Re: Gravity Vehicle C
Posted: February 7th, 2013, 4:42 am
True that a lower start height means slower time, but it's really important to look at/understand the math in the scoring. What it tells you is...dramatic.
Bottom line -180cm is WAY more than you want
Height score is 400 x h/300-h. Time score is 25 pts/sec.
So, for a 180cm h, height score is 600 points.
Go to a 1m (100cm) h, and points go to 200. That's a 400 point difference. 25 goes into 400 16 times. That means it could take 16 seconds longer and you'd still end up with the same height + time score. That's a LOT of time.......
Go to 50cm height, H score goes to 80 points. That's a 520 point difference; almost 21 seconds to get equal h + t score.
The rate at which time score increases w/ h reduction is much lower. Velocity off the ramp is a function of the square root of the difference in h. At 1/2 the height, v(initial) will be about 70% (1/1.414 (sqrt of 2)). Time difference will depend on the.....friction appetite of the vehicle; the rate at which friction losses eat into momentum.
The initial #s above really tell the story most clearly, though- how much slower you can go at a given h reduction and end up with the same h + t score. You obviously need enough h for the vehicle to be able to go 10m. You don't need or want very much more than that. So, optimizing h is pretty simple. Get to the h that gets you 10m. Check out a little more (h score + t score). The way the scoring works REALLY favors a low friction setup- big-time - the ability to go 10m with as little h as possible.
Bottom line -180cm is WAY more than you want
Height score is 400 x h/300-h. Time score is 25 pts/sec.
So, for a 180cm h, height score is 600 points.
Go to a 1m (100cm) h, and points go to 200. That's a 400 point difference. 25 goes into 400 16 times. That means it could take 16 seconds longer and you'd still end up with the same height + time score. That's a LOT of time.......
Go to 50cm height, H score goes to 80 points. That's a 520 point difference; almost 21 seconds to get equal h + t score.
The rate at which time score increases w/ h reduction is much lower. Velocity off the ramp is a function of the square root of the difference in h. At 1/2 the height, v(initial) will be about 70% (1/1.414 (sqrt of 2)). Time difference will depend on the.....friction appetite of the vehicle; the rate at which friction losses eat into momentum.
The initial #s above really tell the story most clearly, though- how much slower you can go at a given h reduction and end up with the same h + t score. You obviously need enough h for the vehicle to be able to go 10m. You don't need or want very much more than that. So, optimizing h is pretty simple. Get to the h that gets you 10m. Check out a little more (h score + t score). The way the scoring works REALLY favors a low friction setup- big-time - the ability to go 10m with as little h as possible.