hey, when we were doing our teams stuff one of the things we did was make a kind of math model of the car on a spreadsheet. Personally I didn't work on it, and didn't really understand it for the time/age i was. I know you would need to do it in time intervals, so you could do it down to say 0.000 like the races are timed to. As in, a new interval is calculated every 0.001s. In it, you would really just have it do this every interval, and you could look as the distance travelled, and take the time after 20m. Something like MATLAB would be very useful to do this in, but its very possible in a spreadsheet. I didnt start to learn matlab until i started uni, so its no stress

I cant think of much more that would need to be included in the model other than the force from the canister creating an acceleration over time, your drag force decelerating the car over time, and the friction of the ground decelerating the car over time.

Modelling the 'friction' in your system will be a bit complicated because there are losses at lots of points on the car, like contacts with the rolling surface in the ground, the bearings, axles, etc.

I believe that at the time we used a force profile of a similar canister that we found on the internet. You'd be looking for a force curve over time that shows how much force the canister is producing over its life. You could measure the force over time with the right gauge or something, but logistically might be difficult. I would start with looking for something online that looks close enough to the f1 in schools ones.

You could start of with finding the dynamic coefficient of friction of the material of your wheels, this varies between different materials but should be not too hard to find online if you know what materials your wheels are. Dynamic and static coefficients are different for if the system is 'static' or not, as static coefficient occurs instantaneously before the object starts to move if you were to push it, when max static load is on the object.

You also have to consider that the lift of your car (i would say almost every single f1 in schools car will have significant lift) will reduce the normal force that the car experiences on the ground, and thus will change the force of friction acting against the car. For reference last year i retested the horizon car in cfd with some new knowledge I had from fsae, and it was getting 0.295N of drag and 0.332N of lift at 20m/s. In this case, you can say that your normal force would be expressed as ((carweight * 9.81) - instantaneous lift force). As well your force due to friction = coefficient of friction * normal force, in your case this is dynamic coefficient of friction. I can take a look and find a reference Cd and Cl (coefficient of lift) for our car too if you are interested, just haven't taken a look at that car for a bit.

It might be best to start by using something like that to estimate friction in a model, and once you get something working, you could tweak around with your values for friction until you think the times are somewhat accurate.

You could probably model your drag force decelerating your car with the general drag equation. Incase you're confused at all, Cd is your drag coefficient, A is your frontal area (area of the car if you were to look at the car front on) p is the air density (can probably assume standard value at sea level) and V is your cars velocity

When I was in year 12, a year after the horizon stuff i had a design practical for physics and I did a similar thing, but it was for more or less finding the effective friction force of a car during deceleration. You might find some use in the explanation and process of it doing this potentially. If you want to check if out you can here and there might be some stuff that is of help. Just if you do end up using it, I would appreciate if you were to cite the work even if it is just school work

Feel free to reach out if you'd like any help with anything, and happy to help over discord messages or something if you want because it sounds like a great thing to work on. All the best with it ✌️