Lower Diffs Actually useful on racetrack?

First: it's clear that lower diff ratios (3.46, 3.73, 3.91, 4.10, etc) are good
if you care how fast you launch off the line. (i don't)
if you care about autocross where you risk bogging in 2nd gear (I don't)
if you care how much power you have in a given gear (rather than the right gear) (I don't)

I'm only concerned about racetracks.

I made up a spreadsheet with speed in gear based on the gear ratios, tire circumference, & diff ratio. I used diff ratios between 2.23 and 4.27. I typed in a dynosheet and used linear interpolation to find power at rpm.
I added something to find optimum gear at rpm. I found power at speed assuming ideal shifting. I found power to overcome wind resistance at speed. I found acceleration at speed, and finally, I found speed at time and distance at time.

If we start at 20mph, there is almost no diff-based difference in your position as a function of time after the first few hundred yards. If you start faster, there is less difference. At the end of a mile, the 3.15 was actually in front, but by a small enough amount that it's probably due to

Lower diff ratios do better when you aren't in the power band in first.
On the m coupe, after you get into the power band in first, you can stay in the power band.
If the band was peakier, you couldn't do this, and lower ratio diffs would put the gears closer together and you'd go faster. I'm sure that this is an important factor in many race cars.

For my use, I can't figure out how a lower ratio diff would help, except perhaps by removing an inconvenient shift point in a particular corner at a particular track.

I'd love to understand why I'm wrong, if I'm wrong.

I can email my spreadsheet to anyone who is interested. It doesn't look like I can attach it here.

-john d

Reply » Lower Diffs Actually useful on racetrack?

PTG Racing seems to think so.

"Differential
BMW (modified) 75% limited slip 3.851:1"

Quoted from their website.
http://www.ptgracing.com/cars.htm

.

Reply » Lower Diffs Actually useful on racetrack?

Quote:

For my use, I can't figure out how a lower ratio diff would help, except perhaps by removing an inconvenient shift point in a particular corner at a particular track.

-john d

Very good point. The Hewland gearbox, used in most formula and sportsracing cars, has interchangable gearsets for all gears. These guys rarely change the final drive, but the tranny gears can be easily changed at the track. At Moroso for example, we used a fairly tall 2nd gear and a short 3rd gear because from turn 2 to turn 6 it's all turns with just a few short straights.

Reply » Lower Diffs Actually useful on racetrack?

On a race track one desires to be in the max power band as much of the time as possible.

On any given track (or even on a straightaway such as Bonneville) there is a maximum speed that a given car can achieve due to hp and wind (and rolling) resistance. Some tracks are configured so that the car cannot reach it's theoretical top speed; on these "slow" tracks a lower-than-normal (higher numerically) final drive ratio than that used at "fast" tracks is beneficial since you won't hit top speed anyway. On tracks that do allow you to hit top speed a lower (higher numerically) ratio than optimum for street use is usually beneficial due to the following.

To maximise performance (i.e. keep the engine in the power band for the most time), one ought to choose a final drive ratio that just allows the car to reach top speed at the rpm that produces max hp --- in practice one would choose a ratio that would produce slightly above top speed at max hp.
This allows the car to get up to the power band quicker. For track use a significantly higher (numerically lower) final drive ratio is useless since it only allows you to reach a speed for which you don't have the hp to attain. On the street it allows greater fuel economy and lower rpms. Also on the street a lower (numerically higher) final drive will make the car easier to drive from a dead stop.

A different final drive ratio does NOT change the rpm difference between gears. If you drop from 6000 rpm to 4000 rpm on a given shift (say 2nd to 3rd) with a 3.15 ratio, you will still drop from 6000 rpm to 4000 rpm with a 2.23, 3.23, 3.46, 3.64, 3.73, 4.10, or any other ratio. You will be going slower but pulling harder with the lower gears. It's just math.

Reply » Lower Diffs Actually useful on racetrack?

Don't forget to allow some headroom for drafting.

By havin gthe gearing set up so that you just reach top speed in top gear and top RPM as you hit the brkaing zone, menas you are accelerating as hard as possible to that point, giving you a bit faster overall speed down the straight.

And since most tin tops (sorry) don't swap the actual tranny gears, you may also swap diff ratios to get the most important corners at the right point in the power band. You dn't want to run out of revs or bog in teh high speed corners leading onto straights as these croerns are where can make the most time up on others.

If you can change everything, you normally start by a gear spread that keeps the engine in the power band for shifts. Then final ratio for the longest straight, and then fine tuune the tranny gears for the important corners.

Or you can plug the info into a computer program and install what it says.

Reply » Lower Diffs Actually useful on racetrack?

I have attached a dyno chart from dinan showing the power band for an M coupe. The slightly lower grey band is stock. You can see that the power band is very flat from 6000 to 7600 and still quite shallow at 5500. I have also attached an rpm & mph in gear chart for the M Coupe for a couple of different diffs. (I can't figure out how to pist the pictures inline).

Tighter gears don't change the difference in rpm when you shift, as Bob points out. The do change the difference in MPH between shifts, making shifts closer together in time, which is good if you aren't in your power band.

The gear chart shows MPH and RPM for the different gears, one chart per diff. If you draw a line straight down from your shift point, you can find your rpm in the next gear. The shaded areas are supposed to be powerband, but it's for some other engine, possibly the S52.

Ignoring 1st to second as not useful on a racetrack, and shifting at 7600rpm, we have
2nd->3rd puts us at 5000 RPM, or about 250HP, about 80% of peak. Not ideal.
3rd->4th puts us at around 5800RPM, or about 290HP, 92% of peak. Nearly ideal.
4th->5th puts us at around 6200RPM, which is effectively at peak HP. Ideal.

A lower diff should completely remove the 2nd-3rd shift from racetrack consideration. You'd spend less time at the bottom of 3rd, which is good, and you'd be moving out of the low end of 4th faster (since you are going slower when you get into 4th.) All good. And 4th->5th doesn't have a problem.

Which implies, as everyone I've ever met seems to believe that a lower diff is better on a track, even for this engine with a relatively wide powerband. So I'll have to spend some more quality time with my giant spreadsheet to figure out what the issue is.

If you could change gears, and everyone does at the highend of racing, you'd clearly move 1st up practically to where 3rd is, and then arrange the rest of the gears so they are all useful, and probably most important so you don't have to shift in any of the turns. But changing gears is beyond what I'm thinking about doing to my car.

thanks for all the input.
-john

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