Knot (Deflection)

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In a field of study renowned for oddities in language and expression, the use of the "knot" as a unit of gun deflection is a topper.

The Royal Navy called its units of deflection "knots", but this was not the familiar unit of speed. A knot of deflection is actually an angle. Odder yet, there is no simple conversion of this to any other angular measure, as a knot of deflection is arbitrary and defined only by similarly arbitrary choices made in the shape of cogs, sights, and fire control charts drafted to describe the performance of a given gun. It's maddening (we can say that here... this isn't Wikipedia)!

History and Etymology

In the early days of gunnery when ranges grew to the point where gunners first realized that some battle scenarios required gunners to laterally lead their target (to account for relative motion during the shell's time-of-flight and other factors), they decided a simple choice for the expression of the angle was to tie it to the enemy's speed across the line of fire in knots if the enemy happened to be at a convenient standard (tactically or mathematically) battle range. For instance, if the range chosen was 5,000 yards and the target ship was steaming at 10 knots left to right across the line of fire, the engineers would calculate the proper lateral aim-off angle to hit him, and the sights for the ship's guns would be cut such that 10 knots equaled this angle. In effect, a knot for this ship's gunnery staff became an angular unit pertaining to this cannon/powder/project combination. Perfect, right? Well... were they allowed to flog engineers in the Royal Navy?

This is an extremely sloppy relationship to have attempted to thusly canonize (if you'll pardon a little gunnery punnery). Any merit it might have briefly possessed relied on the fact that at the fairly moderate ranges in question at the time, a shell's time-of-flight was roughly proportional to the range. Therefore, if you thought the enemy was 4,000 yards away rather than the 5,000 yards the deflection on your sights was graduated for, you could still guess his speed-across in knots and set this on your sights. The reason is that if time-of-flight is truly proportional to range, the proper lateral aim-off angle is insensitive to range owing to similarity of triangles.

However, by World War I, most guns were capable of reaching ranges at which the time-of-flight quickly rose above the linear relationship they had to range at the shorter ranges. This meant that the previously not so shabby rule-of-thumb for converting speed-across to lateral aim-off became a liability. However, the Royal Navy kept its system in place. The result was that the deflection portion of gun sights and numerous other calculating devices in the Royal Navy were needlessly variant.

It was only at war's end that the Royal Navy started to discuss the prospect of standardising the knot for deflection purposes. Oddly, this proposal never mentions the possibility of choosing another word for this unit. I would have proposed "pip".

Wait! So how many degrees is a knot of deflection?

As indicated, it was different for different gun sights. On the 15-inch guns on H.M.S. Queen Elizabeth, 1 knot of deflection was defined as 2.56 arc minutes.

The Sight Manual (1916) at TNA lists this for many weapons of the Royal Navy during this period.

Reference