I love being able to back up my decisions with science, and I got to thinking about tire pressure today.

Just for fun, I did a little burnout the other day, and upon later inspection of my tire marks, I noticed that the marks are much darker at the outside edges of both tires -- a dead giveaway for underinflation.

Two days prior, I had just checked and adjusted my tire pressure to my usual -- 32 psi. I confirmed later that neither is leaking, and that both tires still held exactly 32 psi.

I had the opportunity to weigh my car last fall, and I know that when no significant dynamic loads are present, there are almost exactly 1500 pounds on the rear tires. That was with a quarter tank of gas, and I was full when I did the burnout, so figure an additional 8 gallons and I'm sitting somewhere not much under 1600 pounds on the rear tires.

Assuming a relatively stationary burnout, rearward weight transfer should be minimal (right?), and we should be able to do something productive with that number. Of course, if the tires hook and I accelerate, there would be weight transfer and therefore even more pressure. If anyone has figures on a typical dynamic weight distribution under acceleration or thoughts on ways to calculate or estimate such a thing, I'm all ears.

So anyway, being the nerd that I am, I started doing some math. 1600 pounds being supported by 32 psi means that my contact patch should be 50 square inches. A pair of 245mm tires gives a total contact patch width of 19.3", meaning that the length of the contact patch whould be 2.59".

I then did some basic trig and calculated a tire of diameter 25.64" must deflect 0.066" in order to accomodate a contact patch of that size. 0.066" is perhaps more usefully represented as 1.3% of the sidewall height.

Here's where I'm not sure what to do next. It's obvious that for my tires, that's too much deflection, and consequentially, I am not getting good contact. So I need to go higher. How much higher? 1.3% of the sidewall height doesn't seem like much, but it is evidently too much.

40psi would give me 0.87% deflection. I'm going to try it and see how the burnout marks look.

I've heard many people recommend decreasing tire pressure to the ~20psi area when drag racing on street tires. I think that, at least for my GS-D3's, I have proven that to be anything but a good idea. In fact, it seems that I should be increasing my tire pressure on track days to give a good contact patch during maximum rearward weight transfer.

Maybe that's why my 60' times suck so much...

Here is an Excel spreadsheet I threw together to calculate this stuff. If anyone wants to double-check my math, I'd appreciate it. I minored in Applied Computational Mathematics, but I'm not immune to mistakes.

 

Wow, after reading that I feel like I didn't pay attention in school. I like your math skills

 

I have said numerous times around here that when going to the track, specifically on STREET TIRES, to start with the tires INFLATED to at least ~35-36 psi . If a person really believes that their traction still sucks and wants to decrease pressure, at least you've got the option. But, this has worked fairly well for me, and others too .

I've never tried them as high as ~40 psi, but suppose it wouldn't hurt to try?

Thank you for using "science/math" to prove a point that many people around here have tried to tell others .

 

I inflated the rears to 40psi last night. Now all I have to do is watch for a good burnout opportunity.

 

Weight transfer depends on weight distribution, friction coeff., and CG location. I don't have anything with me at work, but I can get you in the ballpark with equations I have at home.

Anyone have an idea on the CG location? I'm gonna say just behind the engine (firewall area), and just under half the height of the engine. We can use the 1600 lbs. to find front to back location, but just take a guess on height.

 

Agreed. I thought I did pretty well in school, but I'd have a lot more learning to do before I could come up with a solution to that problem. In no way would I consider JakeRobb a nerd for that.

 

One error in your analysis - a 245 tire does not have a 9.65" tread width. That is the section width. Tread width is usually less.

You can put all the weight on the rear wheels if you pull the front end, so weight transfer is a function of how much power you have, to some extent.

 

Good call on tread width vs. section width. Is my best bet for tread width just to measure it?

As far as calculating weight transfer, you've given me an idea. My car doesn't lift the front wheels off the ground, but it does rise an inch or two. If I could measure how much the front suspension lifts when I accelerate, we could use the spring rates to determine how much weight has transferred to the back, right? That way I wouldn't need to know the CG or coefficients of friction, both of which would be difficult at best to calculate.

 

Spring rates aren't truly linear, so you still are "guessing" somewhat with that approach, but maybe the operating range of the springs may be in the linear region. I can't say for sure. You can also have progressive spring rates too.

Also, your dealing with sprung and unsprung mass here. Once the weight of the front suspension is just off the ground, the CG has changed. There are lots of variables and assumptions you will have to make. Along with this, you will have different tire deflections based on how much weight is transferred.

There are standard numbers used for coeff of friction, based on tests. I've seen charts that you can pick off friction coeff based on the weight. (Another vehicle type, not F-Bodies)


I'm being nit picky, but there are lots of factors to consider.

 

Another thing I just thought of, is the tread is not completely flat. You have groves cut out. So you truly won't be using the all of the patch of tire on the ground. That will considerably alter you contact patch dimensions.

How picky can you get?

 

Well, the Excel sheet I put together calculates tire deflection based on tire size and weight on the rear axle. So if you can calculate how much weight is on the axle, then you'll know the deflection.

I'm all about nitpicking.

I thought about that for a moment. I suppose we could include an estimation of the percent of the overall tire tread that will actually touch the ground. I'd call that "tread density". I think that would be good enough for the purposes of these calculations, but it would probably throw off the coefficient of friction.

 

Okay, so I found a nice deserted office park this afternoon and did a little 40psi test:



The stripes seem to be even all the way across. What do you guys think?

The next time I go drag racing, I'm going to experiment with it even more, and we'll see what PSI gives me the best 60' times.