Bombing as a Mathematical Problem

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Until it is released, a bomb travels through the air with the same forward velocity as the airplane, and this velocity relative to the air is called true air speed. The instant the bomb is released, four factors act on it: 1) true air speed; 2) gravity; 3) air resistance; and 4) wind. Calculating their combined effect on a bomb can be a rather complex problem, which increases in difficulty with altitude.

Gravity pulls the bomb downward toward the earth and away from the airplane at a continually increasing speed while the true air speed drives the bomb forward. The airplane continues at the same true air speed, but the bomb immediately begins lagging behind as air resistance pushes against it. Air resistance varies according the size and shape of the bomb. Meanwhile, the airplane travels farther over the ground, and the distance between where the bomb actually hits and the location of the airplane is called the trail.

Accounting for the fourth force, wind multiplies the difficulty of determining a bomb's trajectory to a target. A tailwind causes the bomb to go farther, but a headwind shortens the distance. Furthermore, a crosswind forces the bomb to drift sideways and away from the target.

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