Height Score

Crtomir
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Re: Height Score

Post by Crtomir »

There are three ways to get a higher score:

1. Lower Height
2. Slower Run (up to target time)
3. More Gap distance

These three are opposed to each other.

You need more height for time or for more gap distance, but you need faster speed for more gaps and slower speed for longer time.

So you need to optimize and prioritize among these three trade-offs. However, when you consider the points available for each, it becomes clear that gaps are the ONLY way to go. You just basically have to make the device that achieves the largest total gap distance. That's it. No reason to try to hit the target time or try to reduce your height. 5 points per cm of gap distance is pretty hard to beat.

Then, once you have realized this, you need to figure out how to avoid losing as much energy as possible when translating gravitational potential energy into kinetic energy (speed) of the ball for the jump(s). It seems both what material the track is made of and the shape of the "ski jump" (down slope with a curve at the bottom and a short upward slope at the end to launch the ball at 45 degrees = max projectile range) matter a lot in determining jump efficiency. I define jump efficiency at horizontal range of jump divided by vertical height the ball rolls down the "ski jump" track. The horizontal range is measured at the height of the point the ball leaves the track and the vertical drop distance is measured from the height where the ball starts to roll down the "ski jump" track and the height of the point the ball leaves the track for the jump.

Our students did some experiments with several "ski jump" track shapes and found that the maximum jump efficiency they could get was about 0.95. The maximum theoretical jump efficiency is 2. So about half the potential energy is getting lost somehow.

I am curious, without revealing your designs or track materials and shape, for teams that are getting those really big jumps with lots of gap distance (you know, near 400 points as people are claiming in this forum) - what jump efficiencies are you getting? Is anyone able to get above 1.0? Has anyone done experiments like this?

If you could get a jump efficiency of 1.5, then you could, in theory, get two 60cm jumps with an 80cm vertical distance.

However, with only a jump efficiency of 1.0, then you can, in theory, only get one 60cm jump and one 20cm jump with an 80cm vertical distance.

But you are not going to get that because you have to use up vertical space for other parts of the track.

The only other way I can see of increasing jump distance is to use loops, but the thing is there is a maximum potential energy you can start with, governed by the maximum height of the Roller Coaster = 80cm. And the mass factors out when calculating projectile range, so the only thing that you have to work with is starting height which cannot be more than 80 cm. Everything you do to the ball causes it to lose energy and reduces the amount of horizontal jump distance you can achieve. So everything comes down to your jump efficiency, as I have defined it above. They might have well have called this event Ball Jump instead of Roller Coaster.
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Re: Height Score

Post by knightmoves »

Crtomir wrote:I define jump efficiency at horizontal range of jump divided by vertical height the ball rolls down the "ski jump" track. The horizontal range is measured at the height of the point the ball leaves the track and the vertical drop distance is measured from the height where the ball starts to roll down the "ski jump" track and the height of the point the ball leaves the track for the jump.

Our students did some experiments with several "ski jump" track shapes and found that the maximum jump efficiency they could get was about 0.95. The maximum theoretical jump efficiency is 2. So about half the potential energy is getting lost somehow.
The maximum theoretical jump efficiency is not 2. The ball is rolling, so some of your potential energy goes in to spinning the ball, and you don't get that back in jump height. For a sphere that rolls without slipping, mgh = 0.7 m v^2, so v = sqrt(1.42 g h).
For a 45 degree launch, vertical component of velocity = v/sqrt(2) = sqrt(0.71 g h). Time to reach peak = v/g = sqrt (0.71 h/g)

So horizontal distance for jump = 2*sqrt(0.71 h/g) * sqrt (0.71 g h) = 2*0.71*h

So max theoretical jump efficiency is 1.42.
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IvanGe
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Re: Height Score

Post by IvanGe »

wellOKthen wrote:Do you guys think that it's more important to worry about the Gaps of the height?
Gaps of the height? I'm assuming your talking about gaps or height. Height is definitely less important than gaps.
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RyanMist
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Re: Height Score

Post by RyanMist »

IvanGe wrote:
wellOKthen wrote:Do you guys think that it's more important to worry about the Gaps of the height?
Gaps of the height? I'm assuming your talking about gaps or height. Height is definitely less important than gaps.
I agree. I had 79cm of height but 60 cm of gaps and got 4th at states. Without gaps you could never medal
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Re: Height Score

Post by hippo9 »

Yeah as previously stated, this year's rules mean the higher the coaster in general, the better it will do because it has more potential energy to complete gaps.
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