[BigWalleye]

Dorjun Driver,

1. The diagram in your OP is a correct representation of the trigonometric problem you were addressing.

2. The equation in your OP is a correct solution for the trigonometric problem illustrated in the diagram.

3. The angle labeled ‘theta sub intercept’ in your OP diagram is the intercept angle and inserting a value for that angle in the final equation of your OP will yield a correct solution for the deflection angle.

4. The angle labeled ‘theta sub intercept’ in your OP diagram is not the ‘track angle’ (aka Ta, aka A, aka ‘AoB at intercept’) per SLM-1, Page 1-12. It is the supplement of that angle and equals (180-Ta).

5. The angle labeled ‘theta sub Track’ on your second diagram is equivalent to the angle labeled ‘theta sub intercept’ in your OP diagram. It is on the same side of ownship track. It is not the track angle Ta, at least not as SLM-1 defines the term. Please see the diagram on Page 1-12.

6. The angle labeled ‘theta sub Torpedo Track’ is equivalent to TTa, the “torpedo track angle’” as defined in SLM-1, Page 1-12. The intercept angle for the torpedo track. ‘theta sub intercept’ is the suplement of that “torpedo track angle” and equals 180-TTa. Inserting that intercept angle in the last equation of your OP diagram will yield a correct result for the deflection angle.

7. The OP diagram provides a correct solution for a zero-gyro-angle torpedo run. Your second diagram provides a correct solution for firing at small non-zero gyro angles.

8. Except for the mislabeled ‘theta sub Track’ in your second diagram, which is not essential to the calculation of deflection angle in the non-zero-gyro case anyway, I believe everything you have posted is correct.

9. I believe Dignan’s incorrect results came from confusing Ta and intercept angle. His results are consistent with substituting track angle into your equation in place of the (correct) intercept angle. The error was not yours.


Comparing the deflection angles generated from your equation with deflection angles picked off Plate XVIII from SLM-1 yields small discrepancies, which increase somewhat at higher target speeds. I had always assumed that Plates XVII and XVIII in SLM-1 were accurate. The text implies that they include various correction factors and that they are substantially the results generated by a WW2-vintage TDC. The text does not indicate directly how the curves were generated, or what factors were included in the calculations. I had also assumed that the curves were somewhat more accurate than a first-order trigonometric analysis, such as the one in your OP. Apparently, my assumptions were incorrect. I would appreciate if you could tell me why the SLM-1 data are not to be trusted. I do agree that a first-order analysis is perfectly adequate for our purposes.

(Edit: Sorry, I tried to post data for comparison from an Excel spreadsheet and it didn't post properly. I'll be happy to provide the data some other way.)

Slightly OT: Living in the upper Midwest, I made my last post after 11:00 CST. For this 70-year-old, that is well past my normal bedtime. That’s why I made my comment about it being “too late at night....” and added the Danny Glover quote. Sorry if you mis-interpreted it.