Norm Peterson

There's more than just power and tire diameter involved even if you're only looking to kill off the ability to turn the tires over from a roll. BTW, it's easier to think in terms of torque. Tire tread compounding, inflation pressure, overall gearing, and torque converter characteristics (if applicable)matter.

Crudely, acceleration is something like

{ [Engine torque] * [Gearing] * [Drivetrain efficiency] - [Rolling drag + Aero drag] } / {[Tire Rolling Radius] * ( [Weight] + [Rotating Weight effects] ) }

and the trick is to play with all of the terms to get whatever maximum acceleration the road (or track) surface can support. Without "wasting" too many different gears in wheelspin or requiring an extra shift just before the lights if it's a stick-shift. Launch introduces a few more considerations ("impact loading", anti-squat, shock tuning, . . .).

In a street-driven car, I really don't think that taller tires are the answer. Grippier tires or taller gearing, probably. Let's say that you're right on the edge of traction with 400 ft-lbs and 27" tall tires, but you're about to push the torque up to 475 ft-lbs. To match the torque increase with only a tire diameter increase puts you at 32" tall. Only a 30" would still spin (and be awasted effort if that was all you did). IOW, tire diameter is at best a tool for "fine-tuning" your overall combination.

As far as dragsters are concerned, they're direct-drive (no transmission) and IIRC are limited by technical rules/specs in what final drive ratio they are allowed to run (and I think RPM is limited as well). The only way left to see 300+ mph is with tire diameter - which I assume is also limited in some way (with tire growth perhaps being something of an end-run around it all). That's way too different of a situation to be of any use comparing to.


Norm

RodeoFlyer

for drag guys, having a couple different sets of slicks at different heights is easier than a gear change.

a taller tire's sidewall will wrinkle better as well, allowing better grip on launch(all other factors set aside)

MustangGT0405

I plan to get some 28.8" tall rear tires when I get my 20" wheels. The only reason is I like the look of the 20's with the taller tire. I think it makes the car sit better. I know I am giving up performance. To make up for it slightly I might install 3.73's when I have a tru track put in.

For the track I will run the stock rims (17x8) with slicks.

GotMunchies?

Since we were talking about moment of inertia, I'd like to dive into the math of moment of a simplified rim.

Say there are two parts to the rim, the spokes leading from the hub, which for all intents and purposes can be assumed to be a uniform flat disk. At the outside of the wheel, we have a what is basically a hoop.

Moment of Inertia of a disk: 1/2 * mass * radius^2
Moment of Inertia of a hoop: mass * radius^2

The total moment of the wheel would be the sum of the two.

Relating torque from the drivetrain to the angular acceleration of the wheel, which can then be related to the forward acceleration of the car looks like this:

I*a/r = T (Total Moment * acceleration / Radius = Torque)
Solving for acceleration, we get:

a = r*T/I

So acceleration is inversely proportional to the moment of inertia. Basically, here's the simplified physics that tell us: if, in our search for grip and performance, we increase the radius of our wheels and tires, it has a much greater negative effect on performance than increasing the width of the tire.

Physics says: Light is right, increase width for better acceleration and grip.

RodeoFlyer

But............

Isaac Newton didn't have track conditions and clutch performance to consider. It sounds silly, but strictly going off math is STILL guesswork at best.

Once that sidewall buckles the idea of a uniformed hoop is out the window

Look at NHRA Stock Eliminator cars. They are allowed a max tire height of 30", and a max width of 9". You wont find many with 26 or 28 inch tall tires for a reason.

I'm not trying to be a dick - just throwing another angle at it. I worked on 2 Stock Eliminator cars for 5 years. It weird when experience shows you that what works on paper doesn't always work on pavement. It's kinda like the old road racing addage that you have to slow down to go faster.

GotMunchies?

The uniform hoop estimation still holds true, since the distribution of mass is still a unifrom circle rotating around a central axis. It will change the moment slightly, but as an estimation I stand by it. I also stand by the physics. A smaller wheel will require less torque for an equivalent acceleration. However, when you have abundant torque acting on a racing wheel and rubber (which are lighter than equivalently sized street applications) the taller resultant gearing will allow you to haul more sever ***.

The thing is, you need that abundant torque, which Mustangs tend to have

A lot of my racing philosophy comes from smaller displacement four bangers running much smaller tires. Spec Miata and FSAE racing and whatnot. It really doesn't apply to the drag world.

Norm Peterson

I'll agree, that at least where most of us are concerned the math is at the very best an approximation (simulations developed at the OE-level or by top-shelf racing teams or consultantsbeing a different story). Modeling this sort of event can get crazy complicated the deeper that you try to get into it and try to model all the things that vary with time, gearing, engine rpm, or whatever. If real life doesn't match the simulation, the simulation is either missing something or is inaccurately considering it.

But even a relatively crude cut can point out trends, and just going through some of it forces one to look at both the physics and the time element. For example right here, while modeling the tire as a pair of annular rings plus a hoop isn't entirely accurate once the tire deflects (and the annular rings aren't quite rings any longer), that's still a better approximation than making a hold-your-thumb-up-to-the-sky guess based on the tire as a single mass. And now that tire deflection has come up, the rolling radius term drops, effectively lowering the gearing. There's probably an increase in parasitic drag in the form of that additional sidewall deformation, too. Etc. etc. etc.

Steady-state (or at least quasi-steady state) acceleration isn't that tough to get a pretty good handle on. I've got a1963 Hor Rod publication that presents the formula in what's probably the simplest possible terms. But launch is much more complicated, because there's so much more going on, varying rapidly with time -and you can'tignore it or assume it to be constant. Let's just say that I've been picking away at this particular simulation for . . . decades.


Norm