Copy 3 SSIFIED 1: 4-15 WAR DEPARTMENT COAST ARTILLERY FIELD MANUAL SEACOAST ARTILLERY FIRE CONTROLAND POSITION FINDING 5 November 1943 Pilenination of rmstrleted matter-The information contained in re- tricted document, and the essential characteristics of restricted material may be given to any person known to be in the service of the United States and to persons of undoubted loyalty and discretion who are cooperating in Co.ernment work. but will not be communicated to the public or to the press except by authorized military public relation agencies. (See also par. l8b. R b80-5,28 Sep 1942.) ASSI UNCU SS ID FM 4-15 R cl COAST ARTILLERY FIELD MANUAL SEACOAST ARTILLERY FIRE CONTROL AND POSITION FINDING CHANGES~ WAR DEPARTMENT, No. 1 ~ WASHINGTON 25, D.C., 7 JULY 1944. FM 4-15, 5 November 1943, is changed as follows: * 28. APPROXIMATE FORMULAS.-These formulas may * * . the relationship is: parallax (degrees) = 57 AB AT or parallax (mils) = 1,000 AR * 46. AZIMUTH INSTRUMENT M1910AI (DEGREES) (fig. 17).- a. Description. (2) The base provides * * * the horizontal move- ment. Its principal parts are the yoke, the traversing mech- anism, the azimuth scale, micrometer, and the leveling mech- anism. The telescope is * * two level vials. * 104. DESCRIPTION OF BOARD. c. Ballistic correctionmechanism. (4) The ballistic correction * * (fig. 78), is plotted. On the newer charts, the elevation scale is in the form of an elevation-height of site grid. (See app. XII.) * . * 1 COAST ARTILLERY FIELD MANUAL * 105. MOU NTral. (2) Where the guns are equiped with range drums and utilize range-range relations on the percentage corrector tape, considerable inaccuracy may result in angular travel computation if the range drum setting, as read from the percentage corrector, is set on the range scale of the ballistic correction chart. In this case, * * * percentage cor- rector MI. The procedure is discussed in detail in appendix XII. (3) (Added.) Special corrections must be made on some older type ballistic charts to take care of time of flight errors caused by height of site. On newer charts, an elevation- height of site grid has been added. These modifications are covered fully in appendix XII. b. Ballistic correction chart. (3) Mount the ballistic * tighten the screws. If using a chart having an elevation-height of site grid (see app. XII), set index to zero elevation on the zero height of site line. * 127. CASE III ADJUSTMENT. c. Aiming point and aiming rule.-Azimuth circles are * * * of the gun. If a fixed aiming point is used, this parallax introduces an error into all azimuths except that at which the orientation was made as mentioned in para- graph 124. It is desirable * * * to sight displacement. (See par. 132.) 2 FIRE CONTROL AND POSITION FINDING LNE oF SIGHT HORIZONTALPLANE BOE OF I55SmmGUN I s. 875 FIGURE 108.-Testing target for 155-mm gun G.P.F. equipped with quadrant sight M1918A1. * 211. MECHANICAL SOLUTION. b. Application of data to the computer. (14) The rate of change of range (Ro) and the linear rate of lateral displacement (RoAo) are carried to the predictor mechanism which uses these rates in the solving of the pre- diction formulas. The computer solves * * and adjust- ment corrections. * . 3 COAST ARTILLERY FIELD MANUAL APPENDIX IV MANEUVERABILITY OF NAVAL VESSELS *3. b. When the rudder * *' ' the drift angle. The aver- age drift angle for a battleship is 10°; that for a destroyer, 5° (see fig. 160). 4 FIRE CONTROL AND POSITION FINDING 0 y ~~ ~~~U - zl Co ~ C = 0P v,~~~~~~~ =~~~~~~~4 5 COAST ARTILLERY FIELD MANUAL APPENDIX VI CONSTRUCTION OF CHARTS AND SCALES FOR SEACOAST ARTILLERY FIRE CONTROL INSTRUMENTS * 10. RANGE-ELEVATION SCALE FOR PERCENTAGE CORRECTOR M1. c. A graphical method * * * on the scale. For ex- ample, the elevation marking for 440 mils should be placed opposite the range of 13,790 yards and that for 460 mils opposite the range of 14,100 yards. Figure 178 could * * * the 5-mil marks. * . * * * 6 FIRE CONTROL AND POSITION FINDING APPENDIX VII INSTRUCTIONS FOR OBTAINING CHARTS AND SCALES FOR SEACOAST FIRE CONTROL INSTRUMENTS FROM THE COAST ARTILLERY BOARD, FORT MON- ROE, VIRGINIA. * 3. AVAILABLE CHARTS AND SCALES.-Table I lists charts and scales available at the Coast Artillery Board, Fort Monroe, Virginia. This .list will * * writing these requests. The numerals following each item listed should be used in entering table 11 to determine the information which should be submitted to identify properly the chart or scale desired. The examples cited * all neces- sary information. TABLE I.-Available charts, scales, and plans 4. Deflection board Ml. a. Wind and drift chart (1) (2) (3) (4) (5) (6). Example: 2 each-Wind and drift chart for deflection board Ml for 155-mm guns Ml and MIA1 on mobile carriage M1; firing high- explosive shell M101 with point-detonating fuze M51, normal and supercharge, based on Firing Tables 155-S-1, azimuth in degrees and hundredths, elevation in mils, height of site, 100 feet. 7 COAST ARTILLERY FIELD MANUAL APPENDIX X DERIVATION OF PREDICTION FOR GUN DATA COMPUTER Ml * 1. SYMBOLS.-The following symbols * * 192 and 194): A, Azimuth of the line from G, to To (the present azimuth). Ao Angular rate of change of present azimuth (radians per second). A, Azimuth of the line from G. to T, (the predicted azimuth). R o Distance G, to To (present range). Ro Rate of change of R, (yards per second). Rp Distance G, to T, (predicted range). Rp' Corrected predicted range. RoAo Linear rate of lateral displacement (yards per second). t Time of flight to T,. * 2. PREDICTION FORMULA FOR Rp. T c. From p, the * * * intersects at E. Now ET, rep- resents the product Rot. With G, as * * * with radius G,E. NOTE.-ET is the * . the line G0 Then Rp =R o + ET o + FTp (1) ET=o Rt (see above) (2) FT, = R, - G,F R, - G,E (3) 8 FIRE CONTROL AND POSITION FINDING G,E = Rp cos AA (4) FTp = Rp- R cos AA = R, (1- cos AA) (5) From the power series cos aA = ?-4 ! + A .... (6) ... .. Substituting these values from (2) and (9) in (1) AA' (10) R, = R + Rot R, -- (10) By substitution of * * * (10), we get = R0 + + (R. + R t + RA AA') AA' RP=R,,+Rjt+ 0 R,ti - , + t + RPA = Ro R o t + R o-AA + ~2oR A'2 42 (11) Since Rp AA4 is very small, the term may be dropped. AA' 0 AA Then Rp = Ro + Ro + R A' + R t AA (12) t 20 2 Then, by factoring R, = (R + Rot) ( + -A) (13) Equation (13) gives * * * of the target. If the range o is decreasing, R, will be negative. (See fig. 193.) * 3. PREDICTION FORMULA FOR Ap.-In figure 194, * of range prediction. ET, = RoAoI (14) Rp AA = PTp (15) ET,, = PT, (for small angles, the chord equals its arc) R, AA = ET, (by substitution) (16) 9 COAST ARTILLERY FIELD MANUAL RPAA = RoAot (from (14) ) (17) AA = R° (18) Rp Ap = Ao + AA (by definition) (19) A, = A + RAt (20) a. This assumes an increase in azimuth; that is, Ao is positive. If travel is counterclockwise, A, will be minus. b. Both predicted range and predicted azimuth are cor- rected for nonstandard ballistic conditions in the final solu- tion. 10 FIRE CONTROL AND POSITION FINDING APPENDIX XII (ADDED) MODIFICATION OF RANGE OR ELEVATION SCALES ON BALLISTIC CHARTS FOR DEFLECTION BOARD Ml Paragraphs SECTION I. General ......................................... 1-5 II. Modification of older type ballistic charts ...... 6-8 III. Elevation-height of site grid .................. 9-12 SECTION I GENERAL * 1. GENERAL.-Attention is called in paragraph 105a (2) and (3) to the possible necessity for correcting elevation or range scales on ballistic charts for deflection boards Ml when percentage corrector readings incorporate height of site 'corrections or range-range relation corrections made to accommodate a particular range disk. Attention is also called to the elevation-height of site grid appearing on the newer ballistic charts. The purpose of this appendix is to give a more detailed explanation of such modifications. * 2. PREPARATION OF BALLISTIC CHARTS.-a. In firing tables, time of flight and effects due to nonstandard ballistic con- ditions, as well as drift and rotation of the earth effects, are set forth as values corresponding to various level point ranges or quadrant elevations for zero height of site. Bal- listic charts for deflection boards essentially are graphical representations of firing table data and the ordinate scale used initially in preparing the chart is the firing table range or quadrant elevation. Corresponding time of flight values are plotted opposite this scale. All range corrections for nonstandard conditions, except height of site but including tide, computed on the range correction board and applied on the percentage corrector to obtain corrected range or elevation can also be applied directly to this initial range or elevation scale on the ballistic chart for purposes of obtaining proper deflection ballistic corrections and time of flight values corresponding to the corrected range. 11 COAST ARTILLERY FIELD MANUAL b. Under certain circumstances, ballistic charts prepared in the manner described in a above require modifications. These depend on the form in which range or elevation data are sent to the guns and how height of site correction or corrections for nonstandard ammunition (for guns equipped with range disks) are made. (1) Charts positioned according to range.-In fixed bat- teries that are laid in elevation by means of a range disk, the height of site correction is taken care of in the gradua- tion of the range disk. For batteries of this type, the bal- listic chart on the deflection board is made with a range scale for positioning the chart.