CPSmith

Interesting reading from one of my friends at Bimmerforums
I'd like to see something like this done for our cars, from you geniuses out there (Joe Perez, Sav, Brain, etc.). Just use your own setup for your calculations

gospeed81

iTrader: (51)

I actually have a program written which will do (something like) this. Was part of a project last semester at school (I kick *** at MATLAB). It also takes into account terrain angle of incline, vehicle weight, and various other forces acting on the vehicle.

When I'm done with this load of homework I'll see if I can dig it up and adapt it to the Miata.

Hardest part will be making a vector of torque values from somebody's dyno graph...which isn't really hard. Raw data would be better though. Diff ratio and wheel radius are all knowns.

JasonC SBB

I did something very similar back in 1998 or 1999, I used a torque curve, weight, gearing, and drag as inputs. I used a circuit simulator (PSpice) to do it. I might still have it in my archives somewhere.

With it I proved to my own satisfaction that the best single number to predict the accelerative capability of an engine is the average power in the dyno curve between the upshift RPM, and the RPM after the shift.

The best shift RPM is that after the RPM of power peak (such that power is going down with RPM), where the RPM you drop to after the shift, has the same value of power.

For example, if your peak power RPM is at 6500, with say 250 hp, and then it's 230 hp at 7500 and at 5500, and if shifting at 7500 drops your RPM to 5500, then 7500 is the right RPM to shift. This is true as long as the power curve is bell shaped and you can shift at a high enough RPM for this to be true. Otherwise redline is the best RPM to shift. This is mathematically provable.

gospeed81

iTrader: (51)

Very interesting Jason. The highest average power between the two points is a neat take on it, and would be easy to evaluate with a maxima finding function.

I took a cursory look at my function, and it simply tells a Mars rover which gear is best to be in for a given situation, but can easily be modified.

First person to figure this out gets a cookie?


Truth be told though, the shift points would vary, if not wildly, depending on setup. Those of us running street turbos on stock intake manifolds would surely be shifting a good bit shorter than guys like Savington with huge compressors and better breathing setups.

Anecdotal crap: I do know I would commonly short-shift when running the little IHI turbo as it "felt" faster. When the post-shift RPM would fall between 5000-5500rpm the torque there was noticeably greater than if I'd carried it all the way to 7200rpm to shift.


Really the best way to handle this due to different torque curves amongst us, and several different rear end ratios would be to make an awesome spreadsheet. Everyone has access to Excel and could plug in their own values. I unfortunately am not that good with Excel, and it would take me more time than I could devote figuring out how to make things that take me a half hour in a known programming language work in an Excel macro.

Braineack

iTrader: (62)

In my altima I ran the 1/4 (32) times in one day.

Stupid Honduh people said to shift at 6k to keep my torque up. I said they were retarded and would prove them wrong.

I would consistently see 16.1s if I shifted at redline. When I tried 6K (6500 limiter), I would achieve a mind-blazing time of 16.7s.



shifting below redline has never made sense to me.

JasonC SBB

At any given road speed, (ignoring drag)

acceleration = power / mass / speed

Ergo acceleration is proportional to power.

If you shift at an RPM such that the power after you shift is the same as the power at your shift RPM point, your acceleration will be the same at the moment just before and just after the shift. If you shift early, and the power after the shift is less than just before, your acceleration will drop after the shift, and you should have delayed the shift. If you shift too late, your acceleration before the shift is weaker than after the shift, so you should have shifted earlier.

Again if your revlimit isn't high enough then you shift at redlimit.

Another consequence of this is that because the higher the gear, the less the RPMs drop after the shift, the lower the optimal shift RPM is.

The reason gears have wider spacing at lower speeds/gears, is that the time it takes to shift encroaches on acceleration time, and you don't want to spend that time shifting in lower gears, where acceleration is harder and it takes a lot less time for the motor to pull the car through the RPM range.

Another thing I realized from my simulations is why "low end torque wins races". I mentioned that average power is the single most important indicator of accelerative capability.

If you took 2 motors with the same bell shaped power curve, around the power peak, with the same peak power, the same powerband RPM range (say 5000-7000 RPM), and one of them had more area under the curve, (and thus higher average power) what most people would notice is not the area under the power curve, but that the 2nd motor has a higher torque value at 5000 RPM.

Comparing torque values works only if the 2 motors being compared have the same RPM range. It won't work if one motor say, has a power peak at 6000 RPM, and another is at 9000 RPM. Then you have to compare power curves, or "translate" one motor's torque curve to the other by multiplying its RPM by the ratio of the redline RPMs (or by the ratio of peak-power-RPM), and dividing its torque by the same number.

Also, if you increase your peak power but make the area under the curve smaller, your car will be slower. Racers notice this and then conclude "torque wins races", instead of "more area under the power curve wins races". And then they don't reconcile the fact that to win a drag race one will shift past the peak power point, instead of just past the torque peak point, because they don't know math and physics.

Lastly if two motors have the same area under the power curve, but different shapes, the one that has more meat lower in the rev range will win a drag race.

The reason is that the earlier in the rev range you develop max power, the earlier you accelerate the car, (e.g. coming out of a corner or at the start of a drag race), and this pays dividends throughout the main straight / dragstrip. The car that pulls away early will build up a large lead. It's the same reason the 60 ft time pays dividends in car lengths at the end of a drag race.

If 2 motors had the same power curve from 5000-7000 RPM, but both cars launched at 3000 RPM, assuming they have traction, the one that's stronger at 3000 RPM will win, significantly. Do the thought experiment where one of them had half the output 3000-4999 RPM, and it's like this car sat and waited and let the other car launch first before launching himself.

If your motor spends most of its time on a given track between 5000-7000 RPM, but there is one particular slow corner that you exit at 4000 RPM, and this corner precedes the main straight, the motor's output from 4000-5000 RPM is disproportionately important to lap times. You wouldn't want to sacrifice that RPM range too much in the quest for peak power.

This is where "torque wins races" came from.

If one took 2 motors wherein the 2nd motor had 2x the RPM, then you added a 2:1 reduction gear on the output of the 2nd motor, you could design 'em to theoretically have the same torque and power curves when measured at the output of the reduction gear; in reality, before the reduction gear, the 2nd motor would have 2x the RPM and half the torque, and their performance would be identical, with the right gearing.

You can develop 80 ft-lbs at a lug nut, but you can't accelerate the car down the road like a geo metro motor would, despite matching the engine's torque, because you don't develop anywhere near the power. You can't develop that torque at anywhere near reasonable road speeds.

JasonC SBB

gospeed, the way to find the optimal shift RPM is to start at the RPM of power peak.

Let's say you are doing a 2->3 shift.
Take the ratio of the gearing of 2nd divided by 3rd, let say it's 1.88 and 1.3.

1.888/1.33 = 1.42

Let's say power peak is at 6000 RPM.
If you shift at 6000 RPM, the RPM after the shift will be 6000/1.42=4225 RPM.
Check power value at 4225 RPM vs 6000.
If it's lower, try next higher RPM value. Search until it matches.

This is a linear search. Of course you can do a, what's it called, "linear bisection method"?

Start testing the shift point at the RPM value 6000 * sqrt(1.42)
If the after-shift-RPM's power is lower, search halfway between the last value and the next higher value, if higher, seach at a lower RPM.

sjmarcy

Often it is better to simply measure the thing directly. So, just log the car's acceleration in each gear across the RPM / speed range. Overlay and then choose. Allow for any post shift lag by testing. This nets everything out. Things like each gear's different loss factor, aero, cooling at different road speeds, etc can be accounted for to arrive at better results.