Computing Slant Ranges

Slant Ranges were precomputed on the ground. Three were usually used on the run. The first at 70 degrees to target at which point the rate motor on the bombsight was activated. Two checks were made on the run at 64 and 58 degrees to target. The three values needed are represented by the red lines in the diagram above and designated C1-AP, C2-AP and C3-AP. These ranges were to an aiming point usually on the coast and at these ranges the inland target was at sighting angles of 70, 64 and 58 degrees respectively.

Trigonometry and the Pythagorean Theorem were the tools for solving the six triangles involved. The known values were absolute altitude (A), sighting angles, and the distance from aiming point to target. Sines, Cosines and Square Root are parts of the process. The process is best described by reconstructing the math involved in our strike on Tokyo, May 25, 1945 and offered in the following exhibit. It is a vertical treatment of the horizontal perspective offered in the previous exhibit. Our assigned absolute altitude was 7000 feet, Indicated Air Speed 205 mph, Aiming Point a tip of land on the shoreline with the target 7000 feet inland.

Sine of an angle = side opposite divided by hypotenuse Cosine of an angle = side adjacent divided by hypotenuse In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides....Pythagoras

Slant Range Calculations

Tables were developed from which slant ranges were interpolated for all altitudes eliminating the need for custom calculations. It was a short cut constructed on the above process. It fursnished flexibility for changed conditions and enabled the use of radar bombing on targets of opportunity.