Actually the post tells where the method comes from and the info is a screenshot. It's part of the official US Navy
Submarine Torpedo Fire Control Manual of 1946. And it is self-validating. Just reading it and understanding what it says reveals a proof of concept from within the method.
It's a simple concept of relative motion. You are constantly in motion. In fact, if you are at the equator, you are rotating with the earth at 1,000 mph, while simultaneously orbiting the Sun at about 100,000 mph. However, in our relative motion calculations with the submarine and target, we ignore both of those components and do not end up with a multiple variable solution.
This method simply stops the motion of your submarine and calculates the target speed relative to your stopped submarine. Let's say you calculate 2 knots, Yeah! But the sub is moving 10 knots. Fine. We know he's going 2 knots more than we are. 10 + 2 means our target is moving 12 knots.
If our method "stops" our submarine, we eliminate that variable. The result is that our resulting single variable solution is only calculating the target speed relative to ours. It's the simple method of eliminating a variable by expressing it in terms of another variable, then ending up with a single variable equation.
It works. Don't believe me, it's not my idea. Believe the US Navy!