August 10th, 2017, 01:20 AM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 374 Thanks: 26 Math Focus: Number theory  Ball dynamics  lift, drag
The maximum distance traveled by a ball (without lift, drag or spin) is when it projects 45 degrees from a flat surface. What function of lift vs. drag (with the 45 degree angle of projection) would show the ball to travel that same distance? 
August 10th, 2017, 02:28 AM  #2 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,127 Thanks: 716 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
You'll never be able to get the same distance travelled by introducing air resistance unless you add some other force (e.g. by making the projectile a rocket). If you want to determine what that force should be be in order to get the situation back to the noresistance result, you're going to get a timedependent force that will depend on your air resistance prescription you choose. Since air resistance problems are very difficult to solve analytically, you'll probably have to resort to numerical solutions. 
August 10th, 2017, 09:23 AM  #3 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 374 Thanks: 26 Math Focus: Number theory 
Could just a little friction with considerable lift allow the ball to travel at least the original maximum distance?

August 10th, 2017, 03:07 PM  #4  
Senior Member Joined: Jun 2015 From: England Posts: 853 Thanks: 258  Quote:
https://www.google.co.uk/search?hl=e...26.0soT4Owl0AA  
August 11th, 2017, 01:29 AM  #5  
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,127 Thanks: 716 Math Focus: Physics, mathematical modelling, numerical and computational solutions  Quote:
Studiot's post is interesting, but I don't know if a projectile experiencing bottomspin in a medium would travel further than a projectile with no spin in a vacuum. The result would be interesting  
August 11th, 2017, 03:51 AM  #6  
Senior Member Joined: Jun 2015 From: England Posts: 853 Thanks: 258  Quote:
Compared to a no spin ball, Topspin lowers the vertex of the trajectory but lengthens its length. Backspin raises the vertex of the trajectory but shortens its length.  

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ball, drag, dynamics, lift 
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