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)
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.
3.3 Effects of Shooting Uphill or Downhill
When a gun is sighted in on a level or nearly level range and then is fired either uphill or downhill, the gun will always shoot high. This effect is well known among shooters, particularly hunters, but how high the gun will shoot is a subject of considerable controversy in the shooting literature. In fact, at the present time some literature has information that is simply erroneous. In this subsection, we will try to explain the physical situation carefully so that it can be understood clearly, and then provide some examples using Infinity to perform precise calculations.
Throughout this subsection the terms ―bullet drop‖ and ―bullet path‖ will be used frequently, so we will review the definitions of those terms before we begin to explain the physical situation. One may refer back to Figure 3.0-1 concerning these definitions. Bullet drop is always measured in a vertical direction regardless of the elevation angle of the trajectory. At any range distance measured along either a level range or a slant range, drop is then the vertical distance between the extended bore line and the point where the bullet passes. Drop is expressed as a negative number, denoting that the bullet falls away from the extended bore line as the bullet travels.
Bullet path, on the other hand, is always measured perpendicular to the shooter’s line of sight through the sights on the gun. Thus, it would be where the shooter would ―see‖ the bullet pass at any instant of time while looking through the gun sights, if that were possible. At the gun’s muzzle, the bullet path is negative because the bullet starts out below the line of sight of the shooter. Somewhere near the muzzle, the bullet will follow a path that rises and crosses the line of sight, then travel above the line of sight until the target is reached. The bullet path is then positive throughout this portion of the trajectory. The bullet will arc over and cross the line of sight at the zero range. So, the bullet path is zero at the zero range, and then becomes negative at distances greater than the zero range.
The explanation of the physical situation for uphill/downhill shooting begins with a simple observational fact — that bullet drop at any given range from the muzzle is almost independent of firing elevation angle. What this means is that if the drop of a bullet trajectory at, say, 150 yards is measured when the gun is fired on a level range, then the drop at a slant range distance of 150 yards will be almost the same value when the gun barrel is elevated at +45 degrees, - 15 degrees, - 60 degrees, or any other positive or
negative elevation angle. It is very important to remember that we use ―start range‖ because that is the range that the bullet must actually travel to reach the target. This is true for all range distances practical for small arms fire.
To illustrate this point, Table 3.3-1 has been prepared for a group of five cartridges, three for rifles and two for handguns. The table shows drop numbers at a specific range distance for each cartridge, as a function of the bore elevation angle of the gun at the firing event. These drop numbers have been computed with Infinity. These trajectories have been computed for a firing point altitude of 2500 feet above sea level. The selected cartridges in Table 3.3-1 illustrate typical behavior of drop at a specific (and relatively long) range distance versus the bore elevation or depression angle. The 338 Winchester Magnum cartridge exhibits the worst case in the table. At a range distance of 600 yards, there is only about 0.5 inch difference in drop value between a level trajectory and a trajectory elevated 60 degrees or depressed 60 degrees. This is because the major driving cause of bullet drop is gravity acting over the bullet’s time of flight. There are two other smaller effects on drop as the bullet travels. When a bullet is traveling upward on an elevated trajectory, there is a component of gravity that adds to the drag
deceleration of the bullet, but the bullet is traveling into less dense atmosphere that reduces the
aerodynamic drag. So, these small effects tend to offset one another. The opposite small effects occur when the bullet is traveling downward along a depressed trajectory.
This result is true in general. At practical range distances for small arms fire the change in vertical drop with firing elevation or depression angle is very small, even for very steep angles. However, the bullet path can change dramatically, particularly at steep angles.
Figure 3.3-1 shows how this happens. Ordinarily, a shooter will sight his gun in on a target range that is level or nearly level. Figure 3.3-1 (a) shows this situation. When sighting in, the shooter adjusts his sights so that the line of sight intersects the trajectory at the range (Ro in the figure), which is the range where he wants his gun zeroed in. Ro is called the zero range for level fire. The vertical distance between the line of departure (extended bore line) of the bullet and the point where the bullet passes is the drop (do). This symbol is used to denote the drop at the range where the gun is zeroed in.
Note that the angle between the bullet’s line of departure (extended bore line) and the line of sight is very small. This angle is greatly exaggerated in Figure 3.3-1 for purposes of illustration. Even for very long- range target shooting (1000 yards or more), the angle A is much less than 1.0 degree, and it is typically less than 10 minutes of arc for sporting rifles and handguns.