Speeds, gears, torque, acceleration, rear-ends, etc.

[greg]

I decided to start a new thread here because this is being discussed in various places. One thing that drives me crazy is car guys talking about car stuff - particularly performance - and believing in old wive's tales (like "always shift at the torque peak for best acceleration"). A knowledge of elemental math and physics allows us to figure stuff out without guessing.

The image below is of my latest iteration of a spreadsheet you can download at http://www.bmwm5.com/greg/files/M5_Data.xls (27Kb)

I believe the math is correct, but would certainly appreciate it if someone checks me on this. The most waffled figures are the torque ones - I interpreted a dyno chart where 3 members' stock M5's returned very similar results. I multipled the torque figures (and I had to guess within about 10 lbs on those) by 1.15 since the chart shows torque as measured at the rear wheels and we want engine torque, which isn't a victim of drivetrain loss. If someone has the original M5 factory torque graph, I'd love to make these numbers more accurate. I am confident these numbers are good enough to draw many conclusions, however.

One conclusion is that you have more force at the rear wheels in a lower gear, even after the engine's torque has passed peak, all the way to redline, than if you shift early. Argues for shifting at redline every time, and explains why a shorter gear ratio isn't always a good thing.

Making comparisons between the 3.15 and the 3.45 is easy, but drawing meaningful conclusions is more difficult. For example, you'd have to do more work to figure out who wins in a hypothetical run from 0mph to 100mph - this is where the 3.45 guy has more acceleration in a given gear, but also has to shift to the higher gear sooner, and in fact must shift to 4th to reach 100, where the stock car can remain in 3rd. If someone can help me with THAT math - I surely need it. (Math beyond basic algebra was NOT my strong suit in school!)

SO - comments, observations, corrections, supplements, etc - all welcome.

[BM5VIUS]

Wow Greg, this is great and really appreciated. Already have it on the laptop.

Heck, even for the simple task of knowing what gear is best to pass with on the two-lane roads I play on.
Love that torque at 1,000 RPMS...Geez, no wonder we spin off the line so easily (then again, torque moves weight).

There's less top-end diff in the 3.45 than I thought, might just be an upgrade someday !

Anyway, thanks as it'l come in many uses I'm sure !

[JEM]

Was looking the other day at some numbers on the Supra Turbo gearbox, which is supposed to be the same basic box as ours.

The gear ratios, however, are (according to what I was reading) a little different. Most notably, first is about 10% taller.

Not that I'm advocating tearing down M5 transmissions, but given that our first is basically a granny gear as it is, I wonder if those first-gear gearsets would be swappable?

[EBMCS03]

Wooo Crazy info greg... COOL now i just need to learn what it all means and how to read it hehehe

[Zman]

Greg, you never cease to amaze me. Great work!! I love this place!!

[chazzy]

Greg,

The numbers look good to me. They match the spreadsheet that I created separately just by thinking about the problem, so it's probably safe to say that the calculations are correct. Maybe someone else can chime in about torque corrections?

I think that determining the actual acceleration the car experiences at any given point is a simple enough idea. We would have to take the torque curve, divide out the moment arm (radius of the wheel), and then divide out the mass and we'll be able to get the linear acceleration. Then a computer could be used to try to calculate the final speed after winding out a gear.

There are some difficulties and inaccuracies that would be involved, including shift time, traction, contact patch, etc.

Anyone want to tackle this challenge?

[greg]

BM5VIUS - The torque at 1000 RPM is a GUESS - since it doesn't show on the dyno chart I looked at. I am hoping someone has more accurate info.

JEM - taller 1st would be great. If it were standard, however, I'm afraid it would increase the number of burned clutch stories too.....

Chazzy - AAAAAAhhhh! You're right. I should have divided the "force" calcs by rolling radius of the tire - this truly equals "thrust". Since it is a constant it won't change the conclusions, but it does change the numbers a bit. And, since the rolling radius of our tires is almost exactly 1' (12.8 inches by my calcs) it won't make a big change. We really also should be dividing out driveline losses too..... But I don't understand what you mean by "Then a computer could be used to try to calculate the final speed after winding out a gear. " - The speed in each gear is only a function of RPM, gear ratio and wheel size - and that is already computed (without needing to know anything about torque.) Did I misunderstand?

[Oak]

Yowza! great job! I guess you can blue print numbers till the cows come home, in the end theres only one way to see the difference. Run em!

Most all serious racers blue printed there engines, gears, susp. etc.... and they all think they have a winning combo, but in the end there is only one winner.

[400 PLUS]

Your math looks correct.
Thanks for the data.

[johann]

Originally posted by greg
I believe the math is correct, but would certainly appreciate it if someone checks me on this. The most waffled figures are the torque ones - I interpreted a dyno chart where 3 members' stock M5's returned very similar results. I multipled the torque figures (and I had to guess within about 10 lbs on those) by 1.15 since the chart shows torque as measured at the rear wheels and we want engine torque, which isn't a victim of drivetrain loss. If someone has the original M5 factory torque graph, I'd love to make these numbers more accurate. I am confident these numbers are good enough to draw many conclusions, however.

Very useful stuff!

Not that I understand why you would want to work with engine torque but if you want that you should divide wheel torque with 0.85 (wheel torque = 0.85 x engine torque => engine torque = wheel torque/0.85).

Anyway it really doesn't matter since you'll get the same error for every gear, hence the right conlcusions can still be made.

I made a similar spread sheet comparing GT2 with SL55 earlier that verified my theories.

Cheers,
/Johan

[johann]

Originally posted by Oak
Most all serious racers blue printed there engines, gears, susp. etc.... and they all think they have a winning combo, but in the end there is only one winner.

One of the reasons is because you can't blue print the driver.

Cheers,
/Johan

[woolston]

Greg,

I'm a new member. One of the things that got me most interested in this site/MB was the possibility of sharing information. As it so happens, I was also working on calculating the performance of the E39 M5 but I was looking for torque data. Your spreadsheet supplied that ... thanks!

I have used some of your data to do my own spreadsheet analysis. Much of it closely matches your own, however, I went the additional step of calculating acceleration, tire slippage and O-60 MPH performance based on these calculations . . . I also charted some of the data. Suprisingly, the published 0-60 performance of 4.8 seconds and my calculated performance are very close. Either my model is a decent approximation or I was just plain lucky.

My data also supports your conclusion that there is more torque (thus acceleration) in the lower gears and thus one should shift at or near redline. One can also conclude that much of the available torque (~33%) in 1st gear is unavailable due to probable tire traction/slippage. It tends to argue for putting stickier tires and more weight in the rear end . . . on the other hand, this would upset the 50/50 weight distribution and handling and would add additional inertia. I haven't calculated the trade-offs yet . . . perhaps I'll do that next.

I would be happy to post the excel file but I am not sure how this should be done. Please advise.