How to Use the Mark 2 Navigator’s Slide Rule Bob Goethe Copyright © 2016 by TEOG Industries Ltd. Serial Num: 1 Mark 2 Navigator’s Slide Rule Copyright © 2016 by TEOG Industries Ltd. 0°40’ 0°50’ 1° 10’ 20’ 30’ 40’ 50’ 2° 30’ 3° 30’ 4° 30’ 5° 30’ T0 tan 0.01 → 0.1 T1 tan 0.1 → 1.0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 1 2 3 4 5 6 7 8 9 10 20 30 40 50 60 70 80 90 100 A x2 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 60 70 80 90 sin 0.1 1.0 S →→ 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 65 60 55 50 45 40 30 20 10 0 0°40’ 0°50’ 1° 10’ 20’ 30’ 40’ 50’ 2° 30’ 3° 30’ 4° 30’ 5° 30’ tan 0.01 → 0.1 ST sin 0.01 0.1 →→ 89°20’ 89°10’ 89° 50’ 40’ 30’ 20’ 10’ 88° 30’ 87° 30’ 86° 30’ 85° 30’ cos 0.01 0.1 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 T2 tan 0.1 → 1.0 T3 tan 1.0 → 10.0 45 50 55 60 65 70 75 80 81 82 83 84 30’ 85° 30’ 86° 30’ 87° 30’ 88° 10’ 20’ 30’ 40’ 50’ 89° 89°10’ 89°20’ T4 tan 10.0 → 100.0 natural log Ln 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 1 1 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 1 C y D x 1 1 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 1 m:ft l:USg DL 45 50 55 60 65 70 75 80 81 82 83 84 T5 tan 1.0 → 10.0 T6 tan 10.0 → 100.0 30’ 85° 30’ 86° 30’ 87° 30’ 88° 10’ 20’ 30’ 40’ 50’ 89° 10’ 20’ g n i t t o l p S O - P V h t i w s e t u n i m f o e l a c s e s U . h t a l P & s m e e W y b d e h s i l b u p t e e h s ’ ’ ’ ’ ’ 0 0 0 0 ’ 0 0 0 ’ ’ ’ ’ 2 3 4 5 0 ’ 0 ’ 0 1 2 3 4 5 1 0 0 ’ 0 TACKING DOWNWIND GREAT CIRCLE CALCULATIONS Course to Dest. relative to dead downwind = γ Meridian Angle (H) = ________°___ 4. [cos(W) ÷ cos(Y)] * tan(H) = tan(Az) Course sailed relative to dead downwind = θ E/W Az = ___ ________° ___ Distance Factor DF = cos(γ)/cos(θ) My Latitude (L) = ________°___ N/S E/W Speed on course θ = Sθ N/S Use N if destination is north of you. Speed Factor SF = Sθ/Sγ Latitude of destination (d) = ________°___ Use E if destination is east of you. Time Factor TF = DF/SF N/S 5. cos(Az) * tan(Y) = tan(Hc) Ideal Course = Course with smallest TF 1. tan(d) ÷ cos(H) = tan(W) 6. D = (90° - Hc) × 60 2. Ignore the sign of X (i.e. -60 = 60) - If H < 90° then then use [+ W] if d has If doing sight reduction, d = declination CHART SCALES AND DISTANCE the same name as L. Use [– W] if d of celestial object. L = latitude of AP. has opposite name as L. Nautical Miles Per Inch = Reciprocal of Chart Scale ÷ 72,900 - If H > 90°, use [– W]. If meridian angle > 90°then... (90° - L) ± W = X Use alternate data input: 180°- MA = H 3. If X < 90°, then X = Y. Use alternate Step 2: (90° - L) - W = X If X > 90°, then 180 – X = Y Use alternate Step 6: D = (90°+ Hc) * 60 Inches 0 1 2 3 4 5 6 7 8 9 10 Actual Size = 11.25” x 2.85” Table of Contents Contents Introduction .......................................................................................................................... 1 §1. Abbreviations ........................................................................................................................................... 1 Part I: Navigational Mathematics .......................................................................................... 3 §2. Conversions.............................................................................................................................................. 3 Coastal Navigation .........................................................................................................................3 §3. Chart Scales & Distance ........................................................................................................................... 3 §4. Speed, Time and Distance ........................................................................................................................ 3 §5. Calculate Boatspeed with a Dutch Log .................................................................................................... 3 §6. Solving the Current Triangle .................................................................................................................... 3 §7. Fuel Consumption .................................................................................................................................... 4 §8. Maximum Hull Speed ............................................................................................................................... 4 §9. Distance to Visible Horizon ...................................................................................................................... 4 §10. Calculating Intermediate Tide Heights..................................................................................................... 4 §11. Tacking Downwind ................................................................................................................................... 4 §12. Distance Off by Two Bearings and the Run Between .............................................................................. 5 §13. Distance to Radar Horizon ....................................................................................................................... 5 Offshore Navigation .......................................................................................................................5 §14. Dip ............................................................................................................................................................ 5 §15. Dip for Short Horizon ............................................................................................................................... 5 §16. Scope of a Given Universal Plotting Sheet ............................................................................................... 6 §17. Sight Reduction/Great Circle Route Calculations .................................................................................... 6 §18. Rhumb Line Route Calculation ................................................................................................................. 8 §19. Plotting Longitude .................................................................................................................................... 9 §20. Distance by Vertical Angle of Object Beyond the Horizon ....................................................................... 9 §21. Compass Delta ......................................................................................................................................... 9 §22. Trigonometry and Mental Math ............................................................................................................ 10 Part II: Using the Mark 2 Navigator's Slide Rule ................................................................... 11 First Things................................................................................................................................... 11 §23. Can You Learn to Navigate From This Manual? ..................................................................................... 11 §24. Parts of the Slide Rule ............................................................................................................................ 11 §25. Reading the C & D scales ....................................................................................................................... 12 §26. Speed, Time and Distance ...................................................................................................................... 13 §27. Reading Sines, Cosines and Tangents .................................................................................................... 15 §28. Solving the Current Triangle .................................................................................................................. 15 Using Gauge Points ...................................................................................................................... 18 §29. Converting Liters to Gallons ................................................................................................................... 18 §30. Converting Meters to Feet ..................................................................................................................... 20 §31. Calculate Boatspeed with Dutch Log ..................................................................................................... 21 Multiply and Divide ...................................................................................................................... 22 §32. Multiply .................................................................................................................................................. 22 §33. Chart Scales & Distance ......................................................................................................................... 25 §34. Divide ..................................................................................................................................................... 27 §35. Fuel Consumption .................................................................................................................................. 29 Squares and Square Roots ............................................................................................................ 31 §36. Distance to Visible Horizon .................................................................................................................... 31 §37. Dip .........................................................................................................................................................