Me again! Slight change of a semi-technical and mathematical discussion here, so some of you who don't know much (you know who I mean ) please move along

Right. Gear change point calculation. Easy isn't it. You just find when the wheel torque curves cross, and change at that RPM. Or you do it by feel (or a mixture). Very simple. Doesn't require any extreme thought. Or so I thought...

The other day I happened across a website with a little gear change point calculator (and I can't find it now, which is annoying). You put in your ratios, you put in your power curves and a few other bits and pieces and out pops TWO bits of data.

The first bit is the RPMs when the torque curves cross. It matched mine (+-5rpm). No problem, and it confirms my maths.

The second bit on info was gear change points calculated using calculus - areas under curves (the curves being approximated from the torque data I suppose). And the results were quite different. I normally change gear about 6700rpm, with a 7250rpm rev-limiter, and the area method was suggesting going much much closer to the rev limiter.

So, the question is: Which is correct, and why?

Answers on a postcard (or via the little reply box below)...

the question is pretty pointless without any real info on how the other method calculates its results

I think it works out the areas under the torque curve for different shift points. Check total area when changing at 6000rpm then at 6100rpm. If 6100 is better (bigger area) then check 6200.. I think. Presumably it does it for all gear shifts; I think it gave different figures for each gear, as you'd expect.

I really need to find it again. Bah!

Well that was easy: http://www.bgsoflex.com/shifter.html

My data, if you want to try it:
1st. 2.583
2nd. 2.077
3rd. 1.667
4th. 1.438
5th: 1.222

3500 102hp
4000 133hp
4500 154hp
5000 170hp
5500 183hp
6000 185hp
6500 180hp
7000 169hp
7500 140hp (guessed, but all others derived from rolling road results [not taken straight from the gauge])

Guessing you want this in theory. Otherwise it might just be worth doing a few 0-xxx runs using the two diffrent options for shift points and seeing which one takes less. Or im probably missing the point and your asking why the two results, if so carry on

You want the most torque possible for the particular speed you're traveling. Assuming instantaneous shifts and sufficient grip, I don't see why you'd want to change before or after the tractive force curves intersect.

Quote from robt :

Guessing you want this in theory. Otherwise it might just be worth doing a few 0-xxx runs using the two diffrent options for shift points and seeing which one takes less. Or im probably missing the point and your asking why the two results, if so carry on

I could try running various tests, but race clutches are relatively fragile, and quite expensive, so I'd rather work out why there is a difference in theory before trying it

Forbin - that was my understanding of it. But surely the most tractive effort at any point would also give the largest area under the curve? At what point (assuming the curves are reasonable representations of the power curve) does this change?

Mathematicians - can you shed any light on this? Is it an error in analysis?

The reason you want to change AFTER the torque curves cross is:

You start slowing down the instant you disconnect the drive. No matter what gearbox you have, or how you change, there is always a short delay before the drive is restored. The car decelerates(sp?) during that time and if you change at the cross over point the RPM will drop below the optimum for the next gear.

Now, if you "over rev" it and change after the cross over point the RPM is right for the next gear to provide the maximum acceleration.

IF the gear changes were instant and the drive wouldn't be disconnected, then the cross over point would give the max acceleration.

The amount of over revving depends on the time the drive is disconnected and the deceleration of the vehicle.

^ I think that's pretty clear, but the weird/alternate calculation method Tristan talks about suggests much bigger differences than simple accounting for the gear change loss.

closer to 1000 rpm higher, if my memory serves me. Your way is technically correct, and already factored into my spreadsheet - I have to hold the gear change for about 10rpm. Ten. Not much really (depends on gradient though). My up changes are pretty darn quick!

The difference in rpm between each gear change (e.g. first to second being at higher rpm than 4th to 5th) isn't that much of a problem, because my shift light isn't programmable for each gear. So I tend to set it for 3rd, 4th and 5th because the rate of rpm increase is too high in 1st and 2nd to be accurate anyway - quite frequently I hit the rev limiter in 1st gear because my brain can't quite keep up.

Sorry for stating the obvious

I can't explain it. The first set of numbers are close to what VHPA is telling me with a rough approximation of your torque curve, so I'd stick with them/what you've found from actually testing.

mOOHOAOahahaha

(That's manical laughter btw)

If you are trying the calculus method, you are trying to maximize the area under the curve. That is, torque, plotted with Rpm and vehicle speed as the two axis.

Both methods are similar in theory. Without calculus, you are breaking up the torque plot into vertical standing rectangles. This approximates the area using simple geometry. To be more precise, you could use rectangles having a smaller width, thereby getting close to the actual area. Calculus is a way to do the same thing where the width of each rectangle approaches zero.

I'd rather change gears to my own preference. Knowing your torque curve via a chassis dyno, you can pick out where peak power is and at what point it has dropped past an unacceptable level. With that knowledge in mind you should be able to figure out when to short shift or hold gears longer due to traffic, turn complexes, elevation changes. SOmetimes its better to shift a little early so that you can concentrate on a set of upcoming turns.

i have a feeling that the doods who made that are either confused themselves, or have expressed themselves in a confusing way. they are talking about horsepower curves, not torque, and it's not very clear whether they mean at the flywheel or at the rear wheels, but i'm assuming they mean at the flywheel. if that is the case then their calculation ought to yield similar results to the torque at the wheels calculation, but their accuracy is highly dependent upon good information regarding power in the very highest revs (past the power peak), especially if your gears are far apart.

so basically i'm suggesting that their theory is ok, but their implementation doesn't have enough data points to yield a smooth curve, and so using calculus on it doesn't gain anything. all they end up doing is calculating the area of triangles instead of rectangles, neither of which represents the motor's true characteristics very well.

I've just finished adding a data table output for the engine curves VHPA generates, so I could get the curve to match all those data points Tristan posted. See screeny.

Shift points haven't changed much from my earlier estimated curve, but here they are for reference:
1st to 2nd - 6630 rpm
2nd to 3rd - 6621 rpm
3rd to 4th - 6458 rpm
4th to 5th - 6487 rpm

Quote from PAracer :

If you are trying the calculus method, you are trying to maximize the area under the curve. That is, torque, plotted with Rpm and vehicle speed as the two axis.

Both methods are similar in theory. Without calculus, you are breaking up the torque plot into vertical standing rectangles. This approximates the area using simple geometry. To be more precise, you could use rectangles having a smaller width, thereby getting close to the actual area. Calculus is a way to do the same thing where the width of each rectangle approaches zero.

I'd rather change gears to my own preference. Knowing your torque curve via a chassis dyno, you can pick out where peak power is and at what point it has dropped past an unacceptable level. With that knowledge in mind you should be able to figure out when to short shift or hold gears longer due to traffic, turn complexes, elevation changes. SOmetimes its better to shift a little early so that you can concentrate on a set of upcoming turns.

Thanks very much, but I've known what calculus is since I was 14. And I don't need a lesson on basic shifting theory thanks, I wanted to know why there is a difference. I even said in my first post not to bother posting if you don't understand the question (or words to that effect).

Quote from evilgeek :

i have a feeling that the doods who made that are either confused themselves, or have expressed themselves in a confusing way. they are talking about horsepower curves, not torque, and it's not very clear whether they mean at the flywheel or at the rear wheels, but i'm assuming they mean at the flywheel. if that is the case then their calculation ought to yield similar results to the torque at the wheels calculation, but their accuracy is highly dependent upon good information regarding power in the very highest revs (past the power peak), especially if your gears are far apart.

so basically i'm suggesting that their theory is ok, but their implementation doesn't have enough data points to yield a smooth curve, and so using calculus on it doesn't gain anything. all they end up doing is calculating the area of triangles instead of rectangles, neither of which represents the motor's true characteristics very well.

It doesn't matter where the data is measured (I can put ANY numbers in the boxes), and it doesn't matter if it's power or torque, as both are linked. The accuracy of the information is determined by making a curve to fit the data (explained on the website), so it's unlikely to that inaccurate. There is a reason, probably mathematical, why two ideal shift points can be generated, because there must be only one in real life (assuming flat roads, no tail winds etc).

Quote from Bob Smith :

I've just finished adding a data table output for the engine curves VHPA generates, so I could get the curve to match all those data points Tristan posted. See screeny.

Shift points haven't changed much from my earlier estimated curve, but here they are for reference:
1st to 2nd - 6630 rpm
2nd to 3rd - 6621 rpm
3rd to 4th - 6458 rpm
4th to 5th - 6487 rpm

That's roughly what I get too with the torque (or power) curve crossing point method. But verifying our results using the same equation doesn't explain why maximising the area under the curves gives vastly different numbers.

So the question still stands, and I think I might need a REALLY clever person to help.

I was just considering making something in excel to figure out where to shift when you take torque curves and gear ratios into account, after being annoyed again by car reviews raving about torque without looking at rpm.

I can not see any other way than to plot the torque curves for each gear measured at the driveshaft, and then shift at or slightly beyond where the curves intersect.

There just can't be a way to go quicker with less torque on the driven wheels?!?!

You would think not, wouldn't you...

I might have to get excel out again later and plot some curves using discrete date, approximate them with a formulaeic curve (probably a polynomial I'd expect, as Excel can do that for you ), and then integrate that over various ranges to find out what it is actually trying to tell me...

How hard can it be?

Anyone care to make a small diagram that shows which "area under the curve" is being calculated? I cannot make any sense of this.

it doesnt make any sense whatsoever to integrate the power curves directly (or cross them for that matter)

the only way i can think of to get a shift point from a power curve is to use E = \int P dt but that will leave you with the problem of figuring out what time you spend in each gear

Quote from Shotglass :

what time you spend in each gear

I'm certain he spends tea-time in reverse as most young Britons are accused of doing. But I shouldn't get too technical for this thread.

Quote from tristancliffe :

That's roughly what I get too with the torque (or power) curve crossing point method. But verifying our results using the same equation doesn't explain why maximising the area under the curves gives vastly different numbers.

Agreed, but it's at least good to know that, using the normal method, everyone is in agreement.

The whole area under the curve method only seems relevenant if you are using the algorithm to pick the ideal ratios to optimise acceleration in a certain range of speeds. For which it would need more input data anyway.

Quote from Shotglass :

it doesnt make any sense whatsoever to integrate the power curves directly (or cross them for that matter)

It shouldn't make any difference but I suspect it could be related to this (although, the script could just be converting power back to torque before doing and maths - we just can't tell).

Quote from Bob Smith :

although, the script could just be converting power back to torque before doing and maths - we just can't tell

it must be the power curve isnt influenced by gearing at all (only where in the cruve you are which might lead to a way to come up with a result but i havent thought it through)

In theory, they should both give the same figure. If you change too early or too later (than that cross over point) then you are not using the maximum area. But I'll see what I can make Excel do before I decide that fully.

Android - I'm taking about the wheel torque or tractive effort curves, like this one http://www.reynard883.com/imag ... excel/tractive_effort.jpg (sorry it's black). The question is do you change gear where the lines cross, do you change gear at the points that give the maximum area, or are both methods meant to give the same data and it's just inaccuracies that cause the difference?

Quote from tristancliffe :

The question is do you change gear where the lines cross, do you change gear at the points that give the maximum area, or are both methods meant to give the same data and it's just inaccuracies that cause the difference?

explain to me how exactly the outline of that mountain panorama which maximizes the area isnt exactly the same as the intersection method