How can I make the fastest lap possible?

[DaddyTy]

Through a driving simulator I want to establish the fastest lap possible.

Here are the known variables,
Displacement=5866cc
Max. Power=892HP/9000rpm
Max. Torque=567ft-lb/7000rpm
Weight=1565kg (55% of the weight is in the front of the vehicle, leaving %45 to the rear)
Redline=9500rpm
RPM from TQ-HP=8190.2rpm
Tire Circumference=87.92in
Tire Diameter=28in

The track used is Daytona International Speedway(2.5miles in length).

The transmission adjustments I can make are to gears 1st-4th, and the Final Gear. So mostly I am looking to how I can optimally move this weight with this power and what gear ratios I would need to do that the best and being the fastest entering TURN 3 and crossing the flagstand. I can also make adjustments to the suspension. Ride Height, Spring Rate, Dampers(Extension/Compression), and Sway Bars, as well as Camber and Toe settings to hold the speed in the turns.

I would greatly appreciate any help, and maybe someone can make an equation that uses these variables so I could figure this out on my own for other vehicles available through the simulator.

I've seen guys reach speeds of 225mph entering TURN 3, and turning fast laps. My goal is to be superior to this statistic.

 

[Baluncore]

I don't believe this is an equation problem so much as a search. If you define the track by it's two edges then you can optimise a driving line within those bounds. It should be possible to minimise lap time by making slight changes in the steering radius, acceleration and braking for each segment of the track. Score would be laptime plus a heavy penalty for crossing the track edges.

Track banking could be specified as a difference in hight between the two track edges. If the track is defined as left and right coordinates, L(x,y,z) and R(x,y,z), offset from the centre for every metre along the track, then the length of each segment, the banking and the rise and fall in the track can be interpolated. It then becomes a Newtonian physics question.

 

[AlephZero]

I agree this is basically a "search" type of optimization problem, but you can break it down into subproblems which are more manageable.

For example, if you don't change any of the car parameters, you will get the fastest entry to turn 3 by having the fastest exist from turn 2. So figure out how fast you need to exit turn 2 to meet your target speed for turn 3. You may be able to reduce the turn 2 exit speed by tweaking the gear ratios.

Then figure out how to get around turn 2 with that exit speed - probably by tweaking the suspension. Then work back to turn 1 ...

Most likely this attempt will fail for some reason before you have worked back to the start line. But you will have learned something along the way, so you can decide what to change for your next attempt.

 

[DaddyTy]

The longest straightaway at Daytona is .57 of a mile. Average speed off of TURN 2 is 205mph. Would this be better if it was in the upper part of the powerband of GEAR 3 or the lower part of GEAR 4? I guess I am more so trying to breakdown how to best move 1565kg using 572ft-lb/7000rpm & 892HP/9000rpm(powerband=7000rpm-9000rpm[possibly to the redline of 9500rpm]). The final gear can be anywhere between 2.500-5.000, as well as the other gears can be near whatever of a specific choice. I believe it's safe to assume that the higher the final gear, the more magnified the Torque.

 

[Baluncore]

In effect you are writing code to drive on a simulator. You do not need a real-world physics model of the track, you need a model of their simulator. If your model differs from their simulated model then you will be searching for a false solution in the wrong universe.

That requires you know the fundamental equations used by the simulator writer. You must then replicate those equations, in effect you write your own version of their simulator kernel. You must then write code that can learn to drive.

So this problem is more complex than searching equation solutions. You must identify their model and then write a track simulator kernel to match it, then a learning to drive perfectly program, followed by a vehicle parameter optimisation program.

If you think this is going to be simple, think again because you don't understand the problem. Your solution will need to make some assumptions and take some short cuts to get close to a solution. It is picking correctly what code to economise that will decide if this can be done and how close to perfection your optimum solution will be.

 

[DaddyTy]

Subtract the fact that it's on a simulator. Assuming their design is reality, how do I find the best gear ratios to move that weight optimally with the given assets?

 

[Baluncore]

You will need a torque to RPM curve for your engine and the aerodynamic characteristics of the car.
Convert the torque curve to power through the gearbox to the back wheel, (power = torque * RPM ), and find the optimum speeds to change gear for each change. Engine braking is a complexity.

 

[Kozy]

As Baluncore says, you need to look at the thrust curve for your powertrain, and modify the gearing so that it places the highest drive thrust (wheel torque) exactly where you need it for corner exits, and to minimize the need for unnecessary gear changes.

It only offers basic torque curve manipulation, but this link might be of use. It's aimed at far less powerful cars though, so the parameters will need a lot of tweaking.

http://blackartdynamics.com/Transmission/ThrustIndexMX5.php

ETA: The maximum speed on the chart is only 175mph, so probably a bit slow for your needs. If it would be useful, I could make a specific page tailored to your parameters.

 

[HowlerMonkey]

Aero