A Scientific Basis For Evaluating Variable Crosswinds
If we use the Infinity software to check our math, we find the exact same prediction of bullet drift for a 1,000-yard shot in the presence of a constant 10-mph wind. Obviously, bullet drift for both the Wind Early and the Wind Late scenarios will necessarily be less than this.
In order to find the drift values for the Wind Early and Wind Late circumstances, weíll have to alter the approach somewhat. These situations, as well as all others where the wind speed and/or direction is not constant along the entire range to target, fall into a different category, appropriately described as variable crosswinds. The approximate effect of a variable crosswind can be determined by analyzing the problem as a series of constant crosswinds acting over short intervals, each of which starts at a different down-range distance from the gun muzzle. The Wind Early scenario is comprised of two wind segments: 10 mph over the first 500-yard interval and 0 mph over the second 500-yard interval; for the Wind Late situation, the segments are the same but the wind speeds are reversed. For a variable wind comprised of more than one segment, the following formula can be used to calculate the drift for each segment:
Equation 2 is really a variation of equation 1, allowing for the calculation of the drift observed at the target range [Z(R)] resulting from a particular wind acting during an interval of bullet flight beginning at some point downrange (a) and ending at a point further downrange (b). The symbols Xa and Xb represent the starting and ending ranges of the interval (feet); t(Xa) and t(Xb) refer to the bulletís time of flight to reach each of those ranges (seconds); and Vxa and Vxb are the down-range velocities (feet/ second) of the bullet when it reaches those ranges. The symbol R represents the range to target (feet) and t(R) is the time of flight to the target (seconds).
Table 1 shows the values of these variables, in 100-yard increments, for the present study. The flight times and bullet velocities were taken from Sierraís Infinity software. The fifth column represents the calculated numerical value (seconds) of the bracketed portion of equation 2 at various ranges. To find the bullet drift attributable to a particular wind, the numerical value in column 5 which corresponds with the range where the wind interval ends is subtracted from the value corresponding to the range where the wind interval begins. The resulting quantity is then multiplied by the applicable wind velocity (inches/ second) to give the drift.
To start, letís use Table 1 to calculate the drift for the Wind Early case. Of course, the first wind segment begins at the muzzle and ends at 500 yards. The wind velocity for this interval of flight is 10 mph (176 inches/ second). Therefore, the drift attributable to this segment can be calculated by:
Itís important to note that this figure represents the drift, attributed to this particular wind segment, which will be observed at 1,000 yards (target distance). Since the wind velocity is zero for the second segment of flight, there is no additional contribution to bullet drift. However, if a crosswind was present for the second segment, then that would obviously impact the total amount of drift. The same process would be employed to calculate the drift caused by a second-segment wind. The total drift would be determined by simply adding the drift caused by the two wind segments. Any additional wind segments would be analyzed in a similar fashion, with the total drift comprising the sum of the drift calculated for the individual segments.