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Old Mar 4th 2019, 12:16 PM   #1
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Ball Rolling up then down curved ramp

Good morning everyone,

I need help with solving a problem that is way over my head. I am trying to design and 3D print myself a tool that I can use to practice putting in golf.

What I need help solving is that I want to hit a golf ball up a small curved ramp so that, after it reverses direction, the ball travels the same distance back towards me as it would have continued to roll forward had the ramp not been there.

In other words: A ball is struck in a straight line at X speed on flat ground towards a target and travels Y distance past the target. Now, if I hit the same ball again at the same speed up a curved ramp placed at the location of the previous target, how would I be able to figure out the curve needed to be able to send the ball same Y distance back along its original path (ie. towards me the striker)?

Ideally I would like this ramps final height no more than about 200mm from the ground so there will obviously be a limit to how hard you can strike the ball before it goes flying off the back of the ramp. However, the return travel of the ball (Y) should never really have to go over 1200mm or you would have hit it way to hard in a game anyways.


This may be a simple solve but I have nearly no background in math and I can't seem to refine my googling enough to be able to get me the answers I need.
Thanks for your help!
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Old Mar 4th 2019, 02:31 PM   #2
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This is really quite simple - if we ignore rolling friction between the ball and the ramp, it really doesn't matter what the shape of the ramp is - it will roll up the ramp starting with a certain initial velocity, come to a stop, then roll back down towards you and exit the ramp at the same speed it started with. Hence it should roll the same distance back towards you as it would have rolled forward from the beginning of the ramp if the ramp hadn't been there. Having said that - to minimize losses due to rolling friction you want the shape of the curve to be fairly gradual, so use a fairly large radius of curvature. Also you will need to decide what the max initial velocity of the ball will be, as that will guide how tall the ramp has to be. I can go into the detail of that if you like, but a reasonable approximation of how high the ramp must be is:

h = v_i^2/(2g)

where v_i is the initial velocity of the golf ball as it enters the ramp and g is acceleration due to gravity (9.8 m/s^2). This is a approximate - it ignores the effect of rotational kinetic energy, so in fact the ball will roll a bit higher than that. I can provide more detail if you like.
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Old Mar 4th 2019, 02:35 PM   #3
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Fantastic! That is an even easier answer than I expected! Thank you for the reply.
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Old Mar 4th 2019, 02:54 PM   #4
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My pleasure! I’d love to see what you end up with - I’m a golfer myself, and am always interested in ways to improve my game.
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Old Mar 4th 2019, 06:40 PM   #5
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Originally Posted by bbeaucha88 View Post
What I need help solving is that I want to hit a golf ball up a small curved ramp so that, after it reverses direction, the ball travels the same distance back towards me as it would have continued to roll forward had the ramp not been there.
Well the problem is friction and air resistance slowing the ball ....

It will never return to the distance it would have continued to , it will always fall short ....

You can only know how far it will fall short by experiment ... different surfaces will slow the ball differently , a hard smooth surface must be best...
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