Rick -
Absoulutely fascinating! When I went through FAOCS at Ft Sill, we asked about the calculations of the trajectory. Their answer was that it was a bit too complicated for what we needed to know to launch bullets.
Here he goes step by step - I fit it into the picture in my mind of the bullet leaving the bore aligned with the bore and keeping that alignment (more or less) as it travels through the trajectory (howitzers). Now we see the caluclations of the forces on the bullet throughout the trajectory and how the bullet would somewhat but not completely align with the direction of motion. More math than what I want to go through for each round, but now I know how the trajectory tables were derived.
We plugged into the formulas the gun and target coordinates, altitudes, wind velocities at each 500 feet, powder temperature, charge, rotation of the earth and which way we combed our hair. All that to figure azimuth and elevation of the howitzer - fire two spotting rounds, adjust the coordinates and do it again.
Thanks for providing the answer to a question that has been lurking in my mind since 1972!