Pamphlet on the Effects of Wind in Gunnery
My copy of this document is a black and white photocopy of an original at TNA. It is primarily theoretical, and focuses on high-angle trajectories for anti-aircraft gunnery. I had hoped it would feature discussion of the Wind Dumaresq, but it has no such practical elements.
It is 40 pages long, but the table of contents references the material as it spreads across the 70 sections contained on those pages. Two figures (V and VII) are oversize fold-outs. A black-and-white copy of this, I feel, retains all necessary information.
This book appears more suited to Army than Navy readers, as it is primarily one for battery fire of timed airbursts against aircraft targets (ack ack), but the first section is useful for seeing how the problem of wind was generally considered.
They understood that wind direction and speed varied with altitude at any given moment, and that knowing its behavior at each point in a shell's flight was unknowable in practice. They referred to the overall wind data along the trajectory as the "wind structure". The simplification sought was to think of the wind at any given moment not as a structure but as a wind in a single direction at a single speed which acted on the shell only during a portion of its flight (section 10). The sections A and B of Part I are for examining the wind in 2 components -- that perpendicular to the plane of the trajectory, and that falling in the plane of the disturbed trajectory.
One of the assumptions taken in this work for the most part is that the shell's velocity is at all points substantially greater than the wind velocity. Reference is made to this failing to be the case in high, lofting shots at (say) 60-80 degree elevation where the yaw of the shell's nose from the air it is passing through (induced wind - actual wind) becomes appreciable.
With various simplifications taken into account, the formula derived in Section 12 for the lateral displacement a constant cross-wind of a given speed induces in a shell is taken to be
LateralDisplacement = CrossWindSpeed * (TimeOfFlight - (Range / (MuzzleVelocity * cos(FiringElevation))))
Section 13 notes that if one considers only a portion of the shell's flight, pretending that it is fired from the beginning of this portion, one can work the above equation to determine the lateral displacement that will be imparted during only the segment in question, plugging in the suitable counterparts for TimeOfFlight, Range, MuzzleVelocity and FiringElevation with the values that would be in place at the beginning of the interval being considered. Subtraction of this displacement from that which occurs over the shell's complete flight would yield the displacement occurring during the parts of the trajectory NOT considered.
By breaking down a trajectory into segments where the shell passed through a given 1000 foot altitude strata (and keeping in mind that in a surface-to-surface firing, it will pass through each strata twice), and computing the lateral displacement that is imparted during each passage, one can derive a weighting table for each strata passage which describes the percentage of the entire displacement attributable to the winds in this elevation strata.
This segmenting of the total wind effect gave the means to apply different wind speeds at different altitude strata, and the weighting table gave the means to consider each CrossWindSpeed in the proper proportion in synthesizing a single Equivalent Constant Wind.
Section 17 details that in high angle fire, strata of 2000 or 3000 feet may be sufficient. In low angle, finer strata may be required to accommodate the wind at different altitudes.
The example in Sections 19-23 show a 6-inch gun firing a 4 crh shell at 2,750 feet per second at 35 degrees. It flies about 20,000 yards in 58 seconds. Tabular data shows the shell at various points in its trajectory, and Table III shows the weighting table for which stratum's winds contribute to the total displacement in what proportion. For instance, the shell reaches an apogee of 14,684.5 feet, and the lowest stratum from 0-1,000 feet weighs in at 4.75% and the next-to-highest from 13,000-14,000 feet weighs out at 7.25%, while the winds over 14,000 feet contribute fully 10.75% of the displacement. The reason for these different figures is the amount of time the shell spends within each stratum.
I'm stopping my notes at this point, as this document is a little too heavy for me at the moment. If you are good at maintaining consciousness while reading such matter, I'll gladly offer you a copy if you share your notes with me.