Position, Velocity and Acceleration of a Dragster -- Help please with the math

[Dynamo Hum]

How did you find PF?: Google Search

I have been working on an Excel Program for the better part of 3 years that will take the input from a Time Slip that you get at your local Drag Strip and will extract all the performance information about your car that you would ever want to know. But the calculus I learned in undergrad and grad school does not do a very good job of calculating the non- constant Acceleration the car undergoes over the 1320 feet it travels. I cannot understand why.

 

[berkeman]

Welcome to PF.

Can you post some examples of the time slips and your spreadsheet? Use the "Attach files" link below the Edit window to upload images, and please don't upload the Excel file itself since it can contain macros. Just convert it to a PDF or take a screenshot before uploading it.

Also, how many datapoints does a typical drag strip printout contain? It seems like it would need to contain at least 10 markers to be useful for your calculations.

Do you have access to a car's telemetry to compare to the printouts? The telemetry would give you complete data like you are looking for.

@Ranger Mike @jack action

 

[Dynamo Hum]

Welcome to PF.

Can you post some examples of the time slips and your spreadsheet? Use the "Attach files" link below the Edit window to upload images, and please don't upload the Excel file itself since it can contain macros. Just convert it to a PDF or take a screenshot before uploading it.

Also, how many datapoints does a typical drag strip printout contain? It seems like it would need to contain at least 10 markers to be useful for your calculations.

Do you have access to a car's telemetry to compare to the printouts? The telemetry would give you complete data like you are looking for.

@Ranger Mike @jack action

Thanx for the quick reply.

I am doing something that has never been done before in the Drag Racing Community. Taking a simple Time Slip you get at the end of the track and input time vs position data provided and my program will extract all the car performance you could ever desire. HP and speed and time elapsed at any location on the track.

Here is a typical Time Slip from this past January 27 where I placed 2nd in my class at the 2024 Cadillac Attack in Orlando, Florida

The calculus I learned in undergrad and grad school has failed to correctly provide the non-constant acceleration my car undergoes over the 1320 ft.

Why?

This problem would seem to be the one application where Calculus would provide an exact solution of non-constant acceleration.

It does not.

Elapsed Time (s) Position (ft) Speed (mph)
0 0
1.714 60
4.560 330
6.889 660 104.57
8.893 1000
10.576 1320 133.80

IMPORTANT NOTE: The speeds listed are "trap speeds" ie. AVERAGE speeds.

The 104.57 is measured (trapped) between 594 and 660 ft

The 133.80 is measured (trapped) between 1294 and 1320 ft.

I need the terminal speeds and exact accelerations at any position along the 1320 ft track to calculate HP

 

[berkeman]

Taking a simple Time Slip you get at the end of the track and input time vs position data provided and my program will extract all the car performance you could ever desire. HP and speed and time elapsed at any location on the track.

Of course not. You cannot undersample the data and guess/recreate the full dataset.

I need the terminal speeds and exact accelerations at any position along the 1320 ft track to calculate HP

Um, this ^^^

 

[Dynamo Hum]

Why not...............there is plenty of data on the slip.

I have a program that will do just what I want except there are cases where the acceleration calculated will start to increase at the end of the track when it should not and I have not been able to find the weak link in my math.

It you take the times and positions I gave you and plot them in excel as a 4rth degree polynomial function it will give you a perfect time vs position plot with an R^2 = 1

Take the first derivative of that position vs time function and it will give you a perfect (nearly) plot of the speeds at any position on the track.

Take the second derivative of that position - time function and it will provide a good approximation of the non-constant acceleration but as you get near the 1000' position the acceleration begins to increase when it should not....or at least I don't think it should.

 

[berkeman]

Sorry, this is nonsense. We enforce a very high signal-to-noise ratio here at PF.

If Mike or Jack ask me via PM to reopen the thread, I'll likely do that. As for now, this thread is closed.

 

[berkeman]

Reopening the thread provisionally...

 

[jack action]

but as you get near the 1000' position the acceleration begins to increase when it should not....or at least I don't think it should.

That is expected as you used a 4th-degree polynomial function. At one point the function will either go up or down indefinitely. This approach can only be valid over a certain data range since we know the vehicle will at one point reach a terminal velocity, thus no more acceleration.

it will give you a perfect time vs position plot with an R^2 = 1

This will be true anytime you have only 5 points in your data set. It means you cannot do better with a 4th-degree polynomial, but it might be done a lot better with another function.

You might be better off doing it backward: you know the expected forces acting on the vehicle, and all you have to do is adjust the parameters of those forces to fit your data set. You might find more than one way to define the data set, but you will get a good idea, especially if you already know the type of vehicle used.

That is how I did it with my simulator. All the theory is explained as well.

HP and speed and time elapsed at any location on the track.

You should find out that HP is pretty much constant throughout the track.

 

[Dynamo Hum]

Of course not. You cannot undersample the data and guess/recreate the full dataset.


Um, this ^^^

I wish I had a penny for every physicist who has suggested I am over- fitting or over parametrizing and to chose a 3rd degree polynomial to plot the Time - Position data. but if I do that the second derivative of this function will leave me with a linear acceleration function that implies the acceleration is constant..... which it is not.

That is expected as you used a 4th-degree polynomial function. At one point the function will either go up or down indefinitely. This approach can only be valid over a certain data range since we know the vehicle will at one point reach a terminal velocity, thus no more acceleration.


This will be true anytime you have only 5 points in your data set. It means you cannot do better with a 4th-degree polynomial, but it might be done a lot better with another function.

You might be better off doing it backward: you know the expected forces acting on the vehicle, and all you have to do is adjust the parameters of those forces to fit your data set. You might find more than one way to define the data set, but you will get a good idea, especially if you already know the type of vehicle used.

That is how I did it with my simulator. All the theory is explained as well.


You should find out that HP is pretty much constant throughout the track.

Thanx so much for your help. I can better understand where I am and the limitations of my approach. I have tried using a Power function to describe my data set w/ some success.

 

[jack action]

I have tried using a Power function to describe my data set w/ some success.

If you look at the physics, the function for acceleration $a$ will be at the beginning:
$$a = C_1 - C_2 v^2$$
where $C_1$ and $C_2$ are constants. But since the velocity $v$ will be small at that point, it may just be approximated as a constant:
$$a = C_1$$
This is when the maximum wheel torque depends solely on the friction between the tire and the pavement.

Then the maximum wheel horsepower is not enough to provide the maximum friction force at higher speeds and the acceleration $a$ becomes:
$$a = \frac{C_3}{v} - C_4 - C_2 v^2$$
Bot equations for the acceleration can be modeled as a function of $v$.

This is what it will look like (the black line is the initial quasi-constant acceleration and the red line is the constant wheel power acceleration):

 

[Ranger Mike]

just saw this post, Good job Jack, as usual!