My Math Forum Ball dynamics -- lift, drag

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 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 no-resistance result, you're going to get a time-dependent 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. Thanks from Loren
 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
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Quote:
 Originally Posted by Loren Could just a little friction with considerable lift allow the ball to travel at least the original maximum distance?

August 11th, 2017, 01:29 AM   #5
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 Originally Posted by Loren Could just a little friction with considerable lift allow the ball to travel at least the original maximum distance?
The direction of the drag is always against the motion, so no, you're always going to impede the projectile.

Studiot's post is interesting, but I don't know if a projectile experiencing bottom-spin 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
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 Originally Posted by Benit13 The direction of the drag is always against the motion, so no, you're always going to impede the projectile. Studiot's post is interesting, but I don't know if a projectile experiencing bottom-spin in a medium would travel further than a projectile with no spin in a vacuum. The result would be interesting
Table Tennis is the ultimate sport to demonstrate this.

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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