S 14 AND 17
17B10. Columns 14 and 17

Column 14 is headed “change of range for motion of gun in plane of fire of 10 knots,” and column 17 is headed
“Deviation for lateral motion of gun perpendicular to line of fire, speed, 10 knots.” By “motion of gun” is meant the
velocity imparted to the projectile due to motion of the firing ship, aside from the velocity imparted by the powder charge.

This velocity may be positive or negative. Thus, a ship steaming at 10 knots and firing dead ahead imparts an added
velocity of 16.89 foot-seconds, in the horizontal plane. The same ship firing dead astern reduces the horizontal component
of initial velocity by the same amount.  Firing on the beam causes a velocity component across the line of fire in the
direction of motion of the ship.

If the gun were fired—and the projectile were to travel—in a vacuum, the range error could easily be determined.
In the case of firing dead ahead, the range would be increased by 16.89 X Tf/3 yards.  But this is the value found in
columns 15 and 18, since the target motion was computed by using this very formula and with these same values.

However, the gun is not fired in a vacuum but in the resisting medium of the atmosphere. If no wind is blowing,
a person standing on deck on a moving vessel will feel an apparent wind, equal in force to the speed of the vessel.
It may therefore be said that a projectile fired from a moving vessel, in still air, is opposed by an apparent wind equal
in force but opposite in direction to the motion of the vessel. The effect of such an opposing wind may be found in
column 13 for range wind and in column 16 for cross wind.

The above discussion leads to the statement that “the effect of a given component of gun motion is, numerically,
the equivalent of the effect of an equal component of target motion less the effect of an equal component of wind.”
This does not mean that target motion, as such, enters into the problem in any way. It does mean that the value
of the change of range if the gun were fired in a vacuum, would be computed in the same manner in which the
effect of target motion is computed. This value is found in columns 15 and 18, which are tabulated as target motion.
However, since the gun is fired in air, this effect is opposed by a force which is the same as that of an equal
component of wind blowing against the projectile. This relation should be thoroughly understood, as it will be
employed repeatedly in this text.

This statement may also be expressed as:

Column 14 = column 15 — column 13, and

Column 17 = column 18 — column 16.

Examination of any range table for any range shows that this relation is true. (The occasional difference of 2 or 3 yards
is due to the fact that columns 14 and 17 actually are computed from formulas, the results plotted, and the curves faired.)