Mathematically both algorithms should find the same solution.
My first explanation for the difference, without knowing the actual formulas used, is that the integration-method keeps integrating the approximation-errors and thus ends up with a bigger error in the result than in any of the data-values. I'd hazard the guess that the approximation will only deliver sound results when you have largely more data on the power-curve.

Vain

Quote from Shotglass :

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

No, I was hoping people would explain it to me - the website (which I didn't necessarily trust, but it got me thinking) implied that they are not the same.

Vain - I think I agree with your opinion. I'm still going to check it myself though

i dont think youre getting this
i was trying to get you to stare at the curves long enough to see that anything but exactly the same result must be complete rubbish calculated by some wannabe engineer

Oh I see

I did some sketched graphs earlier at work, and visualised the integration, and I agree. But I'm still going to check it for peace of mind. If you try and prove something wrong you often learn a lot more about the subject. I've been thinking about anti-roll bars for weeks now, and I'm only starting to come to terms with the huge topic that roll-stiffness really is. I'm glad I'm not a suspension designer

If we could get the script off the site we could examine the code and find out where the guy has bollocksed it up.

Okay, just hacked up a quick Excel thingy to compare the two methods. Don't judge my excel skills - it really is a hack

Made up some torque figures and some gear ratios, then got Excel to plot a 3rd order polynomial trend line on each curve of the tractive effort chart (force at the wheels).

The chart shows me, graphically, the optimum gear change points I could make it work it out too, but can't be bothered to put interpolation into it

From looking, I got the shift points. I then intergrated the trend line equations, and put the shift points as the limits (with 20mph and 130mph as the first and top limits).

By editing the shift points in the pale green boxes, it compares the total area under the graph with the original method. If the bottom box is bright green then the visual gear change points are best. If it's red then the calculus method is best. If it's yellow then they are the same.

I can't make it be any better shifting anywhere but where they cross. Thus validating everyone's opinion that both methods SHOULD give the same result and the sample web page is WRONG

Question answered. Mind at rest. Hurrah for maths

Edit: Grrr, can't upload XLS, as if they are more risky than any other type of file... Replaced with thrustworthy .zip

Err, that( wa)'s an empty zip.

Fixed. I think.

Quote from site :

Since the RPM after the shift depends on the "ratios" of the gear ratios, the difference between the RPMs before and after the shift grows with increasing RPMs. This makes the area under the curve method favor higher shift RPMs compared to the first method. Which one is better? You find out......

I believe its saying using the area under the curve method, the estimated RPM droop will be higher, meaning it'll suggest you shift at a higher RPM.

When you shift gears ideally you want the RPM to fall on torque peak correct? I know thats how you set up a car for maximum acceleration using an automatic transmission, because when it falls on torque peak you're getting the most torque multiplication from the torque converter...obviously not the case with a manual transmission, although I'd assume you'd want the RPM to fall on torque peak with both for the best acceleration.


I threw all your data in the site only to find that the "compute" link is broken and I'm going to a blank page...balls

Quote from spanks :

When you shift gears ideally you want the RPM to fall on torque peak correct?

No, totally incorrect. You will be slower in acceleration, elapsed time and peak top speeds if you do this, on drag strips or racing circuits.

Quote from spanks :

I know thats how you set up a car for maximum acceleration using an automatic transmission, because when it falls on torque peak you're getting the most torque multiplication from the torque converter...obviously not the case with a manual transmission, although I'd assume you'd want the RPM to fall on torque peak with both for the best acceleration.

No, you don't do that on an auto or a manual transmission. You want to change gear when you have more motive force (or power) in the next gear than you do in the current gear. Which means revving above peak torque (or power) and the shift will drop you below peak torque (or power), but give you the most force more of the time.

You are however correct in saying that in a given gear you have peak acceleration at peak torque.

With a CVT you maximise the area under the curve by keeping the rpm at peak power and adjusting the gear ratio to suit the speeds.

Quote from spanks :

I threw all your data in the site only to find that the "compute" link is broken and I'm going to a blank page...balls

Can't pin that one on me

Quote from tristancliffe :

No, totally incorrect. You will be slower in acceleration, elapsed time and peak top speeds if you do this, on drag strips or racing circuits.

Well, not quite totally. It depends how far apart the peak torque, power and the limiter are on the rev curve, not to mention how broad the gears are. It is possible the the optimum shift point, can end up at or even below the peak torque. Although that would likely imply badly thought out gear ratios.

Or a very odd engine.

Yes, or that.

Ah shit, broke 8k.