Postby Bill Jurens » Sun Mar 27, 2005 1:28 am
Well, please keep me posted on your results.
It's easy to bury your head so far in theory that you forget that the theory -- at least theoretically -- should lead to practical solutions as well. I suspect that you have somewhat over-emphasised Dr. C's concern regarding yaw effects, or that he is speaking in the context of very long projectiles fired in high crosswind conditions rather than the rather mundane computation of 'stone-age' early Twentieth Century armor-piercing bullets fired from what would now be considered rather low velocity guns at low angles of departure. But that, admittedly, represents mere speculation on my part.
I notice that the material you sent was, at least in part, adapted from McCoy's text, which is used as one of the basic textbooks in the program.
So it might be fair to take two specific quotations right from McCoy's text...
"Modern numerical integration of the 6-DOF differential equations of motion gives the most accurate solution possible, for the trajectory and flight dynamic behaviour of a trotationally symmetric, spinning or non-spinning projectile, PROVIDED THAT ALL THE AERODYNAMIC FORCES AND MOMENTS, AND THE INITIAL CONDITIONS, ARE KNOWN TO A HIGH DEGREE OF ACCURACY. Scientists and engineers who routinely use 6-DOF methods are often heard to say, "GIGO" (Garbage In-Garbage Out!). No computed trajectory or flight dynamic analysis can be any better than the quality of its input data." (Emphasis mine)
This is an almost perfect restatement of the point(s) I was trying to make in my previous post. I've done 6-DOF with old range tables. It's GIGO!
Also:
"It was noted in the first chapter of this book that 6-DOF trajectories are not required for routine work in exterior ballistics. If the total angle of attack is small everywhere along a projectile's flight path, a point-mass trajectory is often sufficiently accurate for all practical purposes."
Couldn't have said it better...
You will find that in practical purposes the yaw for virtually all of these big projectiles was very small throughout the normal flight path, and further that the effects of small angles of yaw on the drag of the projectile are typically quite minimal -- and what's more important -- quite easily predictable. In point of fact, for many of these old range-tables, etc., it's impossible NOT to automatically include the effects of yaw in the trajectory computations, simply because the ballistic test firings on which the original drag functions were based measured actual bullet motion and thus automatically included the effects of flight yaw in the observations. To get the more modern "zero yaw drag coefficient" one has to actually SUBTRACT the effects of yaw from range firing results, and -- somewhat ironically -- add it back in again when running actual trajectories because actual bullets almost never run with exactly zero yaw. (Close though, often...)
The effects of small angles of yaw on armor penetration have been understood for a long time now; at least eighty years. The conditions at the proving ground, which involved firing at odd velocities over short ranges had to be watched carefully to ensure that the projectile was not still experiencing some initial nutation/precession effects when it struck the plate. For this reason, yaw cards were routinely placed in front of the plate to ensure the yaw was within reasonable bounds just before impact. As a rule, the effects of residual yaws under about 3-5 degrees was considered entirely inconsequential, i.e. the differences due to yaw in such situations could not be separated from the effects of random variations in the plate, projectile, and striking velocity. If one wanted to be incredibly picky, a simple linear-extrapolation formula was used to 'adjust' the measured penetration to the effective penetration that would have occurred if the yaw were zero, which was never the case anyway in real life when shells were fired long distances downrange in battle. It was relatively rarely used, and I can, offhand, recall no instances where the correction involved a difference of more than three or four feet per second. Actually about the only time this was done was when a plate or projectile was just on the line between acceptance and rejection, and the addition of that additional few feet per second would bring the whole plate series into the acceptance level.
So far as I know, high-yaw impacts (i.e involving yaw angles exceeding 10 or so degrees) of large projectiles was never studied anywhere by anybody. It was simply too difficult to get the big projectiles to yaw significantly without damaging them before they hit the plate. These projectiles are BIG, and it's not easy to deflect them without breaking something.
Hope this helps. Again, please do keep me informed of your progress. Your attempt to clear the the rain forest of ballistics armed with a computational chain saw may reveal more (or may reveal more faster) than I could with my crude mathematical machete(s) , but I doubt it, as this particular piece of land has been cleared many times before and the map -- for better or for worse -- has already been drawn. At this stage, your chances of finding anything new or significant 'under the bushes' are small...
Good luck!
Bill Jurens