This is the point that all those questioning your data arent understanding: that the direction of force at release (vector) of ALL underhand fastpitches is slightly upward leading to an initial upward trajectory of the ball, not parallel to the groud plane as all seem to think.
The NASA calculations and my own are not so different. There might be small differences due to different assumptions about the air drag, since there can be variations in drag due to temperature, elevation, surface roughness of ball, etc. I guarantee that if air drag were eliminated, we would all get exactly the same trajectory for the gravity-only case. That is a calculation that is done by week 2 of an introductory physics course.their numbers are not close to each other. My question is why?
Agreed! And as I already said, the point is not to predict with precision but to demonstrate the qualitative effects. On the other hand, the technology now exists to obtain precise data on the trajectories of pitched baseballs or softballs in actual game situations. One such technology is the so-called Trackman radar system, which is used in many MLB stadiums and some NCAA games. It is less used in fastpitch softball, but it certainly could be used. The system provides full information on the trajectory of each pitch, including release speed, height, and angles, home plate crossing (including speed and direction), spin rate, and spin axis. In short, it pretty much provides everything you would want to know about the pitch from release to home plate.This is all interesting but it seems much more about theory than real world observations. I would be interested to find out how is the launch angle was determined. Also, in addition to spin rate how is the orientation of the ball with respect to roll, pitch, and yaw which all affect movement taken into account? It would also be interesting to understand an accounting of the affect of drag with respect to the aforementioned.
The NASA calculations and my own are not so different. There might be small differences due to different assumptions about the air drag, since there can be variations in drag due to temperature, elevation, surface roughness of ball, etc. I guarantee that if air drag were eliminated, we would all get exactly the same trajectory for the gravity-only case. That is a calculation that is done by week 2 of an introductory physics course.
However, one should not focus on the differences in these different calculations but rather their similarities. The point of these calculations is *not* to predict with precision the trajectory of the ball but rather to demonstrate the qualitative effects that occur due to backspin, topspin, etc. For example, these calculations clearly show that a rise ball really can rise, meaning it crosses the plate above the release point. Also they show that for any reasonable amount of spin, the trajectory never rises above the projection of the initial direction (the red line in my graphs). The calculations show that the height of the ball as it crosses the plate is very sensitive to the release angle of the pitch, regardless of the spin axis. The calculations also show that the ball drops more with topspin than with gravity alone. These are all useful things to know and understand, at least at the qualitative level.
So you are using a different set of variables vs what the NASA calculator is using, ok. If you will go back to Sluggers post, you are actually at odds with what he is saying. Not only are the numbers off, (1' difference at 40' is huge) but he clearly states a rise ball does not rise it just falls less. In this post you say it does in fact rise. I am not giving you a hard time here, I am just saying that the numbers presented were stated as fact but they aren't and even though you and Sluggers appear to be in agreement, you aren't. Or at least the way the information was presented it appears you aren't.
Can of worms time!