5.3.1 Headwinds and Tailwinds
In Section 2.0 we discussed the two physical forces, gravity and air drag, which act on a bullet traveling through the air. The trajectory of a bullet is completely determined by these forces after it leaves the gun barrel. The gravitational force does not depend at all on wind conditions, but the air drag force does, and it has a very important influence on trajectory. Drag on a bullet is determined by the velocity of the bullet RELATIVE TO THE AIR THROUGH WHICH IT TRAVELS. When the air moves, the drag on the bullet is different from what it is when the air is still. It is just this drag force difference that causes the bullet trajectory in a wind to be different from what it is in still air.
This is quite easy to see when the bullet flies in a headwind or tailwind only (no crosswind). Suppose that you fire a bullet with a muzzle of 3000 fps and a tailwind of 10 mph. When the bullet leaves the muzzle its velocity is 3000 fps relative to the ground, since you are holding the rifle still relative to the ground. The wind at your back blows toward your target with a velocity of 14.67 fps (10 mph). Then, at the instant the bullet leaves the muzzle, its velocity RELATIVE TO THE MOVING AIR is 2985.33 fps. If there were no wind blowing, the bullet’s velocity relative to the still air would be 3000 fps. Since the relative velocity is lower, the drag is a little lower when the bullet leaves the muzzle. As the bullet rides the tailwind, the drag is lower than it would be if the bullet flew in still air all along the trajectory. With less drag, the bullet reaches the target earlier (time of flight decreases), it has more remaining velocity when it gets there, and it suffers less drop (impacts a little high).
If you were firing into a 10 mph headwind instead, just the opposite situation would happen. The bullet velocity relative to the air would be 3014.67 fps at the muzzle. Since the relative velocity is higher than it would be in still air, drag is higher when the bullet leaves the muzzle. As the bullet bucks the headwind, the drag is higher than it would be in still air all along the trajectory. Consequently, the bullet reaches the target later (time of flight increases), it has a smaller remaining velocity when it gets there, and it drops more (impacts a little low).
Tables 5.3-1(rifle) Table 5.3-1(handgun) and Tables 5.3-2(rifle) Table 5.3-2(handgun) have been prepared to show how large headwind and tailwind effects turn out to be for some typical hunting and target shooting situations. The five bullets in Table 5.3-1(rifle) Table 5.3-1(handgun)have ballistic coefficients which pretty well span the range for hunting bullets. The muzzle velocity for each bullet is deliberately chosen to be moderate for typical cartridges in that caliber, in order to show worst case wind deflections.
Table 5.3-2(rifle) Table 5.3-2(handgun) contains, the same information for the Sierra HPBT MatchKing bullets frequently used for long range target shooting. The muzzle velocities chosen for these bullets are typical of the magnum cartridges in the three calibers since many target shooters favor high velocities for this type of competition.
Two points may be noted from these tables. First, the vertical deflections are relatively small, even in comparatively strong headwinds and tailwinds. At normal ranges for hunting, these deflections are completely negligible. For 1000 yard target shooting in a strong headwind or tailwind, a vertical correction might be desirable if the wind were steady. However, with no correction any one of the three bullets, if well aimed, would stand a good chance of staying inside the 20 inch V-ring, and would certainly stay within the 36 inch bull.
Second, both tables show that a headwind usually causes a slightly larger vertical deflection than a tailwind of equal speed. The reason for this has to do with the relatively complicated way that drag depends on the speed of the bullet relative to the air.
It should also be noted that the wind deflection of any bullet depends very much on muzzle velocity. As an example, 2600 fps for the 117 grain .257 spitzer flat base in Table 5.3-1(rifle) Table 5.3-1(handgun) is about a top load for the .257 Roberts. The table shows that in a 30 mph headwind this load would shoot 3.30 inches low at 600 yards. This same bullet can be driven at 3200 fps from a .257 Weatherby Magnum. Our calculations show that this load would shoot 1.35 inches low in a 30 mph headwind.