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Old Dec 26th 2013, 06:42 AM   #11
Pmb
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Originally Posted by dcebb2001 View Post
Thanks. I'm a novice as well so I will have to see if anyone else has any idea.
I didn't say I was a novice. In fact I used to be a computational physicist. I said that I haven't done this for so long that I'm so rusty that it would take me a while to refresh my knowledge of this. However I'd rather let somoene handle this who has it fresh on their mind. I haven't done this kind of thing in over 20 years.

There's something I don't get here - I already told you how to find the answer to your question. I.e. take that table you posted and calculate the velocity and acceleration approximations as I showed you how to. The result is function of acceleration and speed as a function of time. From that table find the largest values of the acceleration and that's your answer. Anything else will simply be a different approximation. It won't give you what you might be thinking of as the "correct" and precise/correct answer.
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Old Dec 26th 2013, 09:39 AM   #12
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Originally Posted by dcebb2001 View Post
For example, a rational function formula time vs. distance for Sprinter A is f(x)=(-0.75637765+7.67424367*x)/(1-0.03552688*x+0.00166922*x^2). The R-Squared value is 0.999, which is pretty good. So now I need to know how I can determine the maximum velocity reached during Sprinter A's run and the rate at which Sprinter A accelerated to reach his top velocity. How can I get those numbers, compare it to sprinter B, and then determine values from 1-99 for both the maximum velocity and acceleration ratings?
If you have a formula like this for distance as a function of time (I assume here that your variable 'x' is time, and f(x) is distance), then velocity is simply the first derivative of the distance function with respect to time and acceleration is the second derivative. This gives you a good approximation of velocity and acceleration as function of time. The max velocity occurs either when acceleration = 0, or if acceleration doesn't equal zero at any point then either at the beginning or end of the run. If you find several values of time where acceleration = 0 then the next step is to take the derivative of the acceleration function and see if that value is negative at the point where acceleration = 0; if it's negative then you have a local max for velocity. As for how to create a rating system - that's a subjective question, as you first need te determine the relative "worth" of top speed versus top acceleration versus best overball time. One way to do it is to divide the slower runner's top velocity and divide by the faster runner's, and exprss it as a percentage.

Last edited by ChipB; Dec 26th 2013 at 09:43 AM.
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Old Dec 26th 2013, 01:21 PM   #13
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Finite Differences

Put these numbers into an excel spreadsheet,
then apply the equations supplied by Pmb:
This gives you the average speed and average acceleration over each 5 meter stretch of the track.

There are various techniques you could use to derive estimates of the instantaneous speeds,
however, these would all require the addition of some assumptions
(for example the acceleration is constant in each 5 meter stretch, or the rate of change of acceleration is linear in each 5 meter stretch, or...)
and I don't think that this would actually tell you much more.
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Old Dec 26th 2013, 02:14 PM   #14
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Originally Posted by Pmb View Post
I didn't say I was a novice. In fact I used to be a computational physicist. I said that I haven't done this for so long that I'm so rusty that it would take me a while to refresh my knowledge of this. However I'd rather let somoene handle this who has it fresh on their mind. I haven't done this kind of thing in over 20 years.

There's something I don't get here - I already told you how to find the answer to your question. I.e. take that table you posted and calculate the velocity and acceleration approximations as I showed you how to. The result is function of acceleration and speed as a function of time. From that table find the largest values of the acceleration and that's your answer. Anything else will simply be a different approximation. It won't give you what you might be thinking of as the "correct" and precise/correct answer.
First and foremost I was not calling you a novice. I was simply stating that I am also a novice in addition to a person with a kinematics problem.

I already know how to take the average velocities and accelerations for each segment. What I really want to do is find the best way to plot a nice smooth line (like a cubic spline or rational function) that best estimates the velocity and acceleration for each sprinter at any given point in time. I suppose I can take the segements and plot those as well and do a spline/rational for each of those too.
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Old Dec 26th 2013, 02:18 PM   #15
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Originally Posted by ChipB View Post
If you have a formula like this for distance as a function of time (I assume here that your variable 'x' is time, and f(x) is distance), then velocity is simply the first derivative of the distance function with respect to time and acceleration is the second derivative. This gives you a good approximation of velocity and acceleration as function of time. The max velocity occurs either when acceleration = 0, or if acceleration doesn't equal zero at any point then either at the beginning or end of the run. If you find several values of time where acceleration = 0 then the next step is to take the derivative of the acceleration function and see if that value is negative at the point where acceleration = 0; if it's negative then you have a local max for velocity. As for how to create a rating system - that's a subjective question, as you first need te determine the relative "worth" of top speed versus top acceleration versus best overball time. One way to do it is to divide the slower runner's top velocity and divide by the faster runner's, and exprss it as a percentage.

I see. I think the graph program I mentioned has a derivitive function built in. I tried it out and it is actually pretty darn close to what I estimated using the 5-yard segments. However, when I then took the derivitive of the velocity v. time equation, I got a peak acceleration of only 0.5 yards per second-squared. Not sure if I did it correctly or not.

You may remember, Chip, that you also helped me with a similar problem a while back regarding sprinters over the course of 40 yards with only 4 data points. Your help, once again, is much appreciated.
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Old Dec 31st 2013, 07:31 PM   #16
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Originally Posted by dcebb2001 View Post
First and foremost I was not calling you a novice. I was simply stating that I am also a novice in addition to a person with a kinematics problem.
Thanks. I understand. It wasn't a biggy anway but thanks for making that clear.
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