Physics and Baseball, relating the two

[CSOleson]

Hey everyone. I've asked a few questions before here, but now I have one not related to my homework or career possibilities. It may be a little difficult.

I am a baseball player and I know classical mechanics and kinematics. However, this question is beyond that. I am trying to find a way to calculate the velocity of a throw when performing long toss. Long toss is a controversial topic in baseball where some try to throw the ball as far as possible to help increase arm efficiency, intent, etc. which overall is theorized to help with velocity. The reason I don't believe that kinematics will properly answer this is that we don't account for air drag, and there are too many unknowns. I don't know the time that it takes to travel the said given distance, I merely assume the angle (45 degrees) and know the distance (calculated by throwing across a football field).

So, knowing simply the distance, the angle, and the acceleration due to gravity and assuming no wind but also accounting for air drag, is it at all possible to figure out the velocity of a thrown baseball? Please let me know!

Also, considering air drag, would 45 degrees actually be the best angle for maximum distance? This would be less horizontal velocity and allow more time for the ball to be subjected to air drag. On top of everything, forgive my inability to do this on my own. I don't remember how to consider air drag into any equation...

EDIT: I forgot, how about elevation in this? I'm sorry, this may be too complicated...

 

[mfb]

So, knowing simply the distance, the angle, and the acceleration due to gravity and assuming no wind but also accounting for air drag, is it at all possible to figure out the velocity of a thrown baseball? Please let me know!

With some approximations or a simulation, sure. The rotation of the ball could be relevant, too.

Also, considering air drag, would 45 degrees actually be the best angle for maximum distance?

The best angle is a bit below that, due to air drag and the non-zero initial height. In addition, the reachable velocity could depend on the angle.

 

[marcusl]

Adair wrote a book called Physics of Baseball that deals with drag, spin and other effects that he uses (if I remember properly) to analyze the distances of hit balls. The same could be applied to throws.

 

[Rap]

I agree with MFB. In my experience, spin is an important effect, throwing the ball with a lot of top spin (I think that's the right term), where the top of the ball is spinning towards you will give you a significantly longer throw. Good pitchers can actually make the ball rise and then drop. To figure this out, along with air drag might not be an overwhelming problem if you make some simplifications, but it won't be as easy as simple force, velocity and gravity with a point particle.