Help me with some gear maths

[Salgar]

Hi all, slightly embarrassed that I can't work this out myself, although I haven't tried very much.

I'm trying to work out which gear I'm in based on the current speed and RPM and gear ratios

e.g.

4090 RPM, 37.9 MPH on my Triumph Street Triple
Gear Ratios: Primary: 85/46 1st: 34/13 2nd: 39/21 3rd: 36/23 4th: 27/20 5th: 26/21 6th: 25/22 Final: 47/16
Rear tyre circumference is 77.896 inches

So, I know that the answer here is 2nd gear, but I'd like to get a formula for it.

I got to a formula that is: gear = RPM x Circ / 1056 x Speed which I got from rearranging the stuff on here http://www.ehow.co.uk/how_6460513_figure-mph-rpm-g...

However sticking all those numbers in doesn't get me anywhere near any of those ratios.

Almost all of what I've said here could be bks, can anyone help out?

[wst]

Working with inches and minutes and hours and miles is messy like fook.

However, I went to wolframalpha.com and came up with a ratio of 7.962. If you came up with similar then it's something else that's wrong with the maths...

[deadtom]

4090 RPM / 60 = 68.167 RPS = W
(37.9 mph * 1.609 * 1000) / 60 * 60 = 16.939 ms^-1 = V
tyre circ. = 77.896 * 0.0254 = 1.979 metres = C
gear ratio = ? = X
primary = 85/46 = 1.848 = Y
final drive = 47/16 = 2.9375 = Z


so....

V = (W/(X*Y*Z))*C (engine speed divided by the overall ratio of primary, gear and final drive, multiplied by the wheel circumference.

=> X = (C*W)/(V*Y*Z)

however this gives you the result of 3rd gear rather than 2nd. If you were in second gear at that engine speed you would be doing 30mph ish

Edited by deadtom on Tuesday 11th December 00:23

[TheEnd]

You can try this is you find out your numbers and input them-
http://www.endtuning.com/gearratios.html

It's set up for some BMWs, but you can use any numbers, (watch out for metric tyres though!)

[mrmr96]

Salgar, why not log rpm and speed in each gear and then review the log and put the ratios into your program? No maths to be done then, and it also takes account of any differences in sensor readings etc. All you need to do if just go up through the gears and make sure the clutch is fully up in each one to generate the log you'll need to get this set up.

[Salgar]

deadtom said:

4090 RPM / 60 = 68.167 RPS = W
(37.9 mph * 1.609 * 1000) / 60 * 60 = 16.939 ms^-1 = V
tyre circ. = 77.896 * 0.0254 = 1.979 metres = C
gear ratio = ? = X
primary = 85/46 = 1.848 = Y
final drive = 47/16 = 2.9375 = Z


so....

V = (W/(X*Y*Z))*C (engine speed divided by the overall ratio of primary, gear and final drive, multiplied by the wheel circumference.

=> X = (C*W)/(V*Y*Z)

however this gives you the result of 3rd gear rather than 2nd. If you were in second gear at that engine speed you would be doing 30mph ish

Edited by deadtom on Tuesday 11th December 00:23

Ello, thanks for this, I knew I'd not got the gear ratio part right. I still don't fully understand the gear ratio maths but I'll look it up sometime.

You are very correct though, I was in 3rd gear, not 2nd.

Interestingly, this calculations gives 1.429 where 2nd is 1.857 and 3rd is 1.5652

I'm assuming the difference is in the fact that I measured the RPM and speed separately with around 0.25-0.5 second difference, and a lot can change in that time, I should be able to make those closer together.

Thanks for this

Edit: Actually, it's closer to 4th gear in absolute terms, where 4th is 1.35. I don't really know which gear I was in. I don't have the log file with me to do more rpm/speed matches.

Edited by Salgar on Tuesday 11th December 09:22

[Salgar]

doogz said:

Engine Speed 4090

Tyre Size Circumference 1978

Gear	Ratio	Final Drive	MPH
1st	2.615384615	5.42798913	21.25
2nd	1.857142857		29.92
3rd	1.565217391		35.50
4th	1.35		41.16
5th	1.23809523		44.88
6th	1.136363636		48.90

They seem awfully close together?

I've included the primary with the FD ratio

Pretified your table.

They are pretty close together, it's for a Triumph Street Triple which has a close ratio gearbox. It can do 85ish in 2nd gear. But yeah it makes working this stuff out a little harder with inaccuracies.

[Mr2Mike]

doogz said:

Engine Speed 4090

Tyre Size Circumference 1978

Gear Ratio Final Drive MPH
1st 2.615384615 5.42798913 21.25
2nd 1.857142857 29.92
3rd 1.565217391 35.50
4th 1.35 41.16
5th 1.238095238 44.88
6th 1.136363636 48.90

They seem awfully close together?

They make more sense when you realise the red-line is around 12600 RPM

[Mr2Mike]

doogz said:

A ratio is a ratio. At 12,600, there's only 12mph between 5th and 6th.

A power curve is a power curve. A 675cc 3 cylinder engine producing 105bhp doesn't do it by having stump pulling torque (though for it's size it's very good). In the Street Triple peak power occurs occurs quite close to the redline (around 11700 RPM), to maximise performance you need to keep the engine speed up around this point.

[Mr2Mike]

doogz said:

I understand that. The actual figure of peak power, or red line, is fairly irrelevant though. That's what I meant. A ratio, is a ratio, regardless of the actual speeds involved.

The point I was trying to make is that the RPM drop when you change gear depends on RPM, i.e. you larger drop at higher RPM for a given gear ratio, so high revving engines tend to need closer ratios.