iloveporsches

Hoping I could get some help here. I have to write a paper and give a presentation for Calc (), and it has to be on how mathematics (calculus specifically) relates to our intended field. I was going to go check out Miliken today, but was wondering if anyone here had any good sources or info I could use. Thanks!

ColorChange

I love porsches

I know nothing about driving and have no experience so you shouldn't listen to anything I say.

But, with that disclaimer, I would suggest looking at the integral of g sum as a quick lap indication (questions remain over line and artificial g-sum creation - you might be able to add nice value here), and the derivative of g sum as a "smoothness" indicator.

Talk with Tim McCarthy down at UofI (FSAE). He might help and would be interested also.

iloveporsches

thanks, that will be perfect. I've talked with Tim a few times too, but I'll see what he says about this.

M758

Another thing could be how to calculate the right gearing for a track. Based on the HP curve and how to get the max acceration.

Remember you can pic a point on the curve for a specific hp point, but that changes as you acclerate.

Or may be use calculus to determine optimium shift points given a specifc HP curve and gear ratio's. I know a thread on shift points came up, but do do an analysis showing/proving the theory might be nice and valuable for us and not too hard for you.

Just some ideas!

SundayDriver

There is a lot of interesting stuff you can do. Realize that data is only useful if you can a) Change driver behavior to get faster and/or b) Change the car setup to be faster. The data we have for that is things like g forces, suspension position, brake pressure, throttle, steering and of course speed, rpm, etc. The most interesting data to play with is usually g's - especailly lateral g's. (Not to say the braking and throttle is not, but those are pretty direct peices of info and I don't think there is a great deal to learn by further processing that data.)

Since you have accelerations and speeds and distance, the first thing that usually happens is to generate a track map. Unless you can map the track, other data has almost no value. I think this is the primary place where you will see calculus used in race cars. Yoiu can dig deeper into that to figure out what math is happening.

Another calculation is to derive what the vehicle is doing without direct measurment. What angle is the car at vs. the carner arc? There is a bunch of math to get this.

Now for a wild chase - In theory, the first and second derivatives of g's should be interesting and valuable. These are quite important in some industries and are called jerk and snap, respectively. From what I understand, they are used in elevator design and it makes sense that in an environmnet where you are going for smoth travel, those would be very important to the passenger.

It happens that my math package is calculating these (someone else built this package to play with those values so I end up with the data for my car as well). So far it is proving to have little value, but with some further processing, it might help. The issue (and this is pretty universal with g data) is that there is a lot of noise in the data stream. But it is not bad noise, rather it is the reality of a race car - it is a violent environment and you do not actually generate smooth g's as you corner. The car is going over bumps and surface changes which change the available grip. So you have a noisy looking signal, but it is really what is happening. If you generate derivatives, they are garbage. There are just a bunch of spikes in both direction that don't tell you anything about smoothness.

So the solution would be to filter the data before processing further. The cahllenge is that if you smooth the data, all drivers are going to look smooth because you have forced that. Like I said, that might be interesting to look at, but so far what I have seen is not valuable.

Kurt R

How about how as you try to decrease lap times or increase hp the money goes quickly to infinity?

OK, but seriously. What's the optimum number of gears for a 1/4 mile? You need to keep the engine in it's power curve, but you lose time every time you shift. (Let's keep this simple with a conventional transmission). So, forgeting aero drag and rolling friction and tire slip, but knowing the hp and torque curve of your target engine, what are the optimum gear ratios, and what is the split between them?

Mike in Chi

Brandon

I remember nothing of calculus, except that it made me give up Math as a major.
So I can't help you.

However, I do want to give you props for your signature line. Very funny.

Geo

How about thinking in terms or aerodynamics or shocks? I'm sure there are applications of calc in those two areas.

Bill_C4S

Oh definitely...if you want to have some real fun..venture into Boundary Layer Theory.

http://ocw.mit.edu/NR/rdonlyres/Aero...weep_taper.pdf

iloveporsches

Haha, nice Bill. I'll just print that off and write "Car Dynamics" on the top and turn it in

I'm looking more at G-sum right now. Involves derivatives and integrals, which is pretty much the scope of a Calc II course. I talked with our FSAE team captain today and anything he could come up with, aside from G-sum involves too much differential equations to be of any use to me. I talked with Tim for a while too while we were tearing apart a Honda CBR head. Hopefully he can give me some good sources or just some insight he might have.

Mike in Chi, I just want to clarify something. Hacker-Pshor (or whatever that beer is called) said that, and I thought it was the funniest thing I've ever read on Rennlist.

adrial

I think the acceleration thing is perfect.

You'd need to find an equation for the horsepower/torque curves (plug data into graphing software and ask for curve of best fit...)...and then use integrals to calculate what gearing/shift points give you the most power laid to the ground taking into account the time it takes to shift.

G-sum I think would be very difficult to do find an equation for the curve, but maybe I'm looking at it the wrong way.

Geo

That's why I think shock data is perfect. It also has very real commercial application (shock dynos).