Zero Gyro Angle-No TDC Required Firing method video

[gumbeauregard]

Here is a film of my Zero Gyro Angle attack method with a graphical explanation of the trigonometric relationship of target speed and torpedo speed.



Notes:

1 knot is 33.7 yards per minute so that is about 100 yards every 3 minutes for each knot.

If you take positions every three minutes the yards moved divided by 100 =knots of speed for the target.

I use two different torpedo speeds in the film.
29 knot Mark 18's and Mark 14's set to run at high speed at 46 knots.

The target speed was found to be 11 knots

Deflection angle for 11 knot target with 46 knot torpedo can be found on the Wiki chart
https://en.wikipedia.org/wiki/Torped...ctionAngle.png

Note this chart is only valid for 46 knot torpedoes.

Or you can use this calculator
http://www.couscouscrabcakes.com/okane.html

The above calculator works great.

Or you can make your own table of values in Excel using =DEGREES(ATAN Target Speed/Torpedo Speed)



Notice there is no need to put anything into the TDC with this method.

Once I know the target speed all I do is get to my shooting position, 1000 yards or less from target track and 100 degrees Torpedo track angle (The angle formed by the target track and the torpedo track)

The calculated firing bearing for 29 knot torpedo and 11 knot target is 21 degrees port which is a bearing of 339 degrees (360 - 21 =339). The 46 knot torpedoes for an 11 knot target is 13 degrees port or 347 degrees (360-13=347)

Range is unnecessary for this method as the ratio of the target speed to torpedo speed remains the same, thus the angle does not change with range to target.

The firing bearings generated by the chart are good for torpedo track angles of 70 to 110 degrees with the ideal angle being 100 as in the video

If you want to use this method at torpedo track angles outside this range there are simple rules of thumb to reduce the firing bearing.

For a 60 degree torpedo track angle, multiple the deflection angle by .75 which is 75% or three quarters of the calculated deflection for a 90 degree shot.
For example, a 29 knot torpedo fired at an 11 knot target is 21 degrees times .75 or a deflection angle of 15 degrees

At 40 degrees use half the table or calculated value. Half of 21 is 10 degree angle using the same example.

For a down the throat shot at 18 degrees, use 25% or one quarter of the calculated angle. 5 degrees in this case.

Be aware that shots deviating from the ideal of 100 degrees torpedo track will be proportionally less tolerant of errors in the target speed and more likely to get duds the further from the ideal you get.

The method demonstrated here was developed by me beginning in 2007 after reading everything available on the historical record, browsing this board and gleaning tidbits and employing my own personal interest in the math involved with shooting accurately.

It WILL NOT work for stern torpedoes in SH4 because you have to input a TDC solution for the stern tubes or the software prevents them from firing.

So no matter what you will have to learn to use the SH4 TDC if you want to shoot stern shots.

[Rockin Robbins]

Up to the 10:57 mark a beautiful job of describing the Vector Analysis Method. You were wrong in stating that the table was correct and the graph was wrong. The actual state was because you didn't measure the angle between target track and your course, and it was not exactly 90 degrees, the trig function was wrong because it didn't apply to your exact situation. Trig only works with 90 degree angles. Vector analysis works with ANY angle.

Try another angle, further away from a 90 degree approach and see what I mean. In fact, when you use the vector analysis method, which you showed excellently and described brilliantly, no trigonometry is necessary at all! You can literally toss the trig tables and lead angle tables out the window.

When you have a disagreement between a calculation and a graph, pick the graph every time. The other thing that gets dispensed with when using a graph is meaningless precision.When your measurements are only good to plus or minus half a degree, then a number like 1.2365 degrees is meaningless. When you're measuring with the protractor on a graph you measure best as you can and automatically get the correct number of significant figures to reflect your accuracy.

Love your presentation. Very measured and clear. You have presented a valid and usable method here, although your later use of trigonometry is not necessary and actually would introduce human error in the process if people used the numbers rather than the graphical solution.

I consider you to have fixed the missing information in the other thread. The only thing I would change is making primary reliance on the graphical solution and using the trig as illustration of how the method works numerically.

Did you know that the TDC actually used a triangle and vector analysis rather than numerical calculation? Yes it actually constructed a scale model of the triangle and measured its properties. So it can rightly be claimed that the TDC itself used the vector analysis method for its solutions.

Here is a page from the TDC Mark III manual showing how a threaded rod was used to measure the length of one of the sides of the solution triangle (in this case the distance to the target track) and the trigonometric justification of the design. But the TDC didn't USE trigonometry. It measured a scale representation made with threaded rods! This is a subassembly of the TDC angle resolver. Fascinating!



And here is the output on the front side of the angle solver:

[gumbeauregard]

Part 2 addresses how this method is used at AOB other than 90 degrees but here is the summary

There are two triangles available to solve allowing precise calculation of the firing angle for any AOB. Before the digital age, solving two triangles was not as easy as it is now so it was not operationally feasible to calculate this on the fly.

However, rules of thumb were developed.

In Part 2 one can see that the 90 degree AOB firing angle is valid for ANY AOB from 90 to 120 degrees. At AOB of 135 the firing angle is about 85% of the 90 degree angle.

At 60 degrees AOB it is 75%
At 40 it is 50%
At 18 it is 25%



So in any case, once you know your 90 degree AOB firing angle you can quickly mentally compute the required firing angle for any AOB.

Or you can build a calculator to solve the two triangles like I did but the rules of thumb are accurate enough inside 1500 yards.

I want to emphasize that I make no claims as to authoring ANY of this. Everything I use comes from the guys who actually did this in WWII and the ancient Greeks who invented trigonometry and figured all this out.