MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Midway Repeats Trafalgar’s Lessons: How Division of Force Defeated a Larger Navy

William Sutherling, Docent Channel Islands Maritime Museum 3900 Bluefin Circle Oxnard, CA 93035

Keywords: massing force, firepower, Mega Joules, Lanchester relations, N-Square Law,

Salvo relations, strategy, victory disease, Schlieffen syndrome, Murphy’s Law.

(Pages 192, Words 36,500)

1 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

This is educational material of the Channel Islands Maritime Museum. Please kindly obtain permission of the CIMM to reproduce this document in electronic or printed format. Thank you. Many thanks go to Jerry Leckie, Doug Adams, Tom Shideler, Doug Russell, Dave Anderson, Tom Danza, Bill Conroy, Heather Behrens and Tom Johnston.

2 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

TABLE OF CONTENTS

INTRODUCTION………………………………………………………… 7 Interesting findings: Realistic equation for Midway outcome Japan could have won with 2 more carriers at Midway, available Villeneuve could have equaled with 94 ships at Trafalgar, not available Less than 1% of total firepower sank five carriers at Midway High USN torpedo failure rate revealed torpedo bombers as a feint PART I: FIREPOWER……………………………………………………… 11 Energy in Mega Joules 12 A. WEAPONS 13 Anti-Aircraft Guns 14 Effectiveness 17 Torpedoes 19 The Great Torpedo Scandal 21 Trafalgar Comparison – Fuses 23 Bombs 26 Mines 27 B. ATTACK CRAFT 28 Warships 28 30 Aircraft 32 IJN aircraft shortage 34 USN aircraft production 34 IJN aircraft range advantage 36 Aircraft Warfare 39 Trafalgar Comparison – Communications 42 C. TOTAL IJN AND USN FIREPOWER COMPARED 44 IJN and USN Mega Joules vs Lanchester Military Effectiveness 45 Decisive firepower, which sank carriers at Midway 47 The question of the ZUIKAKU 48 Trafalgar Comparison – Firepower. 50 PART II: FIREPOWER RATIOS, SALVOS AND TIMELINE 52 A. MODERN FIREPOWER 52 Fewer exchanges in modern warfare 52 The Dynamics of Naval Battles 54 Lanchester’s Equations and Fiske’s tables 54 The N-Square Law 58 The Salvo Equations 63 The Dynamics of the Salvo Equations 66 Trafalgar Comparison – Firepower equations for the two battles 71 Greater massing of force does not avoid M.A.D. 72 Philippine Sea 72 Midway 73

3 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

B. THE TIMELINE AT MIDWAY 74 After Coral Sea 74 IJN Steaming to Midway with four carriers as 1st Kido Butai 75 After first attack on Midway Atoll 75 After decisions to change munitions – “Nagumo’s Dilemma” 77 Trafalgar Comparison – Calculated risk. 82 Were the USN torpedo bombers used as a diversion? 83 Trafalgar Comparison – Reversed decisions during battle 85 Trafalgar Comparison – Commonsense action under pressure 86 Experience and Commonsense 86 Action under Pressure 87 Decision at Pearl Harbor 87 The “Victory Disease” and the “Schlieffen Syndrome” 90 C. CROSSING POINTS 92 Crossing Points of carriers and aircraft in Actual Battle 93 Crossing Point at Nagumo’s Dilemma 95 Realistic Salvo Equations for the Battle give the historical results 97 Trafalgar Comparison – Crossing Points. 99 Crossing Points in other possible scenarios with more IJN carriers 99 Scenario with RYUJO and JUNYO 100 Scenario with RYUJO, JUNYO and ZUIKAKU 102 Trafalgar Comparison – Alternative Possible Scenarios 104 EPILOGUE/CONCLUSION 106

Glossary 107 Bibliography 114 APPENDIX A. Tables (36) 118 APPENDIX B. Solving the Lanchester Equations 160 Calculation of small differences Derivative 161 Derivative as a Limit 164 Integral 166 Solutions to Lanchester’s Equations 168 APPENDIX C. Solutions of Salvo Equation for different scenarios 170 Generic Salvo Equations 170 Scenario 1. Example of Massing of Force 170 Scenario 2. Battle of the Philippine Sea 171 Scenario 3. General Salvo Equations for Midway 171 SCENARIO 4. Salvo Equations for actual carrier numbers at Midway 172 SCENARIO 5. Salvo Equations with RYUJO and JUNYO 174 SCENARIO 6. Salvo Equations with RYUJO, JUNYO and ZUIKAKU 177 APPENDIX D. Text of Yahachi Tanabe, LCDR, IJN, on sinking YORKTOWN 182 APPENDIX E. Text of the Great Torpedo Scandal Investigation 191

4 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

List of Tables in the text Table I. Total firepower in Pacific Operations 44 Table II. IJN and USN total Pacific firepower 45 Table III. Firepower which sank the carriers at Midway 47 Table IV. ZUIKAKU’s full complement potential firepower 48 Table V. ZUIKAKU’s actual immediately available firepower after Coral Sea 48 Table VI. Total firepower at Midway and Trafalgar 50 Table VII. Midway outcomes 52

List of Figures in the text. Figure 1. Radius of IJN and USN strikes. Reverse colors for consistency 37 Figure 2. Two fully constituted, well-coordinated IJN and USN air strikes 39 Figure 3. IJN AAW defense against USN DAUNTLESS dive-bomber 40 Figure 4. Illustration of Lanchester’s Equation for a larger force. 56 Figure 5. Illustration of Lanchester’s Equation for superior 3:1 gunnery. 60 Figure 6. Timeline of Nagumo’s Dilemma before 0753 on 4 June 1942. 77 Figure 7. Timeline of Dilemma after 0753 dive-bomber attack from Midway 79

List of Graphs in the text. Graph 1. Illustration of N-Square Law 58 Graph 2. Timeline of Fleet Carriers available for Midway 93 Graph 3. Timeline of Aircraft available for Midway 93 Graph 4. Timeline of Aircraft firepower during Nagumo’s Dilemma 95 Graph 5. Timeline of carriers in actual Midway Battle by Salvo Equations 98 Graph 6. Timeline of carriers in scenario with RYUJO and JUNYO 101 Graph 7. Timeline of carriers in scenario with RYUJO, JUNYO and ZUIKAKU 102

List of Maps in the text Map 1. . Pacific Ocean 9 Map 2. Battle of Midway. Movement of Forces 10

List of Charts in the text Chart 1. Firepower of AAW guns of IJN and USN at Midway. 14 Chart 2. Anti-Aircraft gun Effectiveness. 17 Chart 3. Firepower of IJN and USN torpedoes at Midway. 19 Chart 4. IJN and USN submarines nominal and actual firepower. 30 Chart 5. Firepower of IJN and USN aircraft types in Mega Joules per minute. 32 Chart 6. IJN and USN aircraft Range (radius = ½ range) 36 Chart 7. Total combined Midway and Aleutian Forces for IJN and USN. 46 Chart 8. Illustration of Lanchester’s Equation for different starting force ratios. 57 Chart 9. Salvo Equations for decreasing IJN defense term 67 Chart 10. Salvo Equations for decreasing IJN staying power term 68 Chart 11. Change in IJN versus USN Effective Aircraft from 0430 to 0745 80 Chart 12. Change in IJN vs USN Aircraft Military Effectiveness from 0430 to 0745 81 5 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Chart 13. Trafalgar: Actual Battle and Scenario with 66 Combined Fleet Ships 104 List of Tables in APPENDIX A X-1 IJN Guns’ Firepower. X-2 USN Guns’ firepower. X-2a Firepower of each gun of IJN and USN at Midway 1942. X-2b Number of rounds to shoot down one enemy aircraft for each USN AA gun. X-3 IJN Torpedoes firepower. X-4 USN Torpedoes firepower. X-4a Firepower of IJN and USN torpedoes at Midway. X-4b TNT equivalents IJN Shimose and USN TNT, with other explosives for comparison. X-5 USN Mark 14 Torpedo performance. X-6 IJN Bombs and Depth Charges firepower. X-7 USN Bombs and Depth Charges firepower. X-7a Aerial Bombs used at Midway. X-8 IJN Mines firepower. X-9 USN Mines firepower. X-10 Firepower by IJN Warship class. X-11 Firepower by USN Warship class. X-12 Total IJN Warship firepower. X-13 Total USN Warship firepower. X-13a Firepower of Ships of IJN and USN at Midway and Aleutians. X-14 Firepower by IJN class. X-15 Total IJN Submarine firepower at Midway. X-16 Firepower by USN Submarine class. X-17 Total USN Submarine firepower at Midway. X-17a USN Submarine offensive firepower reduced at Midway by Mark 6 fuse. X-18 Firepower by IJN Aircraft class. X-19 Firepower by USN Aircraft class. X-19a Comparison IJN and USN Aircraft firepower by class. X-19b Range of IJN and USN Aircraft. X-20 Total IJN Aircraft firepower. X-21 Total USN Aircraft firepower. X-22 Comparison IJN USN Total Aircraft Firepower in numbers N and Mega Joules MJ/’. X-23 AAW gun firepower of IJN carriers. X-24 AAW gun firepower of USN carriers. X-25 Total IJN Firepower. X-26 Total USN Firepower. X-27 Comparison Total IJN and USN Firepower in Pacific Operation. X-28 Total Ship Firepower IJN 1st Kido Butai vs Main Body and Other Groups. X-29 Comparison of IJN and USN Firepower at Midway Battle. X-30 Comparison of Total Firepower at Midway and Trafalgar. X-31 Carriers in the Pacific theater in June 1942. X-32 Military Effectiveness ratios of IJN and USN units for Midway-Aleutians. X-33 Nagumo’s Dilemma: 1st Kido Butai Aircraft. X-34 Military Effectiveness of IJN aircraft united and then divided. X-35 Trafalgar re-analysis with Villeneuve having slow-match fuse but twice as many ships. 6 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

X-36 Trafalgar re-analysis after Nelson cut line but Villeneuve with three times the ships.

7 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

INTRODUCTION AND SUMMARY

The Battles of Midway and Trafalgar were similar in several ways. Both were large naval battles, arising from the expansion of new empires. Both imperial commands were overconfident. Both saw larger forces defeated by smaller ones. And both changed the course of history.

In a study of Trafalgar, Lanchester and Fiske showed that a force with more ships won disproportionately by attrition through the N-Square Law.1 2 Hughes, however, showed that large losses occurred suddenly in modern battles.3 These obeyed the Salvo Equations.4

Midway had different dynamics than Trafalgar, but both dynamics obey the principle of mass, where the largest effective firepower dominates.

In the past, firepower was measured by cannons. But modern weapons use both mechanical as well as high-explosive energy. One must calculate total energy to determine the firepower at Midway. This is also necessary to compare Midway to Trafalgar. The key factors in winning both battles were the principle of mass and commonsense5 action under pressure.

The present study compares the firepower of the IJN and USN at Midway.6 It also compares Midway to Trafalgar. It measures firepower by three measures: numbers of attack

1 Lanchester, Aircraft in Warfare: The Dawn of the Fourth Arm. 2 Fiske, The Navy as a Fighting Machine. Chapter XII. Operating the Machine. Tables I, III. 3 Coral Sea was the first and Midway the second aircraft carrier battle in history. 4 Hughes, “A Salvo Model of Warships in Missile Combat Used to Evaluate Their Staying Power,” in Warfare Modeling 121-143. 5 Commonsense is used in its non-trivial meaning of experience, i.e. memory of obvious mistakes in the past, why they occurred and how to avoid them. Senior officers are expected to have more than junior officers in the Navy. This legal definition was defined in the courts-martial proceedings of the USN disaster off Rio Honda, California. Lockwood and Adamson, Tragedy at Honda 184. en.wikipedia.org/wiki/Honda_Point_disaster 6 IJN , USN Navy. 8 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws craft, military effectiveness and Mega Joules per minute.7 The data reveal a timeline of fleet strengths after each decision point at Midway. This proceeds from superiority of the IJN, to the crossing point of parity and finally to the subsequent retreat of the IJN. The study develops a realistic salvo equation to compare to the actual historical outcome. It then uses this equation to see if the Japanese could have won at Midway with an undivided force.

The analysis reveals interesting findings:

A Salvo Equation with realistic assumptions gives the actual outcome for Midway.

It shows the IJN could have won at Midway with 2 more carriers, which were

available.

At Trafalgar, the N-Square Law shows that Villeneuve would have required 94 ships

just for a draw, but these were not available to him.

Less than 1% of the total assembled firepower sank the five carriers at Midway.

Collected USN torpedo data confirm very high failure rates, revealing that the

torpedo bomber attacks were harmless (but tactically crucial) feints.

7 Easily converted into tons of TNT. 9 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

MAP 1. Battle of Midway. Location and routes of all forces in the Pacific. http://www.worldwar2facts.org/battle-of-midway-facts.html. Major Forces: Japan actually had four (4) fleet carriers (CV’s) at Midway. Japanese OB Midway terminology: First Carrier Striking Force = 1st Kido Butai, Main Force = Main Body. Advanced Force = Submarines. Blue Star = Midway Atoll.

The battle occurred near the home waters of the USN Pacific Fleet. The USN had PBY scout flying boats on Midway Atoll. The PBYs’ early warning eventually led to a USN first strike on the 1st Kido Butai. This changed the odds from 4:3 to 1:3 and gave the USN a major advantage at the start of the Battle. 10 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

MAP 2. Battle of Midway. Movement of IJN and USN forces during battle. https://en.wikipedia.org/wiki/Battle_of_Midway (“4., 4:30” = 4 June 1942 4:30 am) 10:25 Fatal attack on KAGA, SORYU and AKAGI by aircraft from ENTERPRISE and HORNET. 12:05 Kobayashi’s dive-bomber squadron from HIRYU attacks YORKTOWN. 14:30 Tomonaga’s torpedo bomber squadron from HIRYU attacks YORKTOWN. 15:00 I-168 submarine sinks YORKTOWN. The KAGA, AKAGI and SORYU were sunk by aircraft from ENTERPRISE and

HORNET. Due to poor scouting, the IJN never found these two carriers. The IJN only located

YORKTOWN. HIRYU put it out of action, but the submarine I-168 sank it.

11 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

PART I. FIREPOWER

The Japanese high command planned to defeat the U.S. Navy with overwhelming strength at Midway (Map 1). Japan outnumbered the USN in carriers, ships and planes. What was her firepower? Lanchester translated number of ships into military effectiveness or firepower. He showed that, with a certain ratio between opponents, the outcome of a battle was predictable.8 What was the initial ratio of firepower at Midway? How did it change with each decision? When did the IJN advantage disappear?

Firepower can be compared in several ways. Historically, broadsides were compared between opposing fleets, the weight of metal thrown per ship.9 10 This led to the Lanchester N-

Square Law and Fiske’s tables using numbers of ships. In World War II, aircraft carrier battles required the Salvo Equations. These captured the complexity of carrier battles in ten (10) terms.

However, it is difficult to estimate several of those terms.

Neither the N-Square Law nor the Salvo Equations, however, show the actual firepower of modern weapons. For large bore, rifled naval guns, firepower includes both the chemical energy of explosive warheads and the kinetic energy of heavy shells with high muzzle velocity.

Explosive energy is also in torpedoes from submarines, and aircraft as well as aerial bombs. All this energy can be measured in Joules. This complements other measures of firepower.

Energy in Mega Joules.

8 Lanchester, Aircraft in Warfare: The Dawn of the Fourth Arm. 9 en.wikipedia.org/wiki/List_of_broadsides_of_major_World_War_II_ships 10 Sutherling, Trafalgar Influences Navy Tactics 1905-1944 12 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

The Joule is easily understood from examples. One Joule is the work done lifting 1 apple

1 meter. A Mega Joule or one million Joules is the kinetic energy of a one-ton vehicle moving at

100 mph. Six Giga Joules or billion Joules is the chemical energy of burning a barrel of crude oil.11 Sixty-three Tera Joules or trillion Joules was released by the Hiroshima atomic bomb.12

Mega Joules can be calculated directly from the weights of shells and their warheads, available in kilograms.13 The chemical reaction producing an explosion of one gram of TNT releases 4.184 kilo Joules of energy (the same as 1 large Calorie = 1 kilo calorie of heat).14 One kilogram of TNT releases 4.184 Mega Joules and one kiloton of TNT 4,184 Mega Joules.15

Firepower is Mega Joules / time.16 Here Mega Joules / min (MJ/’) is used so that all weapons, rapid- or slow-firing, are included. At Midway, the USN used TNT as an explosive. The IJN used Shimose powder or picric acid, slightly more powerful by weight.17

11 159 liters. 12 https://en.wikipedia.org/wiki/Joule#Practical_examples. Giga billion, Tera trillion. 13 Online, e.g. en.wikipedia.org, www.navweaps.com, www.combinedfleet.com. 14 https://en.wikipedia.org/wiki/TNT_equivalent; http://www.navweaps.com/Weapons; https://en.wikipedia.org. 15 https://en.wikipedia.org/wiki/TNT#Energy_content 16 1 Joule=1 kilogram*meter2/sec2. Mechanical or kinetic energy can be calculated from mass, speed and change of speed. This comes from the relations: Energy or work = force*distance, and Force = mass*acceleration. In concrete terms: Joules = (m*a)*d = (kg*meter/sec2)*meter. The Glossary gives more discussion under Joule and Energy. 17 As an important example, the calculation is given for the anti-aircraft IJN 5”/40 12.7cm Type 89 naval gun. The High Explosive shell of the IJN 5”/40 had a velocity of 710 meters per second, a projectile weight of 23 kg, a warhead weight of 1.8 kg of Shimose (picric acid)7 high explosive and a firing rate of 8 rpm.7 Picric acid has a relative TNT equivalent of R.E. = 1.17. One ton of picric acid has the same energy as 1.17 tons of TNT.7 Thus, each warhead had a chemical energy of 1.8 kg * 4.184 * 1.17= 8.8 Mega Joules (MJ). Each projectile had a kinetic energy of 23 kg * (712m/s)2/1,000,000 = 11.9 (MJ). With a firing rate of 8 rpm, the 5”/40 gun’s total firepower = (8.8+11.9) * 8 = 155 MJ/min. The firepower of all the IJN and USN weapons were calculated this way. 13 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

A. WEAPONS

This study proceeds in the standard sequence of battle monographs: weapons, attack craft and battle. With the additional common denominator of Joules, the firepower of all weapons at

Midway will be added up to compare one side with the other. The most important offensive weapons were the bombs and torpedoes on aircraft. The busy reader may skip to those sections.

The most important guns in the battle were Anti-Aircraft Warfare defense (AAW), against enemy planes that made it past the carrier’s own defending aircraft.

14 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Anti-Aircraft Guns.

The shipboard rifled gun provided AAW defense at Midway, defense against the most

CHART 1. Firepower of AA guns of IJN and USN at Midway 1942. important offensive attack craft – the airplane. The USN had better anti-aircraft guns. Chart 1 compares the firepower of the main anti-aircraft guns at Midway.18 The IJN relied primarily on ship maneuver to evade attacking aircraft. The USN relied mostly on AA guns, avoiding maneuver since it dispersed the force and risked collisions.19

Chart 1 shows that the USN 5-inch gun had almost twice the firepower of the IJN equivalent. The 5”/38 DP gun mated to the Mark 37 Fire Control System had long range and was a very effective AAW weapon. This combination was a common feature on USN ships by mid-1942.20 The USN Bofors 40 mm and the 1.0-inch had four times the power of their IJN

18 The MegaJoules/min (MJ/’) are calculated from the combined explosive and kinetic energy in Tables X-1, X-2 and X-2a of Appendix A. The I.J.N used 1.0” 25 mm, the USN 1.1” 28 mm guns. 19 Parshall and Tully, Shattered Sword 144 15 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws counterpart. The IJN 40 mm was a variant of the British Vickers pom-pom but had less firepower than the Vickers, for which data is available.21 22 23 24 25 The USN 20 mm Oerlikon autocannon had five times more firepower than its IJN equivalent.

Rate of Fire. Mega Joules per minute allows comparison between guns of different bore.

The contribution to firepower is adjusted by rate of fire. For example, the projectile of the 0.52- inch machine gun was light, but 250 rounds were fired per minute; whereas, the IJN 18.1-inch projectile fired 1.5 rounds per minute but was heavy. The 5.5”/50 gun of the I.J.N had almost the same firepower of 332 MJ/’ as the much larger 14”/45 gun of 340 MJ/’, because the smaller gun had a faster rate of fire.26 The benefit of the larger gun was range and armor penetration by a heavy shell.

The practical rate of fire of IJN guns was less than the nominal rate. This was due to small magazines and strips inserted into the breech. The 30-round magazines reduced the 0.52- inch MG from 500 rpm to 200 rpm.27 28 The strips reduced the 0.303-inch MG below 450 rpm.29

30 This degraded their AAW effectiveness, already reduced by the shorter range of these lower calibers and their lower stopping power.

20 http://www.liquisearch.com/ship_gun_fire- control_system/us_navy_systems/mk_37_gun_fire_control_system_gfcs/fire_control_radar 21 https://en.wikipedia.org/wiki/QF_2-pounder_naval_gun 22 https://en.wikipedia.org/wiki/QF_2-pounder_naval_gun#cite_note-21 23 Campbell, J. (1986) Naval Weapons of WW II. Naval Inst. Press, Annapolis: 403 pp. 24 The Royal Navy ultimately decided that this gun was half as effective against IJN torpedo bombers as the Bofors 40 mm, and about equal against the suicide bombers. The IJN 40 mm/62 (1.575”) “HI” Type 91 variant had a slower rate of fire 60-100 rpm, a slower muzzle velocity 600 mps and smaller projectile (0.90 kg) and explosive (0.071 kg) weights, than the Vickers. This made the IJN 40 mm anti- aircraft weapon less effective than the Vickers. 25 The USN 1.1-inch (28mm) Mark 1 gun was useful but prone to jamming. The Bofors 40 mm gun had superior range and power and was substituted for the 1.1” gun. 26 Table X-1 Appendix A. 27 http://www.ibiblio.org/hyperwar/Japan/IJA/HB/HB-9.html#II 28 http://www.navweaps.com/Weapons/WNJAP_13mm-76_mg.php 29 http://www.navweaps.com/Weapons/WNJAP_77mm-87_RU.php 30 https://en.wikipedia.org/wiki/Type_92_heavy_machine_gun 16 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Range. Kinetic energy depends on striking velocity. For anti-aircraft guns, muzzle velocity was used for striking velocity due to the short ranges. Enemy aircraft was sighted at two nautical miles or 3,700 meters.31 Although adequate for slower torpedo bombers, it was a not enough warning for faster dive bombers.32 There was a 3,000-meter effective ceiling of the IJN

5-inch gun. Since 10-20 seconds were required to obtain a solution from the fire control director, the plane would be lower, and shell velocity still near muzzle velocity.33 Thus the default muzzle velocity was used here for anti-aircraft weapons, usually bores ˂ 6 inch. 34 35

31 Taught to general aviation pilots today. FAR AIM (Federal Aviation Regulations). Japan did not have at Midway. 32 See Figure 3 below. 33 A more precise estimate of striking velocity might be from a correction factor from the 18.1-inch gun. The ratio of striking velocity/muzzle velocity for at 5,000 meters 2.4 degrees elevation is 690mps/780mps= 0.885. The range for anti-aircraft shells was shorter, since the gunner had to elevate the gun and train on a moving plane diving on the ship, shortening the range, possibly to half the visual sighting distance. These complications indicate that attempting to obtain a more precise estimate may not get a more accurate one. 34 Table X-1 shows each gun’s kinetic energy and explosive energy. For all guns, the kinetic energy was higher than the high explosive energy, though some were close. Explosive charge was different between armor piercing (AP) and high explosive (HiEx) shells. AP is shown for guns with bore of 6 inch and higher, usually employed against another ship. Smaller bore guns were usually anti-aircraft weapons. The 6.1-inch gun was also used for anti-aircraft, where the HiEx explosive charge was 3.1 kg. There was less explosive in AP shells than in HiEx, due to the thick armor casing. 35 Over a longer range, the shell has more exposure to air friction, slowing it down. For instance, the IJN 18.1-inch/46 cm rifled gun had a muzzle velocity of 780 meters/second, a striking velocity of 690 m/s at 5,000 meters with 2.4 degrees elevation but a much lower striking velocity of 475 m/s at 30,000 m with 23.2 degrees elevation. Angle of fall compensated for decreased velocity at longer range. The smaller elevation gave a smaller angle of fall of 3.3 degrees, the largest gave a fall of 31.4 deg. The largest angle could penetrate thicker deck armor of 230 mm (9.06”), detonating the charge inside deep inside a ship for maximum effect. encounters were long range, so 25,000 m to 30,000 m were chosen as the ranges for large bore guns. The range determined the kinetic energy. The striking velocity decreased for larger bores at a longer range. At longer range, the angle of fall compensated for the decreased striking velocity. This was relevant for surface ship battles, but not for the carrier battle at Midway. 17 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

AAW gun effectiveness.

Chart 2 shows the effectiveness of each Anti-Aircraft Gun of the USN.36

CHART 2. Anti-Aircraft Gun Effectiveness. RPB = to down 1 aircraft. 5” Com = explodes before target - shock wave expanding cone shrapnel 5” VT = variable time proximity fuse 40mm=Bofors 20mm=Oerlikon This shows the dominant role of the 5-inch, Bofors 40 mm and the Oerlikon 20 mm guns. The top part of the Chart shows that over 80% of the 2,250 IJN aircraft shot down in WW II were by the 5-inch at a distance and the 40 mm and 20 mm close-in. The Oerlikon 20 mm autocannon

36 From Table X-2b Appendix A. 18 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws accounted for 42% of aircraft downed by USN shipboard AA by the end of 1942.37 IJN guns were generally inferior AAW weapons, often due to limited capacity of magazines.

The left lower part of Chart 2 shows many rounds expended for the 40 mm and 20 mm due to their rapid firing rate, 85 rpm and 280 rpm respectively.38 The right lower part shows the rounds needed to shoot down one enemy aircraft.39 40 41 The smaller calibers shot many rounds but this was desirable close-in against a fast moving aircraft. The 20 mm Oerlikon shot many more rounds than the .30 cal but needed fewer rounds per bird, i.e. it was more effective. The carriers contributed substantial defensive AAW gun firepower by themselves.42 They had about half the AAW firepower in the 1st Kido Butai formation. 43 44

37 https://en.wikipedia.org/wiki/Anti-aircraft_warfare#Second_World_War 38 Table X-2, Appendix A. 39 http://www.ibiblio.org/hyperwar/USN/rep/Kamikaze/AAA-Summary-1045/index.html 40 https://en.wikipedia.org/wiki/5%22/38_caliber_gun#Ammunition 41 Actual numbers in Table X-2b, Appendix A. 42 Tables X-23 and X-24 in Appendix A. 43 By calculations from the firepower in Mega Joules. 44 Parshall and Tully, Shattered Sword 144 (40%-60%). 19 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Torpedoes.

Japan had superior torpedoes in the first half of the war. The IJN torpedoes had bigger warheads, greater reliability, faster speed and longer range. Chart 3 compares torpedoes of the

IJN and USN.45 The USN’s torpedoes were designed with less firepower, shown in orange as

“nominal.” Due to a faulty fusing mechanism, their firepower was substantially worse, shown in

CHART 3. Firepower of IJN and USN torpedoes Midway. Aircraft torpedoes: IJN Type 91, USN Mark 13. Submarine torpedoes: IJN Type 95, USN Mark 14. Destroyer torpedoes: IJN Long Lance Type 93, USN Mark 15. The USN torpedoes’ nominal firepower was not the actual firepower (grey), reduced due to the faulty Mark 6 fuse. Both are shown. Actual was reduced to 30% for the Mark 13 and 50% for the Mark 14 and 15. grey as “actual.” Japan had a 3:1 advantage in torpedo firepower.

Japan and the US used different explosives: Shimose powder and TNT, respectively. 46

Shimose powder was more stable than nitroglycerin and more powerful than TNT by 17%.47

45 Calculations of Mega Joules per minute is in Tables X-3, X-4 and X-4a in Appendix A. Torpedo tubes are given a firing rate of about one per minute aboard submarines. 46 https://en.wikipedia.org/wiki/TNT_equivalent 47 Table X-4b in Appendix A. 20 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

TNT was more stable and safer than Shimose in the hectic environment of battle or a rolling ship. TORPEX was not used by the USN until late 1942.

The IJN’s Type 93 “Long Lance” was the most powerful, reliable torpedo in WW II, with a long range and high speed. The Type 91 Mod 2 aerial torpedo was used by Tomonaga’s torpedo bombers. They paralyzed YORKTOWN with a large list. Four Type 89 torpedoes, older and weaker model, were fired by I-168 to sink YORKTOWN.48 49 IJN torpedoes were faster than USN ships, which could not outrun them. Most IJN ships, however, could outrun

USN torpedoes. Torpedoes after 1911 had more firepower than naval guns. The massive firepower of the IJN’s torpedo distinguished it as their most powerful weapon.50 The IJN had the advantage in torpedoes until mid-1943 when the USN started addressing its torpedo deficiencies.

The USN’s Mark 13 torpedo was used by the DEVASTATOR and AVENGER torpedo bombers. It was unreliable and had to be delivered at 110 mph at 50 feet above the water, exposing the plane to AAW fire. Many lives were lost in USN torpedo planes with very few hits or ships sunk.51 52 Faulty USN torpedoes finally motivated an investigation within the Navy.

The Great Torpedo Scandal.53 While the IJN pushed its torpedo technology to the limits, the USN Bureau of Ordnance deliberately balked due to budget and shortage of torpedoes. The Bureau performed only two

48 See Table X-3 in Appendix C. 49 Yahachi Tanabe, LCdr, IJN, C.O., I-169, “I sank the YORKTOWN at Midway”, Appendix D. 50 Only the No. 80 1,760 lb. land bomb came close with 1608 MJ/’, but it was rarely used by the IJN. 51 http://archive.hnsa.org/doc/torpedomk13/index.htm#toc 52 U.S. Navy Torpedoes Mark 13, 13-1&2. Description, adjustment, care and operation. Ordnance pamphlet no. 629(A). U.S. Naval Torpedo Station, Newport, Rhode Island. July 1942: 9. Available at above internet site. 53 Milford, U.S. Navy Torpedoes. Part Two: The great torpedo scandal, 1941-1943 in Appendix E. 21 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws live firings: one succeeded and one failed, in the smallest weapons’ sampling test in history.54

Not surprisingly, USN torpedo performance was poor during the first half of the war.

Most data are available from the submarine Mark 14 torpedo.55 Under near perfect non- combat conditions at Santa Cruz, when torpedoes were fired on a derelict carrier and destroyer, one source states that only 9/18 torpedoes actually hit their target and exploded.56 Another study states that only 10/16 torpedoes hit and exploded on the damaged Hornet .57 The results are like flipping a coin. Even all these the hits did not sink the carrier. Still another source states that, early in the War, 96 well-aimed shots by US submarines in combat sank only 3 enemy ships.58

The poor performance data for torpedoes is available in detail for multiple WWII submarines from TROUT to TARPON in a standard history.59 60 From analysis of this data, these submarines fired a total of 116 torpedoes with 43 hits (37%) and sank 24 ships (21%) with those hits.61 62 HALIBUT’s hit rate of 47% was probably representative of the torpedo’s performance under ideal combat conditions. Its aiming was probably the best with SJ radar. The hit rate was only slightly less than the reports from Santa Cruz of 50% under ideal non-combat conditions. The worst report of the dysfunctional torpedo was that it failed to detonate 90% of

54 Kimmet and Regis, U.S. Submarines in World War II. An Illustrated History 31. 55 Submarine Mark 14 torpedo attacks were performed in stealth and less hurried than surface destroyer attacks, where waiting to confirm each Mark 15 hit was risky. 56 Stille, USN Destroyer vs IJN Destroyer. The Pacific 1943 18-19. 57 Stille, Santa Cruz 1942. Carrier Duel in the South Pacific 88-89. 58 Kimmet and Regis, U.S. Submarines in World War II. An Illustrated History 30-31. 59 Morison, Coral Sea, Midway and Submarine Actions. May 1942-August 1942 198-204. 60 This data is listed Table X-5 in Appendix A, extracted from Morison above.

61 One biased interpretation is that 43 torpedoes sank 24 ships, a success rate of 56%, or conversely, a 42% failure rate. The Bureau may have used this failure rate in the Navy Assessment that 37.5% of fleet torpedoes were defective. But this type of “failure rate” does not include torpedoes missing the target by running too deep. It underestimates the deficiencies of the torpedoes. The Bureau assumed torpedoes missing were due to faulty aim by the skipper. 62 Ibid: 214. 22 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws the time.63 Thus, the Mark 14 torpedo had at best a 50% reliability rate, like the Bureau of

Ordnance testing. The Mark 15 on destroyers was probably similar.

The aerial Mark 13, however, was worse. During a controlled exercise by torpedo bomber squadron VT-6 in July 1941, only one of ten Mark 13 Mod 1 torpedoes worked properly.

Four sank and five experienced erratic runs.64 It subsequently had a 70% failure rate when dropped faster than 150 knots.65 66 It was designed for drop from 50 feet at 110 knots. Impacting water caused problems. Slow speed and low altitude made the pilot a sitting duck. It ensured that most torpedo bombers never made it through IJN defenses to deliver their torpedoes.

The torpedoes’ Mark 6 magnetic fuse was defective. The fuse made the torpedo run deeper than set depth, detonate prematurely or not detonate with a direct hit due to its firing pin.

When submarine captains disabled the fuse, the torpedoes worked better. There were three problems: location of the hydrostatic detector port, the magnetic sensor of the earth’s field distortion by the ship’s metal and a faulty contact trigger. The interactions invited ever- increasing contributions from Murphy’s Laws. The only effective alternative would have been to resort to multiple, costly test trials for useful data. This was not done. Budget constraints in war time are usually inappropriate, where confusing war with business and warriors with customers cost lives.67 Historically, Congress has considered defensive war as a justification to

63 Orr, T. Battle 360: Midway. www.history.com. 64 http://www.navweaps.com/Weapons/WTUS_WWII.php 65 https://en.wikipedia.org/wiki/Aerial_torpedo#World_War_II 66 https://en.wikipedia.org/wiki/Aerial_torpedo#cite_note-NavWeaps-25 67 In retrospect, all excuses pale for not correcting the faulty torpedoes early. The budgetary due to the consequent loss of planes and pilots. The torpedo shortage as well - the torpedo system was faulty anyway. In retrospect, there may be a recent parallel of budget dominance in war, which is instructive. The Vietnam War was directed by Robert McNamara, a business systems analyst focusing on economic efficiency rather than a military strategist focusing on victory. From his experience in the 1962 Missile Crisis, he did not see victory as a goal in a modern war. Cuba had impressed on him the risk of nuclear annihilation from misunderstandings. Instead, he focused on negotiation and graduated pressure communicating toward peace, while trying to achieve proxy metrics in the most cost-effective way. He 23 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws increase taxes and national debt.

The faulty Mark 6 fuse compels an adjustment to USN torpedo firepower at Midway.

The Mark 14 and 15 torpedoes merit a firepower reduction factor of 50%. The Mark 13 actual firepower should be reduced to about 30%. USN submarines, destroyers and torpedo bombers were clearly at a disadvantage.

Trafalgar Comparison – Fuses: Mark 6 exploder and slow-match fuse.

A remarkable similarity in inferior fuses spanned a century. The difference in torpedo performance at Midway can be compared to the difference in cannon performance at Trafalgar, a century earlier. Although British gunnery was three times faster than the French-Spanish fleet, the latter also had an inferior fuse for their cannon.

The British cannon used flintlocks to fire instantly at the aimed target. But the Combined fleet still used slow-matches to fire their guns. The slow-match produced a variable, unpredictable delay after they had aimed at the target.68 On land, this would not have been significant but at sea it was.

The problem with the slow-match fuse was due to ship roll. During the battle the

Combined Fleet was directed on a north-south axis and ocean waves came from the side, causing the ship to roll. The ships were subjected to “heavy swells”. A 30-degree to 48-degree roll would not be unheard of in heavy swells.69

restricted offensive attacks on North Vietnamese anti-aircraft weapons, fearing political repercussions. This cost U.S. lives. His lack of a coherent offensive strategy guaranteed defeat against the committed, opposing North Vietnamese forces, intent on victory, whatever the cost. Ignorance of Vietnamese and Chinese history was a weakness of US Indochina policy. Better understanding of history may have allowed decision makers to distinguish Cuba and Vietnam as two very different situations, early. 68 Howarth, Trafalgar. The Nelson Touch 132. 69 Shideler, Personal communication. Although there is no quantification of the “heavy swells” in degrees at Trafalgar, rolls of 15-20 degrees are common and 30 degrees occur near coastal waters. LCDR T. 24 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

The roll moved the axis of a cannon bore up and down in a large arc. The cannon pointed down at the ocean one second, then up at the horizon the next and then up again at the tops of the oncoming ships. After the variable delay from a slow-match firing, one source concludes that the cannon pointed in a “random” position when fired.70 This degraded the gunnery performance beyond its slower rate of fire.

How many “random” shots would hit their target? A ship’s roll caused the cannon bore to trace a sine wave. It spent about 50% of its time above the horizon, where it would hit somewhere in the rigging or hull of the ship, doing damage. By shooting at any time during a swell, they had about a 1/2 chance of hitting a British ship at 400 yards.71 Their 1/3 slower firing rate combined with the 1/2 chance of hitting the target gave only a 1/6 hitting rate for the

Combined fleet’s gunnery compared to the British.72

In summary, the inferior USN torpedoes at Midway were reminiscent of the less accurate

Combined Fleet’s cannon. The USN’s Mark 14 and 15 torpedoes’ poor performance of 50% was like Villeneuve’s poor aiming effectiveness of 50%. Ironically, both these deficiencies were due to inferior fuses.

Shideler, aboard the USS McDermut DD-677, a Fletcher-class destroyer, experienced 48-degree “heavy rolls” in shallow seas on patrol in the Taiwan Straits in the 1950s-1960’s. 70 Howarth, Trafalgar. The Nelson Touch 132.

71 A sine wave spends more time at the upper and lower parts of its excursion: 1/3rd of its time in the top 25% and 1/3rd in the bottom 25% % of the arc, at the extremes. The combined fleet tactic was to hit the sails and rigging of Nelson’s fleet.71 By shooting at any time during a swell, they had a 50% chance of hitting above the horizon and hitting somewhere on the ship, and a 33% chance of hitting the top 25% of the arc, near the sails and rigging of Nelsons fleet above the horizon. But they could not further constrain the time of fire due to the unpredictable instant of firing of the slow match. 72 Calculations in Table X-35, Appendix A. 25 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

26 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Bombs.

Aerial bombs were the most important weapon at Midway. They sank all four IJN carriers. The two sides had about the same advantage in bombs. The IJN had 500 lb. bombs, armor piercing and high explosive. The USN had general purpose high explosive bombs, 500 lb. and 1000 lb.73

All the IJN carriers were sunk by general purpose, high-explosive bombs from USN dive bombers.74 The AKAGI was destroyed by one 1000 lb. bomb, aimed near an elevator.75 The

KAGA was sunk by four 500 lb. bombs and one 1000 lb. bomb.76 The SORYU was sunk by three 1000 lb. bombs.77 Finally, HIRYU was sunk by four 1000 lb. bombs.78 Even though the

USN bombs were not armor-piercing, they landed near the elevators on all four carriers causing fires, which spread to the carriers’ hangars. These fires raged out of control and all carriers eventually sank.79

Lt Kobayashi Michio armed his dive-bomber squadron from HIRYU with 250 kg 500 lb. bombs. By doctrine, two-thirds of the bombs were armor piercing, to penetrate the decks and detonate inside a carrier’s vital spaces, and one-third were high explosive bombs, to hit exposed anti-aircraft batteries.80 YORKTOWN was hit with two 250 kg AP bombs and one 242 kg high explosive bomb.81 Her damage control teams repaired the effects in two hours.

73 Tables X-6, X-7 and X-7a, Appendix A. 74 Parshall and Tully, Shattered Sword 242. 75 Dick Best’s DAUNTLESS dive bomber from ENTERPRISE 76 Wade McClusky’s squadron of DAUNTLESSes from ENTERPRISE 77 Max Leslie’s squadron of DAUNTLESSes from YORKTOWN 78 DAUNTLESSes from ENTERPRISE and YORKTOWN 79 Parshall and Tully, Shattered Sword 262. 80 Ibid 262. 81 Ibid 295. 27 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Mines.

Mines played little part in the battle but had much available firepower of about 2,400

Mega Joules and were stealth weapons.82 83 84 They could be placed in large numbers by minelaying submarines such as the I-121 class. Mines were used mostly in Japanese coastal waters – the IJN to protect shipping, the USN to sink it.85 Mines were not used at Midway, possibly for two reasons: 1) there was little time for their deployment due to the time constraints of the operation and 2) they could not be concentrated as effectively as aerial bombs.

B.

82 2,400 MJ for Japan’s Type 82, and 2,100 MJ for the US’s Mark 12. Both had 500 kg of explosive. 83 Kimmet and Regis, U.S. Submarines in World War II. An Illustrated History 54. 84 http://www.navweaps.com/Weapons/WAMUS_Mines.php 85 The IJN and USN mines with their firepower are listed in Tables X-8 and X-9 in Appendix A. 28 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

ATTACK CRAFT

The attack units were armed with the above weapons. The most important attack unit was aircraft. The busy reader may skip to Aircraft below.

Warships

Warships in a battle line had always been the main strength of a naval fleet. The warships still had most of the firepower at Midway but played little role in the battle. Their function was different than in past wars. They were to provide AAW defense for the carriers and coastal bombardment prior to invasion of the island.86 The IJN force had 1,900,000 MJ/’ at

Midway and 400,000 MJ/’ in the Aleutians, a total of 2.3 Tera Joules/’ of firepower. USN warship firepower was 240,000 MJ/’ at Midway and 190,000 MJ/’ in the Aleutians, a total of

0.43 TJ.87 At Midway the IJN warship force was six times larger than the USN force.88 89

It is important to stress that not all firepower could be brought to bear at once.90 Rather, it was available to use in concentrated, aimed attacks. Yamamoto peeled off one-fourth of IJN

86 They sank only two (2) aircraft carriers in WW II. Hughes and Girrier, Fleet Tactics and Naval Operations 117. 87 From Tables X-10, X-11 and X-12, summarized in Table X-13a in Appendix A. 88 Total firepower was obtained by multiplying the number of ships in class by the average firepower of the class, since most ships in class are similar in armament. This has been reviewed in: 89 Sutherling, Two Influences of Trafalgar on Navy Tactics 1905-1944 42, 48. The Fletcher-class destroyers at Samar were probably the most homogeneous group. There were 24. The most heavily armed could throw 15,093 lbs. of metal per min. the least heavily armed 13,439 lbs. per min. The average was 14,680 lbs. with a standard deviation (S.D.) of 731 (5% of the average). The standard error of the mean (S.E.M.) was 149 (1%). S.E.M. = standard deviation / (square root (number in sample)). The SEM predicts how much the average of a limited sample varies from the true average of a population. Thus, adding up firepower using the average for a class times the number of ships in that class gives a reasonable estimate of the total firepower of the group of ships. For Fletcher destroyers, there would only be about 2% difference, 95% of the time, from any other average of 24 ships from the total population of 175 ships of that class. With such a small difference between different samples, the other variables of malfunction, downtime for maintenance, etc., probably introduce errors of similar magnitude. Thus, the assumption is made here that other ship classes in the USN and IJN have small average variability. 90 Shideler, personal communication. 29 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws ship firepower (and one-fifth of IJN air power) to the Aleutians. He divided his force. Nimitz did not order USN to Midway since they would have slowed down the carriers en route to Point Luck.

The massive firepower of IJN surface warships, 2.3 Tera Joules, is impressive. This explains some of the zeal of battleship proponents and their inertia to aviation. But range must be considered with firepower. A battleship’s firepower was restricted to about 15 miles, an area of 700 square miles. An aircraft can attack over a radius of 300 miles, an area of 283,000 square miles. The aircraft shoots 20 times farther over an area 400 times larger. Battleships were outgunned.91

91 Since Midway, surface ships and submarines have both extended their range. Today, they can shoot missiles as far as aircraft. The long range of ICBMs has made the fleet ballistic missile submarine the most powerful modern attack craft in nations’ arsenals. A potential surprise attack from their stealth adds to the submarines’ power and deterrence capability. 30 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Submarines.

Submarines were very important in WW II. They sank Imperial merchant shipping and starved Japan of needed industrial resources.92 Furthermore, submarines sank fifteen aircraft carriers in WW II,93 only slightly less than aircraft at twenty. But the only offensive submarine action at Midway was when I-168 sank the badly crippled YORKTOWN after a devastating attack by torpedo bombers.94

Although USN submarines had more nominal firepower than those of the IJN, Chart 4 shows that their actual firepower was much less due to the faulty Mark 6 exploder.95 Their actual firepower is shown in grey. The submarine’s torpedo was its only offensive weapon, 99% of firepower. Chart 4 shows that, due to faulty torpedoes, USN submarines at Midway went from a nominal 2:1 advantage to an actual disadvantage. The Aleutian situation was even worse.

CHART 4. IJN and USN submarines nominal and actual firepower (grey).

92 Kimmet and Regis, U.S. Submarines in World War II. An Illustrated History. 93 Hughes and Girrier, Fleet Tactics and Naval Operations 117. 94 Shideler, audio interview of letter of LCDR Yahachi Tanabe, C.O. of I-168, in Appendix D. 95 From Tables X-14, X-15, X-16, X-17 and X-17a in Appendix A. 31 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

The IJN had attack submarines, minelaying submarines and submarines with float planes with substantial firepower.96 Each of the three I-121 minelaying submarines at French

Shoals had the potential of 42 mines with 22,000 MJ/’. They were used, however, for refueling and scouting, the latter late and ineffective. The IJN’s anti-submarine warfare (ASW) was poor.97

In an ironic twist of fate, the Imperial Japanese Army reduced the offensive power of the

IJN’s submarine force. It diverted many submarines to housekeeping duties of troop and supply transport to isolated outposts. This was a lucky break for the USN since “every time a US carrier was hit by a torpedo in the carrier battles of 1942, the carrier ended up being lost.” 98

96Table X-14, Appendix A. 97 https://en.wikipedia.org/wiki/Anti-submarine_warfare#Pacific_Theatre. 98 Stille, Midway 1942: 62. Tomonaga’s B5N2 Type 97 Carrier Attack Aircraft from HIRYU shot two Type 91 torpedoes into YORKTOWN producing a 23-degree port list. I-168 sank YORKTOWN with a spread of Type 89 torpedoes. The Type 89 had 1256 MJ/’ firepower, Table X-3. 32 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Aircraft.

The most effective arm at Midway was aircraft. The Battle of Midway was decided during the phase to control the air prior to invasion, in an aircraft carrier battle.99 100 101 It was a

CHART 5. Firepower of IJN and USN aircraft types (MJ/’). preview of the rest of the Pacific War, where aircraft carriers were sunk mostly by aircraft (20) and submarines (15). Surface ships sank only two (2) carriers.102

Chart 5 compares the firepower of the equivalent aircraft of the IJN and USN, side by side in Mega Joules per minute.103 The ZERO A6M was the best fighter aircraft in the first years of WW II. The KATE B5N delivered its dreaded torpedo. The USN DAUNTLESS SBD dive bomber outclassed the IJN VAL D3A and new JUDY D4Y in firepower. The CATALINA PBY and EMILY H8K had the largest firepower and the longest range.104 The PBYs did the early

99 Adams, personal communication. 100 Stille, Midway 1942. 101 Parshall and Tully, Shattered Sword. 102 Hughes and Girrier, Fleet Tactics and Naval Operations 117. 103 Comprehensive calculations are in Table X-19a Appendix A. 104 PBY 170 knots and 2200 nm. 33 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws scouting and detection of the IJN fleet.

The IJN had the H6K and H8K flying boats on Jaluit and Wotje Atolls and smaller float planes on cruisers. Two H8Ks were sent on a second raid to Pearl Harbor in March 1942. One flew reconnaissance to Midway Atoll about the same time, where it was shot down by a

Brewster F2A Buffalo. But the H6Ks and H8Ks were apparently not used at Midway. Their speed and range would have improved the IJN’s scouting, a critical weakness.105 Wake and

Midway were within the 1,500 nm radius of the H8K flying boats from Wotje.106 107 108

The US Army’s land-based B-17 FLYING FORTRESS and B-26 MARAUDER dwarfed the other aircraft in firepower, at 9,200 MJ/’ and 4,700 MJ/’ respectively.109 They were, however, big targets, less maneuverable and dropped bombs from high altitude with low accuracy. They were knocked out without hitting any carriers at Midway.110

The IJN had 467 planes with 370,000 MJ/’ firepower at Midway, compared to the USN with 345 planes and 450,000 MJ/’. Several distant land bases could have supported IJN carrier aircraft, but apparently supplied only spares.111 Nearby Midway Atoll supplied a large part of firepower and scouting to the USN Task Forces 17-Fletcher and 16-Spruance.

IJN Aircraft Shortage.

There was an aircraft shortage in the 1st Kido Butai. Each IJN carrier had fewer planes at

Midway than Pearl Harbor.112 Their total complement had decreased from 267 to 225 planes. https://en.wikipedia.org/wiki/Consolidated_PBY_Catalina#Specifications_(PBY-5A) 105 H8K Speed 160-252 knots, range 3862 nm. H6K 138-180 knots and 3280 nm. The floatplanes used by the 1st Kido Butai for scouting were biplanes: E7K2 115-149 knots and 1000 nm and E8N1 100-160 knots and 485 nm. https://en.wikipedia.org/wiki/Kawanishi_H8K#Specifications_(Kawanishi_H8K2) etc. 106 Wake 615 nm, Midway 1314 nm. H8K 3,862 nm range. 107 Google Earth Pro 108 https://en.wikipedia.org/wiki/Kawanishi_H8K#Specifications_(Kawanishi_H8K2) 109 Comprehensive data in Table X-22, Appendix A 110 Parshall and Tully, Shattered Sword 176-188. 111 Stille, Midway 1942 29. 34 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

There were twenty-one extra ZEROs aboard as spares.113 The ratio of Pearl to Midway for aircraft complement was 1.19. By the N-Square Law, the military effectiveness of IJN aircraft at

Pearl was 1.41 times larger than at Midway. Thus, 1st Kido Butai had lost 1/3 of its military effectiveness in aircraft.114 Why?

Mitsubishi was still manufacturing ZEROs on time. But Nakajima and Aichi were behind schedule for KATEs and VALs. These latter two affected strike power most, since they delivered the ordnance on target. Nakajima had redirected all its efforts from the KATE to build a new type of torpedo bomber. Only after a direct request from the government did it restart manufacturing the KATE. Production priority had also shifted from the VAL to the new D4Y dive-bomber. In 1942 only fifty-six new carrier attack aircraft would be sent to the fleet to replenish its losses.115 But the IJN lost many more carrier aircraft in the first half of the year: 80 at Coral Sea and 250 at Midway.116 117

USN Aircraft Production.

In the US, on the other hand, Ford turned out ten bombers a day in 1943 and one bomber every hour in 1944.118 In an apocryphal story, FDR asked Henry Kaiser to produce as many war machines as possible. Kaiser said he would, on one condition. Slowly removing his ivory cigarette holder from his lips, FDR asked: “What exactly is that?” “You stay out of my way,” responded Kaiser. FDR didn’t blink an eye. He was a consummate politician, the fourth time we really needed one.119 FDR resolved the confrontation in a win-win. The two parted friends.

112 AKAGI 6654, KAGA 7563, SORYU 6354 and HIRYU 6354. 113 AKAGI 6, KAGA 9, HRIYU 3 and SORYU 3, Stille, Midway 1942 29. 114 Parshall and Tully, Shattered Sword 91. 115 Ibid 89. 116 https://en.wikipedia.org/wiki/Battle_of_the_Coral_Sea 117 https://en.wikipedia.org/wiki/Battle_of_Midway 118 Overy, Why the Allies Won: 197. 35 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Soon, Kaiser was producing Liberty Ships every 41 days in 1943 and later every 8 days.120 He manufactured larger, more complex Escort (Jeep) Carriers every month. Yamamoto knew that

Japan could not win a long war against US Industry.

119 First three: Rebellion against George III, War between the States and the (failed) Versailles Treaty. 120 Ibid 194. 36 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

IJN Aircraft range advantage.

Chart 6 shows that IJN carrier aircraft had longer range.121 This gave them a unique advantage.122 They could attack safely from outside the range of USN aircraft. The range limit was due to the torpedo bombers. The IJN had a striking radius of about 264 nm, some sources indicate 300 nm.123 The USN striking radius was about 189 nm, between 150-200 nm.124 The

Chart 6. Aircraft range in nautical miles. Striking radius = ½ range. IJN could launch a well-constituted, coordinated strike from outside the radius of USN torpedo bombers. The USN could not launch a similar well-constituted counterstrike due to the distance.

Figure 1 below illustrates the advantage of range.

121 Comprehensive data in Table X-19b, Appendix A. 122 Determining the combat radius of WWII aircraft is non-trivial, since the multiple factors of warm-up, rendezvous, climb, and combat time must all be included. These are not reflected in the manufacturer’s, Anacostia’s or Patuxent’s description of performance. Realistic aviator annotated spec sheets for the USN are available at http://www.wwiiaircraftperformance.org/f4f/f4f-4.pdf and http://www.wwiiaircraftperformance.org/japan/aug42intelrep-0.jpg. They indicate also that fuel consumption also was more, 15% above that anticipated for the F4F-4 Grumman WILDCAT. Detailed combat aviator annotations for IJN aircraft are more difficult to find. 123 Stille, The Philippine Sea 1944 32. 124 Ibid 20. 37 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

FIGURE 1. Range advantage of IJN strike. IJN carrier in blue has strike radius of 264 nm, USN carrier in orange has 189 nm. IJN can strike USN carrier from the safety of a distance, which is outside the range of a USN strike.

Neither Nagumo nor Yamaguchi used this to their advantage at Midway. Instead, after the USN attack, Nagumo charged and closed with the enemy, a feudal or World War I tactic, suicidal in modern battle.

His behavior is not surprising, since Nagumo had been a sea admiral with expertise in torpedo tactics. He had no personal aviation experience or interest in the “intricacies of carrier warfare.” 125 Nagumo had to rely heavily on his staff for perspective. Yamamoto did have aviation experience, but it did not rescue him from his overly detailed plans without worst-case

125 Stille, Midway 1942 12. 38 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws scenarios. Ironically, lack of aviation experience did not handicap the three USN admirals,

Nimitz, Fletcher and Spruance.

39 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Aircraft Warfare.

Aircraft produced a new type of warfare.

20,000 ft (Fighters) A6M ZERO   F4F WILDCAT

15,000 ft (Dive Bombers) D3A VAL   SBD DAUNTLESS

2,000ft (Torpedo Bombers) B5N KATE   TBD DEVASTATR

Sea level IJN Carriers USN Carriers

FIGURE 2. Two fully constituted, well-coordinated IJN and USN air strikes are shown after launching from the carriers. Each type aircraft represents a squadron (~ 18 planes).

A fully constituted, well-coordinated strike was the most powerful tactic. Figure 2 shows the three types of aircraft flying together at different altitudes. It was more difficult to defeat all three before they could attack the carriers. The fighters protected the planes that delivered ordnance. It was IJN doctrine to mass a full-strength, fully constituted, well-coordinated strike.

This meant three squadrons of eighteen planes each.126 Nagumo at Midway tended to adhere to the doctrine of full-strength. On 4 June 1942, Yamaguchi recommended a partial strength attack on a USN contact to the northeast at 0745. Earlier on that day, Spruance had sent out a strike as soon as possible, in parts as soon as they were ready, to catch the IJN during recovery of its aircraft from their bombing of Midway Atoll.

126 See Glossary. 40 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

At Midway USN dive bombers won the battle. The overwhelming advantage of the

DAUNTLESS is demonstrated in Figure 3. A constituted coordinated strike with fighter cover protected the dive bomber up to its pushover point when it began to dive.

FIGURE 3. IJN anti-aircraft defense (AAW) at left against USN dive-bomber at right. It is only after the dive bomber has reached its pushover point to dive that it comes in range of the AAW guns. It must accelerate for only 60 seconds before dropping its bomb. The IJN 5” gun needs 20 seconds for fire control. Parshall and Tully, Shattered Sword 141.

Then the USN DAUNTLESS presented a small head-on target briefly to IJN 5-inch and

25 mm AA guns. Gravity reduced the effective range of both guns. If immediately aimed, each

5-inch gun could fire eight (8) rounds during the 1-minute dive.127 But the Type 94 fire control director took 10-20 seconds to give a solution to the target.128

127 The duration of the dive depends on the altitude at the pushover point. Dives of 20 seconds are often mentioned in the literature. 41 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

The 25 mm AA gun of the IJN could fire 120 rpm. But it could only reach the bomber in the brief, terminal phase of its dive for < 1000 meters. Here the bomber’s speed was 225 mph

(360 kph), so the time window was only 10 seconds. The gun could shoot only 20 rounds.

Furthermore, at that point the DAUNTLESS was rushing past and changing direction. Even aiming these rounds assumes high readiness and instant sighting of the bomber. The smaller calibers had shorter ranges and less stopping power.129

If there were an anvil attack from both sides of the carrier, the complexity increased.

Worse, each IJN fire control director aimed a group of guns. The carrier’s fire control could only defend against eight aircraft at once.130 The ZERO fighter CAP was more effective against the DAUNTLESS. However, with F4F WILDCAT cover and the “Thatch Weave”131, the CAP was saturated with its own defense.

The IJN 25 mm gun was more effective against torpedo bombers, which came in low and slow. But the unreliable Mark 13 torpedo made the torpedo bombers more of a diversion. This diversion was a crucial one at Midway.

Likewise, the USN shipboard .30 caliber and .50 caliber machine guns were not effective

AAW weapons with a range of only 300 to 400 yards. At Pearl Harbor the USN .50 cal machine guns did account for 27 of the 43 attacking IJN planes shot down.132 But only 43 out of the 350 planes in the raid were destroyed. The same machine guns were most effective by aircraft against other aircraft, in short range .

128 Parshall and Tully, Shattered Sword 142. 129 Table X-1, Appendix A. 130 Ibid 143. 131 Glossary. An effective USN F4F WILDCAT tactic against the faster IJN A6M ZERO used in one exchange at Midway to down four ZEROs. This tactic became more important after Midway. 132 http://www.ibiblio.org/hyperwar/USN/rep/Kamikaze/AAA-Summary-1045/index.html 42 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

In summary, the Aircraft Arm was formidable. The DAUNTLESS dive bomber with fighter cover was the most powerful USN offensive arm against the 1st Kido Butai. The four carriers of the 1st Kido Butai were destroyed by DAUNTLESS dive bombers. AKAGI was sunk by Dick Best of ENTERPRISE. KAGA was sunk by Wade McClusky’s squadron of

ENTERPRISE. SORYU was sunk by Max Leslie’s squadron of YORKTOWN. Finally,

HIRYU was sunk by squadrons of both ENTERPRISE and YORKTOWN.133

Trafalgar Comparison – Communications: language and radio

At Midway, the IJN had poor radio contact with and between its aircraft. This was due to the quality of the equipment and the procedure of using one channel for all aircraft communications.134 Poor ship to ship communications caused the MOGAMI and MIKUMA to collide when MOGAMI sighted the USS Submarine TAMBOR.135 The USN had better radio equipment and procedures.

At Trafalgar, the Combined French-Spanish Fleet had a language barrier. The national code books were different. The Spanish translation of the French code book was not available at the battle. The Fleet agreed to use general signal books in French, one for day and one for night.

All the repeating ships were French to the French flagship, but there remained problems with lack of training and experience, especially at night.136

The British signal flag system was sophisticated and the signal officers well trained.

Nelson met frequently with his officers to keep them updated on his plans. Villeneuve apparently did not communicate as much with his own officers, much less the Spanish. The

133 Parshall and Tully, Shattered Sword 262. 134 Ibid 136, 146 135 Kimmet and Regis, U.S. Submarines in World War II 45. 136 Adkin, The Trafalgar Companion 451. 43 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Combined Fleet made 17 pre-battle signals, the British 31. Most of Nelson’s signals gave additional tactical guidance for the battle; whereas, most of Villeneuve’s signals were to get his ships back into a line, after wearing back to Cadiz.137 Better communications were shown by the winning side at Trafalgar and Midway.

137 Ibid 446-451. 44 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

C. TOTAL IJN AND USN FIREPOWER COMPARED

All firepower on all attack craft is summarized in Table I.138 Each force had Tera Joules of firepower (1012 or one trillion Joules). The IJN had a potential 2.9 Tera Joules /’ and the

USN 1.0 TJ/’.

Aircraft contributed only 16% of total IJN firepower at Midway, but 56% of total USN firepower. Although aircraft was a fraction of total firepower, the battle was decided in the first phase of the battle, to control the air. This smaller fraction of mobile, fast and accurate firepower was the deciding factor at Midway. A full-strength, fully constituted, coordinated strike was very hard to defend against.

TABLE I. Total firepower of IJN and USN in Pacific Operation.

138 Table X-27, Appendix A. 45 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

46 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

IJN and USN Mega Joules per minute versus Lanchester Military Effectiveness

Comparing Mega Joules to “Military Effectiveness” is instructive.

TOTAL IJN AND USN PACIFIC OPS FIREPOWER

MIDWAY ALEUTIANS TOTAL BOTH MegaJ/' MegaJ/' MJ/'

IJN 2,386,769 529,978 2,916,747

USN 810,633 197,536 1,008,169

TABLE II. IJN & USN Pacific Total Firepower.

Total Firepower in Mega Joules. Table II reiterates the physical measure of firepower in

Mega Joules per min for the two forces, for comparison to Chart 7 below, which shows the

Lanchester-derived military effectiveness. Mega Joules are calculated from known firing characteristics of weapons with chemical explosive and mechanical kinetic energy. These objective numbers have a solid basis in physics and chemistry.

Lanchester-derived Military Effectiveness. Chart 7 compares the IJN to the USN by the number of units in each class of attack craft. The numbers of attack craft are easily available and verifiable. With these numbers, military effectiveness (M.E.) can be analyzed by Lanchester’s

N-Square Law (see “Lanchester’s equations” below). By the N-Square Law, M.E. = (rate of fire) * (number of units)2.

CHART 7 shows the number of IJN and USN units.139 The M.E. of one force is compared to the other by a ratio.

139 From Table X-32 in Appendix A. 47 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

In Chart 7

lower right,

before the split

to the

Aleutians, the

M.E. for

carriers is 7.11.

The IJN had a CHART 7. Total Midway + Aleutian Forces. Numbers of Carriers all types, Ships and Aircraft compared for IJN and USN. Military effectiveness ratios for each type of attack craft compared. M.E. ≈ N2. On approach to Midway, the M.E. ratio favored the IJN in all but submarines. (CVE/2 gives better estimate for carrier M.E.) large advantage and would be predicted to win. Instead of calculating the firepower for each weapon, the N-Square Law uses a single value for the firing rate of the entire force. Here, as below in the beginning of Part II, similar firing rates (α=β=1) are assumed for the Lanchester and

48 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Salvo Equations. Chart 7 shows that the IJN dominated in carriers, ships and aircraft, with near parity in submarines. But this does not tell the whole story, as will become apparent below.

Decisive Firepower, which sank carriers at Midway.

Of the massive firepower of the two opposing fleets at Midway, only a small, targeted fraction was responsible for sinking the carriers. Table III shows the 23 weapons which sank the

DECISIVE FIREPOWER AT MIDWAY (MEGA JOULES / MIN)

kg no. MJ/' Tot MJ/' kg no. MJ/' Tot MJ/' YORKTOWN AKAGI bomb 455 1 1127 1,127 A/C Bombs 250 3 497 1,490 KAGA bombs 455 1 1127 1,127 A/C Torp 91/2 837 2 1004 2,008 227 4 500 2,000 SS Torp 89 1,668 5 1469 7,345 SORYU bombs 455 3 1127 3,381 HIRYU bombs 455 4 1127 4,508 10,843 12,143

TABLE III. The 23 weapons which sank the carriers at Midway carriers. Dive bombers sank all 4 IJN carriers. YORKTOWN was hit by dive bombers, torpedo bombers and a torpedo spread by I-168 before she sank. carriers at Midway. Only 12,000 MJ/’ of the USN’s total firepower of 1,008,000 MJ/’ wiped out the four fleet carriers of the 1st Kido Butai. This was about 1%. Only 11,000 MJ/’ of the IJN’s total firepower of 2,916,000 MJ/’ sank the YORKTOWN. This was less than ½ of 1%. The average firepower to sink an IJN carrier at Midway was 3,036 MJ/’. It took about three times more to sink the YORKTOWN, from three types of attack craft.

49 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

The question of the ZUIKAKU

The ZUIKAKU was undamaged at the Battle of the Coral Sea in May 1942 but lost many of her Air Group. She did not take part in the Battle of Midway a month later. The IJN followed the doctrine that an Air Group was integral to a Carrier and not moveable one to another.140 The

ZUIKAKU full complement firepower No. MJ/' Tot MJ/' A6M2 18 391 7,038 D3A1 27 871 23,517 B5N2 27 1,005 27,135 Subtotal 72 57,690

TABLE IV. ZUIKAKU full complement potential air firepower with reconstituted air wing. doctrine prevented replacements. ZUIKAKU had a reduced Air Group and the command had her stay in port in June.

Although perhaps good for perfectly constituted strikes and morale, this IJN doctrine was a key operational weakness preventing the ZUIKAKU from participating with the 1st Kido Butai at Midway. Table IV shows the additional airpower this carrier with replacements could have added to the Pacific Operation. There would have been another fleet carrier, another 72 aircraft, another 60,039 MJ/’ firepower with the 3,000 MJ/’ from the carrier’s AAW guns.

ZUIKAKU actual firepower Jun 1942 No. MJ/' Tot MJ/' A6M2 24 391 9,384 D3A1 9 871 7,839 B5N2 6 1,005 6,030 Subtotal 23,253 Repairable aircraft (unkwn types) 17 756 12,846 TOTAL 56 36,099

TABLE V. ZUIKAKU air firepower remaining on board after Battle of the Coral Sea and which could have been used at Midway.

140 Stille, Midway 1942 17-18. 50 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

But the actual details of ZUIKAKU tell an even more intriguing story. After Coral Sea, the carrier retained 39 aircraft that were operational and another 17 that were repairable. This was a total of 56 aircraft - about the same complement as the other carriers in the 1st Kido Butai.

The operational aircraft included 24 A6M fighters, 9 D3A dive bombers and 6 B5N torpedo bombers.141 142 Table V shows the immediately available firepower in June 1942 that ZUIKAKU would have added to the battle.

The exclusion of the aircraft of the ZUIKAKU will have importance for Midway scenarios in Part II.

141 Stille, Midway 1942 18. 142 The seeming discrepancy between a full complement of 18 A6M fighters versus the remaining 24 A6M2 fighters can be explained. There were “12 spares” which were carried in ZUIKAKU, but not included in the usual striking force of the active combat aircraft. The extra fighters could have been used for CAP or scouting as well as fighter cover for attacking squadrons of dive bombers and torpedo bombers. CAP varied from 4-6 aircraft. 51 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Trafalgar Comparison- Firepower.

Technology produced a dramatic increase in firepower since Trafalgar. How much increase? Table VI shows the firepower in Mega Joules per minute available to the commanders at Midway and the firepower a century before at Trafalgar.143 Total British firepower at Trafalgar was equal to two USN 1000 lb. ordinary bombs (2 x 1127 MJ/’) or one IJN Type 93 Long Lance

Torpedo (2,405 MJ/’). From Trafalgar to Midway, total firepower increased a thousand-fold.

The measure of firepower is revealing for the odds at Trafalgar. At Trafalgar, despite the larger total broadside weight of the French-Spanish Fleet, the British had more than twice the offensive firepower due to superior gunnery. At Midway rate of fire also was important for the

USN advantage in defensive anti-aircraft weapons (AAW). At Trafalgar, the victors approached the field with an offensive firepower advantage, but at Midway the reverse was true.

Trafalgar was dominated by maximum firepower expended in the battle line at 500 yards

TABLE VI. Firepower at Midway (1942) and Trafalgar (1805) - mps meters per second, MEGA J Mega Joules, RPM rounds per min, MJ/’ Mega Joules per min

143 Table X-30 in Appendix A. 52 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws or in the mêlée at close range. At Midway, massing of force was still the goal. But this was so that just a few aircraft could get through enemy defenses to deliver their weapons from 200 miles away.

Over the century naval firepower increased three orders of magnitude. This mushroomed on 9 August 1945 at Nagasaki to 88,000,000 Mega Joules per second (88 Tera Joules, 21 kilotons TNT) with the implosion uranium fission bomb, and again on 30 October 1961 to

210,000,000,000 Mega Joules per second (210 Peta Joules, 50 megatons TNT) with the largest thermonuclear weapon.144

144 https://en.wikipedia.org/wiki/Tsar_Bomba 53 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

PART II: FIREPOWER RATIOS, SALVOS AND TIMELINE

A. MODERN FIREPOWER

Fewer Exchanges in Modern Warfare

There were major changes in warfare during the century and a half that separated

Trafalgar and Midway. Up to 1905, ships of the line traded broadsides, raking fire or crossing the T, with gradual attrition. This occurred at Tsushima 1905, Cape Esperance 1942, Surigao

Straight 1944 and the initial actions off Samar 1944. All were surface ship battles.145

But with aircraft carrier battles, first at Coral Sea, attrition was big and quick. The air wing of a carrier delivered a massive pulse of firepower.146 Table VII shows Midway outcomes.

One air wing of three squadrons was enough to sink one carrier (18 dive bombers, 18 torpedo bombers and 18 fighters = 64 aircraft).147 Survival depended on the active and passive defense of the carrier.148 First strike was paramount, from early warning by scout planes, submarines and

Theoretical Survivors After U.S. After Japanese After U.S. attack Counterattack re-attack A Japan 1 1 0 B U.S. 3 2 2 Battle Synopsis Initial Forces Actual Survivors CV Aircraft CV Aircraft A Japan 4 272 0 0 B U.S. 3 233 2 126

Hughes, W.P., Girrier, R.P. (2018): Table Midway, June 1942 p87. intelligence.149

145 Sutherling, Two Influences of Trafalgar on Navy Tactics 1905-1944 36-51. 146 Hughes and Girrier, Fleet TacticsTABLE and Naval VII. Operations Midway 84.Outcomes 147 See Glossary. 148 Parshall and Tully, Shattered Sword 144. 54 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Instead of gradual attrition, Table VII shows three massive losses from USN and IJN attacks. After the first attack, the USN reduced the IJN from four carriers to one. During the counterattack, the remaining Japanese carrier took out one USN carrier. Finally, the last IJN carrier is sunk. To emphasize, after the USN strikes, it has a decisive advantage. It reduces the

IJN force from a 4:3 advantage to a 1:3 disadvantage. The tables are instantly turned, due to the element of surprise allowing a first strike. These massive losses in carrier attacks strain

Lanchester’s Equations and led to the Salvo Equations.

The USN surprise attack arose from the USN’s more thorough scouting and a little luck

(Murphy’s Law or the laws of probability). McClusky’s attack on the IJN carriers occurred during persistent scouting on vector. He continued despite low fuel and subsequently sighted the

IJN destroyer ARASHI. Due to unrelated events, the ARASHI just happened to be south of the

Japanese carriers. McClusky sighted the ship after it broke off pursuit of the submarine USS

NAUTILUS and rushed to rejoin the 1st Kido Butai. He followed it back and his squadron finally sank two carriers. Yet another squadron sank a third carrier.

149 Ibid 84. 55 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

The Dynamics of Naval Battles.

The next sections show in visual form the dynamics of naval battles from Trafalgar to

Midway. There is just enough detail to allow the reader to gain a deeper understanding of why the battles turned out the way they did. There are more details in Appendix B and C. The busy reader can skip this part now, go directly to TIMELINE and come back later.

Lanchester’s Equations and Fiske’s Tables.

Lanchester in 1916 studied Trafalgar and other sea battles to show how destruction of the enemy’s forces by attrition worked.150 His relations were simple. He modeled concentrated fire, when each gun aimed at an enemy ship. This is aimed fire, different than barrage fire. He knew that the number of enemy ships sunk was in proportion to the number of friendly ships firing.

He used the effective firing rate, the number of successful hits that a friendly ship made in one hour. He concluded that the number of enemy ships sunk per hour was equal to the effective firing rate times the number of friendly ships. This relation can be more concise:

This is Lanchester’s Equation. There are two of these equations for each battle: one for one side, another for the other side. He named one side A, with firing rate α, and the other side

B, with firing rate β. Thus, B’s guns sink A’s ships. The number of A-ships sunk is due to the hits by B-guns. This is β x B or βB. The number of B ships sunk per hour is α x A or αA.

These same relationships were apparently discovered independently and listed in tables in the same year by Fiske.151 He showed a disproportionate, stepwise decimation of a smaller force due to its loss of ability to counterattack.

150 Lanchester, Aircraft in Warfare. 151 Fiske, The Navy as a Fighting Machine Tables I, III. 56 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

The following figures illustrate the dynamics of Lanchester’s equations, first for a larger force then for a faster firing rate:

57 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

FIGURE 4. Illustration of Lanchester’s Equation for a larger force: 48 ships vs 24 ships. Both have same gunnery. The larger blue force rapidly decimates the smaller red force, with disproportionate survival of the larger force. Here α = β = 10%.

A. Time 0000.

B. Time 0100 hour.

A. Time 0200 hours.

A. Time 0300 hours.

58 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

In Figure 4, the larger force sinks more ships of the smaller force with the same gunnery, in the first hour. In the next hour, the smaller has lost enough ships that it sinks fewer of the larger.

But the larger still has enough ships to sink about the same number of the smaller. At 0300 hours, the smaller force has lost 14 ships with 10 remaining, while the larger has lost only 7 with

41 remaining. The size ratio started out at 2:1, but it is now 4:1.

CHART 8. Illustration of Results of Lanchester’s Equation for many different starting force ratios, due to different numbers of ships. The first block on the left shows the case of Figure 4 above, the columns for the blue and red ships at 0300 hours: there are 41 blue ships remaining and 10 red. The grey column shows that at the end of the battle at 0600 hours, 40-41 blue ships remain after all red have been sunk.

Chart 8 shows the Lanchester results for seven separate battles with different initial force sizes, emphasizing that size is paramount. The first block on the left shows the case of Figure 4 above, 48 blue ships to 24 red ships - a starting ratio of 2-1. There are 41 blue ships remaining and 10 red at 0300. The grey bar shows that 40-41 blue ships remain after the battle, when all the red ships have been sunk. Each of the next blocks to the right shows the results for fewer and fewer starting ships for the larger force, but the same 24 ships for the smaller. With each step to

59 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws the right, more red ships at the 0300-hour mark are expected with a more equal ratio, and the chart shows this.

But what is totally unexpected is the last block to the right – the result with a small two ship advantage, a 26-24 ratio. This results in fully nine ships surviving of the larger force. Thus, even a small number advantage is useful to win a battle and preserve the ships of one’s fleet.

This is the remarkable insight from Lanchester’s Equations and Fiske’s Tables.

The N-Square Law.

Graph 1 illustrates by example the behavior of Lanchester’s N-Square Law. It shows the data from Chart 8 in a different form. The colors represent different things in this graph. The

GRAPH 1. This shows the ship and firepower ratios between the larger and smaller navy in Chart 8. The colors are different than in the chart. The ratio of the numbers at the start is blue and at the end is grey. The start ratio squared is orange and is virtually the same as the end ratio. The start number ratio squared approaches the firepower ratio. The blue, orange and grey colors are used differently here than in Chart 8.

60 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws relative fleet sizes at the beginning for the seven separate battles are shown on the horizontal axis, as in Chart 8. The blue line shows these same relative sizes as ‘start ratios’ on the vertical axis. A line is used for clarity instead of seven dots. Thus, the 48/24 relative size gives a start ratio of 2.00, via the blue line. The grey line shows the final relative fleet sizes or ‘end ratio’ at the end of each battle at 0300. Thus, the final relative sizes of 41-10 gives an end ratio of 4.10, via the grey line. If one squares the values on the blue line, one gets the orange line. The square of the number of ships is proportional to the firepower. The Graph shows that the grey and orange lines overlap.

In these examples, the end ratio is related to the firepower ratio at the beginning. The end ratio is due to attrition or loss of ships during the battle. The two sides have different losses due to the different sizes of their navies. The smaller has greater losses. This is due to the difference in firepower between the two navies, the ratio of firepower.

Firepower ratio ≈ end ratio ≈ (start ratio)2.

Start ratio = B/A

(start ratio)2 = (B/A)2 = B2/A2 ≈ firepower ratio.

This does not prove conclusively that firepower is related to B2 or A2, but it suggests it.

61 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

FIGURE 5. Illustration of Lanchester’s Equations for faster 3:1 gunnery. Trafalgar: 27 British vs 33 French-Spanish ships. British superior gunnery outweighed its fewer ships. The effect was even more, after Nelson cut the line in two to defeat in detail.

A. Time 0000.

B. Time 0100 hour.

A. Time 0200 hours.

A. Time 0300 hours.

62 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Figure 5 shows that Lanchester’s Equations show a similar effect for faster firing rate, superior gunnery. Larger size and/or better gunnery can win battles.

Lanchester solved the equations for the overall firepower or “military effectiveness” of a force. The example in Graph 1 suggested the answer. The solution for the effect by the B-guns was βB2 and by the A-guns was αA2. This resulted in the “N-Square” Law:

βB2 – αA2 = constant 152

Here βB2 is the firepower or “military effectiveness” of B. In this term, the number of ships B is the most important. This number is squared and dominates. For 2 ships firepower is

4, for 3 ships firepower is 9, 416, 525, etc. Therefore, concentrating mass or number of ships is paramount. This is the proof of the principle of mass.

At first the squared term B2 seems strange. But the example in Figure 4, Chart 8 and

Graph 1 showed this. The battle starts with 48:24 ships or a 2:1 ratio. Then 3 hours later, there are 41:10 ships or a 4:1 ratio, this is 22:1. There is a disproportionate reduction in the size of the smaller, which produces a disproportionate reduction of its hitting power against the larger. The smaller size results in a smaller hitting power. The smaller hitting power allows the larger force to shoot more incoming hits. These hits result in an even smaller size of the smaller force, etc.

There is a vicious cycle, where the smaller size seems to reduce itself even more. So, the squared term is not so strange after all.

If βB2 > αA2, the military effectiveness of B is greater than A, the constant is positive, and

B wins the battle. If αA2 > βB2, then A wins the battle. The solution of the Lanchester equations to reach the N-Square Law requires a calculation method of small differences. One derivation of

152 Derivation of solution is in Appendix B, from Sutherling, Two Influences of Trafalgar on Navy Tactics 1905-1944 64-65. 63 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws the solution is given in Appendix B. Lanchester and Fiske used this approach to analyze naval battles of surface ships.

64 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

The Salvo Equations.

The Lanchester equations worked well for naval battles between surface ships, ships of the line and dreadnoughts. However, in modern carrier battles the new feature of squadrons of multiple attack aircraft introduced dynamics different from gradual attrition by cannon. Instead, there were interchanges of sudden, massed pulses of firepower with bombs and torpedoes. One carrier’s airwing of 60-80 aircraft was enough to knock out an enemy carrier. The salvo equations are more predictive of the outcome of carrier battles. They show how many carriers are sunk by each massive aircraft salvo.153 154 The Salvo Equation can be concise:

This is like the Lanchester Equation. Those terms that are similar are in black. On the left side of the equation is the number of enemy ships sunk per salvo, the rate of ships sunk. On the right side of the equation, there is the striking force, or the firing rate x the number of friendly carriers. But then there are new terms. These are shown in blue. The striking force is decreased by the defensive force of the enemy carriers. Then that combined result is divided by the staying power term. If the staying power is 1, then the combined result is not reduced. If it is

2, then the result is reduced by half. This means that the effect of the striking force is further decreased. Although the added terms used in the equation are a bit unusual at first, the underlying relationships are logical and commonsense. There are two salvo equations for a battle, just like the two Lanchester equations, one for each opposing navy.

153 Hughes and Girrier, Fleet Tactics and Naval Operations 264. 154 Hughes, “A Salvo Model of Warships...” In Warfare Modeling 125. 65 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

The salvo equations still follow the same logic as the Lanchester equations. The number of enemy carriers sunk are still in proportion to the effective firing rate times the number of friendly carriers. If the enemy is A and the friendly is B, then the number of A sunk is still related to βB, the striking power of B. But with aircraft, there arise additional terms.

Defensive power = defend rate x enemy carriers (a3A) – The defense rate a3 multiplies by the number of enemy carriers A. The force A defends against the aircraft of B by its fighter

Combat Air Patrol (CAP) and its AAW guns. Thus, the striking power of βB is reduced by A’s defensive power of a3A.155 Again, size or number of carriers is paramount, since it determines both offensive and defensive power. Lanchester’s fundamental insight remains true.

Staying power (a1) - This is how many salvos a carrier can sustain before it sinks. The unit of strength A, the aircraft carrier, is massive and difficult to sink. The larger the staying power is, the more hits required and the smaller loss of A. Staying power reduces the effect of striking power. Striking power is divided by a1. For example, a carrier with a1 = 4 can sustain four times as many hits as a carrier with a1 = 1. The goal is to sink the carrier. A damaged carrier can be repaired and fight again. Staying power is a new term, without analogy in

Lanchester. Note the difference in putting it out of action and sinking it. Damaging a carrier is important tactically for the battle. Sinking a carrier is important strategically for the war.

Were the IJN and USN equivalent in defensive power? The main offensive attack craft at

Midway was aircraft. The primary defense against aircraft was other aircraft, fighter cover. The

IJN had the ZERO, the USN the WILDCAT.156 157 Although the WILDCAT had more armor, the

155 Hughes and Girrier, Fleet Tactics 264 used IJN a3=1/7 and USN b3=1/2 in Battle of Philippine Sea. 156 In a subsection of one squadron at Midway, one pilot, John Thach, and his wingman repeatedly crossed horizontally in their WILDCATS to allow his wingman to shoot down an attacking ZERO following on his tail. Together they shot down four ZEROs. The “Thach Weave” became the great equalizer of the 66 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

ZERO was generally accepted as the best fighter early in the war and at Midway. Aircraft was the primary defense. On the other hand, the IJN had inferior anti-aircraft guns (Chart 1), mostly ineffective against the DAUNTLESS dive bomber (Figure 3). The IJN relied on maneuver rather than AAW guns. This was useful against high altitude bombing, but less against dive bombers. The USN had radar for early detection for defense, in addition to superior AAW guns.

Overall, then, the strengths and weaknesses balanced out. With these considerations, in applying the salvo equations to Midway, it is logical to select a3=¼ and b3=¼, where the USN (B) and

IJN (A) had similar defensive firepower (see its footnote above).

Hughes (1995) considered staying power a1 = b1 for the Battle of the Philippine Sea.158 In that battle, however, a recent study shows that IJN damage control training, doctrine and procedures remained inferior; three carriers were sunk after failed damage control.159 160 At

Midway only one 1000 lb. general purpose bomb sank AKAGI.161 It caused a fire, which spread and destroyed the carrier. KAGA was sunk by four 500 lb. and one 1000 lb. bombs,162 SORYU by three 1000 lb. bombs163 and HIRYU by four 1000 lb. bombs.164 The only USN carrier hit at

Midway was YORKTOWN, which was repaired in two hours after three 500 lb. bombs hit.165 166

ZERO and the WILDCAT. Although it was not used widely at Midway, where the ZERO generally outperformed the WILDCAT, afterwards it became a standard tactic. 157 https://en.wikipedia.org/wiki/John_Thach 158 Hughes, “A Salvo Model of Warships” in Warfare Modeling 121-143. 159 Stille, The Philippine Sea 1944 77, 87. 160 The carriers lost were TAIHO, SHOKAKU and HIYO. 161 Parshall and Tully, Shattered Sword 253. 162 Ibid 249. 163 Ibid 251. 164 Ibid 327. 165 Ibid 292-298. 166 YORKTOWN (Coral Sea) bombs unsinkable, (Pearl) repaired 48 hr  (Midway) bombs unsinkable repaired 2 hr  aerial torpedoes listing  submarine torpedoes sunk. YORKTOWN was repaired in 48 hours after Coral Sea. Kobayashi’s dive bomber attack from HIRYU produced damage which was repaired by YORKTOWN’s crew in 2 hours underway at Midway. It took another attack by Tomonaga’s torpedo bombers to put her out of action with a 23-degree list so she could not launch or land aircraft. 67 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Even a squadron of torpedo bombers did not sink the carrier. A submarine did. These data support better USN damage control and a difference in survivability at Midway. As an initial estimate for Midway, it would be logical that, conservatively, the USN b1= 2 and the IJN a1 = 1.

The Dynamics of the Salvo Equations.

The following charts illustrate the dynamics of the Salvo Equations. Some results are like the Lanchester equations, due to numbers and effective firing rate. But the new terms for defensive and staying power introduce new dynamics. The following charts show the effects of different values of defensive power a3 and staying power a1 during a first salvo interchange in ten and eight separate simulated battles between the IJN and USN:

Chart 9 shows different battle outcomes for ten different values of defensive power a3 but with the same

CHART 9. Salvo Equations for decreasing IJN defense term a3 but constant USN defense term b3 = 0.5. Each horizontal block represents a separate case. Other terms for the IJN and USN are the same: both have the same number of original carriers (4), same striking power of 1 and same staying power of 1.

Only the final attack of torpedoes by submarine I-168 finally sank her. These data compel the estimate that, for YORKTOWN at Midway, the b1 ≈ 2. 68 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

starting numbers and variables. The numbers are shown after the initial salvo exchange between an IJN force and a USN force. Each block of two pillars is for a specific value of a3. The first block shows the effect of a3 = 0.45, while b3 remains constant at 0.50. After the initial salvo, the USN is reduced from four carriers to two carriers. But the IJN is reduced from four carriers to 1.8 carriers. The next block shows the effect of a3=0.40 while b3 remains at 0.50. The IJN is reduced from four carriers to 1.6 carriers. The chart shows that progressively smaller values of a3 gives a linear reduction in the surviving IJN carriers after the initial salvo exchange. Since a1,

69 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws and b1 are both set equal to 1.00, the dividing term does not affect the result. In this case the salvo equation becomes the equation of a straight line.

Chart 10 shows a different effect. It shows different battle outcomes for eight different values of staying power a1. The equations behave differently here. With progressively smaller values of a1, the numbers change in a non-linear way. For clarity, both sides are given a large original value of a1=b1=10.00. Both sides start with 4 carriers, a3=b3=0.50 and α=β=1. The chart shows the values, when the difference begins to have a visible effect. The block on the left

show the results for a1=6.00 and b1=10.00. After the initial salvo exchange with these values for staying power, the IJN drops from 4.00 to 3.67 carriers remaining and the USN drops from 4.00

CHART 10. Salvo Equations for decreasing IJN staying power term a1 but constant USN b1 = 10.00. Other terms for IJN and USN same. to 3.80 carriers. Since b1 doesn’t change, the USN keeps the same 3.80 carriers in all other blocks to the right. The overall effect is small from 6.00 to 3.00. After that it becomes more prominent with a big drop at a1=1.00. The chart has been extended to the right to show values for a1 equal 0.75 and 0.50, on the horizontal axis. When a1=0.50, all the IJN carriers are sunk

70 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws with the first salvo interchange, while the USN retains 3.80 carriers. In this last case, three USN carriers remain operational, and the 0.80 damaged carrier can be repaired and sent back to the fleet. The chart shows that with progressively smaller values of a1, representing worse damage control and/or carrier design, there is a larger and larger, non-linear loss of IJN carriers during the initial salvo exchange.

The above examples of the salvo equations show the effects of variation of only one term at a time. But all four terms can vary between opposing navies: starting number, striking power, defensive power and staying power. As a result, these equations can show more complex interactions than the Lanchester equations.

The solutions to the salvo equations are more complicated than those of Lanchester, since the equations are more complicated. They are given here once for completeness and comparison.

They have a similar term (in bold) as the Lanchester solutions but with additional terms:

a1αA2 – a1Ab3B

b1βB2 – b1Ba3A

If the first solution is larger than the second, then A wins the salvo exchange.

If the second is larger, then B wins the salvo exchange.

This is like the Lanchester Equations.

In both solutions, which are enclosed in squares, the first term is related to striking power and the second term to defensive power.

The salvo equations confirm conventional wisdom and have implications for the disposition of forces at Midway. The equations show that a force inferior in other ways can compensate by increasing its size, A or B. Massing a larger force against a smaller force is

71 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws usually paramount. This will be important below during the analysis of alternative scenarios for

Midway.

Scouting. There are other “embellishments,” which can be made to the salvo equations.

They capture other variables important in battles. These are scouting effectiveness (σ), readiness, seduction chaff, evasion, distraction chaff and training.167 Each of these terms take a value between 0 and 1 and then multiplies by one of the more comprehensive variables α, β, a3 or b3.

The latter thus become composite terms with more than one variable affecting them. The composite terms are then used as before, as multipliers of A or B.

Scouting was crucial. The IJN had worse scouting. At Midway they had too few scout planes assigned, their scouting plan was porous, and their launch delayed.168 Only by two unrelated errors exactly canceling each other fortuitously, did the IJN search pattern detect

YORKTOWN at 0728, although one hour after it came in range.169 Captain Minoru Genda, an otherwise skilled officer, was responsible for scout planning and the inadequate number of search planes.170 Due to the faulty scouting, the IJN never located ENTERPRISE or HORNET.

On the other hand, the USN had excellent scouting. This was due, in large part, to the long-range PBY’s from Midway Atoll. They first detected the IJN fleet. The IJN made little effective use of its it many land-based long-range flying boats, the H6K and H8K. Although these were farther away from the battle than Midway Atoll, these flying boats had been used near

French Frigate Shoals in the vicinity before. A prior conflict at FFS may have deterred them.

They certainly had adequate range of 4,000 nm.

167 Hughes, “A Salvo Model of Warships” in Warfare Modeling 129. 168 Parshall and Tully, Shattered Sword 147-148. 169 Ibid 160. 170 Ibid 401. 72 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

The difference in scouting compels modification of the salvo equations to include factors

for sigma σA multiplied times α and for σB multiplied times β. If scouting effectiveness for the

USN was σB = 1.0, then σA for the IJN would have been smaller. The absolute number can be

argued, but here it is proposed conservatively that, at the most, σA = 0.75. The resultant

reduction of α, from 1.0 to 0.75, due to σA = 0.75, is important. The IJN could not attack what it could not see. They could not see ENTERPRISE or HORNET. Thus, for Midway, α = 0.75 and

β = 1.0 are used in the salvo equations

Trafalgar Comparison – Firepower equations for the two battles

The Lanchester equations apply to ships at Trafalgar. The Salvo equations apply to aircraft carriers at Midway. Lanchester considered force size B (number of ships/cannon) and gunnery β (effective rate of fire) at Trafalgar. The salvo equations have similar terms - number of carriers B and effective hits per carrier air wing β.

What about the other two terms in the salvo equations? Did they have any analogs at

Trafalgar? There is no defensive term a3 in the Lanchester equations for Trafalgar, no destruction of “incoming cannon balls”. The only parallel in the 1800s might be the 21-inch thick hull of the USS CONSTITUTION, which could deflect the usual cannon ball.171 What about staying power a1, the number of hits to sink a French ship? This was moot at Trafalgar.

Once a sailing ship was put out of action, it was in the mêlée near at hand and not hundreds of miles away. It could not escape back to port without masts. The French-Spanish ships were captured and then either sunk or commandeered by the British to be refurbished as HMS vessels.

171 https://en.wikipedia.org/wiki/USS_Constitution 73 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Put out of action was the same as lost to its fleet at Trafalgar. But some of the embellishments to the salvo equations were important at Trafalgar: scouting effectiveness, readiness and training.

Greater massing of force does not avoid M.A.D.

Massing larger firepower wins battles. But it is not always the answer to survival. This paradox is illustrated by the following example taken from Hughes.172 Consider two forces, A and B, with the following features. A has two carriers and B has six, so A=2 and B=6. Each A has four times more striking power than B, so α=24 and β=6. Each A has sixteen times the defensive power, so a3 =16 and b3=1. Each A has twice the staying power, so a1=2 and b1=1.

The results from the salvo equations are enlightening.173 Due to its superior striking power, defensive power and staying power, A can sink the 6 units of B seven times over with one salvo. But, due to its larger size, B can also sink both units of A with its first salvo. This would result in a stand-off. A and B will avoid the battle; it is suicide for both. There must be enough ships to win and survive largely intact. B will only have survivors if it has more than 42 ships. This is relevant to modern missile warships and mutually assured destruction.

Philippine Sea.

The salvo equations were used to model the Battle of the Philippine Sea.174 The Japanese,

A, had 9 carriers and the US, B, had 15 carriers. A carrier’s salvo was its air wing. The values for α, β, a1, and b1 were set equal to one. The values for defensive power were b3 = ½ for the

US and a3 = 1/7 for Japan. These reflect the better USN anti-aircraft defensive weapon systems and the inexperienced IJN pilots after Japan had lost its best air crews, later in the war. The result of the above variables in the salvo equations show that its superior numbers and

172 Hughes, “A Salvo Model of Warships” in Warfare Modeling 127-128. 173 Detailed analysis in Appendix C. 174 Hughes and Girrier, Fleet Tactics and Naval Operations 264. 74 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws defensive power gave the USN a 15 to 1 advantage.175 The superior striking power, defensive power, staying power and size of the USN force made a US victory very likely in the

Philippine Sea “turkey shoot.”

Midway.

The salvo equations reveal the effect of force sizes or number of carriers during the timeline at Midway. The values for defensive power, however, should reflect the more experienced IJN pilots at Midway, compared to the inexperienced ones later in the Philippine

Sea. The equations should also show the same relative weakness of the IJN surface ships’ anti- aircraft weapon systems. At the Philippine Sea in 1944, the USN had a 3.5 to 1 advantage in defensive power [3.5 to 1 = a3 / b3 = (½)/(1/7)]. At Midway in 1942, the initial assessment in the salvo equations above indicated equivalent defensive power at Midway with a3= ¼ and b3=

¼ . The USN’s better damage control and carrier design gave it a staying power advantage, with a1=1 and b1=2. During the battle, all these variables would remain constant except the number of operational carriers A and B. These variables are inserted into the salvo equations in

Appendix C. The results are illustrated in the Timeline at Midway, which follows.

175 Appendix C. 75 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

B. THE TIMELINE AT MIDWAY

A half-century has elapsed since Midway and a century and a half since Trafalgar. New data on Midway has recently been published, after access to IJN records. Midway is still a work in progress for naval historians. The following relies primarily on these main sources: Parshall and Tully’s Shattered Sword (2005) and Stille’s Midway 1942 (2010) for the battle and Hughes’

Salvo Model of Warships in Missile Combat (1995) and Fleet Tactics and Naval Operations

(2018) for quantitative analysis.176 These works are up to date at this time. These sources for

Midway are analogous to the two main ones for Trafalgar: Adkin’s Trafalgar Companion (2005) and Lanchester’s Aircraft in Warfare (1916).

Most supporting data and existing opinions have been taken from Parshall and Tully.

What is attempted here is to collect the salient features of the dynamics of the Battle, put them together and compare them to assess the effect of the principle of mass. Then Midway is compared to Trafalgar.

After Coral Sea

Yamamoto planned a knock-out blow early before the United States could gear up its industry. He wanted a decisive battle to destroy the USN carriers in the Pacific. The Imperial

Japanese Army and Naval General Staff agreed on condition that he launch a simultaneous

Aleutian operation. This political constraint reduced his effective forces at Midway. Yamamoto acceded to a division of force to get approval for his Midway operation.

176 Stille Midway 1942 and en.wikipedia.org have already been noted extensively in the first part of this study. Stille gives a detailed order of battle. Parshall and Tully, Shattered Sword reveal a more detailed and favorable view of Nagumo from the Japanese sources available to them than the conventional story reviewed in Stille. Both views are worth reading on Nagumo and Yamamoto. 76 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

This dilemma was analogous to the political constraint on the Younger Moltke of neutral

Belgium, which stood in the path of the Schlieffen Plan advance. The excellent railroad network of Belgium sped up the great wheel of the German attack on France in 1914. But invading

Belgium brought in the Allies against Germany. The fatal consequences of the political decisions were self-defeating in 1914 on the Somme by increasing the opposing force. The political constraints were self-defeating in 1942 by dividing IJN forces at Midway.

But given Yamamoto’s concession to the Aleutians, were carriers required in the

Aleutians simultaneously with the initial attack on Midway? Alternative scenarios are reviewed below.

IJN Steaming to Midway with four carriers as 1st Kido Butai

This was the actual situation. Yamamoto sent two carriers to the Aleutians. This reduced the IJN military effectiveness.

After first attack on Midway Atoll

The 1st Kido Butai attacked Midway Island. When Spruance was informed of this, he rapidly realized that a window of opportunity had opened. Nagumo would soon have to recover the attacking planes onto his carriers. During that time, he would be vulnerable. Soon thereafter

Spruance launched his own strike on the Japanese carriers.

Tomonaga, the flight attack leader, radioed that a repeat attack was needed. Nagumo’s force was indeed counterattacked first at 0710 by six TBF Avenger torpedo planes and four B-26

Marauder bombers from Midway. These planes did not hit the carriers, but one B-26 did have an important and lasting effect. It was disabled and shot down, but its pilot made a toward AKAGI’s “island” nearly hitting it.177 This frightened Nagumo enough to make the

77 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws remaining Midway aircraft the most important threat to eliminate.178

Nagumo changed Yamamoto’s order. Instead of keeping half his aircraft as a reserve to engage enemy carriers, he ordered the reserve to be rearmed with land bombs to reattack

Midway Atoll. This required a lengthy process of removing torpedoes from the forty-three torpedo bombers in the hangers of AKAGI and KAGA and refitting them with bombs. The thirty-four dive-bombers on SORYU and HIRYU were not affected.

The torpedo bombers required different fittings on its fuselage for torpedoes versus land bombs. It took 30 minutes to rearm every 6-plane chutai division, 1½ hours for an 18-plane squadron.179 180 It took this long because there were a limited number of carts and mechanics to service each squadron of planes. The first chutai was serviced with 3 carts, then the second chutai and finally the third chutai with the same 3 carts. With more carts and technicians, the entire squadron could have been armed faster, but that would have exceeded the manpower available on the carrier.

177 Superstructure to the right of the flight deck, where Admiral and Captain monitored flight operations. 178 Parshall and Tully, Shattered Sword 152-153. 179 Ibid 157. 180 Glossary. A shotai had 3 planes. A chutai had 6 planes for the Type 97 torpedo bomber and 9 planes for the Type 99 dive bomber. A squadron had 3 chutai. 78 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

After decisions to change munitions – “Nagumo’s Dilemma.”

Then began a pivotal time. At 0745, after he ordered a change of weapons to reattack

Midway, Nagumo received a message of USN ships to the Northeast. Much has been written about 1) when Nagumo received this information, 2) what he received and 3) the appropriateness of his decisions. This is shown in Figure 6 and has been called “Nagumo’s Dilemma.” This has been analyzed, from both the Japanese and the American sides.181 182 183 184

There was a limited time window for decision. It was 0745 and Tomonaga’s planes would return about 0830 and needed to land. Caught by surprise, Nagumo immediately stopped

FIGURE 6. Timeline of Nagumo’s Dilemma before 0753, 4 June 1942. It works backward from 0915, when Tomonaga would run out of fuel and ditch. Launching armed Type 97s then Landing Tomonaga’s aircraft. Montemayor “The Battle of Midway 1942” his order to change armament. By this time, one third of the torpedo bombers aboard AKAGI

181 Parshall and Tully, Shattered Sword 153-175 182 Stille, Midway 1942 48-50. 183 Montemayor “The Battle of Midway 1942: Told from Japanese Perspective” YouTube 21:54-41:45. 184 Comprehensive data on the situation is shown in Table X-33, Appendix A. 79 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws and KAGA had been rearmed by the lengthy task of switching torpedoes to bombs. Yamaguchi recommended an immediate strike with the two-thirds of the bombers still fitted with torpedoes on AKAGI and KAGA and the ready bombers on SORYU and HIRYU. If Nagumo had made a

“Yes” decision at this point, he might have launched a well constituted strike of about 64 attack aircraft185 by about 0845, in time to recover Tomonaga’s aircraft returning from Midway.186 187

The time constraints of Nagumo’s Dilemma are generally agreed on.188 189 They are clearly shown in Figure 6 from a new analysis.190 Nagumo had 15 minutes to decide.

Then a dive bomber attack occurred at 0753 by 16 marine DAUNTLESS dive-bombers from Midway Atoll.191 This changed things, shown in Figure 7. Nagumo could still launch a partial strike with few fighters to provide protective cover, he believed only six.192 He could launch under attack, but the need to perform radical ship defensive maneuvers would extend the launch from 45 to 60+ minutes.193 Many of Tomonaga’s aircraft would run out of fuel and have to ditch. The 1st Kido Butai would lose substantial firepower early in the battle. Nagumo had to decide to launch the partial strike and let Tomonaga ditch or to recover Tomonaga and risk vulnerability with the worrisome but still unknown and nebulous threat of enemy carriers out there.

185 Numbers differ slightly between sources, so totals here agree generally. 186 Parshall and Tully, Shattered Sword: 168 187 Table X-33, Appendix A. 188 Ibid 189 Stille, Midway 1942 9-11, 49. 190 Montemayor “The Battle of Midway 1942: Told from Japanese Perspective.” YouTube. 191 Stille, Midway 1942 49. 192 Ibid 49. 193 Launching planes into the wind. 80 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

But Nagumo recalled that, at the Coral Sea, due to a nebulous threat he had squandered a

FIGURE 7. Timeline changed by 0753 dive bomber attack from Midway Atoll. strike on an oiler and destroyer.194 Nagumo now judged it more logical to delay launch of his aircraft. An argument can be made that other commanders in the same situation would have made the same decision.195 The reconstructed timelines from Montemayor clarify Nagumo’s logic.

After this decision, Nagumo followed standard doctrine to mass a full-strength, combined arms, coordinated strike against any USN force. This put the larger strike after Tomonaga’s planes landed. It took 35 minutes from 0837 to 0912 to land Tomonaga’s planes.196 The reserve could not begin spotting on the flight deck until more than 45 minute later, after 1000, putting a launch about 1030-1100. In the meantime, the reserve force was isolated from the planes aloft in the action. This immediately divided forces during battle.

194 NEOSHO and SIMS, Stille, The Coral Sea 55-57. 195 Montemayor, “The Battle of Midway 1942: Told from Japanese Perspective” YouTube. 196 Parshall and Tully, Shattered Sword 165. 81 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

The effect was the same as dividing a massed force into multiple parts, of which each could be defeated in detail. The torpedo bombers were below, separated by space due to bulkheads enclosed in the hangars, and by time due the 45 minutes to lift them to the flight deck by elevator. It would take two hours to return these planes to action. In addition, the planes in the hangars created a fire hazard if the carriers were attacked.197

In an ironic twist of fate, effort to mass a greater force divided it (Chart 11).198 At 0745 half of the IJN aircraft are in the hangars or on standby. This lasted for two hours.

CHART 11. Change in effective IJN v USN aircraft 0430 to 0745. After delayed launch at 0745, IJN is divided - torpedo bombers in hangars, dive bombers waiting, Tomonaga’s return flight landing.

CHART 12. Aircraft Military Effectiveness in MJ/’ at 0430 and 0745.

197 Ibid 166. 198 Comprehensive data in Table X-34, Appendix A. 82 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

The division of Nagumo’s aircraft reduced its military effectiveness, shown in Chart 12.

The advantage shifted from the IJN to the USN. This decision was a major factor that doomed the 1st Kido Butai. Nagumo’s force was split into two equal parts, by 45 minutes in time and by a steel bulkhead in space. The IJN went instantly from an advantage to a major disadvantage. The situation was even worse since Tomonaga’s returning planes were low on fuel and arms.

The two hours were crucial. At 1002 the VS-6 and VB-6 Dauntless dive bombers from

ENTERPRISE were led by McClusky onto KAGA. Best led three dive bombers onto AKAGI.

Leslie’s VB-3 dive bombers from YORKTOWN hit SORYU. All three carriers were mortally wounded. This whittled down the 1st Kido Butai to HIRYU. In a few minutes, the odds changed dramatically from an IJN advantage of 4 to 3 to a USN advantage of 3 to 1.

Some have attributed this to Nagumo’s rigid adherence to doctrine, working for a perfect strike instead of striking immediately, as Yamaguchi recommended. They consider this due to inflexibility or the fog of war under pressure. But the details in Figures 6 and 7 tell another story. Time was the real enemy. Nagumo appeared to have made logical choices. The decisions taken were affected by multiple contingent factors.

Trafalgar Comparison - Nelson’s and Nimitz’s “calculated risk”

Nelson and Nimitz both took calculated risks. Nelson used his knowledge of the enemy to take the “calculated risk” to run the gauntlet of Villeneuve’s battle line. He knew his fleet would take casualties. But he calculated that he would cause more damage to the enemy, if he could close and exploit his superior gunnery on the French and Spanish in a mêlée. He calculated that the HMS fleet would survive the battle. And he calculated that this battle would end Napoleon’s gambit to invade Britain. History has proved him right.

83 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Compare Nimitz’s advice to Spruance and Fletcher before Midway:

“In carrying out the task assigned in OPERATION PLAN 29-42

you will be governed by the principle of calculated risk which you shall

interpret to mean the avoidance of exposure of your force to attack by

superior enemy forces without good prospect of inflicting, as a result of

such exposure, greater damage to the enemy. This applies to a landing

phase as well as during preliminary air attacks.”

C. W. Nimitz, Commander in Chief, Pacific Fleet. 27 May 1942.199

Next, compare Spruance’s application of the principle during the attack on Midway.

When Fletcher and Spruance received word of the IJN carriers and the inbound air strike on

Midway Atoll, Fletcher ordered Spruance to launch from ENTERPRISE and HORNET as soon as practical. Spruance then made several calculations of risk. First, although the IJN carriers were at the outer limits of his aircrafts’ range with the risk they would run out of fuel and ditch, he calculated that it was vital to launch immediately to neutralize the carriers. He would reduce the range to recover the pilots afterwards. He determined the calculated risk justified and acted.

Second, Spruance knew the IJN carriers were vulnerable to attack for the next 2-3 hours during recovery of their planes from the Midway strike. Although his force would sustain more casualties and have less military effectiveness if he sent an uncoordinated strike with separated groups of planes, he calculated that a strike as soon as possible would keep the IJN carriers busy.

It would prevent them from launching a counterattack against the USN carrier force. He thus

199 https://atloa.org/the-calculated-risk-27-may-1942 84 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws committed his forces in smaller groups as soon as they were ready, without a fully coordinated strike. Again, he calculated the risk justified and acted. History has proved him right.200 At 0905

YORKTOWN launched her strike against the 1st Kido Butai.

Were the USN torpedo bombers planned as a diversion, a sacrificial “feint”?

In the air attacks on the IJN carriers at Midway, the ZERO fighters were drawn down to low altitude to defend against the attacking torpedo bombers. This left an undefended approach for the DAUNTLESS dive bombers that sank the IJN carriers. The USN torpedo bombers had little chance of sinking the IJN carriers. Most of the carriers could out-maneuver and outrun the slower Mark 13 aerial torpedoes.201 In any case, the Mark 13 had only a 30% chance of actually hitting and exploding on contact. Although the IJN may not have been aware of all these defects, the USN command probably was. Was Spruance aware of the futile mission of his torpedo bombers? If so, why did he launch them?

A decision had to be made fast - “calculated risk.” The 1st Kido Butai was vulnerable for a short time, while it recovered Tomonaga’s planes. Spruance sent a partially constituted strike piecemeal as soon as possible to get it in the air, with the plan to constitute as much as possible as soon as possible on the way. The thinned out IJN CAP would be defending the recovering planes from the USN WILDCATS, and the WILDCATS could provide some cover for the torpedo bombers. Although USN torpedoes were unreliable, only a few needed to get through and explode on target.

Finally, some have criticized Nagumo for not making a difficult decision fast enough during “Nagumo’s Dilemma” below. Thus, it seems a bit disingenuous to criticize Spruance for

200 https://en.wikipedia.org/wiki/Battle_of_Midway#Attacks_on_the_Japanese_fleet 201 The Mark 13 Mod 0 torpedo had a speed of 30 knots. The AKAGI 31.5 knots, HIRYU 34 knots and SORYU 34 knots. Only the KAGA had a slower speed of 28 knots, but it could maneuver away from the torpedo. 85 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws making a difficult decision too fast. In the end, his decision sank three IJN carriers. The torpedo bombers drew down the CAP fighters, albeit at a major loss in life of the torpedo bomber pilots.

But if this had not happened, the dive bombers may not have got through to sink the carriers.

Did Spruance know that the torpedo bombers would take casualties? Yes. Most sorties did.

Were the torpedo bombers planned as a diversion? There is no evidence for this. They were planned as part of a strike but sent off as soon as possible. It was a calculated risk - the damage to the enemy would be greater than the loss to the USN.

Trafalgar Comparison - reversed decisions of Nagumo and Villeneuve.

Villeneuve and Nagumo reversed decisions. Although there were other factors that led to the defeat of the 1st Kido Butai at Midway, Nagumo’s decisions for multiple ordnance changes looms large as a factor. Some point to his rigid adherence to doctrine in stark contrast to

Spruance’s flexible application of calculated risk. 202 Others are more forgiving and recognize that maximum massing of force was virtually a religious dogma at the time. 203 Still others show how the timeline during his dilemma virtually compelled his decisions.204 Yamaguchi the firebrand was unforgiving. But all sources recognize that the results of his decision at that time were catastrophic. It soon contributed to the destruction of SORYU, KAGA and HIRYU.

Likewise, many factors resulted in Villeneuve’s defeat at Trafalgar. However, the French

Admiral’s last-minute decision to order the entire fleet to wear back to Cadiz also looms large as a factor. To Captain Churruca of the San Juan Nepomuceno, it was the critical factor. He exclaimed, “the fleet is doomed. The French Admiral does not know his business. He has compromised us all.” 205 Perhaps Admiral Yamaguchi muttered the same thing when Nagumo

202 Stille, Midway 1942. 203 Parshall and Tully, Shattered Sword. 204 Montemayor “The Battle of Midway” YouTube and Figures 6 and 7 above. 86 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws did not launch what he had. Villeneuve, like Nagumo, was faced with battle where he had to decide and act rapidly, with some unknowns.

Villeneuve was faced with a dilemma. He could proceed to Gibraltar with a cohesive fleet but possibly be caught between two large HMS forces. If he were caught, there would have been certain annihilation. Or he could reverse direction back to the safe harbor of Cadiz, reducing cohesion of his fleet temporarily, risking loss of part of his fleet. Villeneuve chose the latter, safer alternative. For a similar time of 2 hours, Villeneuve like Nagumo reduced the military effectiveness of his force. While changing direction from south to Gibraltar back north to Cadiz, he broke the cohesion of his fleet. They drifted apart, not in a column. Some ships were behind others or bunched up in groups. For 2 hours, they had to focus on sailing maneuvers. During this time, they could not direct maximum concentrated broadsides from a well-formed, tight battle line to rake the bows of the approaching columns of Nelson and

Collingwood. Villeneuve lost much of his fleet, but not all.

Trafalgar Comparison – Commonsense action under pressure.

Experience and Common Sense.

Commonsense is a word used often with various meanings. The clearest definition emerges in legal cases. When the courts-martial were held after the Honda destroyer catastrophe in 1923, one witness stated that senior officers should have prevented it.206 By their experience they should have acquired the most valuable lesson – common sense. From their experience of past mistakes, they should have learned what caused those mistakes and how to avoid them. At

205 Adkin, M. The Trafalgar Companion: 477. 206 Lockwood and Adamson, Tragedy at Honda 184. 87 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Midway it appears that common sense graced one side more than the other, despite the equal seniority of commanders.

Hindsight is always 20/20. The following should be more of a learning exercise than judgment. It is unfair to judge unless one has been in the commander’s shoes at the time. Even then there are different opinions.

Action under Pressure.

At Midway, Nagumo had reasons for his actions. He was sleep deprived, lacked aviation experience and was distracted by a noisy, cramped bridge on AKAGI.207 These factors would have detracted from exercise of commonsense and action. The pressure to make rapid decisions further increased the distraction. Sudden threat of unexpected USN ships was disorienting and anxiety-provoking. He was on the horns of a dilemma to prioritize two threats. Yet, looking at the timeline during Nagumo’s Dilemma, he chose a logical alternative.208

But what of Yamamoto? Was it commonsense for Yamamoto to make overly detailed plans? Experience showed that no plan survived contact with the enemy. Although the string of

Japan’s victories was impressive, was it likely this would continue, even against the United

States? Would Nagumo succeed with vague rather than detailed instructions, considering his known limitations and lack of background in aviation?

Decision of Pearl Harbor.

What about the biggest decision of the war – a stealth, surprise attack on ships of the world’s great industrial power, serving up a casus belli on a silver platter? History showed that

207 Parshall and Tully, Shattered Sword 161-162, 259. 208 Montemayor “The Battle of Midway: Told from the Japanese Perspective” YouTube. 88 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws the United States was naturally isolationist and had to be pushed into war. In recent history, this had occurred only after a direct attack on ships with loss of American lives.

Yamamoto must have read about the USS MAINE209 and the SS LUSITANIA.210 211 212 The

US concluded that Spain had sunk the MAINE with a stealth mine and killed 261 American sailors, starting the Spanish-American War. A US warship is an icon of American patriotism.

The LUSITANIA was torpedoed by U-20 in a surprise attack in 1915, killing 128 Americans.

This incident inflamed propaganda so that when Germany declared unrestricted submarine warfare in 1917, the US immediately declared war. Yamamoto planned a sneak attack, which sank or damaged 9 US battleships and killed 2,335 American sailors.

What factors obscured his comparison to the MAINE and LUSITANIA? At Pearl

Harbor, he pushed the US President into a corner, giving him no choice but to declare total war on Japan. He did the one and only thing that could produce what he did not want. Furthermore, he did it extremely well on a grand scale– a sneak attack, nine capital ships and ten times more

American lives. It is hard to imagine a greater insult.

With the daggers drawn, could Yamamoto have done more to locate the carriers, instead of just sinking battleships? LEXINGTON was on its way to Midway Island to deliver a squadron of Marine bombers. ENTERPRISE was returning from a supply mission to Wake.213

These were the two nearest American bases. Both carriers were within the search radius of the

H8K flying boats at Wotje Atoll in the Marshall Islands.214 Sources report that Japan knew the

209 The MAINE sank in Havana Harbor in February 1898 with loss of three-fourths of her crew. The press blamed sinking and loss of life on the Spanish. This precipitated the Spanish-American War. 210 German torpedoes sank LUSITANIA in May 1915, with the loss of 128 American lives. This turned the US public against Germany. Unrestricted U-Boat warfare finally brought the US into World War I. 211 https://en.wikipedia.org/wiki/USS_Maine_(ACR-1) 212 https://en.wikipedia.org/wiki/SinkingoftheRMSLusitania#BritishandAmerican_actions 213 Kimmet and Regis, The 36. 89 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws carriers were out of the harbor. This would have been reported to him by the master spy Takeo

Yoshikawa on Oahu215 giving him reports twice weekly, supported by an entire family of German spies working with him.216 But the IJN top command wanted to destroy the maximum number of battleships and Yamamoto went ahead.217 Could his H8K flying boats have scouted more territory and located LEXINGTON and ENTERPRISE? Searching the routes from Pearl to

Wake and Midway would appear logical.

In any event, Yamamoto pushed the US into a war, while missing the most powerful offensive force, the carriers. Although Yamamoto was not under acute time pressure like

Nagumo and Spruance, he was under a long-term time pressure to incapacitate the US before its industrial power could ramp up. He was also subject to the less visible pressure of the “victory disease.” So, in a general way, Yamamoto’s actions during the war in general and at Midway in particular can also be evaluated by the standard of commonsense action under pressure.

At Trafalgar, Villeneuve expected the tactics of Nelson but not the timing. He was caught halfway from Cadiz to Gibraltar, from a temporary but safe harbor on the way home to his permanent harbor, Toulon. But the way was guarded by British ships. He knew Nelson had superior gunnery. He was on the horns of a dilemma. He chose what he thought was the safer route, return to Cadiz to preserve the fleet. Under pressure, did he draw on his experience that wearing back would disorganize and weaken his battle line for hours? We have no indication of sleep deprivation, lack of confidence or noisy, cramped quarters on BUCENTAURE.

Did the trade-off seem worth it due to fear of British gunnery and the anvil of two forces,

Nelson’s and a fleet near Gibraltar? Or did anxiety obscure his commonsense? In all fairness to

214 See footnote on distances under Aircraft, Weapons. 215 https://en.wikipedia.org/wiki/Takeo_Yoshikawa#cite_note-Time-7 216 https://www.trivia-library.com/a/pearl-harbor-and-the-japanese-spy-family-part-3.htm 217 https://en.wikipedia.org/wiki/Attack_on_Pearl_Harbor#cite_ref-61 90 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Villeneuve, however, what was his alternative? What would have happened if he had not turned back but gone on to Gibraltar? 218 If he were caught between Nelson and another British force at

Gibraltar, it would have been just as bad if not worse. In retrospect, Villeneuve’s actions have logical explanations.

But what of Napoleon? He did not have the short-time pressures of field generals219 but he made some decisions, which seem to defy commonsense. Again, it is easy from the armchair to wise about war. Napoleon marched or rode with his troops. In those days it was, to say the least, uncomfortable. He was undoubtedly cold, sleep deprived and intermittently ill. But the big picture seemed to get the better of him. He tried to beat a stronger, faster and smarter British fleet on the high seas with a combined force of lower quality. He fought a multifront war. He invaded the vast land mass of Russia in winter. In any event history may be more forgiving to

Villeneuve than Buonaparte.

The “Victory Disease” and the Schlieffen Syndrome.

It’s been described throughout history - arrogance, the victory disease. It was extremely difficult, if not impossible, to see the early string of Japanese victories in proper perspective.

Without such arrogance, would Yamamoto have made back up plans for the worst scenario?

Napoleon with his early successes also was affected by the victory disease. Villeneuve at

Trafalgar probably was not. Nagumo at Midway probably was not.

Yamamoto and Napoleon had lost sight of Murphy’s Law. The law is not new. They must have seen it happen sometime. Murphy’s Law has a sound basis in physics. It’s the tendency of a system to reach the most random, disorganized state. Engineers state it: If

218 Adams, Personal Communication. 219 But sometimes forced himself into them. 91 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws anything can go wrong, it will at the worst possible time.220 221 Planners ignore worst-case scenarios to their peril. The improbable happens.

The Imperial General Staff did not think this way. They believed that they could predict the enemy with certainty and then plan to defeat that behavior. Yamamoto, especially, made ever more intricate plans, time constrained and unrealistic. He repeated the error of an officer of the German General Staff. It is called the “Schlieffen Syndrome.”222 223 224 225 Schlieffen’s plan failed when its great wheel could not avoid invading neutral Belgium and meet the tight timetables of logistics support. For if Schlieffen invaded Belgium, the Allies would enter the war against Germany, upsetting the balance of force and sacrificing the advantage of the wheel.

That should have suggested to Yamamoto that he, too, would have problems with complex operational plans.226

That such a brilliant and educated mind as Yamamoto should fall into such traps should serve as a warning. It is not strange that he fell into them. Many had before him. In the same year, Germany showed that it had not learned the lessons of Napoleon’s disastrous invasion of

Russia. Perhaps brilliance, education and common sense are not inextricably connected…

220 https://en.wikipedia.org/wiki/Murphy%27s_law 221 Result of the Second Law of Thermodynamics dealing with entropy or randomness. “At the worst possible time” because that’s when it sticks in the memory. 222 Zuber, Inventing the Schlieffen Plan. 223 Schlieffen, Cannae. https://www.armyupress.army.mil/Portals/7/combat-studies-institute/csi- books/cannae.pdf 224 Ritter, The Schlieffen Plan: Critique of a Myth. 225 Taylor, War by Timetable. 226 Peterson, The Schlieffen War Plan: What Impact did Logistics contribute to the Plan’s Failure? 92 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

C. CROSSING POINTS

This final section pulls it all together in graphs. These graphs illustrate the progress of the Battle of Midway. It’s difficult to compare opposing navies during a conflict. The interactions can be vague and ambiguous. But graphs highlight relationships. Graphs with two lines, one for each navy, show crossing points. If one side starts out stronger than the other, or one line is higher than the other, the lines cross when firepower becomes equal.

These graphs also have other benefits. A crossing point indicates the stronger has lost its advantage and is usually on the way to defeat. Where there is no crossing point, the larger force maintains its advantage and wins. This suggests that the initial conditions have predetermined the outcome. Crossing points also allow evaluation of alternative scenarios. What would happen if Japan had more carriers at Midway? Graphs allow sharper analysis of causes.

93 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

The Crossing Point of Carriers and Aircraft in the Actual Battle

The first graphs here depict the actual battle. Graph 2 shows the carriers and Graph 3 the aircraft. They show the crossing point when the 1st Kido Butai hit parity with the USN. This occurred during rearming of AKAGI’s and KAGA’s torpedo bombers. Graphs 2 and 3 show the

GRAPH 2. Timeline of Fleet Carriers of IJN and USN in Pacific.

GRAPH 3. Timeline of Attack Aircraft of IJN and USN in Pacific.

94 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws two navies from the time before the Coral Sea up to the time of the USN repeat attack, which sank the last IJN carrier. Before the Coral Sea, the IJN had a two-to-one advantage in carriers and a four-to-one advantage in military effectiveness.

By June 1942, the IJN had the equivalent of about six fleet carriers. It had the five fleet carriers KAGA, AKAGI, SORYU, HIRYU and ZUIKAKU. It had the three light carriers

RYUJO, JUNYO and ZUIHO and additional aircraft platform HOSHO.227 228 The aircraft complements equaled about six fleet carriers. The USN had only three: HORNET,

ENTERPRISE, and YORKTOWN. SARATOGA was in drydock in .229 230 231

At Coral Sea, the ZUIKAKU had lost much of its air group. IJN doctrine required that a carrier sail with its own, full air group. ZUIKAKU did not go to Midway. This reduced the carriers at Midway. Then, both RYUJO and JUNYO were sent to the Aleutians. This divided the force further. These two light carriers had a total of 63 aircraft, the same as the airwing of

KAGA. Together they were equivalent to one fleet carrier.

Why did Yamamoto send his carriers simultaneously to Midway and the Aleutians? If he won Midway, the Aleutians would easily follow. If he lost Midway, the Aleutians were moot. It would take RYUJO 54 hours at 29 knots and JUNYO 60 hours at 25.5 knots to steam 1765 miles from Midway to the Aleutians. They could get to the Aleutians soon after June 5th. In two days, they would be within 200 miles to launch a strike.

Support ships could have been sent ahead of time to the Aleutians. JUNYO and RYUJO could have followed, after Midway. If the General Staff insisted on attack with two carriers in

227 RYUJO 30 aircraft, JUNYO 33, ZUIHO 24, HOSHO 8 B4Y1 torpedo bombers ( capacity 15). 228 Stille, Midway 1942 30. 229 https://en.wikipedia.org/wiki/List_of_aircraft_carriers_of_World_War_II 230 See TABLE X-31 in Appendix A. 231 It had been damaged at Wake Island by torpedoes in January 1942 and was not back in action until Guadalcanal. 95 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws the Aleutians, was there not enough concern from submarine intelligence and missed deadlines for Yamamoto to alter slightly tactical plans? The split of the carriers to attack simultaneously at two distant points was a weakness in planning. Why Yamamoto did this the way he did remains puzzling, considering the principle of mass.

Crossing Point at Nagumo’s Dilemma – Quick dip in MegaJoules

When Nagumo committed firepower to attack Midway, he temporarily reduced the discretionary firepower available to him. If not before, this became clear to him when he was out of contact with Tomonaga until the latter reported a repeat attack was needed.232

GRAPH 4. Timeline of Aircraft Firepower during Nagumo’s Dilemma.

Graph 4 shows when the available firepower of aircraft in the 1st Kido Butai dipped below that of Task Forces 16 and 17, at a crossing point. Nagumo’s advantage decreased by the attack on Midway when he went to a 5:7 disadvantage. His firepower could have been reconstituted by rearming Tomonaga’s planes, but he had to recover them first.

232 Parshall and Tully, Shattered Sword 146. 96 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

When Nagumo was informed of a USN force within striking range, he was faced with a dilemma to launch or not. Then, during that critical 15 minutes, at 0753, the Marine

DAUNTLESS dive-bombers attacked. The increasingly tight time constraints compelled

Nagumo to delay launch to recover his aircraft before ditching. In the meantime, his torpedo bombers in AKAGI and KAGA lay amid bombs which had just been removed. The firepower of these planes was now not accessible. During a crucial two hours, Nagumo went to a 1:2 disadvantage. Spruance took advantage of this. He launched an attack when the IJN carriers were recovering aircraft and vulnerable.

97 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Realistic Salvo Equations, which give the actual historical results

The above give the actual historical facts of the battle. Now an attempt is made to determine if the Salvo Equations fit the facts. This is important. If the equations fit the facts, then they can be used to assess other scenarios: Could Japan have won Midway with more carriers?

The Salvo Equations give slightly different transient numbers than those evolving during the battle. Nevertheless, they give the correct final outcome of annihilation of the IJN force.233

The same realistic values given above are used for the variables:

Number of units AJapan = 4 BU.S. = 3 Staying power a1 = 1 b1 =2 Defensive power a3 = ¼ b3 = ¼ Striking power α = 0.75 β = 1

USN staying power is double that of the IJN, due to better damage control and carrier design. Defensive power is equal. The USN had better AAW guns but the IJN ZERO was a superior fighter. The USN had a larger hitting rate β, due to better scouting σA.

Graph 5 shows the salvo equation results with these variables. The USN knocks out half the IJN fleet in its first USN attack. The equations show two IJN carriers surviving, instead of one as occurred in the actual battle (see note). The proportion of USN knocked out by the IJN counterattack is 0.13. The two IJN air wings counterattack but are unable to sink a USN carrier, instead they knock out half a carrier. They damage it and put it out of action.

233 The detailed solution of the salvo equation is shown in SCENARIO 4 in APPENDIX C. The Salvo Equations would not take into account the temporary lack of aerial defense of the KAGA and AKAGI. This was due to Nagumo’s Dilemma and the independent torpedo bomber attack prior to the dive bombers. The Salvo Equations predict two carriers surviving without these factors. 98

GRAPH 5. Timeline of actual Midway Battle by the Salvo Equations. MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

The final results correctly show the loss of all four IJN carriers. But the results show the survival of 2.6 USN carriers. This shows that Kobayashi’s dive bomber damage did not sink

YORKTOWN. Tomonaga’s torpedo planes caused a severe list in the carrier and put it out of action but did not actually sink it.234 These are both correct. This appears to be where the salvo equations end. It was in fact the Japanese submarine I-168, which finally sank the

YORKTOWN. But submarine torpedoes are not included in these salvo equations. So, it appears that the salvo equations give correct results for aircraft exchanges, but not submarines.

The two operational USN carriers in a second attack reduce the IJN to 0.5 carriers. From then on, the IJN cannot counterattack. The third USN attack sinks the remaining IJN floating hulk, consistent with the historical outcome.

The outcome of victory by these salvo equations corresponds with the outcome using the specified variables for α, β, a3, b3, a1 and b1. The variables selected appear reasonable,235 if there are no other submarines involved.236 Thus, this realistic salvo equation is used below to investigate other possible scenarios.

Trafalgar Comparison – Crossing Points.

The crossing point at Trafalgar occurred when Nelson and Collingwood divided the line of the Combined Fleet, during the two hours when it wore back to Cadiz. This was analogous to the two hours after Nagumo’s Dilemma at Midway, when his decision kept the reserve aircraft in the carrier hangars. The effective IJN aircraft were divided; the torpedo bombers in the hangars were isolated from the battle. The dive-bombers on SORYU and HIRYU were kept waiting.

234 Stille, Midway 1942. 235 Another, different selection of variables could give the same outcome. Nevertheless, the selection of variables was reasonable as explained above. 236 There were no USN submarines active in the battle and only one IJN submarine, I-168. 99 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Once the two-hour countdown started, there was little that Villeneuve or Nagumo could do to correct the situation.

Crossing Points in Other Possible Scenarios with more IJN Carriers.

Would more IJN carriers have saved the Japanese? The realistic salvo equations developed above showed the final historical outcome. They can be used to show the outcomes of other possible scenarios, without submarine intervention. The I-168 was the only submarine action in the Battle.

There were three other carriers available. Each of these could have accompanied the 1st

Kido Butai. Adding them in the salvo equations is instructive.

Scenario with RUYJU and JUNYO.

The total aircraft on both RYUJO and JUNYO totaled 63. They were the equivalent of one fleet carrier. With them, the IJN would have had 5 carriers to the 3 of the USN. But they were diverted to the Aleutians. What if they had sailed to Midway and then gone to the

Aleutians?

By the N-Square Law, the IJN would have had firepower proportional to αA2 = 0.75*52

= 19.237 The USN firepower was proportional to βB2 = 32 = 9. Without the simultaneous split to the Aleutians, the firepower ratio would have been 19/9 or 2:1, in favor of the IJN. A two-fold firepower advantage goes a long way towards victory. The N-Square Law would have predicted victory for the IJN. This is more than the actual battle where the firepower ratio for 0.75*42/32

= 12/9 = 1.33.

237 Alpha (α) is 0.75, reduced by the worse IJN scouting. 100 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

By the simple formula of one wing destroys one carrier, the scenario of 5 IJN fleet carriers vs 3 USN fleet carriers would have resulted in two IJN carriers surviving rather than one.

After the USN attack, the two surviving IJN carriers could have destroyed two USN carriers with a counterattack, restoring the IJN vs USN advantage to 2:1. A second USN attack would knock out one IJN carrier, but the remaining one IJN carrier would destroy the only USN carrier, leaving Japan the victor on the field with one carrier. The simple formula predicts the IJN wins.

What about the Salvo Equations? They show something different. Graph 6 shows that 5

GRAPH 6. Timeline of Salvo Equation result with RYUJO and JUNYO.

IJN carriers lose against 3 USN carriers.238 If RYUJU and JUNYO had accompanied KAGA,

AKAGI, SORYU and HIRYU, there would have been 5 carriers. But even with the aircraft complement of another fleet carrier, the IJN still would suffer complete annihilation. The extra

IJN carriers do prolong the Battle with multiple crossing points but the IJN loses. One USN

238 The salvo equations calculations are shown in SCENARIO 5, APPENDIX C. 101 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws carrier remains operational and the second sustains damage but does not sink. The results are due to the IJN’s worse scouting and less staying power. These terms are not considered in the N-

Square Law or the simple formula above but are included in the salvo equations. The addition of

RYUJO and JUNYO to the 1st Kido Butai does not change the outcome of the Battle. The two simpler formulas show IJN victory: 1) one wing knocks out one carrier and 2) Lanchester’s N-

Square Law. But the more realistic salvo equations do not.

Scenario with RYUJU, JUNYO and ZUIKAKU.

But add ZUIKAKU. This gives the IJN six carriers. There is now a two-to-one IJN carrier advantage. The salvo equations with 6:3 numerical superiority are shown in Graph 7.239

GRAPH 7. Timeline Salvo Equations with RYUJO, JUNYO & ZUIKAKU.

As before, the N-Square Law and simple formula show the IJN wins, but now the Salvo

Equations do as well. And the Salvo Equations include all relevant factors. They are realistic.

239 The salvo equations and their solutions are shown in SCENARIO 6 in APPENDIX C. 102 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Graph 7 shows their results at Midway, if RYUJU, JUNYO and ZUIKAKU had accompanied

KAGA, AKAGI, SORYU and HIRYU. With these carriers, the IJN would have a 2:1 advantage in numbers and 0.75*62/32=27/9=3:1 advantage in firepower and military effectiveness. The

IJN has the initial advantage and keeps it throughout the Battle. The third IJN counterattack wipes out the last USN carrier. The IJN wins.

The 2:1 numerical advantage in the realistic salvo equations changes the outcome of the

Battle. The USN suffers repeated attrition to complete annihilation by repeated IJN air strikes.

The IJN suffers the loss of two carriers, but the damage to a third can be repaired in the dockyards of Japan. The addition of the ZUIKAKU compensates for the IJN’s poor scouting and less staying power. The realistic salvo equations show that Japan could have won at Midway.

She could have retained 4 of her 6 carriers, to dominate the Pacific strategically. This was

Yamamoto’s original aim. This outcome with more carriers demonstrates the principle of mass.

103 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Trafalgar Comparison - Alternative Scenarios.

One can apply the principle of mass to Trafalgar for alternate scenarios, as well.240 The

British had 27 ships, the French-Spanish 33. Nelson’s superior gunnery and cutting Villeneuve’s line won the battle. The Combined Fleet had inferior gunnery performance. It had 1/3 slower rate of fire. The slow match reduced the accuracy by ½.241 This produced an overall degraded

(Actual) Before cut After cut

CHART 13. Trafalgar Actual Battle (left) and Alternative Scenarios with a draw - before (center) and after (right) Nelson cut Villeneuve’s line in half, which required more ships to produced same firepower. British β = 6.0, Combined α = 1.0. Firepower = βB2 and αA2. gunnery performance of 1/6 in comparison with the British. Chart 13 shows that Villeneuve required many more ships to overcome this gunnery disadvantage. By Lanchester’s N-Square

Law, he would have needed 66 ships at the start to make up for his gunnery, just for a draw

(Chart 13).242 He would have needed 94 after Nelson cut his line in half.243 But this many ships

240 Sutherling, Two Influences of Trafalgar on Navy Tactics 1905-1944: 42-48, 56-65. 241 Howarth, Trafalgar. The Nelson Touch: 132. 242 Table X-35, Appendix A. 243 With 27 ships and 6:1 gunnery, Nelson had (6)*(27)2 = 4,374 firepower (in arbitrary units). Villeneuve had 33 ships, (1)*(33)2 = 1,089 firepower. Before the cut, Villeneuve needed twice or 66 ships, (1)*(66)2 = 4,356 firepower, to equal Nelson. After Nelson cut the line, and divided its force in half, Villeneuve 104 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws were not available.

needed 94 ships: (1)*(47)2 [=2209] + (1)*(47)2 [2209] = 4,418 firepower, with split forces. After the force is split, Nelson can attack each in detail, separately. Thus, Villeneuve’s split force needs to add up to the total of Nelson’s force. 105 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

EPILOGUE/CONCLUSION

Midway’s outcome was decided by multiple factors. Nevertheless, two factors loom large – the principle of mass and commonsense action under pressure.

The principle of mass was simpler at Trafalgar. It corresponded to Lanchester’s N-

Square Law and Fiske’s tables. They show that Trafalgar would have been a draw if Villeneuve had three times the ships. But these were not available.244 The carrier battle at Midway had more variables and corresponded to the Salvo Equations. They show that Japan could have won with the air wings of two more fleet carriers, which were available.245

The other factor was subtle - commonsense action under pressure. Many have found

Villeneuve and Nagumo at fault, but circumstances may justify their actions. Not so for

Napoleon and Yamamoto. Napoleon sent an inferior fleet against the British, fought a multi- front war and invaded Russia in winter. Yamamoto did the only thing that would push the

United States into total war, the outcome he most feared. Then he split his forces.

Trafalgar occurred at the peak of Napoleon’s First Empire on the continent. Midway occurred after repeated victories by Japan in Asia and the Pacific. Both new empires suffered the “victory disease,” which obscured commonsense. Then Napoleon and Yamamoto immersed themselves in detail, which distracted from Grand Strategy.

Trafalgar stopped the Grande Armée’s invasion of Britain. Midway stopped the Imperial

Navy’s conquest of the Pacific. Both battles changed the course of history.

244 http://www.napoleonguide.com/navy_balance.htm 245 In the RYUJO, JUNYO and mostly constituted ZUIKAKU. 106 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Glossary.

Joule (J)= unit of energy or work. The work done lifting an apple one meter (3.28 feet). 1 Joule

= 1 kilogram*meter2/sec2, i.e. E=kg*m2/s2. Explicitly, as follows:

Energy (E) = ability to do work. The mechanical or kinetic energy of a shell thrown against an

enemy or the chemical energy released during an explosion.

Energy=Force*distance. Force = mass*acceleration=m*a. acceleration = (Δ velocity) /

(Δ time) = (meters/sec)/sec=m/s2.

E=(m*a)*d=(kg*m/s2)*m. E=kg*m2/s2.

Mega Joule (MJ) = one million Joules. There are 4.184 MJ in a kilogram of TNT. There are

4,184 MJ or 4.184 Giga Joules in a kiloton.

Mega Joule / min = power.

Power = ability to do work in a short time.

Concentration of Mass = important military concept, massing of force usually wins battles

Lanchester Equations = show that the time rate of decrease in size of a force by attrition is

related to the firing rate and number of guns of the enemy. They show with the same

firing rates on both sides that a larger force will a battle of attrition, all other things equal.

Furthermore, they show that the larger force retains an unexpectedly large number of its

ships after a battle, to fight another day.

N-Square Law = shows that military effectiveness (M.E.) is related to the square of the number

of ships.

Military Effectiveness (M.E.) = (rate of fire) * (number of units)2. The fleet with the greater

M.E. will win the battle, all else equal.

107 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Salvo Equations = modern equations, which show that aircraft carrier battles decided by a few

massed pulses of firepower. This is different than many small interchanges of fire in a

battle of attrition, which can be described by the older Lanchester equations.

Commonsense = experience, i.e. memory of obvious mistakes in the past, why they occurred

and how to avoid them. Senior officers are expected to have more than junior officers in

the Navy. This definition comes from the courts-martial proceedings of Honda Point

USN Destroyer disaster of 8 September 1923, off the coast of California. Subordinate

officers did not think through the consequences of their ships’ course and blindly

followed the ship ahead, leading them to founder on the rocks.

IJN = Imperial Japanese Navy

USN =

TNT = Tri-nitro-toluene. Three nitro groups (-NO2) added to toluene. Toluene is the hexagon

structure of the carbon ring benzene with a methane group (-CH3) attached at the top.

These the additions to the carbon ring markedly increase the amount of gas atoms trapped

in the compound. When a molecule of the solid TNT undergoes combustion, it produces

multiple molecules of nitrogen gas (N2), hydrogen gas (H2) and carbon monoxide gas

(CO), which instantly occupy a much larger space, i.e. explode.

During detonation of the explosive TNT the reaction is:

2 C7H5N3O6 → 3 N2 + 5 H2 + 12 CO + 2 C

Two molecules of TNT produce 3 molecules of nitrogen gas, 5 molecules of hydrogen

gas and 12 molecules of carbon monoxide gas, a total of twenty new gas molecules. To

calculate how much gas a kilogram of TNT makes we need to use the concept of molar

mass or “mole.” It is known that one mole of a gas occupies 22.4 liters of volume at

108 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

standard temperature and pressure. As a solid, one mole of TNT occupies a small

volume. When converted into gas, TNT occupies a very large volume. This is the basis

of explosives.

The element hydrogen has one proton and a mole of hydrogen is one gram. Most

of the familiar gases have two atoms bound into one molecule of gas. One mole of

hydrogen gas (H2) weighs two grams (one gram for each H atom, with 2 H atoms for

every molecule of gas), one mole of nitrogen gas (N2) weighs 28 grams (14 grams for

each N atom) and one mole of carbon monoxide gas (CO) weighs 28 grams (16 for O and

12 for C).

One mole of TNT is 227 grams and two moles, or 454 grams, are in the above

chemical reaction. So, the detonation of 454 grams of TNT generates 20 moles of new

gas. These instantly occupy 20 * 22.4 L = 448 liters. The instant expansion of the gas

blasts everything out of its way. The detonation of 454 kilograms generates a thousand

times more – 4,480 liters. The USN AN-M66 2000 lb. bomb had 482 kg TNT, a bit

bigger (Table X-7). It generated 4,756 liters of gas instantaneously. This chemical

explosion produced 2,026 Mega Joules of energy.

Because TNT has an excess of carbon, explosive mixtures with oxygen-rich

compounds can yield more energy per kilogram than TNT alone. During the 20th

century, amatol, a mixture of TNT with ammonium nitrate was used as a military

explosive. Amatol exploits synergy between TNT and ammonium nitrate. TNT has

higher explosive velocity, but is deficient in oxygen. The oxygen surplus of ammonium

nitrate increases the energy release of TNT. Ammonium nitrate’s formula is NH4NO3 ,

simplified to N2H4O3 .

109 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

https://en.wikipedia.org/wiki/TNT

https://en.wikipedia.org/wiki/Amatol

https://en.wikipedia.org/wiki/Ammonium_nitrate.

Mole = molecular weight. A mole is based on the number of atomic weights (protons and

neutrons) in a molecule. Hydrogen has one proton. A mole of hydrogen weighs one

gram.

Picric Acid = powerful explosive with 1.17 times the power of TNT. P.A. is like the TNT

molecule but with the substitution of a hydroxyl group (-OH) for the methane group (-

CH3) on the top of the hexagon benzene carbon ring.

Shimose powder = a safer preparation of picric acid, less subject to accidentally detonation by

movement, but still not as safe as TNT.

Tactics = maneuvers to win in a local battle

Doctrine = intermediate between tactics and strategy. More comprehensive than tactics,

doctrine weaves together multiple tactics by a continuous thread into the predictable

behavior of a fleet. Thus, each ship in a fleet can confidently determine what its role and

the roles of the other units in the force will be under changing circumstances during

battle. This ensures synchronous application of firepower and, if need be, independent

action if communications are lost.

Strategy = overall plan to win a conflict. It includes strategy to win a war through multiple

battles in different areas or “theatres.” Grand Strategy includes the political, economic

and social dimensions to enhance the effects of military effectiveness. Political

considerations were paramount when the offensive movement of the troops in the

Schlieffen plan was constrained to avoid the neutral low countries.

110 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

SHIPS:

CV = fleet carrier

CVE = escort carrier

BB = battleship

CA =

CL = light cruiser

DD = destroyer

DE = destroyer escort

SS = submarine

AIRCRAFT:

A6M = Mitsubishi carrier fighter aircraft ZERO or ZEKE

B5N = Nakajima carrier attack bomber KATE, usually used as a torpedo bomber with Type 91/2

torpedo. Termed “kanko.”

D3A = Aichi carrier dive bomber VAL. Termed “kanbaku.”

D4Y = upgrade replacement for the D3A dive bomber. Manufactured by Yokosuka.

B4Y = carrier attack plane, torpedo bomber, JEAN. Manufactured by Yokosuka.

A5M = an older version of the A6M carrier fighter ZERO

Type 0 fighter aircraft = A6M2 Mitsubishi ZERO fighter. Best all-around fighter in the early

years of WW II. Outclassed USN in speed, ceiling and

111 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

maneuverability, but had less armor. F4F developed effective counterattack to the

ZERO’s agility with the tactic of the “Thach Weave.”

Type 97 carrier attack aircraft = B5N KATE torpedo bomber, could also be fitted with bombs.

Type 99 carrier bomber aircraft = D3A VAL carrier dive bomber

Type 95 aircraft = E8N Nakajima reconnaissance aircraft DAVE float plane catapult launched

H6K and H8K = large flying boats used for scouting, anti-submarine warfare, search and rescue

and transport.

F4F = Grumman WILDCAT carrier fighter

SBD = Douglas DAUNTLESS dive bomber

TBD = Douglas DEVASTATOR torpedo bomber

TBF/M = Grumman AVENGER upgraded torpedo bomber

PBY = Consolidated CATALINA American flying boat used for scouting, anti-submarine

warfare, search and rescue and transport

E8N = Consolidated CATALINA American flying boat used for scouting, anti-submarine

warfare, search and rescue and transport

PBY = Consolidated CATALINA American flying boat used for scouting, anti-submarine

warfare, search and rescue and transport

Range = the maximum distance an aircraft can fly from and return to the carrier with a specific

fuel reserve. Limited by payload carried.

Radius = the combat radius is ½ the range. This is the maximum distance at which a plane can

attack and still return home to the carrier.

112 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Endurance = the maximum time an aircraft can remain in the air before landing with a specified

fuel reserve. Limited by payload carried.

Bingo Fuel = the minimum amount of fuel needed to return to the ship and have a specified fuel

reserve, if any.246

Japanese Aircraft Formations = shotai, chutai and squadron.

Shotai = 3 aircraft flying in triangle formation. Analogous to USN section or element.

Chutai = 6-9 aircraft or 2-3 shotai flying in triangle formation. At Midway the carrier attack

torpedo bombers used a 6-plane chutai and the dive bombers used a 9-plane chutai.247

Analogous to a USN division.

Squadron = 18-27 aircraft or 3 chutai flying in triangle formation

AAW = anti-aircraft warfare.

ASW = anti-submarine warfare.

Thach Weave = aircraft fighter tactic. Two planes fly next to each other. When an enemy

fighter gets on the tail of one and starts shooting, the two weave repeatedly into each

other’s direction so that the enemy fighter comes into the sights of the other’s machine

guns. In this way two slow WILDCAT fighters could protect themselves against one

faster, more maneuverable ZERO fighter.

246 Adams, Personal Communication. 247 Parshall and Tully, Shattered Sword 80-82. 113 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

Bibliography

Adams, D., MJR, USMC (2020). Personal Communication. 20 January Adkin, M. (2005) The Trafalgar Companion. Aurum Press, London. 560 pp. Campbell, J. (1986) Naval Weapons of WW II. Naval Inst. Press, Annapolis: 403 pp. Feynman RP, Leighton RB, Sands M. The Feynman Lectures on Physics. Vol I: Mainly Mechanics, Radiation and Heat. Addison-Wesley. Reading, MA. 1963: 8.5-8.10 Fiske, B.A. (1916) The Navy as a Fighting Machine. Chapter XII. Operating the Machine. Tables I, III. U.S. Naval Institute Press, Annapolis, MD. http://www.gutenberg.org/files/17547/17547-h/17547-h.htm#chapter%20XII Fort, B., Cdr, USN. (2006) “Midway Is Our Trafalgar.” U.S. Naval Institute Proceedings June Vol 132/6: 1240 Hoag, M. (2001) Jaws of Honda. Rev. Ed. Hoag, Lompoc, California: 48 pp. Howarth, D. (1969) Trafalgar. The Nelson Touch. Collins, London. Jarrold & Sons, Norwich, UK. 254 pp. Hughes, W.P. (1995) “A Salvo Model of Warships in Missile Combat Used to Evaluate Their Staying Power,” in Warfare Modeling. J. Bracken, M. Kress, R.E. Rosenthal. Eds. Military Operations Research Society. John Wiley & Sons, Inc., Danvers, MA.

Hughes, J.P. Jr, Girrier, R.P. (2018) Fleet Tactics and Naval Operations. 3rd Ed. Naval Inst. Press, Annapolis, MD: 96-97 Kimmet, L., Regis, M. (1996) U.S. Submarines in World War II. An Illustrated History. Navigator Publishing, Seattle, Washington. 159 pp. Kimmet, L., Regis, M. (1999) The Attack on Pearl Harbor. Rev Ed. NavPublishing, Seattle, Washington: 127 pp. Lanchester, F.W. (1916, 2009). Aircraft in Warfare: The Dawn of the Fourth Arm. Constable & Co. Ltd., London. Reprint Bibliolife, www.bibliolife.com/opensource: 272 pp. Lockwood, C.A., Adamson, H.C. (1997) Tragedy at Honda. Valley Pioneer Pub., Clovis, CA.: 184. Milford, F.J. (2009) US Navy Torpedoes. Part Two: The great torpedo scandal, 1941-43. www.geocities.com/Pentago/1592/ustorp2htm&date=2009-10-25+09:26:02 Montemayor (2020) “The Battle of Midway 1942: Told from the Japanese Perspective (1/2).” YouTube 24 February 2020.

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Morison, S.E. (1948, 2010) The Rising Sun in the Pacific. 1931-April 1942. History of United States Naval Operation in World War II. Volume 3. Naval Institute Press. Annapolis, MD. 411 pp. Morison, S.E. (1949, 2010) Coral Sea, Midway and Submarine Actions. May 1942-August 1942. History of United States Naval Operation in World War II. Volume 4. Naval Institute Press. Annapolis, MD. 307 pp. OPERATION PLAN 29-42 (Declassified, From Box #101 (1-40 Series) 6-10-52, Division of Naval Records and History. Orr, T. Prof. Old Dominion Univ. History Chan. Battle 360: Midway. www.history.com. Overy, R.J. (1997) Why the Allies Won: W.W. Norton & Norton. New York: 416 pp. Parshall, J.B., Tully, A.P. (2005) Shattered Sword. The Untold Story of the Battle of Midway. Potomac Books, Inc., Univ. Nebraska Press: 613 pp. Peterson, C.O. Major, USMC. (2008) The Schlieffen War Plan: What Impact did Logistics contribute to the Plan’s Failure? Master’s Thesis. U.S. Marine Corps Command and Staff College, Quantico, VA.: 36 pp. Accessible online as pdf.

Ritter, G. (1958) The Schlieffen Plan: Critique of a Myth. Oswald Wolf, London: 195 pp.

Rubel, R.C. (2015) Deconstructing Nimitz’s Principle of the Calculated Risk, Lessons for Today. Naval War College Review 2015; Winter: 31-46.

Schlieffen, A. von. Genl. (1913) Cannae. Command and General Staff School Press, Fort Leavenworth, KA. 1931: 420 pp. https://www.armyupress.army.mil/Portals/7/combat- studies-institute/csi-books/cannae.pdf

Shideler, T. LCDR, USN. (2020) Personal Communication. 31 January

Shideler, audio interview of letter of LCDR Yahachi Tanabe, C.O. of I-168, read by his daughter, text reproduced in Appendix D.

Stille, M. (2009) The Coral sea 1942. The first carrier battle. Osprey Publishing, Oxford. 96 pp.

Stille, M. (2010). Midway 1942. Turning point in the Pacific. Osprey Publishing, Oxford. 96 pp.

Stille, M. (2012) USN Destroyer vs IJN Destroyer. The Pacific1943. Osprey Publishing, Oxford. 80 pp.

Stille, M. (2012) Santa Cruz 1942. Carrier Duel in the South Pacific. Osprey Publishing, Oxford: 88-89

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Stille, M. (2017) The Philippine Sea 1944. The last great carrier battle. Osprey Publishing, Oxford: 96 pp.

Sutherling, W. (2019). Two Influences of Trafalgar on Navy Tactics 1905-1944: 42-48, 56-65. Channel Islands Maritime Museum Research Paper. Go to www.maritime-museum.org (archived under volunteer training syllabus).

Tanabe, Y. (1963) “I sank the Yorktown at Midway.” U.S. Naval Institute Proceedings Vol 89/5: 723. Taylor, A.J.P. (1969) War by Timetable: How the First World War Began. Macdonald & Co., London: 128 pp.

Taylor, J.G. (1980) Lanchester-Type Models of Warfare, (Monterey, CA: U.S. Naval Postgraduate School).

Thomas GB. (1966) Calculus and Analytic Geometry. 3rd Ed. Addison-Wesley. Reading, MA:26- 39, 155-164.

Zuber, T. (2002). Inventing the Schlieffen Plan: German War Planning 1871-1914. Oxford Univ. Press, Oxford: 340 pp. http://www.history.com/battle360/midway military.wikia.org/wiki/Shell_(projectile) http://www.navweaps.com/Weapons/WNUS_4cm56_mk12.phphttp://www.navweaps.com/Wea pons/WNUS_5-38_mk12.php http://www.navweaps.com/Weapons/WNJAP_18-45_t94.php www.google.com www.wikipedia.org en.wikipedia.org/wiki/Imperial_Japanese_Navy_Technical_Department#6th_Year_Type_Torpedo_(1917 http://www.combinedfleet.com/torps.htm http://faculty.nps.edu/awashburn/Files/Notes/Lanchester.pdf http://faculty.nps.edu/awashburn/Washburnpu/aggregated.pdf https://en.wikipedia.org/wiki/Aerial_torpedo#World_War_II https://en.wikipedia.org/wiki/Aerial_torpedo#cite_note-NavWeaps-25 https://atloa.org/the-calculated-risk-27-may-1942 (Logistics Officers Association) https://en.wikipedia.org/wiki/Battle_of_Midway#Attacks_on_the_Japanese_fleet 116 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws https://www.pearlharboraviationmuseum.org/pearl-harbor-blog/nakajima-b5n2/ http://www.fischer- tropsch.org/primary_documents/gvt_reports/USNAVY/USNTMJ%20Reports/USNTMJ-200E- 0551-0578%20Report%200-25.pdf http://www.warbirdsresourcegroup.org/IJARG/arm-type99.html https://en.wikipedia.org/wiki/Honda_Point_disaster http://www.pwencycl.kgbudge.com/J/a/Japanese_7p92mm_Type_1_gun.htm http://www.lonesentry.com/ordnance/20-mm-aircraft-cannon-type-99-mk-ii.html https://en.wikipedia.org/wiki/Nakajima_B5N#Specifications_(Nakajima_B5N2) https://military.wikia.org/wiki/List_of_Japanese_World_War_II_army_bombs TM 9-1985-4, Japanese Explosive Ordnance, Departments of the Army and the Air Force, 1953. https://archive.org/details/TM9-1985-5/mode/2up https://military.wikia.org/wiki/List_of_Japanese_World_War_II_navy_bombs#cite_note-3 http://www.worldwar2facts.org/battle-of-midway-facts.html https://en.wikipedia.org/wiki/Midway_order_of_battle https://www.ibiblio.org/hyperwar/USN/ref/ORD-ONI-9/index.html#depth. ORD-ONI Intelligence Bulletin. 1 Dec 1944. A Statistical Summary of Japanese Naval Matériel (REV. 2) https://en.wikipedia.org/wiki/List_of_aircraft_carriers_of_World_War_II https://en.wikipedia.org/wiki/John_Thach https://en.wikipedia.org/wiki/Anti-submarine_warfare#Pacific_Theatre.

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APPENDIX A. TABLES

JAPANESE NAVAL GUNS Firepower Bore/cal kg TNT m/s* meters rpm mag MegaJ Total kg all range drum /min MJ/' 18.1"/45 46cm AP HE 33.9 1.5 249 744 KE 1,463 475 30,000 1.5 495 16.1"/45 40cm AP HE 14.9 2 146 581 KE 1,020 462 30,000 2 435 14"/45 35.6cm AP HE 11.1 2 109 340 KE 674 414 30,000 2 231 8"/50 203mm TypII/3rdYr AP HE 3.1 3.5 53 117 KE 126 380 25,000 3.5 64 7.9" 20cm HE 2.8 3.5 48 104 KE 110 380 25,000 3.5 56 6.1"/60 155mm Type 3rdYr AP HE 1.2 5.5 31 69 KE 56 350 25,000 5.5 38 5.5"/50 14cm Type 3rdYr HiEx HE 2.9 8 112 332 KE 38 850 19,100 8 220 5"/40 12.7cm Type 89 HiEx HE 1.8 8 70 165 KE 23 710 9,400 8 95 4.7"/45 120mm Type 10thYr HiEx HE 1.9 7 65 162 KE 20 825 10,000 7 97 3.9"/65 10cm Type 98 HiEx HE 0.95 18 84 318 KE 13 1000 11,000 18 234 3"/40 80mm Type 88 HiEx HE 0.6 16 47 90 KE 6 670 10,800 16 43 1.6"62 40mm HI Type91 Vick pompom HE 0.07 80 28 54 KE 0.90 600 4,000 80 26 1.0" 25mm/60 Type 96/1 15rd mag HE 0.01 115 15 5.6 28.9 KE 0.25 900 3,000 115 23 20mm autocannonT99 Ship KE 0.13 600 600 520 24 24 20 mm autocannon A/C 60rd mag KE 0.13 600 600 60 60 2.8 2.8 0.52" 13mm/76 Type 93 30rd mag HE 0.004 250 4.3 12.4 KE 0.05 805 1,500 250 8.1 0.303"7.7mmMGTy94 HI KE 0.011 745 300 900 5.5 5.5 0.303"7.7mmMGTy97 Ship KE 0.011 724 540 500 2.9 2.9 0.303"7.7mm Ty97 Aircraft MG 500rd mag KE 0.011 724 540 500 500 2.9 2.9 0.303"7.7mmMGTy92 30rd strips KE 0.011 732 800 450 30 2.6 2.6 0.303"7.7mmMGTy92 A/C 97rd drum KE 0.011 732 800 97 97 0.6 0.6 7.92 mm Type 1 MG 30rd feed trays Ship KE 0.012 789 1,000 425 3.0 3.0 7.92 mm Type 1 MG A/C 75rd mag KE 0.012 789 1,000 75 75 0.5 0.5

Table X-1. IJN Guns’ Firepower. HE high explosive Energy. KE Kinetic Energy. MegaJ/’ = MegaJoules/min=(HE+KE)/min. m/s=meters/sec. Total firepower reduced for aircraft guns due to limits of drums. On ships, drum limits reduce rate of fire, but not total output per minute. AP armor-piercing shell. HiEx ordinary shell with high explosive 118 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

TABLE X-2. USN Guns’ firepower. For HiEx shells, an accepted optimum explosive ratio was about 20% of projectile weight (15% to 25%). There is a smaller percentage for IJN shells, the maximum being about 10% for 3” 80 mm or 1.6” 40 mm shells. Military.wikia.org/wiki/Shell_(projectile)

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TABLE X-2a. Firepower of each gun of IJN and USN at Midway 1942 in Mega Joules per minute (MJ/’)

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TABLE X-2b. Number of rounds to shoot down one enemy aircraft for each USN AA gun. R.P.B. is “rounds per bird.” “Kills” are aircraft shot down, with % of total 2,250 aircraft shot down. 5” Com = fuse set to explode just before it reaches target, with detonation shock wave and expanding cone of shrapnel increases chance of target destruction. 5” VT = variable time or proximity fuse 40 mm = Bofors gun 20 mm = Oerlikon autocannon

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IMPERIAL JAPANESE NAVY TORPEDOES

SURFACE/SUBMERG TORPEDOES kg EXP Speed Range rpm MegaJ Total kg all m/s meters /min MJ/' Type 93 LL 61cm 24" HE 491 40,000 1 2,404 2,405 Shimose, O2 LongLance KE 2,705 18.5 1 0.93 Type 95 53.3cm21" HE 406 12,000 1 1,987 1,988 Shimose, O2 KE 1,669 23.2 1 0.90 Type 92 53.3cm21" HE 300 7,000 1 1,469 1,469 battery KE 1,724 15.4 1 0.41 6th yr Torpe53.3cm21" HE 203 15,000 1 994 994 1917 keros air KE 1,432 13.4 1 0.26 Type 89 53.3cm21" HE 300 10,000 1 1,255 1,256 1929 Type 91 exp KE 1,668 18.0 1 0.54 Type 8/1 61cm24" HE 300 10,000 1 1,469 1,469 1920 KE 2,215 19.0 1 0.80 Type 8/2 61cm24" HE 346 20,000 1 1,694 1,694 1920 KE 2,362 13.9 1 0.46 Type 90 61cm24" HE 375 15,000 1 1,569 1,570 1930 Type 97 exp KE 2,605 18.0 1 0.84 Type 44/2 53.3cm21" HE 160 10,000 1 783 784 1911 surshp keros air KE 2,851 13.9 1 0.55

AIRBORNE TORPEDOES kg EXP Speed Range rpm LaunSp MegaJ Total kg all m/s meters Knots /min MJ/' Type 91/1 Type 97 exp HE 150 21 2,000 1 260 734 734 KE 785 1 0.00 Type 91/2 Type 97 exp HE 205 21 2,000 1 260 1,004 1,004 Apr-41 KE 837 1 0.00 Type 91/3 Type 97 exp HE 240 21 2,000 1 260 1,175 1,175 Jul-42 KE 851 1 0.00

en.wikipedia.org/wiki/Imp_Jap_Nav_Tech_Dept#6th_Year_Type_Torpedo_(1917) http://www.combinedfleet.com/torps.htm TABLE X-3. IJN Torpedoes firepower available during Pacific campaign. There are different values for some warheads. NavWeaps gives 300 kg for Type 89 and 406 kg for Type 95, while Yahachi Tanabe give 446 lbs. or 203 kg, and 991 lbs. or 450 kg, respectively. http://www.navweaps.com/Weapons/WTJAP_PreWWII.php Yahachi Tanabe. “I sank the Yorktown at Midway.” US Nav Inst Proc 723

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US NAVY TORPEDOES

SURFACE/SUBMERG TORPEDOES kg TNT Speed Range rpm MegaJ Total kg all m/s meters /min MJ/' MARK 13 57cm22.5" HE 182 5,762 1 761 762 TNT KE 1,007 17.2 1 0.30 MARK 14 53cm21" HE 292 8,232 1 1,222 1,222 1942 TNT KE 1,490 16.0 1 0.38 MARK 15 53cm21" HE 375 13,720 1 1,569 1,569 1940 TNT KE 1,746 13.6 1 0.32

TABLE X-4. USN Torpedoes firepower in 1942. Increased weight HE warheads occurred with advance in model number. This is nominal firepower. Nominal firepower is reduced to actual deliverable firepower when these are added to the attack craft. This is due to the USN’s torpedo unreliability. Reduction factors are: ships 50%, submarines 50% and aircraft 30%. Nominal data from https://en.wikipedia.org/wiki/American_21-inch_torpedo, and other data on Wikipedia. Dates and model numbers helpful for Midway

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TABLE X-4a. Firepower of IJN and USN torpedoes. Type 91 Mark 13 aircraft Type 95 Mark 14 submarines Type 93 (LL) Mark 15 destroyers (I-168 sank YORKTOWN with four Type 89 torpedoes, each with 1,256 Mega Joules

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TABLE X-4b. TNT equivalents IJN “Shimose” and USN TNT, along with other explosives for comparison. RE = relative effectiveness. Rho (ρ) is density. Trinitroanisole (TNA) is Type 91 explosive. Hexanite (TNT 60%, HND 40%) is Type 97 explosive. It was developed to extend the amount of explosive when TNT was in short supply. Its R.E. is slightly less than TNT.

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TABLE X-5. USN Mark 14 Torpedo performance. * -- incomplete data. ** DRUM includes data from 05/01/42. **SJ = more accurate SJ Radar. DRUM and HALIBUT number of attacks estimated but proportional and likely about right. Overall GUARDFISH had 11 hits which sank 8 ships, unknown no. shots. RATE is the hit rate or HITS/SHOTS. Morison, Coral Sea, Midway and Submarine Actions 198-204.

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I.J.N. BOMBS AND DEPTH CHARGES

kg TNT m/s rpm MJ/' MJ/' kg all Total Type 98 No 25 532lb HE 96 1 470 472 Midway 400mmconcrete AP KE 242 92 1 2.0 No. 80 1760LB HE 383 1 1,874 1,880 Midway 400mmconcrete AP KE 800 92 1 6.7 No. 25 Mod 2 HE 104 1 507 509 Midway ordinary KE 253 92 1 2.1 No. 3 Mod 2 Ordinary bomb HE 11 1 51.4 52 KE 30 92 1 0.3 Type 99 No.6 Mk2 140lb HE 39 1 189 190 KE 64 92 1 0.5 No.50 Mod 2 1080lb HE 208 1 1,018 1,022 ordinary bomb KE 491 92 1 4.1 No. 25 550lb land bomb HE 150 1 734 736 KE 250 92 1 2.1 Type 99 No.25 550lb HE 60 1 294 296 ordinary bomb KE 250 92 1 2.1 Type 1 No.25 Mk2/1 572lb HE 144 1 705 708 KE 260 92 1 2.2 Depth charge T 95 T88explo100kg HE 130 1 636 639 KE 260 92 1 2.2 Depth charge T 99/6/2 T88explo 60kg A/C HE 78 1 382 384 KE 260 92 1 2.2 Depth charge T 1/25/2 T88explo 250kg A/C HE 325 1 1,591 1,593 KE 260 92 1 2.2

TABLE X-6. IJN Bombs and Depth Charges Pacific Campaign. https://www.ibiblio.org/hyperwar/USN/ref/ORD-ONI-

9/index.html#depth

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UNITED STATES NAVY BOMBS & DEPTH CHARGES kg TNT m/s rpm MJ/' MJ/' kg all Total AN-M30 100lb HE 25 1 103 103 KE 45 92 1 0.4 AN-M57 250lb HE 56 1 234 235 KE 114 92 1 1.0 NA-M64 500lb HE 119 1 498 500 KE 227 92 1 1.9 Mark 65 AN-M65 1000lb HE 268 1 1,123 1,127 gen purpose SBD KE 455 92 1 3.8 AN-M66 2000lb HE 482 1 2,018 2,026 KE 909 92 1 7.7 AN-M58A1 500LB LIGHT AP HE 66 1 276 278 KE 227 92 1 1.9 AN-M59 1000lb LIGHT AP HE 138 1 576 580 KE 455 92 1 3.8 AN-MK33 1000lb HEAVY AP HE 65 1 274 278 KE 455 92 1 3.8 AN-MK1 1600lb HEAVY AP HE 98 1 409 415 KE 727 92 1 6.2 AN-MK47 350 DEPTH A/C HE 115 1 479 479 KE 159 4 1 0.0 AN-MK29 650 DEPTH A/C HE 211 1 882 885 KE 295 92 1 2.5 Depth Charges Mark7 HE 272 1 1,138 1,138 KE 338 4 1 0.0 http://www.navweaps.com/Weapons/WAMUS_ASW.php http://www.303rdbg.com/bombs.html

TABLE X-7. USN Bombs and depth charges firepower. HE for Mark 65 was averaged from Navweaps 295kg and 303rd Bomb Group 303rdbg 241kg.

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TABLE X-7a. Aerial Bombs used at Midway. http://www.navweaps.com/Weapons/WAMUS_ASW.ph p h // db /b b h l

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JAPANESE MINES kg EXP No. MJ/' kg all Aircract Typ 3 Mk 1 Mod 1 HE 80 1 392 KE 640 Shimose 5 Mod 1 moored contact HE 83 1 406 KE 520 Mark 6 Mod 1 moor contact HE 215 1 1,052 KE 1156 Type 93 Mod 4 moor contact HE 110 1 538 KE 710 Type 82 shore-controlled acoustic HE 500 1 2,448 KE 1300

http://www.navweaps.com/Weapons/WAMJAP_Mines.php

TABLE X-8. IJN Mines firepower available Pacific.

US NAVY MINES kg TNT No. MJ/' Total kg total

MARK 12 21"/533mm HE 500 1 2,092 2,092 Submarine KE 655 MARK 13 magn pistol HE 290 1 1,213 1,213 Air KE 475

http://www.navweaps.com/Weapons/WAMUS_Mines.php

TABLE X-9. USN Mines firepower available Pacific.

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I.J.N. WARSHIP CLASSES

Armament size kg Armament size kg Armament size kg MJ/' No. MJ/' MJ/' No. MJ/' MJ/' No. MJ/' HE+KE Total HE+KE Total HE+KE Total 1 BB KONGO 6 CA TONE 13 KAGERO DD 14"/45 35.6cm 340 8 2,720 8"/50 TypII 203mm 117 8 936 5"/40 12.7cm 165 6 990 6.1"/60 155mm 69 8 552 5"/40 12.7cm 165 8 1,320 1.0 in 25mm/60 28.9 4 116 5"/40 12.7cm 165 8 1,320 1.0 in 25mm/60 28.9 12 347 Torp Ty 93LL 24"61cm 2405 8 19,240 1.0 in 25mm/60 28.9 122 3,526 Torp Ty 93LL 24"61cm 2405 12 28,860 Type 95 depth charges 18 639 6 3,834 8,118 31,463 24,180

2 BB YAMATO 7 CA TAKAO 18.1"/45 46cm 744 9 6,696 8"/50 TypII 203mm 117 10 1,170 14 YUGUMO DD 6.1"/60 155mm 69 12 828 5"/40 12.7cm 165 8 1,320 5"/40 12.7cm 165 6 990 5"/40 12.7cm 165 12 1,980 1.0 in 25mm/60 28.9 60 1,734 1.0 in 25mm/60 28.9 4 116 1.0 in 25mm/60 28.9 24 694 Torp Ty 93LL 24"61cm 2405 16 38,480 Torp Ty 93LL 24"61cm 2405 8 19,240 0.52 in 13.2mm/70 12.4 4 50 42,704 Type 95 depth charges 18 639 6 3,834 10,247 24,180

3 BB NAGATO 8 CA MYOKO 15 FUBUKI DD 16.1"/45 40cm 581 9 5,229 8"/50 TypII 203mm 117 10 1,170 5"/40 12.7cm 165 6 990 5.5"/50 14cm 332 6 1,992 4".7/45 120mm 162 6 972 0.52 in 13.2mm/70 12.4 2 25 5"/40 12.7cm 165 24 3,960 Torp Ty 93LL 24"61cm 2405 12 28,860 Torp Ty 90 24"610mm 1837 9 16,533 Torp Ty44 21"53cm 784 2 1,210 31,002 Type 95 depth charges 36 639 6 3,834 12,391 21,382

4 BB ISE (1933) 9 CA MOGAMI 16 SHIRATSUYU DD 14"/45 35.6cm 340 12 4,080 8"/50 TypII 203mm 117 6 702 5"/40 12.7cm 165 5 825 5.5"/50 14cm 332 16 5,312 5"/40 12.7cm 165 8 1,320 0.52 in 13.2mm/70 12.4 2 25 5"/40 12.7cm 165 8 1,320 1.0 in 25mm/60 28.9 30 867 Torp Ty 93LL 24"61cm 2405 8 19,240 1.0 in 25mm/60 28.9 20 578 Torp Ty 93LL 24"61cm 2405 12 28,860 Type 95 depth charges 16 639 6 3,834 11,290 31,749 23,924

5 BB FUSO 10 CL NAGARA 17 HATSUHARU DD 14"/45 35.6cm 340 12 4,080 8"/50 TypII 203mm 117 10 1,170 5"/40 12.7cm 165 6 990 6.1"/60 155mm 69 14 966 4".7/45 120mm 162 6 972 1.6" 40mm 54 2 108 5"/40 12.7cm 165 8 1,320 5"/40 12.7cm 165 8 1,320 Torp Ty 90 24"610mm 1837 6 11,022 1.0 in 25mm/60 28.9 59 1,705 0.52 in 13.2mm/70 12.4 2 25 Type 95 depth charges 18 639 6 3,834 8,071 Torp Ty 93LL 24"61cm 2405 12 28,860 15,954 32,347

11 CL SENDAI 18 ASASHIO DD 5.5"/50 14cm 332 7 2,324 5"/40 12.7cm 165 6 990 3"/40 80mm 90 2 180 1.0 in 25mm/60 28.9 28 809 Torp Ty 93LL 24"61cm 2405 4 9,620 0.52 in 13.2mm/70 12.4 4 50 12,124 Torp Ty 93LL 24"61cm 2405 8 19,240 Type 95 depth charges 18 639 6 3,834 24,923 12 CL KUMA 19 MINEKAZE DD 5.5"/50 14cm 332 6 1,992 4.7"/45 120mm 162 4 648 1.0 in 25mm/60 28.9 10 289 0.303" 7.7mm Ty92 MG 2.6 2 5 Torp T92 21"533mm 1469 4 5,876 Type 44/2 21"533mm 784 6 4,704 Torp T44/2 21"533mm 784 4 3,136 Type 95 depth charges 18 639 6 3,834 11,293 9,191

TABLE X-10. Firepower by IJN Warship class. BB Battleship, CA Heavy Cruiser, CL Light Cruiser, DD Destroyer. MJ/’ is Mega Joules per minute. Size No. is number of guns of caliber size. HE+KE is sum of explosive and kinetic energy.

131 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

USN CLASS SHIPS FIREPOWER

MJ/' No. MJ/' MJ/' No. MJ/' MJ/' No. MJ/' HE+KE Total HE+KE Total HE+KE Total 1 CA NEW ORLEANS 6 CL BROOKLYN 11 DD MAHAN 8"/55 Mk203mm 83 9 747 6"/47 152mm 106 15 1,590 5"/38 127mm DP 315 5 1,575 5"/25 127mm AA 286 8 2,288 5"/25 127mm 286 8 2,288 .50cal 12.7mm MG AA 83 4 332 20mmOerlikonAA 17 28 476 Bofors 40mm AA 251 28 7,028 Torp Mk15 21"533mm* 785 12 9,414 3,511 20mmOerlikonAA 17 18 306 Depth charges 2054 2 4,108 11,212 15,429 2 CA PORTLAND 8"/55 Mk203mm 83 9 747 7 DD SIMS 12 DD BENHAM 5"/25 127mm AA 286 8 2,288 5"/38 127mm 286 5 1,430 5"/38 127mm DP 286 4 1,144 20mmOerlikonAA 17 17 289 .50 cal/90 MG 14 4 56 .50cal 12.7mm MG AA 14 4 56 3,324 Torp Mk15 21"533mm* 785 8 6,276 Torp Mk15 21"533mm* 785 4 3,138 Depth charges Mk7 1138 2 2,276 Depth charges Mk7 1138 2 2,276 3 CA NORTHAMPTON 10,038 6,614 8"/55 Mk203mm 83 9 747 5"/25 127mm AA 283 8 2,264 8 DD GLEAVES 13 DD GRIDLEY 1.1"/75 27.9mm 174 4 696 5"/38 127mm DP 286 5 1,430 5"/38 127mm DP 286 4 1,144 3,707 .50 cal 12.7mm MG AA 14 6 84 .50cal 12.7mm MG AA 14 4 56 Torp Mk15 21"533mm* 785 10 7,845 Torp Mk15 21"533mm* 785 16 12,552 4 CA PENSACOLA Depth charges Mk7 1138 2 2,276 (not receive Bofors) 8"/55 Mk203mm 83 10 830 11,635 13,752 5"/25 127mm AA 283 4 1,132 1.1"/75 27.9mm 174 4 696 9 DD PORTER 14 DD BAGLEY 20mmOerlikonAA 17 8 136 5"/38 127mm SP 286 8 2,288 5"/38 127mm DP 286 4 1,144 2,794 Bofors 40mm AA 251 2 502 .50cal 12.7mm MG AA 14 4 56 20mmOerlikonAA 17 6 102 Torp Mk15 21"533mm* 785 16 12,552 5 CL ATLANTA Depth Charges Mk7 1138 2 2,276 Depth charges Mk7 1138 2 2,276 5"/38 127mm Mk 12 286 16 4,576 5,168 16,028 1.1"/75 27.9mm 174 12 2,088 20mmOerlikonAA 17 8 136 10 DD FARRAGUT 15 DD CLEMSON Torp Mk15 21"533mm* 785 8 6,276 5"/38 127mm DP 286 4 1,144 4"/50 102mm 35 4 140 13,076 Bofors 40mm AA 251 4 1,004 3"/23 76mm AA 14 1 14 20mmOerlikonAA 17 5 85 Torp Mk15 21"533mm* 785 12 9,414 Torp Mk15 21"533mm* 785 8 6,276 9,568 Depth charges Mk7 1138 2 2,276 10,785 16 DD WICKES 4"/50 102mm 35 4 140 3"/23 76mm AA 14 1 14 Torp Mk15 21"533mm* 785 12 9,414 9,568

TABLE X-11. Firepower by USN Warship class. No battleships. * The firepower of the Mark 15 Torpedo is reduced by 50% from 1569 MJ/’ to 785 MJ/’, to reflect its reduced reliability of 50%.

132 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

IMPERIAL JAPANESE NAVY MIDWAY FORCE ALEUTIANS FORCE 1st Mai Gua Inv Sup Xpt Tdr Σ MJ/' Tot MJ/' 2nd Mai Attu Kiska Tdr Σ MJ/' Tot MJ/' Kid Bod For For Kid Bod Adak Inv But But Inv For

BB CC DD DIVISIONS BD3 BD1 BD2 BD3 CD4 SHIP CLASS KONGO BB 2 2 4 8,118 32,472 YAMATO BB 2 2 10,247 20,494 NAGATO BB 1 1 12,391 12,391 ISE BB 2 2 11,290 22,580 FUSO BB 2 2 8,071 16,142 TONE CA 2 2 31,463 62,926 NAGARA CL 1 1 2 32,347 64,694 1 1 32,347 32,347 SENDAI CL 1 1 2 12,124 24,248 KUMA CL 2 2 11,293 22,586 2 2 11,293 22,586 TAKAO CA 2 2 42,704 85,408 2 2 42,704 85,408 MYOKO CA 2 2 31,002 62,004 1 1 31,002 31,002 MOGAMI CA 4 4 8 31,749 253,992 KAGERO DD 9 8 1 18 24,180 435,240 YUGUMO DD 3 3 24,180 72,540 FUBUKI DD 8 4 12 21,382 256,584 3 2 2 7 21,382 149,674 SHIRATSUYU DD 6 4 10 23,924 239,240 HATSUHARU DD 2 2 15,954 31,908 4 4 15,954 63,816 ASASHIO DD 3 2 2 7 24,923 174,461 MINEKAZE DD 1 1 2 9,191 18,382 1,889,910 403,215

TABLE X-12. Total IJN Warship firepower Pacific Operation. Kid But=Kido Butai.

133 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

UNITED STATES NAVY MIDWAY FORCE ALEUTIANS FORCE No. MJ/' Tot MJ/' No. MJ/' Tot MJ/' BB CC DD DIVISIONS SHIP CLASS CA NEW ORLEANS 4 3,511 14,044 PORTLAND 1 3,324 3,324 1 3,324 3,324 NORTHAMPTON 1 3,707 3,707 1 3,707 3,707 PENSACOLA 1 2,794 2,794 CL ATLANTA 1 13,076 13,076 BROOKLYN 11,212 3 11,212 33,636 DD SIMS 5 10,038 50,190 GLEAVES 2 11,635 23,270 PORTER 3 5,168 15,504 FARRAGUT 4 10,785 43,140 MAHAN 1 15,429 15,429 2 15,429 30,858 BENHAM 2 6,614 13,228 GRIDLEY 1 13,752 13,752 2 13,752 27,504 BAGLEY 2 16,028 32,056 CLEMSON 9,568 6 9,568 57,408 WICKES 9,568 3 9,568 28,704

TOTAL 243,514 185,141

TABLE X-13. Total USN Warship firepower Pacific Operation. *The firepower of the destroyers and light cruisers has been corrected for the reduced reliability of the Mark 15 Torpedo. This reduced the Midway firepower from 457,000 MJ/’ to 243,000 MJ/’ and the Aleutians firepower from 313,000 MJ/’ to 185,000 MJ/’.

134 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

TABLE X-13a. Firepower of ships of IJN and USN at Midway and Aleutians.

135 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

IMPERIAL JAPANESE NAVY SUBMARINES

Armament MJ/' No. MJ/' MJ/' No. MJ/' HE+KE Total Armament HE+KE Total

1 Kaidai III A Submarine I-153, I-154, I-155 6 Kaidai VIA Submarine I-171, I-172, I-73 "later mod" Torpedo Type6th YR 994 8 7,952 Torpedo Typ89 533mm 1469 6 8,814 gun 4.7" 120mm 162 1 162 gun 4.7" 120mm 162 1 162 gun 7.7mm MG 2.6 1 3 gun .52" 13.2mm AA 12.4 1 12 8,117 gun 7.7 mm MG 2.6 1 3 8,991

2 Kaidai III B Submarine I-156,I-157,I-158,I-159,I-60,I-63 7 Kaidai VIB Submarine I-174, I-175 Torpedo Type6th YR 994 8 7,952 Torpedo Type89 533mm 1469 6 8,814 gun 4.7" 120mm 162 1 162 gun 4.7" 120 mm 162 1 162 gun 7.7mm MG 2.6 1 3 gun .52" 13.2mm AA 12.4 1 12 8,117 8,988

3 Kaidai IV Submarine I-61, I-162, I-164 8 I-121 Minelaying Submarine (I-121, I-122, I-123, I-124) Torpedo Ty89 533mm 1469 6 8,814 Torp 6th yr Type 21" 994 2 1,988 gun 4.7"120mm 162 1 162 Gun 5.5"/40 14cm 11th yr 332 1 332 gun 7.7mm MG 2.6 1 3 Total without mines 2,320 8,979 Mine average T93/4 m c 538 42 22,596 Total with mines 24,916 4 Kaidai V Submarine I-165, I-166, I-67 Torpedo Typ89 533mm 1469 6 8,814 9 TYPE A1 SUBMARINE (I-9, I-10, I-11) gun 3.9" 100mm Ty88 318 1 318 Ty95 533mm21" Torpe 1988 6 11,928 gun 7.7 mm MG 2.6 1 3 5.5"/50 14cm gun 332 1 332 9,135 1.0"25mmAAgun 28.3 2 57 12,317

5 Kaidai VIA Submarine I-168, I-169, I-70 "earlier mod" 10 TYPE B1 SUBMARINE (I-15, I-17, I-19, I-25, I-26) Torpedo Typ89 533mm 1469 6 8,814 Ty95 533mm21" Torpe 1988 6 11,928 gun 3.9" 100mm Ty88 318 1 318 5.5"/50 14cm gun 332 1 332 gun .52" 13.2mm AA 12.4 1 12 1.0"25mmAAgun 28.3 2 57 gun 7.7 mm MG 2.6 1 3 float plane 12,317 9,147

TABLE X-14. Firepower by IJN Submarine class, I-121 without and with mines.

136 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

IMPERIAL JAPANESE NAVY SUBMARINE FORCES

MIDWAY FORCE Advance Force MJ/' No. Total MJ/' Total MJ/' SUBRON 3 w/o mines w mines I-168, I-169 KAIDAI VIA 9,147 2 18,294 I-171 KAIDAI VIA 8,991 1 8,991 I-174, I-175 KAIDAI VIB 8,988 2 17,976 SUBRON 5 SUBDIV 19 I-156, I-157, I-158, I-159 KAIDAI IIIB 8,117 4 32,468 SUBDIV 30 I-162 KAIDAI IV 8,979 1 8,979 I-165, I-166 KAIDAI V 9,135 2 18,270 SUBDIV 13 (OP K) I-121, I-122, I-123 MINELAYING 2,320 3 6,960 24,916 3 74,748 MIDWAY 111,938 179,726

ALEUTIANS FORCES Submarine Detachment I-9 TYPE A1 SUB 12,317 1 12,317 SUBDIV 2 I-15, I-17, I-19 TYPE B1 SUB 12,317 3 36,951 SUBDIV 4 I-25, I-26 TYPE B1 SUB 12,317 2 24,634 ALEUTIANS 73,902

MIDWAY + ALEUTIANS 185,840 253,628

TABLE X-15. Total IJN Submarine firepower at Midway.

137 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

US NAVY SUBMARINES MJ/' No. MJ/' MJ/' No. MJ/' HE+KE Total HE+KE Total 1 V-8 CACHALOT SS-170 4 V-5 NARWHAL SS-167 Mark 14 Torpedo* 611 6 3,666 Mark 14 Torpedo* 611 6 3,666 3"/50 76mm deck gun 14 1 14 6"/53 152mm MkXIIM2 deck gu 106 2 212 3,680 3,878

2 GATO SS-212 5 V-7 DOLPHIN SS-169 Mark 14 Torpedo* 611 10 6,110 Mark 14 Torpedo* 611 6 3,666 4"/50 102mm deck gun 35 1 35 4"/50 102mm deck gun 35 1 35 Bofors 40mm 251 1 251 3,701 Oerlikon 20mm 17 1 17 6,413 6 PORPOISE SS-172 Mark 14 Torpedo* 611 6 3,666 3 TAMBOR SS-198 3"/50 76mm deck gun 14 1 14 Mark 14 Torpedo* 611 10 6,110 .30 cal 7.62mm MG 4 2 8 3"/50 76mm deck gun 14 1 14 3,688 Bofors 40mm 251 1 251 Oerlikon 20mm 17 1 17 7 S-1 HOLLAND S-18 23 27 28 35 SS-123 6,392 Mark 14 Torpedo* 611 4 2,444 4"/50 102mm deck gun 35 1 35 2,479

TABLE X-16. Firepower by USN Submarine class. *Mark 14 torpedo firepower decreased by 50% to reflect unreliability due to Mark 6 fuse

138 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

USN TOTAL SUBMARINE FORCE MIDWAY FORCE ALEUTIANS FORCE SUBMARINES* MJ/' SUBMARINES* MJ/' TASK GROUP 7.1 MIDWAY PATROL GROUP SUBMARINE GROUP CACHALOT SS V-8 CACHALOT 3,680 S18 SS-123 2,479 FLYING FISH SS GATO 6,413 S-23 2,479 TAMBOR SS TAMBOR 6,392 S-27 2,479 TROUT SS TAMBOR 6,392 S-28 2,479 GRAYLING SS TAMBOR 6,392 S-35 2,479 NAUTILUS SS V-5 NARWHAL 3,878 GROUPER SS GATO 6,413 DOLPHIN SS V-7 DOLPHIN 3,701 GATO SS GATO 6,413 CUTTLEFISH SS V-8 CACHALOT 3,680 GUDGEON SS TAMBOR 6,392 GRENADIER SS TAMBOR 6,392 TASK GROUP 7.2 MIDWAY SHORT STOPS NARWHAL SS V-5 NARWHAL 3,878 PLUNGER SS PORPOISE 3,688 TRIGGER SS GATO 6,413 TASK GROUP 7.3 NORTH OF OAHU TARPON SS PORPOISE 3,688 PIKE SS PORPOISE 3,688 FINBACK SS GATO 6,413 GROWLER SS GATO 6,413

TOTAL 100,319 12,395

TABLE X-17. Total USN Submarine firepower at Midway. *The firepower of the submarines has been reduced from 196,000 to 100,000 at Midway and from 24,000 to 12,000 in the Aleutians, due to the unreliable Mark 14 torpedo and Mark 6 fuse.

139 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

TABLE X-17a. USN submarines lost half their firepower advantage due to unreliability from their defective Mark 6 fuse.

140 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

I.J.N. AIRCRAFT TABLE X-18. MJ/' No. Tot MJ/' Firepower by IJN Aircraft class. 1 A6M2b Typ 0 Mod 21 ZERO Mitsubishi Carrier Fighter 20mm autocannonT99 60rds 2.8 2 5.6 0.303"7.7mmMGT97 500rds 2.9 2 5.8 T99/6/2 60 kg bomb 190 2 380 two 60 kg bombs or fuel tanks 391

1a A5M4 0.303"7.7mmMGT97 500rds 2.9 2 5.8 No 3 Mod 2 Ordinary 30kg bomb 52 2 104 two 30 kg bombs or fuel tanks 110

2 B5N2 KATE Nakajima Carrier Attack Torpedo Bomber 0.303"7.7mmMGT92 97rds 0.6 1 0.6 Type 91/2 800kg Torpedo 1004 1 1,004 1,005

3 D3A1 VAL Aichi Type 99 Carrier Dive Bomber 0.303"7.7mmMGT97 500rds 2.9 2 5.8 forward 0.303"7.7mmMGT92 97rds 0.6 1 0.6 rear Type 98 No 25 250 kg bomb AP 472 0.67 315 2/3 semi-armor piercing deck No25/2 250 kg bomb HiEx 509 0.33 170 1/3 knock out AA batteries T99/6/2 60 kg bomb 190 2 380 871

4 D4Y1 JUDY Yokosuka Carrier Dive Bomber 0.303"7.7mmMGT97 500rds 2.9 2 5.8 fuselage Type 1 7.92mm MG 75rds 0.5 1 0.5 rear Parshall and Tully:483 Type 98 No 25 250 kg bomb AP 472 1.00 472 2/3 semi-armor piercing deck No25/2 250 kg bomb HiEx 509 1.00 509 1/3 knock out AA batteries 987

5 H6K Kawanishi Flying Boat slower, shorter range 20mm Type99 autocannon 60rds 2.8 1 2.8 assume same magazine as A6M 0.303"7.7MGT92 97rds 0.6 3 1.8 1 spine, 2 waist blisters Type 91/2 800kg Torpedo 1004 2 2,008 or carry 1000 kg bombs 2,013

6 H8K Kawanishi Flying Boat faster, longer range 20mm Type99 autocannon 60rds 2.8 5 14.0 0.303"7.7MGT92 97rds 0.6 5 3.0 Type 91/2 800kg Torpedo 1004 2 2,008 or carry 2000 kg bombs/depth ch 2,025

7 B4Y1 JEAN Yokosuka Type 96 Torpedo Bomber Biplane 0.303"7.7mmMGT92 97rds 0.6 1 1 Type 91/2 800kg Torpedo 1004 1 1,004 1 torpedo or 1 bomb 1,005

TABLE X-18. Firepower by IJN Aircraft class. 141 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

US NAVY AIRCRAFT

MJ/' No. Tot MJ/' MJ/' No. Tot MJ/'

1 TBF/M GRUMMAN AVENGER (6-10) 6 TBD-1 DOUGLASS DEVASTATOR 0.50"12.7mmM2Brown MG 14 2.0 28 0.50"12.7mmM2Brown MG fwd 14 0.5 7 0.30"7.62mmBrownMG M1919 4 0.5 2 0.30"7.62mmBrownMG fwd 4 0.5 2 0.30"7.62mmBrownMG 4 0.5 2 0.30"7.62mmBrownMG rear 4 0.5 2 Mark 13 Torpedo* 229 1 229 Mark 13 Torpedo* 229 1 229 261 240

2 SBD DOUGLASS DAUNTLESS 7 PBY-5A CONSOLIDATED CATALINA 0.50"12.7mmM2Brown MG 14 0.5 7 0.50"12.7mmM2Brown MG fwd 14 2.0 28 0.30"7.62mmBrownMG 4 0.5 2 0.30"7.62mmBrownMG rear 4 3.0 12 bombs 1020kg 1,362 1 1,362 4000lbs 1818kg bombs, d/c, torp 1,371 Bombs 1000lb. 455kg 1,127 1.00 1,127 Depth charges 650lb. 295kg 850 1.00 850 3 F4F-4 GRUMMAN WILDCAT Mark 13 Torpedo* 229 1.00 229 0.50"12.7mmM2Brown MG fwd 14 3 42 2,246 AN-M30 100lb bomb 103 2 206 248 8 F2A-3 BREWSTER BUFFALO 0.50"12.7mmM2Brown MG nose 14 2.0 28 4 SBU2-3 VINDICATOR 0.50"12.7mmM2Brown MG wing 14 2.0 28 0.50"12.7mmM2Brown MG fwd 14 2 28 56 Mk65 AN-M65 1000LB 454KG BO 1,127 1 1,127 1,155 9 B-26G MARAUDER 0.50"12.7mmM2Brown MG 14 12 168 5 B-17E FLYING FORTRESS Mk65 AN-M65 1000LB 454KG BO 1,127 4 4,508 0.50"12.7mmM2Brown MG 14 13 182 4,676 Mk65 AN-M65 1000LB 454KG BO 1,127 8 9,016 9,198

TABLE X-19. Firepower by USN Aircraft class. *The firepower of the Mark 13 Torpedo has been reduced to 30% of its nominal value due to the faulty Mark 6 fuse and water impact problems. Some sources would use 10% of nominal value, e.g. http://www.navweaps.com/Weapons/WTUS_WWII.php .

142 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

TABLE X-19a. Comparison IJN and USN Aircraft firepower by class.

TABLE X-19b. Range of IJN and USN Aircraft.

143 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

IMPERIAL JAPANESE NAVY AIRCRAFT

MIDWAY FORCE ALEUTIANS FORCE 1st Main Invas Exp Σ MJ/' Tot MJ/' 2nd Σ MJ/' Tot MJ/' Kido Body Force Land Kido Butai AF Butai

AIRCRAFT DIV: CVD1 CVD4 (AKAGI, KAGA, HIRYU, SORYU) (RYUJO, JUNYO) A6M2 93 6 72 171 391 66,861 A6M2 30 30 391 11,730 A5M4 6 6 110 660 D3A1 72 82 154 871 134,134 B5N2 81 12 93 1,005 93,465 B5N2 36 36 1,005 36,180 D4Y1 2 2 987 1,974 B4Y1 8 8 1,005 8,040 H6K (Flyboats) 33 2,013 66,429

Total 467 371,563 66 47,910

TABLE X-20. Total IJN Aircraft firepower.

144 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

TOTAL USN AIRCRAFT FIREPOWER MIDWAY FORCE YORK ENT HORN ATOLL No. MJ/' Tot MJ/' CV-5 CV-6 CV-8 F4F WILDCAT 25 27 27 6 85 248 21,080 SBD-3 DAUNTLESS 37 38 37 18 130 1,371 178,230 TBD-1 DEVASTATOR 13 14 15 42 240 10,080 SBU2 VINDICATOR 14 14 1,155 16,170 TBF AVENGER 6 6 261 1,566 B-17E Flying Fortress 15 15 9,198 137,970 B-26G Marauder 4 4 4,676 18,704 F2A BUFFALO 20 20 56 1,120 PBY-5A CATALINA 29 29 2,246 65,134 Total 450,054

TABLE X-21. Total USN Aircraft firepower. The unreliable Mark 13 Torpedo has reduced the DEVASTATOR and AVENGER firepower by 70%. This reduces total aircraft firepower from 491,000 to 465,000, by 5%. Even worse, it reduces by 11% the combined firepower of the attack arm, the carrier dive bombers and torpedo bombers, of a fully constituted, well-coordinated strike.

145 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

IJN USN MIDWAY ALEUTIANS MIDWAY No. MJ/' No. MJ/' No. MJ/' A6M2 171 66,861 A6M2 30 11,730 F4F 85 21,080 A5M4 6 660 SBD-3 130 178,230 D3A1 154 134,134 TBD-1 42 10,080 B5N2 93 93,465 B5N2 36 36,180 SBU2 14 16,170 D4Y1 2 1,974 TBF 6 1,566 B4Y1 8 8,040 B-17E 15 137,970 H6K Fly Boats 33 66,429 B-26G 4 18,704 F2A 20 1,120 PBY-5A Fly Boats 29 65,134 Total 467 371,563 66 47,910 Total 345 450,054

TABLE X-22. Comparison IJN USN Total Aircraft Firepower in numbers N and Mega Joules per minute MJ/’. *IJN H6K Flying Boats: N=24 in Stille, M. (2010): 30-31 but N=42 in https://en.wikipedia.org/wiki/Midway_order_of_battle. The Figure above, N=33, is average of these two. ImperSomeial Jap asourcesnese N astatevy - thePac iH8Kfic Op waserat itheon flying boat at Midway. The firepower of the H6K andM H8KegaJ/ 'are similarNo withMe gtorpedoes,aJ/' (gun) M 2,013egaJ/ 'MJ/’ (ship and) 2,025Mega JMJ/’./' (for ce) MIDWTheAY -difference 1st Kido B uist a396i - C AMJ/’,RDIV less1 A Athan gun 1%s difference. The H8K’s advantages AKAGwereI more bomb carrying weight, faster speed and longer range. The USN 20cm7had.9" more firepower104 with fewer6 planes, 6since24 Midway Atoll added 12cm4substantial.7"AA potential162 firepower12 in the B-17s1,944 and PBYs. 25mm 1" 28.9 28 809 3,377 KAGA 20cm7.9" 104 10 1,040 127mm5"DP 165 16 2,640 25mmT96 .98"AA 28.9 22 636 4,316 HIRYU 12.7cm5"T89DP 165 12 1,980 25mmT96AA 28.9 31 896 2,876 SORYU 12.7cm5"T89DP 165 12 1,980 25mmT96AA 28.9 28 809 2,789 13,358

ALEUTIANS -2nd Kido Butai - CARDIV 4 AA guns RYUJO 12.7cm5"DP 165 12 1,980 13.2mm0.5"AAMG 12.4 24 298 2,278 JUNYO 12.7cm5"DP 165 12 1,980 25mm1"AA 28.9 24 694 2,674 4,951 146

TABLE X-23. AAW gun firepower of IJN carriers. MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

UNITED STATES NAVY CARRIERS MegaJ/' No MegaJ/' (gun) MIDWAY YORKTOWN class 5"/38 cal 286 8 2,288 1.1"/75 cal 174 16 2,784 20mm Oerlikon 17 30 510 5,582 YORKTOWN ENTERPRISE HORNET 3 Total 16,746

TABLE X-24. AAW gun firepower USN carriers.

147 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

148 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

IMPERIAL JAPANESE NAVY

MIDWAY ALEUTIANS TOTAL BOTH

MegaJ/' MegaJ/' MJ/' MJ/' w/o mines w mines w/o mines w mines BB CC DD DIVISIONS 1,889,910 1,889,910 403,215 2,293,125 2,293,125

UBMARINES w/o min 111,938 73,902 185,840 w mines 179,726 253,628

AIRCRAFT 371,563 371,563 47,910 419,473 419,473

ARRIERS (guns) 13,358 13,358 4,951 18,309 18,309

TOTAL FIREPOWER 2,386,769 2,454,557 529,978 2,916,747 2,984,535 2.9 TeraJ/'

TABLE X-25. Total IJN Firepower.

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TOTAL UNITED STATES NAVY FIREPOWER

MIDWAY ALEUTIANS TOTAL BOTH MegaJ/' MegaJ/' MJ/'

CC DD DIVISIONS 243,514 185,141 428,655

SUBMARINES 100,319 12,395 112,714

AIRCRAFT 450,054 450,054

CARRIERS (guns) 16,746 16,746

TOTAL FIREPOWER 810,633 197,536 1,008,169

TABLE X-26. Total USN Firepower.

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TOTAL FIREPOWER OF IJN AND USN PACIFIC OPERATION IJN USN MIDWAY ALEUTIANS BOTH MIDWAY ALEUTIANS BOTH Ratio MI Ratio All MJ/' MJ/' MJ/' MJ/' MJ/' MJ/' IJN USN IJN USN

BB CA CL DD 1,889,910 403,215 2,293,125 243,514 185,141 428,655 7.8 5.3

SS 111,938 73,902 185,840 100,319 12,395 112,714 1.1 1.6

A/C 371,563 47,910 419,473 450,054 450,054 1.2 1.1

CV guns 13,358 4,951 18,309 16,746 16,746 1.3 1.1

2,386,769 529,978 2,916,747 810,633 197,536 1,008,169

Carriers 4 2 6 3 3 1.3 2.0

TABLE X-27. Comparison Total IJN and USN Firepower in Pacific Operation.

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IMPERIAL JAPANESE NAVY MIDWAY FORCE 1st MJ/' Tot MJ/' MB Gua Inv Sup Xpt Tdr Σ MJ/' Tot MJ/' Kid Bod For For But

BB CC DD DIVISIONS BD3 BD1 BD2 BD3 SHIP CLASS KONGO BB 2 8,118 16,236 2 2 8,118 16,236 YAMATO BB 2 2 10,247 20,494 NAGATO BB 1 1 12,391 12,391 ISE BB 2 2 11,290 22,580 FUSO BB 2 2 8,071 16,142 TONE CA 2 31,463 62,926 NAGARA CL 1 32,347 32,347 1 1 32,347 32,347 SENDAI CL 1 1 2 12,124 24,248 KUMA CL 2 2 11,293 22,586 TAKAO CA 2 2 42,704 85,408 MYOKO CA 2 2 31,002 62,004 MOGAMI CA 4 4 8 31,749 253,992 KAGERO DD 9 24,180 217,620 8 1 9 24,180 217,620 YUGUMO DD 3 24,180 72,540 FUBUKI DD 8 4 12 21,382 256,584 SHIRATSUYU DD 6 4 10 23,924 239,240 HATSUHARU DD 2 2 15,954 31,908 ASASHIO DD 3 2 2 7 24,923 174,461 MINEKAZE DD 401,669 1,488,241

TABLE X-28. Total IJN Ship Firepower IJN of 1st Kido Butai versus of Main Body, Guard Force, Invasion Force, Support Group, Transport Group and Tenders.

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TOTAL FIREPOWER OF IJN AND USN AT MIDWAY BATTLE IJN USN 1st Kido Butai Other Total MIDWAY Total Ratio MI MJ/' MJ/' MJ/' MJ/' MJ/' IJN USN

BB CA CL DD 401,669 1,488,241 1,889,910 243,514 243,514 1.6

SS* 111,938 73,902 185,840 66,138 66,138 1.7

A/C 182,454 189,109 371,563 450,054 450,054 2.5

CV guns 13,358 13,358 16,746 16,746 1.3

709,419 1,751,252 2,460,671 776,452 776,452 1.1

Carriers 4 4 3 3 1.3

TABLE X-29. Comparison of IJN and USN Firepower at Midway Battle. * Sources differ on the number of IJN submarines: Stille, Midway 1942 gives 12, pp. 30-31. Morison, Coral Sea, Midway and Submarine Actions gives 13, pp. 87-88.

153 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

FIREPOWER AT MIDWAY AND TRAFALGAR (MEGA JOULES / MIN

MIDWAY

MJ/' MJ/' IJN Total 2,916,747 USN Total 1,008,169

TRAFALGAR

FR-SPAN 909 BRITISH 2,254

lb kg mps MEGA J RPM lb kg mps MEGA J RPM Cannon 66,164 30,075 396 4,716 0.19 896 49,578 22,535 396 3,534 0.60 2,120 Obusiers 3,924 1,784 197 69 0.19 13 12,630 5,741 197 223 0.60 134

Sutherling, W. (2019)Two Influences of Trafalgar:24. Adkin, M. (2005)The Trafalgar Companion:225-268

TABLE X-30. Comparison of Total Firepower at Midway and Trafalgar. Calculations for Trafalgar include mechanical kinetic energy and power; whereas, Midway includes chemical explosive as well as mechanical kinetic energy and power.

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TABLE X-31. Carriers in the Pacific theater in June 1942.

The IJN had ZUIKAKU 39 operating aircraft (24 fighters, 9 dive bombers and 6 torpedo bombers) plus 17 repairable aircraft = 56, KAGA, AKAGI, SORYU, HIRYU, RYUJO and

JUNYO. Light carriers HOSHO (15 capacity) had 8 B4Y1 carrier attack aircraft at Midway and

ZUIHO had 24. (SHOKAKU was severely damaged at Coral Sea and out of the fight.) (SHOHO was sunk at CORAL SEA) (CHITOSE 30 AND CHIYODA 30 were seaplane tenders, only became light carriers after Midway) ( RYUHO seaplane tender became light carrier after

Midway)The two-to-one advantage in carriers persisted even after the Coral Sea. The USN had

HORNET, ENTERPRISE, YORKTOWN, (LEXINGTON sunk at Coral Sea), (WASP in

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Atlantic xfer to Pacific after Midway then sunk at Guadalcanal by I-19 Sept 1942))

(SARATOGA damaged at Wake Island by torpedoes before Midway, returned after Midway to

Guadalcanal), (RANGER in Atlantic too slow to keep up with Pacific CVs).

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TABLE X-32. Military Effectiveness. On approach to Midway, IJN dominated in carriers, ships and aircraft with near parity in submarines versus USN.

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TABLE X-33. Nagumo’s Dilemma: 1st Kido Butai Aircraft. 3 June Original Complement of aircraft steaming to Midway (top left) 0430 4 June Tomonaga’s attack group against Midway Atoll (bottom left) Reserve aircraft in hangars for defense. (top right) 0745 4 June Time after decision to launch Type 97 carrier attack torpedo bombers with Type 99 dive bombers. (bottom right). Attack at 0753 changed this. Original Complement from Stille, Midway 1942. Launch against Midway and Reserve in Hangars from Parshall & Tully, Shattered Sword. Different sources may explain slight differences in numbers, in table and text.

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TABLE X-34. Military Effectiveness of IJN aircraft united and then divided. When united they have advantage in military effectiveness. After delay launching aircraft, the IJN is divided with the reserve Type 97’s in the hangars and Type 99’s waiting for Type 97’s. The IJN is even weaker, since Tomonaga’s planes are low on fuel and weapons.

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British Combined British Combined Rate of fire 3 1 3 1 Aiming 2 1 2 1 β α 6 1 6 1 B A 27 33 27 66 [B]2 [A]2 729 1,089 729 4,378 β[B]2 α[A]2 4,374 1,089 4,374 4,378

TABLE X-35. Trafalgar re-analysis. Military Effectiveness of British and Combined Fleet with adjustment for slow match fuse delay in aiming reducing accuracy to 50% but Villeneuve having twice as many ships. It is a draw before Nelson cuts the line.

British Combined British Combined British Comb N Comb S Rate of fire 3 1 3 1 3 1 1 Aiming 2 1 2 1 2 1 1 β α 6 1 6 1 6 1 1 B A 27 33 27 66 27 47 47 [B]2 [A]2 729 1,089 729 4,378 729 2,209 2,209 β[B]2 α[A]2 4,374 1,089 4,374 4,378 4,374 2,209 2,209

N 27 33 27 66 27 94 β[B]2 α[A]2 4,374 1,089 4,374 4,378 4,374 4,418

TABLE X-36. Trafalgar re-analysis. Far right: After Nelson cuts Villeneuve’s line into a Comb North half and a Comb South half, the military effectiveness of 33+33 ships divided is less than Nelson’s 27 ships together. Villeneuve then would have needed 94 ships for a divided 47+47 ship force to have the same military effectiveness or firepower as Nelson’s 27 ships massed together. But when Villeneuve left Toulon, that number of ships was not available to him. Given these circumstances, it is difficult to imagine a situation under which Villeneuve could even achieve a draw versus the British fleet.

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APPENDIX B. SOLVING THE LANCHESTER EQUATIONS.248

The Lanchester equations for concentrated aimed fire are:

To solve these equations and get the results for firepower βB2 and αF2, it’s necessary to understand the derivative, represented by and , and then the ‘integral’, which just reverses the operation of the derivative. Those acquainted with this know it as calculus.

APPENDIX B consists of two parts. First, a brief review of the concepts of derivative and integral, copied from the clearest pedagogical sources that the author could find.249 250 251

Second, a clear derivation of the solution to the Lanchester equations, from a book review of

Lanchester’s work.252

If you are familiar with derivative and integral, go to “Lanchester Equation Solutions.”

Usually a general introduction to the derivative and integral takes a semester in

University. However, there are examples of focused applications, for instance, early in courses in

Physics, where a well-written and illustrated chapter reviews the essentials, even as students are beginning their calculus course.253

248 Reproduced from Sutherling, Two Influences of Trafalgar on Navy Tactics 1905-1944: 56-65. Available on-line: www.maritime-museum.org (volunteer syllabus) 249 en.wikipedia.org, www.google.com, 250 Feynman, Leighton, Sands, The Feynman Lectures on Physics I 8.5-8.10 251 Thomas, Calculus and Analytic Geometry 26-39 155-164. 252 www.amazon.com/books Lanchester, Aircraft in Warfare. Comment Viktor Blasjo FN below. 253 Feynman, Leighton, Sands, The Feynman Lectures on Physics I 8.5-8.10. 161 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

The text here is not original but was extracted from the internet and standard textbooks.

Once understood, the concept will get us to the results for firepower.

Derivative.

This is a brief application of just enough of the derivative and integral, borrowing generously from Wikipedia and standard sources, to get a solution of Lanchester’s equations. There are many clear introductions, includingGraph Thomas 2. andSlope the of first a linear chapters function: of Feynman (see References).

The derivative of a straight line is its slope.

Graph 1 shows a straight tangent line (red) which touches the curved line (black) at one point. The tangent line is the slope of the curved line at that point and is also the derivative of the curved line or function at that point.

Graph 1. The graph of a function, drawn in black, and a tangent line to that function, drawn in red. The slope of the tangent line is equal to the derivative of the function at the marked point. Wikipedia entry on derivative shown here and graphs below.

Graph 2 shows the details of the slope of a line, or linear function. The slope is the

change in y divided by the change in x, at the point x. This would be Δy = y2 - y1 divided by Δx

= x2 - x1 . The slope is m = Δy / Δx . The slope of the line is its derivative. But you can see that if we only take the derivative, we are losing some information about the line, the constant b. This constant shows where the line intersects the y-axis below or above the origin.

In the measurement of the slope of the line

there is a visible distance between x1 and x2

. So, Δx = x2 - x1 is more than just one Graph 3. The line intersects a parabola y=f(x)=x2 at (x) and (x+h). 162 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws point, it is a line segment on the x axis. In the figure it is the base of a right triangle. We can only use this type of approach on a straight line, where the slope is the same at all points along the line. Using a right triangle won’t work on a curved line, where the slope changes from one part of the curve to the next.

Graph 3 shows a line intersecting a parabola at the points x and x+h. We can estimate the slope or derivative as ( f(x+h) – f(x) ) / ( (x+h) – (x) ), but this is obviously not the derivative for any one point on the curved line of the parabola. Finding the slope of the line at any one point on a parabola is where we really need a general form for the derivative.

Graph 4. The intersecting line gets Graph 5. Tangent line intersects the closer to the tangent line at (x) as: curve at one point when Δx=0. (x+h) becomes a smaller or Derivative is the slope of the line, a new function f ′(x). (x+h) approaches (x) or (h) approaches (0) or (Δx0). When Δx=0, the tangent line When the intersecting lines in Graph 4 cut across less and less of the parabola, they eventually touch the curve at just one point. This is shown in Graph 5. Then the line becomes a tangent line. It intersects the function at x (Δx=0) and is the slope of the curve, which is its derivative f ′(x) at that point.

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Derivative as a Limit.

The derivative for y=x2 is the value of the slope of the tangent line at a specified point, at the point x on the parabola above in Graph 5. The numerical value changes or is variable depending on the value of x on the parabola. The derivative is the limit of the variable when the line goes from Graph 4 to Graph 5. The equation to find the value of the derivative is:

Just as the graphs above showed the lines getting closer and closer to a tangent line intersecting one point on the curve, where (x+h) became smaller and smaller until it approached

(x) and (h0), the algebraic quantity is made to do the same thing. The quantity is evaluated as (

. The Limit of is calculated as ( . The slope of the tangent line goes from the simple situation of intersecting multiple points to the precise situation of intersecting just one point on a parabola.

At that point, x2 = x1 , so, Δx = x2 - x1 = 0 , or . By a series of successive approximations, the

slope is calculated as Δx = x2 - x1 goes from multiple points to just one point where The equations below show the steps leading to the answer:

Now ( x2 ) = ( x1+Δx ) or ( x+ Δx ) and ( x1 ) = ( x ), so the above equation becomes:

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Multiplying it all out, one gets:

Canceling out the terms:

Dividing by :

As , the goes to zero, and the Limit becomes 2x. This is the final answer for the derivative of y = x2. This is the instantaneous or point derivative, the slope of a tangent line intersecting only one point of the function y= x2 .

Note that the derivative can be obtained from most any variable x. It can be distance (dx) or time

(dt). In the Lanchester equations the variable x is time (dt) and the variable y is what is changing with time (dB), number of ships, guns or pounds-of-metal.

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Integral.

The Integral is obtained by reversing the operation for the derivative. Lanchester solves his equation in a certain way by infinitesimals. The more common way today is by integration.

In reversing the operation, remember that obtaining the derivative took away a constant b. When calculating the integral, one must put back a placeholder for that constant, C. The symbol for the integral254 is a long, sinuous S, . The Integral sums up the values of a function over a range of x’s. The integral acting on a function f(x) looks like this:

The little dx at the end indicates that the Integral is summing up f(x) over many small changes in x (or dx’s), a range of x’s. If one then lets the derivative be the function inside the Integral, it shows a clear picture of what’s really going on.

The same derivative analyzed above can be put inside the new Integral symbol just introduced here. When that is done, it looks like this:

Then the (dx) on the right end of the Integral and the (dx) in the denominator of the derivative will be able to cancel out to give a simple expression:

The Integral and derivative symbols are now side by side on the right. They operate in opposite ways. They cancel each other out to give the original function f(x) = y , but one must also add back the placeholder constant:

254 The process to calculate the derivative is called differentiation, to calculate the integral is integration. 166 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

In summary, the Integral of the derivative 2x gives the original function y = x2, with a placeholder C as needed.

That is outline of the Derivative and Integral as far as it is applied in the Lanchester equations.

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Solutions to Lanchester’s Equations.

The derivative and integral can solve the Lanchester equations for British and French:

Victor Blasjo has clarified steps in a solution, in a review of Lanchester on the internet.255

These steps are repeated here. If you understand the footnote, no need to read further…

Otherwise:

Dividing the first by the second equation, the dt and minus sign drop out:

Rearranging:

Using the Integral to sum up and get rid of the dB and dF terms (β and α are constants):

By integrating:256

255 Viktor Blasjo. www.amazon.com/books comment: Lanchester, Aircraft in Warfare. 1 Jan 2007: “Personally, I was interested only in a particular part of this book, namely Lanchester's battle model. It goes like this. There is a battle between two armies, one with A soldiers and one with B soldiers. Each army has a constant efficiency coefficient (determined by weaponry, training, etc.): a [one] side A soldier takes out a [α] enemies per unit time while a side B soldier takes out b [β] enemies per unit time. The battle is then described by the differential equations dA/dt = - bB and dB/dt = - aA. Dividing the first by the second gives aAda = bBdb, which we integrate to get aA2 - bB2 = constant. (Lanchester avoids mentioning integration and uses a direct infinitesimal argument.) The sign of this constant determines the outcome of the battle, since if, for example, there are side A troops still standing when B reaches zero then the constant must be positive (indeed we see that the number of side A troops surviving the battle can be calculated by setting B=0 and solving for A). Also, the fact that the strength of an army is proportional to the square of its size has an important strategical implication: never divide your forces. For example, assuming equal efficiency a=b=1, an army of 5000 could handle an army of 7000 split into two, 50002=40002+30002, but if the 5000 army faced the full 7000 army at once it would be destroyed after having killed only about 2100 enemies, 70002 - 50002 = 49002 .”

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Subtracting from both sides:

These are the solutions to the Lanchester differential equations. The terms βB2 and αF2 are the military effectiveness or firepower of the B-guns and F-guns, respectively. If βB2 is larger than αF2, then the military effectiveness of the B Navy is larger than the F Navy and the constant

C is positive, and B should win the battle. The term βB2 shows that military effectiveness is proportional to β in a linear fashion, but proportional to the square of B. This is the Lanchester

N-Square Law. In other words, the difference in force sizes will usually dominate the outcome.

We suspected this from the Excel worksheets in specific cases,257 but here it is proven in general.

This has been recognized for a long time. “Do not divide one’s force in battle.” “Divide and conquer.” “Defeat in detail.”

256 When one does the integral, the results are actually (1/2)βB2 and (1/2)αF2. But one can get rid of the factor (1/2) by adjusting the constant without changing the fundamental solutions or relationships. 257 Sutherling, Two Influences of Trafalgar on Navy Tactics 1905-1944: 26, 28, 29, 31, 55. 169 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

APPENDIX C. SOLUTIONS OF SALVO EQUATIONS FOR DIFFERENT SCENARIOS

The following are the details of the solutions to the Salvo Relations for different scenarios. They show the generic equation, up to equation for the Battle of Midway and possible scenarios for more IJN carriers. These same solutions are shown in the main text in the Graphs.

The Generic Salvo Equations.

The salvo equations show how many carriers (ΔA) are sunk by each aircraft salvo:258 259

258 Hughes and Girrier, Fleet Tactics and Naval Operations 264. 259 Hughes, “A Salvo Model of Warships” in Warfare Modeling 125. 170 MIDWAY REPEATS TRAFALGAR’S LESSONS CIMM/ws

A = total number of IJN carriers B = total number of USN carriers = hits (salvos) by each A = hits (salvos) by each B = hits (salvos) which each A deflects = hits (salvos) each B deflects = number of hits to sink each A = number of hits to sink each B αA – b3B = striking power of each A βB – a3A = striking power each

(a3=defensive power, a1=staying power, αA-b3B how many B put out of action).

Scenario 1. Example of Massing of Force.

Consider two forces. The fraction of each force that can be sunk by a salvo is:

Number of units A = 2 B = 6 Staying power a1 = 2 b1 =1 Defensive power a3 = 16 b3 = 1 Striking power α = 24 β = 6

A can destroy B seven times over, but A will also be destroyed by B.

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Scenario 2. Battle of the Philippine Sea (Hughes). 260

Number of units AJapan = 9 BU.S. = 15 Staying power a1 = 1 b1 =1 Defensive power a3 = 1/7 b3 = ½ Striking power α = 1 β = 1

260 Hughes and Girrier, Fleet Tactics and Naval Operations 264. 172 Sutherling/MIDWAY REPEATS TRAFALGAR’S LESSONS

Due to larger mass and better defense, B destroys A, but A cannot destroy B.

Scenario 3. General Salvo Equations for Midway

The following salvo equations would thus apply for Midway:

Number of units AIJN = BUSN = Staying power a1 = 1 b1 =2 Defensive power a3 = ¼ b3 = ¼

Scouting σA = 0.75 σB = 1.0 Striking power α = 0.75 = (0.75*1) β = 1 = (1.0*1)

For staying power, USN had better damage control and carrier design. For defensive

power, IJN and USN were about equal. IJN defense was better at Midway than in the

Philippine Sea. It had more experienced pilots than later in the war for its air defense.

Thus, a3 at Midway is increased from 1/7 to ¼ . USN was worse at Midway than later,

with an inferior fighter, b3 decreased from ½ to ¼ . Scouting was better USN than IJN.

During battle, the YORKTOWN was bombed and repaired in 2 hours. In these salvo

equations, a cut-off of 0.85 carrier is assumed as the lower limit for launching strikes.

173 Sutherling/MIDWAY REPEATS TRAFALGAR’S LESSONS

SCENARIO 4. Salvo Equation solutions for actual carrier numbers at Midway

Following is the application of the given variables for the Midway Battle:

Number of units AJapan = 4 BU.S. = 3 Staying power a1 = 1 b1 =2 Defensive power a3 = ¼ b3 = ¼ Striking power α = 0.75 β = 1

The USN first strike reduces the IJN by the following proportion:

The IJN is reduced from 4 carriers to 2. The USN has 3 carriers.

The IJN counterattack reduces the USN by:

The USN loses 0.38 carrier, reduced to 2.63 carriers, 2 operational.261 IJN has 2 carriers.

The second USN attack gives:

The IJN loses 1.5 carriers, reduced to 0.5 carriers, none operational. The USN has 2.63 carriers, 2 operational. IJN can no longer attack.

The third USN attack annihilates the IJN:

The IJN 0.5 carrier hulk is destroyed three times over, shown in Graph 5 below.

The USN wins, with retention of 2.63 carriers. The damaged 0.63 carrier can be repaired and returned to service for the war. The results from the salvo equations give a different outcome than the historical battle. The results of the equations show the plight of the badly listing YORKTOWN after Tomonaga’s torpedo bomber attack. The YORKTOWN was actually sunk by the submarine I-168. Since the submarine variable is not considered in the salvo equations, the results of the salvo equations, as far as they go, appear accurate.

261 0.63 carrier is below the assumed cut-off of 0.85 for a carrier to launch strikes. 174 Sutherling/MIDWAY REPEATS TRAFALGAR’S LESSONS

Time IJN Carriers USN Carriers

Before 4.00 3.00 USN Attack 2.00 3.00 IJN Counterattack 2.00 2.63 USN 2nd Attack 0.50 2.63 USN 3rd Attack 0.00 2.63

GRAPH 5. The actual Midway Battle by the Salvo Equations.

175 Sutherling/MIDWAY REPEATS TRAFALGAR’S LESSONS

SCENARIO 5. Midway Salvo Equation solutions with RYUJO and JUNYO.

In this scenario, RYUJO and JUNYO accompany the 1st Kido Butai to the Midway battle.

RYUJO and JUNYO together equal one fleet carrier’s air wing. With poor IJN scouting, the

USN still struck first, starting the sequence of calculations.262 The starting assumptions are:

Number of units AJapan = 5 BU.S. = 3 Staying power a1 = 1 b1 =2 Defensive power a3 = ¼ b3 = ¼ Striking power α = 0.75 β = 1

The first USN attack on the IJN would result in the following fraction of IJN loss:

262 Also, the IJN force did not locate two of the USN carriers. 176 Sutherling/MIDWAY REPEATS TRAFALGAR’S LESSONS

The IJN loses 1.75 carriers, with 3.25 IJN carriers left. The USN has 3 operational carriers. With the assumption that ¼ of a carrier could not launch offensive aircraft, the IJN operational force would be 3 carriers at this point.

The IJN counterattack would reduce the USN by the factor:

The IJN sinks 0.75 USN carrier, resulting in 2.25 USN carriers left, 2 operational, with 3.25 IJN carriers, 3 operational. It’s unlikely 0.25 carrier could launch aircraft. In order to launch, a carrier needs to be in good shape. Destroying three-fourths of it would affect flight operations with disruption of the flight deck and elevators. This leaves the USN with two operational carriers.

The second USN attack would reduce the IJN by a factor of:

The repeat USN attack would destroy 1.19 IJN carriers. After the USN repeat attack, there would be 2.06 IJN carriers, 2 operational, and 2.25 USN carriers, 2 operational.

The second IJN counterattack:

The IJN destroys 0.47 USN carriers, with results that USN would have 1.78 carriers,263 1 operational, and the IJN 2.05 carriers, 2 operational.

177 Sutherling/MIDWAY REPEATS TRAFALGAR’S LESSONS

The third USN attack would reduce the IJN by a factor of:

2630.78 carrier is below the 0.85 limit, which is taken as the cut-off to launch aircraft strikes. 178 Sutherling/MIDWAY REPEATS TRAFALGAR’S LESSONS

The USN sinks 0.48 IJN carriers, reducing the IJN to 1.58 carriers, one operational, with the USN 1.78 carriers, 1 operational.

The third IJN counterattack would reduce the USN by a factor of:

The USN loses 0.15 carrier down to 1.63 carriers, one operational. The IJN has

1.58 carriers, one operational.

The fourth USN attack would reduce the IJN by a factor of:

The USN sinks .61 IJN carrier. The IJN has .97 carriers remaining, operational

(≥0.85). The USN retains 1.63 carriers, one operational.

The fourth IJN counterattack would reduce the USN by a factor of:

The USN loses 0.16 carrier down to 1.47 carriers, one operational. The IJN has

0.97 carrier, operational.

The fifth USN attack would reduce the IJN by a factor of:

The USN sinks 0.76 IJN carrier. Only .21 IJN carrier remains, non-operational.

The IJN cannot counterattack. The USN retains 1.47 carriers.

179 Sutherling/MIDWAY REPEATS TRAFALGAR’S LESSONS

The sixth USN attack would reduce the IJN by a factor of:

The USN sinks the IJN hulk four times over. The IJN fleet is annihilated. The

USN retains 1.47 carriers. With the addition of RYUJO and JUNYO, the IJN still loses the battle. But with the extra IJN carrier aircraft, it takes longer, there are multiple crossing points and the USN has fewer carriers at the end of the Battle. This is shown in Graph 6 below:

Time IJN Carriers USN Carriers

Before 5.00 3.00 USN Attack 3.25 3.00 IJN Counterattack 3.25 2.25 USN 2nd Attack 2.06 2.25 IJN 2nd Counterattack 2.06 1.78 USN 3rd Attack 1.58 1.78 IJN 3rd Counterattack 1.58 1.63 USN 4th Attack 0.97 1.63 IJN 4th Counterattack 0.97 1.47 USN 5th Attack 0.22 1.47 USN 6th Attach 0.00 1.47 SCENARIO 6. Midway Salvo Equation solutions RYUJO JUNYO & ZUIKAKU.

180

GRAPH 6. With RYUJO and JUNYO. Sutherling/MIDWAY REPEATS TRAFALGAR’S LESSONS

In this scenario, RYUJO, JUNYO and ZUIKAKU, accompany the 1st Kido Butai to the

Midway battle. ZUIKAKU is a fleet carrier. RYUJO and JUNYO together equal one fleet carrier’s air wing. Poor IJN scouting still allows USN to strike first. Starting assumptions:

Number of units AJapan = 6 BU.S. = 3 Staying power a1 = 1 b1 =2 Defensive power a3 = ¼ b3 = ¼ Striking power α = 0.75 β = 1

The first USN attack on the IJN would result in the following fraction of IJN loss:

USN sinks 1.5 IJN carriers, with 4.5 IJN carriers, 4 operational, and USN 3 carriers.

The IJN counterattack would reduce the USN by the factor:

The IJN sinks 1.12 USN carriers, resulting in 1.88 USN carriers operational

(1+.88, since ≥0.85 carrier can function), with the IJN retaining 4.5 IJN carriers, 4 operational.

Then the second USN attack would reduce the IJN by a factor of:

The repeat USN attack destroys 0.75 IJN carriers, reducing the IJN to 3.75 carriers, 3 operational, with the USN retaining 1.88 carriers operational.

The second IJN counterattack:

The IJN sinks 0.90 USN carrier, reducing the USN to .98 carrier operational

(≥.85), with the IJN retaining 3.75 carriers, 3 operational.

The third USN attack: 181 Sutherling/MIDWAY REPEATS TRAFALGAR’S LESSONS

The third USN attack destroys 0.03 IJN carriers, reducing the IJN to 3.72 carriers, 3 operational, with the USN retaining .98 carrier operational.

The third IJN counterattack would reduce the USN by a factor:

The IJN sinks the remaining .98 USN carrier. The USN force is annihilated, with the IJN retaining 3.72 carriers, 3 operational. This is shown in Graph 7.

Time IJN Carriers USN Carriers

Before 6.00 3.00 USN Attack 4.50 3.00 182 Sutherling/MIDWAY REPEATS TRAFALGAR’S LESSONS

IJN Counterattack 4.50 1.88 USN 2nd Attack 3.75 1.88 IJN 2nd 3.75 0.98 CounterattackUSN 3rd Attack 3.72 0.98 IJN 3rd 3.72 0.00 Counterattack

GRAPH 7. With RYUJO, JUNYO & ZUIKAKU.

With the equivalent of six fleet carriers, the IJN could have won at Midway. The salvo equations support this with multiple combinations of a3, b3, a1, b1, α and β. Most simulations

183 Sutherling/MIDWAY REPEATS TRAFALGAR’S LESSONS show that the addition of RYUJO, JUNYO and ZUIKAKU result in IJN victory at Midway. This is not surprising. There would have been more aircraft for scouting. There would have been more aircraft available for launch during Nagumo’s dilemma. There would have been more CAP fighters to defend simultaneously against torpedo bombers and McClusky’s and Leslie’s dive bombers.

The results for these three scenarios use the variable values likely from historical records and studies. It’s possible that other values might result in different outcomes.

184 Sutherling/MIDWAY REPEATS TRAFALGAR’S LESSONS

APPENDIX D. Recount of Yahachi Tanabe, LCDR, IJN, on sinking YORKTOWN.

I Sank the Yorktown at Midway By Yahachi Tanabe, formerly Lieutenant Commander, Imperial Japanese Navy, With Joseph D. Harrington May 1963

US Naval Institute Proceedings (Courtesy of LCdr T. Shideler, USN)

Vol. 89/5/723 ARTICLE

“The tension in I-168's conning tower had been steadily building up for six and a half hours. In the cramped command post, I stood, palms out, waiting to grip the rising periscope's handles. We were all perspiring heavily. My torpedo petty officer was scanning his switch panel, and a nervous helmsman wiped clammy hands frequently on his pants. Lieutenant (jg) Nakagawa, pencil in hand, mopped his damp brow between looks at the compass and speed indicator. But my gunnery officer, Ensign Watanabe, seemed almost unconcerned. Of the five, his job was by far the simplest. Our submarine was creeping straight toward the crippled American aircraft carrier Yorktown. There were no ballistics problems for Watanabe to work out- the range was point-blank, and target speed was nearly zero. The whine of the periscope's lift motor died away as I sighted through the eyepiece. I had been allowing myself a maximum of five seconds on each sight check and I didn't intend to change the tactic. One quick glance would give me the range, and I could give the order to fire torpedoes. The periscope stopped. I looked and then stepped back. "Down periscope! Right, twenty degrees rudder! Maintain full silence! Maintain speed of three knots!" My navigator and gunnery officer were astounded. "What has happened, Captain?" they asked, "Aren't we attacking?" They knew we were at that moment so close to Yorktown that we could not possibly miss. "We are going around again." I told them, knowing full well that four, and maybe as many as seven, American destroyers were prowling overhead. "The range is too short! I'm going to open the range and try again. I want to be sure of this kill!" An odd series of events had put I-168 where she was on 6 June 1942, deep inside the Yorktown’s protective circle of American destroyers whose crews were listening for a Japanese submarine. Although I would soon write a last line in that bloody chapter of Japanese history called the Midway Island Battle, the portion I had originally been scheduled to carry was small, indeed. Of the 160-odd ships that gathered from all parts of the Empire to strike at Midway, and the Aleutians, I-168 had the simplest assignment of all—scouting. 185 Sutherling/MIDWAY REPEATS TRAFALGAR’S LESSONS

I had missed the war's opening battle. While nearly 30 other submarine commanders were deployed around Oahu, I was plodding our Inland Sea in RO-59. My boat trained officers and crews for duty in larger submarines. We knew nothing; about the proposed attack on Pearl Harbor, although we did suspect something was afoot because of the heavy radio traffic and many ship movements throughout November 1941. All ships had been on wartime readiness for weeks. When in port we had a number of surprise drills, during which all hands ashore were ordered quickly back to their ships. On 8 December 1941, we had such a drill. But when all ships at Kure reported "manned and ready for sea," we were not given the usual order to secure. Instead, we were told that we were at war with America. Our First Air Fleet had made a very successful attack on the U. S. Fleet at Pearl Harbor, I learned, and we then realized where so many of our first-line units had gone. Some officers were disappointed at not being in on this battle, but I felt that it would be a long war. Therefore, a highly trained officer like myself, with six special service schools behind him, would eventually see his full share of sea action. Nor was I disappointed five months later when my part in the Midway operation was explained to me at Combined Fleet Headquarters. I had meanwhile relieved Lieutenant Commander Otoji Nakamura as commanding officer of I- 168, in January. Since then we had been exercising in the Inland Sea. I-168 was designed to make 23 knots on the surface, eight submerged. She carried ten torpedoes, with four forward tubes and two in the stern. I was satisfied with her. The Midway-Aleutian force was to be commanded by Admiral Isoroku Yamamoto, who would sail with it in the mighty Yamato, the world's biggest warship and our national pride. A total of 13 submarines were to form the Advance Expeditionary Force, most of them strung out along two lines east of Midway. They were to report any enemy warships coming out of Hawaii to counterattack, then intercept, and sink them. Four carriers, Akagi, Kaga, Hiryu, and Soryu, veterans of many successful engagements, were to launch two quick air strikes against Midway, after which 5,000 troops in heavily protected transports would move in and seize the island. This would advance Japan’s perimeter well to the east of the homeland. It might even entice the remains of the American fleet to fight. If so, defeating that fleet would give Japan control of the Pacific Ocean. I-168's task was to scout to the southward of Midway, and report on as much of the enemy's activities as we could observe. According to the basic plan, we were to see no action at all. We would be near when the troops landed, but by then, our job would have been done. We were the van ship of the entire operation, coming in sight of Kure Island, west of Midway, on 31 May 1942. Part of the over-all strategy called for seizing this island, too. It was to be a seaplane and midget submarine base. After radioing a report that nothing appeared to be happening on that island, I proceeded to Midway, and spent the first three days of June making observations there. We would spend daylight hours on periscope watch, on Midway's southern horizon. After dark each night, we moved in within five miles, and continued to watch through powerful binoculars. Our observations made us think that the Americans were expecting imminent attack. I radioed the information that 50 to 100 planes were making landings daily. This meant that American forces on Midway were getting ready to fly extensive patrols, or else were bringing in air protection from Hawaii. 186 Sutherling/MIDWAY REPEATS TRAFALGAR’S LESSONS

The four carriers of our striking force, although detected at the last, got near enough to launch planes against the island. I-168 had a front seat, or at least I did, at the day periscope, when 108 of our planes hit the island. Divided into equal numbers of fighters, dive bombers, and torpedo bombers, the last of which operated as level bombers and carried a 1,770-pound bomb each, this force did heavy damage. My crew grew more and more excited as I described the action to them, and a great cheer went up as I described some fuel tanks being blown sky high. This portion of the attack appeared to be successful, even though Midway's airplane had been warned. We saw them take off before ours arrived and watched them land after that first attack ended. At this point Japan was doing very well. More than 100 of our 108 planes made it safely back to their carriers, while our Zeros shot down or badly damaged two dozen American fighters. Readers are aware of what transpired after that. The Americans counterattacked, with Grumman torpedo bombers, Martin bombers, and Boeing Flying Fortresses, as well as Douglas and Vultee dive bombers. A total of 52 planes attacked our striking force. All were either shot down or driven off, none of them able to do more than get a few machine gun bullets into one Japanese ship. The American aircraft carriers had slipped into the battle area before our submarine scouting lines had gotten into position. Their planes came next. They sent in an additional 41 planes, 32 of which were shot down. At that point, practically no damage had been done to our side. The 4th of June seemed to be a great day for Japanese arms. Then the tide of battle turned. While our Zeros were at low level, defending against torpedo bombers, 54 American dive bombers plunged out of the sky against loaded flight decks. They made a shambles of Kaga, Akagi, and Soryu. No hits were made on Hiryu. She soon got away two strikes. They put three bombs and two torpedoes into USS Yorktown, but a return attack by the Americans hurt Hiryu so badly that her crew had no choice but to abandon and sink her. By midnight of 4 June, the Midway Battle was lost, though we did not know it yet. Admiral Yamamoto still had hopes of finding the American ships and sinking them in a surface engagement. It was only the cautiousness of the America's Admiral Spruance that prevented this. Having lost one carrier, Spruance decided it was better to fight again another day, and he turned his ships eastward after a short run westward. Comparison of ships’ logs after the war showed that, bad he continued westward, his two carriers, eight cruisers, and 15 destroyers would have run into a Japanese force that included seven battleships! While Yamamoto's main body was steaming eastward, hoping to catch the American striking force, I-168 was given orders to close in on Midway and open fire with her 4-inch deck gun. I was to continue this until joined by the cruisers Mikuma, Mogami, Suzuyu, and Kumano. These were the world's most powerful heavy cruisers then. Their 40 big guns might easily have smashed Midway’s defenses with a bombardment in the early hours of 5 June, paving the way for an easy landing of the 5,000 troops in the transport force. I obeyed orders, taking I-168 in. We surfaced about 0130 on 5 June but got off only six rounds before a pair of shore searchlights picked us out. We submerged immediately. Meanwhile, the four cruisers had their order changed, and were withdrawing. In the morning we

187 Sutherling/MIDWAY REPEATS TRAFALGAR’S LESSONS were sighted by plane and attacked by them, suffering no damage. We were pursued for a short while by an American ship. I-168 slipped back onto station as soon as I thought it was safe. We were supposed to watch the enemy and I intended to do so. The next time our radio antenna poked above the waves frightening news came through it. Soryu and Kaga had gone down the evening before. Akagi and Hiryu had followed them not long before the American planes attacked I-168. One of the messages gaveI-168 a new role to play. Scout planes from Japanese cruisers had sighted the American aircraft carrier Yorktown lying dead in the water about 150 miles northeast of Midway. My orders came through quite clearly: "Submarine I-168 will locate and destroy the American carrier." We set off at once, running submerged in daylight hours at the best speed we could make and still nurse our batteries. After dark I ran on the surface but could not use top speed for fear of missing our target in the blackness. So it was that, at 0530, on 6 June, the 12-mm. binoculars of my best-trained lookout picked up Yorktown. She was a black shape on the horizon, about 11 miles distant. It was the easiest intercept a submarine commander ever made. My course had not changed, from beginning to end. I ordered a dive, a course change to 045 degrees, and then reduced speed to six knots, leveling off I-168 at 90 feet. As we shortened the range, I reduced speed until we were never doing more than three knots. At intervals I moved I-168 up to 60 feet and took sightings. It required only a few course adjustments to set her heading straight for Yorktown's beam. Our screws were barely turning over, and I hoped they were not giving off enough turbulence for the American ships to detect us. I had sighted one destroyer ahead of the carrier with a towline out to her, and another destroyer nestled close to Yorktown's side. Three more kept station on the side I was approaching, which made me feel certain there must be at least two more on the opposite side. This meant seven of them against one of us. * It never occurred to me to do anything except continue my approach and attack, in spite of the odds. Our intelligence said the American Fleet had seven carriers. Two of them, Ranger and Wasp, were reported in the Atlantic, and we had word that Saratoga was on the U. S. West coast. One more, and perhaps two, had been sunk in the Coral Sea Battle a month before. That left the United States with no more than three carriers operating against us, and one of them was dead ahead. Sinking her would mean that the enemy would be left with no more than two to use against us for some time, a vital point now that we had just lost four of our first- line aircraft carriers. Each time I took a sight, the sun was higher in the sky. Yorktown appeared to be making just a little headway. I kept making minor changes of course to keep I-168 headed at her amidships section. We might get sunk in this action, but before that happened, I meant to do the maximum possible damage to this ship. I wanted my torpedoes to plow into her midsection, not her bow or stern.

188 Sutherling/MIDWAY REPEATS TRAFALGAR’S LESSONS

In those moments, a lot of faith was being placed by my crew in shrine charms previously given to each I-168 man by Lieutenant Gunichi Mochizuki, my chief electrical officer. Mochizuki, a deeply religious man, spent much time at shrines ashore, praying. My crew fervently hoped that his piety had given him some extra influence with the gods. When there was time to turn my thoughts in that direction, so did 1. All I-168 men limited their movements to the most necessary ones only, fearing to create some sound which the American detectors might pick up. By 1100, I had decided that the enemy equipment was not very sensitive. This gave me confidence as the range shortened; I kept moving in. Suddenly my sound operator reported that the Americans had stopped emitting detection signals I couldn't understand this but, since it was now nearly noon, I tried to make my voice light and told my crew, "It appears the Americans have interrupted their war for lunch. Now is our chance to strike them good and hard, while they are eating!" There were small jokes made about what to give them for dessert. Shortly thereafter I raised the periscope again. Abaft my beam, each about 1,000 yards distant, were a pair of American destroyers, one to port, one to starboard. I-168 had safely pierced the protective screen of escorts; I could now give the order to fire. Then I took another look. Yorktown and her hugging destroyer filled my periscope lens. I was too close! At that moment I estimated my range at 600 yards or less. It was necessary to come around and open up the range. What I had to do now was try to escape detection by those destroyers above us and get far enough away so that my torpedoes, fired from a 60-foot depth, would have enough running space to stabilize themselves at a 19-foot depth for hitting. Whatever was the reason, enemy sound detectors could no longer be picked up by our equipment, I knew the destroyer men above were not asleep. I kept I-168 in a right-hand circle, easing the rudder a little so that I could return to my original track at a point about one mile from Yorktown. I didn't dare put up the periscope until the compass showed us back on our original course. So, I concentrated instead on a torpedo tactic I wanted to use. Though some submarines in 1942 had Model 95 torpedoes—underwater versions of the very powerful Model 93 "Long Lance" used on surface ships—my torpedoes were an older type. Model 95's had 991-pound warheads, mine had 446pound ones. So, I planned to make two torpedoes into one.

189 Sutherling/MIDWAY REPEATS TRAFALGAR’S LESSONS

Listing badly from the effect of Japanese air strikes, Yorktown was virtually helpless as the I-168 moved in for the kill. Four torpedoes, the last two following the wake of the first pair, finished off the six-year-old carrier. U.S. NAVAL INSTITUTE PHOTO ARCHIVE If I followed the usual procedure and fired my four torpedoes with a two-degree spread, they would cover six degrees. But I wanted very badly to deprive the Americans of this carrier. I intended to limit my salvo to a two-degree spread I would fire No.1 and No.2 first, then send No.3 and No.4 in their wakes, on the same courses. That way, I could achieve two large hits instead of four small ones. I could thus deliver all my punch into the carrier's midsection, rather than spread it out along her hull. When I was back on my approach course, I took another look, and wagged my head at how the destroyers still seemed unaware of us. Either they were poor sailors, had poor equipment, or I-168 was a charmed vessel. At a range of 1,200 yards, my periscope up, I sent my four torpedoes away as planned. I did not lower the periscope then, either. The wakes of my torpedoes could be seen, so their source could be quickly established. And, if I-168 was going to die, I at least wanted the satisfaction of seeing whether our fish hit home. Less than a minute later we heard the explosions. "Banzai!" someone shouted. "Go ahead at full speed!" I ordered, then, "Take her down to 200 feet!" My conning tower officers were surprised when I ordered speed cut back to three knots a short time afterward, but by that time we were where I wanted to be, directly beneath the enemy carrier. I didn't think she would sink at

190 Sutherling/MIDWAY REPEATS TRAFALGAR’S LESSONS once, so had no fear of her coming down on us. And one of our torpedoes had run shallow and hit the destroyer alongside Yorktown. There would be men in the water. Her destroyers wouldn't risk dropping depth charges for a while, for fear of killing their comrades. Meanwhile, I hoped to creep out of there. I ordered left rudder and tried to ease away at three knots. My plan didn't work. The American destroyers were on us in no time, dropping depth charges. They had I-168 pinpointed, and took turns making runs, according to my sound operator. We had torpedoed Yorktown at 1330. By 1530, the enemy had dropped 60 depth charges at us, one or two at a time. They were much more sparing with these than they were later in the war, and I took advantage of this by trying to keep an opposite course to whichever destroyer attacked us. The tactic worked a number of times, many depth charges dropping well astern of us as the enemy passed directly overhead. One of the destroyer captains must have estimated that I was doing this, though. The last depth charge of the two-hour barrage landed just off my bow, putting out all lights, springing small leaks in many places, and causing the danger of chlorine gas forming in my forward battery room. This was serious. I-168 had only ten gas masks for a crew of 104 men. But Lieutenant Mochizuki took a small group of men into the forward battery room, closed it behind them to protect the rest of us, and began disconnecting damaged batteries. Before long they had the situation under control, but more trouble was occurring in the bow. Both the outer and inner doors of No. 1 Torpedo Tube were sprung. I-168 was partly open to the sea; water was entering the bow section. We couldn't work on the outer door, of course, so men tried to seal off the inner one, that last depth charge having distorted it. Instead of lying flat in its seal, it bulged into the torpedo room, while water jetted from leaks around its edge. Torpedomen finally plugged the leaks with wedges, however, and everything came under control. By now we had taken on enough water to weigh the bow down considerably. I ordered all crewmen possible to move aft a counterweight. This did not remedy the situation, so I employed a tactic used by other Japanese submarines in the war. Every man walked forward again, picked up a sack of rice from our supplies, and carried it aft. This helped considerably, and I-168 was on an even keel by the time full electrical power was restored. Now we had been operating nearly 12 hours submerged. The destroyers had continued to fire depth charges after 1530, but only sporadically. That sixtieth one had hurt us and made us bob up from 200 feet nearly to 60 feet. A few more like it, and we might have broached, a perfect target for the searchers. But it seemed as if they were hoarding charges for a final attack, knowing we would have to surface and charge batteries before long. There were five pistols and ten rifles in I-168's armory. I ordered these issued and told my deck gun crew to stand by near the tower. Sunset was not far off. If we could surface then, and run long enough to charge our batteries, I-168 might have a chance to reverse the situation, for we still had six torpedoes and five usable tubes left. We might even be able to dive and counterattack, using the darkness to our advantage.

191 Sutherling/MIDWAY REPEATS TRAFALGAR’S LESSONS

It was still daylight when I ordered "Surface!" There had been a long lull in the firing, and I thought the enemy destroyers might have given up when no sounds could be heard on our detectors. When I got to the open bridge, there was no sign of Yorktown on the eastern horizon. I was sure she was somewhere beyond it, sinking, for I had seen the torpedoes hit. Between myself and the horizon, I could sec three American destroyers, running in line abreast to the east, on an opposite course from my own. I guessed they were looking for other possible submarines, or else had been summoned back to help with survivors of the carrier. We were not long on the surface before two of the three ships swung about in pursuit. I estimated their distance at about 11,000 yards. We ran west at 14 knots, the best speed I could make while charging batteries and taking in air. I ordered smoke made, using the heavy black clouds for cover. It helped for a while, and the enemy ships did not appear to be gaining on us very much during the first 30 minutes. I couldn't understand this at all, because of the speed I knew they could make. When they closed to about 6,500 yards, they opened fire and not long afterward I- 168 was straddled. All a good gunnery officer had to do now was "walk" across me a few times and all would be over. I can remember the moment of the straddle most vividly. My lookouts began darting quick looks at me, their faces strained and pale. They were anxious to be back in the hull and diving I could also detect a high note in the voices below as reports on the progress of the battery charge were called up to me. The men above wanted to dive, though they dared not say so, and the men below wanted to remain surfaced as long as possible while dials and gauges made higher readings. Finally, tile enemy silhouettes growing ever larger, I called down, "Do you have enough air and power for short time operations?" A reluctant "Yes, sir," came up. "Stand by to dive!" I shouted and cleared the bridge. I followed all hands into the hatch, ordering I-168 swung about for a dive into her own smoke. The tactic worked. Both destroyers over-ran us. They soon had our location fixed again but dropped only a few charges before breaking off the action and making toward the east at high speed. I looked at my watch. Only a few minutes until sunset. Whether the enemy ships departed because they feared a night encounter with us, or whether they had no more depth charges, I did not know. In either case, I-168 was going to get out of this now. We surfaced a little while after sunset. Assuming that patrol planes from Midway would be seeking us out, we headed north. I hoped they would think I had set a course for Truk, and thus be thrown off the scent. After a few hours, we changed course for Hokkaido, our northernmost island, it then being the nearest to us on a great circle course. I-168 cruised at her most economical speed, for we were not out of trouble yet. Oil was the Imperial Navy's lifeblood and strictly rationed. I-168 had been given only enough for cruising to Midway and operating there for a few days. All submarines were supposed to have refueled from captured stores when the island was taken. By practicing severe economies, however, we were able to set Yokosuka, then Kure, as our final destination.

192 Sutherling/MIDWAY REPEATS TRAFALGAR’S LESSONS

A great crowd greeted our arrival. There were cheers, music, congratulations, and speeches in abundance as we tied up. A special news broadcast had told earlier how I-168 had torpedoed the carrier Yorktown, and that she had sunk the following morning. A special report of the exploit was rendered His Majesty, The Emperor—something done only when the war news was of great magnitude. I was given command of a new submarine, I-776, at once and granted special permission to hand-pick only men who had factory and machine experience as civilians. This guaranteed me a crack crew. There were to be other exciting times in the war for me. In I-776, I made the first submarine reinforcement of Guadalcanal after the Americans landed there, and with one torpedo knocked out the heavy cruiser Chester for a year. Later, after surviving a tenacious attack on I- 776 in the Solomons, I was received in audience by the Emperor himself. But all I could think of that day at Kure, while being hailed as a hero, was that as yet no news of Kaga, Akagi, Hiryu, and Soryu had been released to the public. All the Japanese people thought we had scored another Pearl Harbor at Midway. They didn't know that four of our fighting carriers, together with hundreds of Japan's best planes and pilots, were gone forever. My sinking of the USS Yorktown was small revenge for that loss.”

* The Yorktown had been abandoned for about 24 hours on 4 June. The "destroyer" that Lieutenant Commander Tanabe thought he saw towing her was the minesweeper Vireo (AM-52), which had begun a slow tow on the afternoon of the 5th. The other destroyers were real. They were Benham (DD-363), Hughes (DD-410), Gwin (DD-433), and Monaghan (DD- 354); Hammann (DD-412) was alongside to provide power and a salvage crew.

193 Sutherling/MIDWAY REPEATS TRAFALGAR’S LESSONS

APPENDIX E. Text of Great Torpedo Scandal Investigation

Post War Resolution. Midway highlighted the poor performance of the Mark 13 torpedo:

42 of the 51 attacking USN torpedo bombers were lost without scoring a single hit.264 B.

Rowland reviewed the government’s assessment in “U.S. Navy Bureau of Ordnance in World

War II”:

“[After Midway] Despite the complications that were attending the other phases of

torpedo development, the Bureau of Ordnance considered the aircraft torpedo problem

so important that it was assigned the highest priority at the Newport Station. The

improvements and modifications of 1942 and 1943 still left the weapon unpopular,

however, and production problems were as great as those stemming from incomplete

development. In mid-1943 an analysis of 105 torpedoes dropped at speeds in excess of

150 knots showed clearly why aviators distrusted the Mark 13: 36 percent ran cold, 20

percent sank, 20 percent had poor deflection performance, 18 percent gave

unsatisfactory depth performance, 2 percent ran on the surface, and only 31 percent

gave a satisfactory run. The total in excess of 100 percent proved that many torpedoes

were subject to more than one of the defects, just as the bulk of the problems were still

due to the effects of poor air stabilization on water behavior. Better performance at

reduced aircraft speeds was small comfort since aviators could not be held down by

paper restrictions that imposed serious and dangerous handicaps in combat. And even

when they accepted the limitations, the water entry behavior of the torpedo produced

frequent hooking and broaching. Time promised to complicate the problem still further.

264 https://en.wikipedia.org/wiki/Mark_13_torpedo 194 Sutherling/MIDWAY REPEATS TRAFALGAR’S LESSONS

Unsatisfactory for existing planes, the torpedo would certainly fail to utilize the

potentialities of aircraft then under development.

“Confronted with such a problem, the Bureau felt that it had two alternatives: it

could accept the Mark 13 as an interim weapon with recognized tactical limitations and

initiate the design of a new torpedo, or it could concentrate on eliminating the known

defects in the existing weapon. To attempt both might spread effort too thin to assure

success in either venture. The first alternative involved predictable delay, since the

Bureau estimated that 2 years would be required to move a weapon from conception to

production. On the other hand, 12 known defects seemed to preclude immediate

success in converting the Mark 13 into an effective aircraft torpedo. Neither alternative

was considered alone, so the Bureau decided to increase its resources and follow both

at once. The National Defense Research Committee was appealed to for aid, and in late

1942 it accepted a double-barreled order from the Bureau. The Committee was given a

blank check to produce a new aircraft torpedo, the Mark 25, for tactical use at 350

knots launching speed, and it agreed to aid the Bureau in making immediate

improvements to the Mark 13.” 265

265 http://www.ibiblio.org/hyperwar/USN/Admin-Hist/BuOrd/BuOrd-6.html 195