3.2 Effects of Winds

A “wind” is a movement (relative to the ground) of the air mass through which the bullet flies. The effect of a wind on a bullet’s trajectory depends on the speed of the wind and the direction in which it blows. Every shooter is familiar with headwinds, tailwinds and crosswinds. A headwind is a wind that blows from the target toward the shooter. A tailwind is a wind that blows in the opposite direction, from the shooter toward the target. A crosswind, of course, blows from right to left or from left to right across the line between the shooter and the target. These winds are always considered to blow horizontally.

Some shooters are not aware that there also can be vertical winds. These are winds that blow vertically upward or downward across a line between the shooter and the target. Vertical winds are especially important for hunters in hilly or mountainous country. Anytime a wind is blowing against a hillside or mountainside, a vertical component of wind must occur. Long-range target shooters also may suffer from vertical air currents. Mirage is an effect caused by vertical air movements. Mirage makes a distant target “hazy and jumpy” when viewed through the gun sights, in turn making aiming extremely difficult. And the vertical currents also move the bullets upward or downward as they fly downrange.

A wind can blow from any direction, and the wind needs to be separated into components in order to compute its effect on a bullet trajectory. Infinity characterizes any wind as a combination of a horizontal wind from any direction together with a vertical wind, if there happens to be one. For a horizontal wind, Infinity makes it particularly easy for a user to enter the wind conditions. A horizontal wind is specified in the “Environmental Parameters” list inInfinity by two parameters, wind direction and the wind speed. The horizontal wind direction is specified as an hour angle on an imaginary clock face denoting the direction from which the wind is blowing. The clock is imagined as lying in the horizontal plane with 12 o’clock being the direction from the shooter to the target, 6 o’clock being the opposite direction (from the target to the shooter), 3 o’clock being the direction from the shooter’s right to left as he or she views the target, and 9 o’clock being the direction from the shooter’s left to right as he or she views the target. Infinity recognizes minutes as well as hours in the data input to specify the horizontal wind direction. For example, a horizontal wind direction entered as 1.30 (denoting 1:30 o’clock) signifies a wind blowing from a direction halfway between 1 o’clock and 2 o’clock, that is a quartering wind blowing toward the shooter. After a horizontal wind direction and speed are entered, Infinity will compute a headwind (or tailwind) component blowing toward (or away from) the shooter, and a crosswind component blowing from the shooter’s right or left.

The speed of the horizontal wind must be entered into Infinity in statute miles per hour in English units, or in kilometers per hour in metric units.

When the wind has a vertical as well as a horizontal motion, separating the wind into vertical and horizontal components is a more complex task. Every situation is different. If the wind is simply blowing up or down a hillside with a known slope angle, then simple trigonometry can be used to separate the total wind speed into horizontal and vertical components. But such a simple case is not usual. The vertical wind analysis feature of Infinity is most widely used to determine the sensitivity of any trajectory to vertical winds. This knowledge will help a hunter or target shooter to understand the effect of a vertical wind, and to compare performances of different cartridges in windy shooting situations. Hunters should be especially aware that vertical winds are encountered when hunting in hilly or mountainous terrain, in ravines and close to steep hillsides. A vertical wind component will cause a bullet to shoot high or low, just as a crosswind will cause a bullet to shoot left or right.

The direction of a vertical wind component, of course, is known, up or down. So, in Infinity, the vertical wind speed is entered as positive for an upward wind or negative for a downward wind. The vertical wind speed also is entered in statute miles per hour in English units, or kilometers per hour in metric units.

The effect of each of the three components of any wind is quite different. This is because the aerodynamic drag on a bullet is a function of the bullet’s speed with respect to the air through which it flies. Therefore, if the air is moving, the drag on the bullet is different than it would be if the air were still. For example, in the case of a headwind acting alone and blowing from the target toward the shooter, the speed of the bullet relative to the air would be greater than it would be if the air were still. Then, the drag on the bullet would be higher, and the bullet would travel slower relative to the ground and drop more than it would if the air were still. On the other hand, for a tailwind acting alone and blowing from the shooter toward the target, the speed of the bullet relative to the air would be less than it would be if the air were still. Then, the drag on the bullet would be lower, and the bullet would travel faster relative to the ground and drop less than it would if the air were still. Generally, unless the wind speed is high and the range is very long, a headwind or tailwind causes only a small deflection of the bullet relative to the still air trajectory.

A crosswind acting alone would cause primarily a horizontal deflection (wind drift) of the bullet relative to the trajectory in still air. [Later in Section 4 we will describe how a bullet turns to follow a crosswind because it is spin-stabilized, and how a small vertical deflection of the bullet also occurs in the presence of a crosswind.] The deflection caused by a crosswind is quite large, even for moderate ranges and high velocities of the bullet.

In a similar manner, a vertical wind acting alone causes a vertical deflection of the bullet that is quite large relative to the still air trajectory, and also a small horizontal deflection. [These deflections also occur because the bullet turns to follow the wind, as explained in Section 4.] The sensitivity of vertical bullet deflections to vertical wind speeds is just equal to the sensitivity of horizontal bullet deflections to crosswind speeds.

A wind that blows from any direction can always be resolved into not more than three components, (1) a headwind or tailwind, (2) a crosswind, and (3) a vertical wind. If a wind blows such that two or all three components occur and act simultaneously on the bullet trajectory, the net effect is somewhat different than simply combining the effects of the components acting separately. Two examples, one for a rifle and one for a handgun, have been prepared to illustrate the effects of the separate wind components and the combined effect of all three components of a wind acting simultaneously. Table 3.2-1 has been prepared, using Infinity, for a 308 Winchester (7.62 NATO) cartridge loaded with Sierra’s 30 caliber 175 grain MatchKing bullet at 2550 fps for a High Power target match with military service rifles, and at the 600-yard stage of competition. Suppose that the rifle has been sighted in at 600 yards under still air conditions (no wind), and the firing range is located at an altitude of 1000 feet above sea level. Suppose also that during the competitive firing a wind blows from a direction of 10:30 o’clock relative to the line of sight from the firing point to the target, and that this wind has a horizontal speed of 15 mph. Suppose also that there is an updraft along the firing range estimated at 1.5 mph.

The total wind speed for this example is then:

Total wind speed = Square root [ 15.02 + 1.52

] = 15.075 mph Resolving this wind into three components for the purpose of analysis gives the following: Headwind component = 10.60 mph (from target toward shooter) Crosswind component = 10.60 mph (left to right) Vertical wind component = 1.5 mph (upward) The data in Table 3.2-1 then show the effects of these three wind components, first with each component acting alone, then with two horizontal components acting together, and finally with all three components acting together. The first row in the table shows the effect of a headwind with a speed of 10.6 mph acting alone. The increased drag on the bullet caused by the headwind would make the bullet strike the 600 yard target just 0.62 inch lower than it

Table 3.2-1 Wind Deflections at 600 yards Range Distance for 308 Winchester with Sierra’s .308 dia 175 grain MatchKing Bullet Loaded to 2550 fps Caused by a 15 mph Wind Blowing from 10:30 o’clock and with a Small Vertical Speed

Wind Direction and Speed Bullet Deflection at 600 yards
Headwind Crosswind Vertical Wind Horizontal Vertical
         
10.6 mph 0.0 mph 0.0 mph 0.0 in - 0.62 in (more drop)
         
0.0 mph 10.6 mph (L to R) 0.0 mph 32.76 in (R) 0.0 in
         
0.0 mph 0.0 mph 1.5 mph (upward) 0.0 in + 4.64 in (less drop)
         
10.6 mph 10.6 mph (L to R) 0.0 mph 33.03 in (R) - 0.62 in (more drop)
         
10.6 mph 10.6 mph (L to R) 1.5 mph (upward) 33.03 in (R) + 4.05 in (less drop)

would if there were no wind at all, and there would be no horizontal deflection. The second row in the table shows the effect of a crosswind blowing from the shooter’s left to right with a speed of 10.6 mph acting alone. In this case, the bullet would turn to follow the wind, and at 600 yards, it would be deflected nearly 33 inches to the right. A small vertical deflection also would occur, caused by the spin stabilization of the bullet, but Infinity computes a value of 0.0 inches for this small effect for reasons explained later in Section 4. The third row in the table shows the effect of a vertical updraft with a speed of 1.5 mph acting alone. The bullet would turn upward to follow the wind, resulting in a vertical deflection of the bullet on the target of 4.64 inches. A small horizontal deflection also would occur, caused by the spin stabilization of the bullet, but Infinity again calculates a value of 0.0 inches for this small effect for reasons explained in Section 4.

It is interesting to note that the sensitivity of the vertical deflection caused by a vertical wind is the same as the sensitivity of the horizontal deflection caused by a crosswind. That is, referring to the second and third rows in Table 3.2-1, 32.76 inches divided by 10.6 mph gives a sensitivity of 3.09 inches horizontal deflection per mph of crosswind. The vertical deflection 4.64 inches divided by the vertical wind speed of 1.5 mph also gives 3.09 inches of vertical deflection per mph of vertical wind speed. This specific sensitivity number applies only to this example bullet fired at this example velocity, but in general the sensitivity to crosswinds and vertical winds is very large for all bullets.

The deflections caused by headwinds (or tailwinds), however, are much less sensitive to wind speed, as the example in Table 3.2-1 shows.

Furthermore, the vertical deflections caused by headwinds or tailwinds are not linearly related to wind speed. That is, it cannot be said that the vertical deflection caused by a 10 mph headwind is ten times more than the deflection caused by a 1.0 mph headwind. This same statement is true for tail-winds.

Returning to Table 3.2-1, the fourth and fifth rows show the effects of the wind components acting together. If a headwind of 10.6 mph acts with a crosswind of 10.6 mph (a horizontal wind of 15.0 mph blowing from the 10:30 o’clock direction), comparing the fourth row to the second row and then the first row shows that the crossrange deflection grows from 32.76 to 33.03 inches. The vertical deflection remains the same, compared to the effects of the wind components acting separately. The reason that the crossrange deflection grows is that the time of flight of the bullet is slightly longer when the headwind acts on the bullet, and this longer time of flight increases the effect of the crosswind. The same increase in the time of flight, of course, occurs when the headwind acts alone, and so the vertical deflection (0.62 inch) does not change.

When all three components of wind act together in this example, the last row in Table 3.2-1 shows that the downward deflection caused by the head-wind component just reduces the upward deflection caused by the vertical wind. Again, there is an interaction among the wind components that changes the time of flight to the target, and so the effects of the wind components acting separately cannot be simply added (or subtracted) to exactly get the effects of the wind components acting simultaneously.

Table 3.2-2 has been prepared for a 44 Magnum handgun cartridge with Sierra’s .4295" dia 240 grain Jacketed Hollow Cavity Sports Master bullet loaded to 1300 fps muzzle velocity. Suppose that the handgun has been sighted in at 100 yards under still air conditions (no wind), and the firing range also is located at an altitude of 1000 feet above sea level. Suppose also that during a target shooting session on a different day, a wind blows from a direction of 4:30 o’clock relative to the line of sight from the firing point to the target, and that this wind has a horizontal speed of 15 mph. Suppose that there also is an updraft along the firing range estimated at 1.5 mph.

The total wind speed for this example is then:

Total wind speed = Square root [ 15.02 + 1.52] = 15.075 mph

Table 3.2-2 Wind Deflections at 100 yards Range Distance for 44 Magnum with Sierra’s .4295" diameter 240 grain Jacketed Hollow Cavity Bullet Loaded to 1300 fps Caused by a 15 mph Wind Blowing from 4:30 o’clock and with a Small Vertical Speed

Wind Direction and Speed Bullet Deflection at 100 yards
Tailwind Crosswind Vertical Wind Horizontal Vertical
         
10.6 mph 0.0 mph 0.0 mph 0.0 in + 0.08 in (less drop)
         
0.0 mph 10.6 mph (R to L) 0.0 mph 4.62 in (L) 0.0 in
         
0.0 mph 0.0 mph 1.5 mph (upward) 0.0 in + 0.66 in (less drop)
         
10.6 mph 10.6 mph (R to L 0.0 mph 4.48 in (L) + 0.08 in (less drop)
         
10.6 mph 10.6 mph (R to L) 1.5 mph (upward) 4.48 in (L) + 0.71 in (less drop)

As before, resolving the total wind into its three components for the purpose of analysis gives the following: Tailwind component = 10.60 mph (from shooter toward target) Crosswind component = 10.60 mph (right to left) Vertical wind component = 1.5 mph (upward) In this handgun example, the horizontal wind has been reversed from the previous rifle example, but the vertical component of the wind is still an updraft of 1.5 mph.

The data in Table 3.2-2 show the effects of these three wind components, first with each component acting alone, then with two horizontal components acting together, and finally with all three components acting together. The first row in the table shows the effect of a 10.6 mph tailwind acting alone. The decreased drag on the bullet caused by the tailwind would make the bullet strike the 100-yard target 0.08 inch higher than it would if there were no wind at all, and there would be no horizontal deflection. The second row in the table shows the effect of a 10.6 mph crosswind blowing from the shooter’s right to left acting alone. The bullet would turn to the left to follow the wind, and at 100 yards it would be deflected 4.62 inches to the left. A very small vertical deflection also would occur, but Infinity does not compute this deflection, as noted above in the rifle example. The third row in the table shows the effect of a 1.5 mph vertical wind acting alone. The bullet would turn upward to follow the wind, resulting in a vertical deflection of the bullet on the target of 0.66 inch. A small horizontal deflection also would occur, but Infinity again calculates a value of 0.0 inches for this small effect as in the case of the rifle example.

Again, we note that the sensitivity of the vertical deflection caused by a vertical wind is the same as the sensitivity of the horizontal deflection caused by a crosswind. In this specific example the sensitivity is 0.44 inch per mph of wind speed. This specific sensitivity number applies only to this example bullet fired at this example velocity, but in general the sensitivity to crosswinds and vertical winds is very large for all bullets, handgun as well as rifle.

The fourth and fifth rows in Table 3.2-2 show the effects of the wind components acting together. If a tailwind of 10.6 mph acts with a crosswind of 10.6 mph (a horizontal wind of 15.0 mph blowing from the 4:30 o’clock direction), comparing the fourth row to the second row and then the first row shows that the crossrange deflection decreases from 4.62 to 4.48 inches. The vertical deflection remains the same, compared to the effects of the wind components acting separately. The reason that the crossrange deflection decreases is that the time of flight of the bullet is slightly shorter with the tail-wind acting on the bullet, and this shorter time of flight decreases the effect of the crosswind.

When all three components of wind act together in this example, the last row in Table 3.2-2 shows that the upward deflection caused by the tailwind component slightly increases the upward deflection caused by the vertical wind. Again, there is an interaction among the wind components that changes the time of flight to the target, and so the effects of the wind components acting separately cannot be simply added (or subtracted) to exactly equal the effects of the wind components acting simultaneously.

To summarize this subsection: A wind from any direction can be resolved into at most three components, a horizontal headwind (or tailwind) component blowing along the line of sight between the shooter and the target, a cross-wind component blowing in a horizontal direction across the shooter’s line of sight to the target, and a vertical wind component blowing upward or downward across the shooter’s line of sight to the target. Headwinds or tailwinds generally have a quite small effect on bullet trajectories, unless the wind is very strong and the range is very long. Crosswinds and vertical winds, however, have serious effects on bullet trajectories. The effect of each component wind can be analyzed separately, and this approach gives insight into wind effects. However, to get accurate calculations of the wind’s effects from any direction, all three components must be analyzed simultaneously, because the wind effects interact, primarily by changing the time of flight of the bullet to the target. Infinity can be used to calculate the effect of any wind component, or to calculate the effects of all components acting simultaneously.

There is a common misconception among shooters that a wind “blows” a bullet off its course as it travels downrange. It is very important to realize that a wind does not “blow” a spin-stabilized bullet off its course. Rather, because of its spin stabilization a bullet turns to follow the wind if the wind direction is perpendicular to the line of sight between the firing point and the target. This will be described in greater detail in Section 4. In the case of a headwind or tailwind, the moving air simply changes the drag on a bullet, because drag depends on the speed of the bullet relative to the air and not the ground. A headwind will increase the drag a small amount, in turn increasing the time of flight and causing the bullet to shoot low. A tailwind will decrease the drag a small amount, in turn decreasing the time of flight and causing the bullet to shoot high.