View Full Version : gearing calculations--a lil brain teaser.

FROSTY

14th March 2006, 22:19

A bike is running 15/47 gearing as standard.

The owner has access to 46 and 45 tooth rear sprockets and 14 and 16 tooth fronts.

To gear the bike up by 4%-or closest to it which combination of sprockets would YOU suggest??

Likewise to gear the bike DOWN by 5% what would you do

A lil test of KB brains

cowpoos

14th March 2006, 22:35

I've been think about getting sky for a while now...but I'm still undecided...I wanna see the superbike races but really theres not much more that would interest me I don't think.

so I'm still pondering...

Jantar

14th March 2006, 22:46

A bike is running 15/47 gearing as standard.

The owner has access to 46 and 45 tooth rear sprockets and 14 and 16 tooth fronts.

To gear the bike up by 4%-or closest to it which combination of sprockets would YOU suggest??

Likewise to gear the bike DOWN by 5% what would you do

A lil test of KB brains

Original ratio = 0.319

To gear up by 4% 15/45 Ratio = 0.333

To gear down 5% 14/46 Ratio = 0.304

FROSTY

15th March 2006, 07:25

aww jant--spoil my fun

Ok calculate all variables with sprockets available then

Flyingpony

15th March 2006, 07:27

Original ratio = 0.319

To gear up by 4% 15/45 Ratio = 0.333

To gear down 5% 14/46 Ratio = 0.304

Second that.

Flyingpony

15th March 2006, 07:44

Ok calculate all variables with sprockets available then

14/45 Ratio = 0.311 -2.519%

14/46 Ratio = 0.304 -4.638%

14/47 Ratio = 0.298 -6.667%

15/45 Ratio = 0.333 4.444%

15/46 Ratio = 0.326 2.174%

15/47 Ratio = 0.319 Original

16/45 Ratio = 0.356 11.407%

16/46 Ratio = 0.348 8.986%

16/47 Ratio = 0.340 6.667%

Percentages are a change over/under original.

The Stranger

15th March 2006, 07:45

So you have worked out the ratio using the number of teeth.

NOT arguing, however when I did the my CBTA at Ride Rite the guy taking it stated that this was incorrect. He stated that that approach was an approximation. He said that the correct way was as a ratio of the radius of the sprockets.

Just put it forward it as a thought.

vifferman

15th March 2006, 07:48

Never mind the calculations - 15T is about the limits of how small you want to go on a front sprocket for a 525 or 530 chain, at least. The smaller the sprocket, the more stress on the chain having to change direction traversing it. Yes, front sprockets are cheaper, but (a) rear sprocket changes give you smaller graduations of gearing changes, and (b) a larger rear sprocket is easier on your chain (and probably robs less power) than a smaller front sprocket.

vifferman

15th March 2006, 07:50

So you have worked out the ratio using the number of teeth.

NOT arguing, however when I did the my CBTA at Ride Rite the guy taking it stated that this was incorrect. He stated that that approach was an approximation. He said that the correct way was as a ratio of the radius of the sprockets.

True, but it's not much of an approximation, so it's close enough, and easier to measure.

FlyingDutchMan

15th March 2006, 07:54

So you have worked out the ratio using the number of teeth.

NOT arguing, however when I did the my CBTA at Ride Rite the guy taking it stated that this was incorrect. He stated that that approach was an approximation. He said that the correct way was as a ratio of the radius of the sprockets.

Just put it forward it as a thought.

Actually, its dead on. If the front sprocket turns one tooth, the rear sprocket turns one tooth - chain don't slip (if they do, you're in the shit). The amount it turns is determined angular distance between each tooth, which can be directly determined by the number of teeth.

TwoSeven

15th March 2006, 07:59

A bike is running 15/47 gearing as standard.

The owner has access to 46 and 45 tooth rear sprockets and 14 and 16 tooth fronts.

To gear the bike up by 4%-or closest to it which combination of sprockets would YOU suggest??

Likewise to gear the bike DOWN by 5% what would you do

A lil test of KB brains

First of all it depends on the internal gearing of the bike, the rpm its going to run on average, whether acceleration is desired over speed and the driving force (power being applied to the rear wheel).

You cant just knock up a sprocket change (of +/- 5%) and expect it to solve the problem, the tradeoffs being given away may end up being bigger penalties than the benifit that is being expected.

What is the bike and scenario you are trying to solve the gearing for ?

The Stranger

15th March 2006, 08:01

Just changed the YZF750 from 15/41 to 15/47.

Pretty wicked.

5500 at 100kph in top so should topout at about 235kph (assuming redline), awesome pickup in any gear and great for wheelies and burnouts.

TwoSeven

15th March 2006, 08:04

So you have worked out the ratio using the number of teeth.

NOT arguing, however when I did the my CBTA at Ride Rite the guy taking it stated that this was incorrect. He stated that that approach was an approximation. He said that the correct way was as a ratio of the radius of the sprockets.

Just put it forward it as a thought.

I suspect he is using pitch circle diameter. I think tho, that given a certain chain type, the PCD can be worked out by the number of teeth on the sprocket.

far queue

15th March 2006, 08:59

Never mind the calculations - 15T is about the limits of how small you want to go on a front sprocket for a 525 or 530 chain, at least. The smaller the sprocket, the more stress on the chain having to change direction traversing it. Yes, front sprockets are cheaper, but (a) rear sprocket changes give you smaller graduations of gearing changes, and (b) a larger rear sprocket is easier on your chain (and probably robs less power) than a smaller front sprocket.

My bike came standard with 15/41, which was OK on the road but way too high off road. I now run a 45 on the rear all the time and vary the front between 13, 14, 15 depending on the riding I want to do. 13/45 is great off road, gives me good engine revs at low low speeds and close gear ratios, but top speed suffers a lot on the road. 15/45 gives me good road speeds, and wider gear ratios which is fine on the road, but low speed off road suffers. 14/45 is a compromise between the two. I regurlary change the front sprocket, it's only a 10 minute job.

Also the chain is 525. The 14 & 15 sprockets are 525. The 13 & 45 sprockets are 520. You can run a 525 chain on 520 sprockets with no problem as the only difference is chain width, and in fact it helps to clear mud from the chain & sprockets.

nadroj

15th March 2006, 10:01

Remembering back to my cycling days - by multiplying the number of teeth on the front sprocket by the diameter of the rear tyre (rolling diameter) then divide that by the number of teeth on the rear sprocket will give you the distance covered by the bike per revolution of the front sprocket. Hence by knowing the final drive ratio of the gearbox in any gear the top speed of any gear can be calculated at redline. How good is my memory?

FROSTY

15th March 2006, 23:57

this is an exersize only --there are always going to be limitatations to every senario.

Doogal and I had been through the exersize for black ice. calculating gearing up and down and the effect on how it punches out of corners etc.

TwoSeven

16th March 2006, 10:20

Well here is a model I created - not sure if its accurate - so take it with a pinch of salt. I'm trying to show the affect on a machine from changing the gears (final drive gearing).

14/45: 66(2.44) - 98(1.64) - 124(1.30) - 157(1.03) - 178(0.91) - 193(0.84)

14/46: 64(2.50) - 96(1.68) - 121(1.33) - 153(1.05) - 174(0.93) - 189(0.85)

14/47: 63(2.55) - 94(1.71) - 119(1.36) - 150(1.08) - 170(0.95) - 185(0.87)

15/45: 70(2.28) - 105(1.53) - 133(1.21) - 168(0.96) - 191(0.85) - 207(.78)

15/46: 69(2.33) - 103(1.57) - 130(1.24) - 164(0.98) - 187(0.86) - 202(.80)

15/47: 67(2.38) - 101(1.60) - 127(1.27) - 161(1.00) - 183(0.88) - 198(.82)

16/45: 75(2.14) - 112(1.44) - 142(1.14) - 179(0.90) - 204(0.79) - 221(.73)

16/46: 73(2.19) - 110(1.47) - 139(1.16) - 175(0.92) - 199(0.81) - 216(.75)

16/47: 72(2.23) - 107(1.50) - 136(1.19) - 171(0.94) - 195(0.83) - 211(.76)

The first pair on numbers is the gear ratio eg. 16/45

The rest of the numbers are the speed km.hr(driving force kN) in each gear

I think a key thing to remember is that the driving force (at the rear wheel) determines the rate of acceleration of the bike. In 1st gear, there is not much speed but the bike will accelerate up to that quickly. In 6th gear, there is heaps of possible speed, but the bike would take ages to accelerate to that speed.

The pattern seems to indicate to me that the front sprocket determines the initial top speed in each gear. The rear sprocket is reducing that speed, but giving better acceleration instead (so the trade off). In effect as I see it, the faster one goes, the slower the acceleration will be.

I think while some of the numbers look impressive, there is a point in that table where the bike will wheelie chronically, and/or the rear wheel will just slip too much. That would mean the rider shutting the throttle which reduced both max possible speed and acceleration.

One day I shall get off my ass and validate the model on the dyno and see if I have done the math correctly. Until then I take it as a wild theoretical guess :)

imdying

16th March 2006, 11:25

So what sort of gearing would an early CBR900 require to get to 215mph?

TwoSeven

16th March 2006, 13:11

I think standard sizes for sprockets on a 900Fn (92) were 16/42. I couldnt find the internal engine sprocket sizes (I need driver/driven from primary thru to 6th), so I used the 600Fn (92) ratios (its almost the same engine).

I dont think the stock bike would do it - from memory I think that the sprockets wont fit and/or allow a workable chain run angle. But in theory if the peak power was moved up the rev range to 14k rpm instead of 10krpm, then it might be possible to be able to use a 17/40 sprocket combo with roughly 0.94kN in 6th - at a very very rough guess.

Edit: I suspect that one would need to calculate the dynamic pressure of air against the machine and subtract that force form the one given above. If the result is negative, then I think that the machine wouldnt have enough power to reach the speed (likely a stock cbr900 wont be able to). So I figure that one would need to boost the power the machine is generating until the driving force is greater than they dynamic pressure pushing against it. Then I suspect a trip to the bonny salt flats and lay flat on the tank at full throttle and wait a heck of a long time for the bike to accelerate to the desired speed.

You can do the math for that :)

onearmedbandit

16th March 2006, 13:49

Huh? What bike are you talking about Mr Watson?

Brian d marge

17th March 2006, 14:36

Huh? What bike are you talking about Mr Watson?

Cbr900 I assume

But 27 is on the right track, If you are setting up from scratch , take a photo of the front of the bike draw lots of squares over it estimate the frontal area. This will give you the force pushing against the bike wind pressure or what ever,

Work out the gearing and the force in each gear just like he has done. If you have a dyno chart you can find estimate the optimum shift points.

I would look at the track figure out where I am going to make the most time and gear accordingly ( I not sure about you road racing fellas but I would be maxed out about 3/4 down the back straight assuming that gearing combo doesnt hurt the rest of the track , ie losing drive out of the rest of the corners. )

Shes a bit of number crunching, and changes for the conditions ( well it does in MX , if you run low big rears in wet clay you just spin up out of the corners but then you have problems getting the punch for the jump, )

At the end of the day I will estimate it using, me pen and paper Ala 27, then slap on what I think is best and test.

Stephen

cowpoos

17th March 2006, 14:51

if you run low big rears in wet clay you just spin up out of the corners but then you have problems getting the punch for the jump, )

its a bitch you can't short shift on strokers eh!

Brian d marge

17th March 2006, 16:12

its a bitch you can't short shift on strokers eh!

Dont rub it in ,,,, Yup the fours just dig holes and launch ...

Stephen

I still prefer to get things done in 2 strokes rather than 4

cowpoos

17th March 2006, 19:15

I still prefer to get things done in 2 strokes rather than 4

I bet your wife doesn't agree with that theory?

motobob

17th March 2006, 22:10

Remembering back to my cycling days - by multiplying the number of teeth on the front sprocket by the diameter of the rear tyre (rolling diameter) then divide that by the number of teeth on the rear sprocket will give you the distance covered by the bike per revolution of the front sprocket. Hence by knowing the final drive ratio of the gearbox in any gear the top speed of any gear can be calculated at redline. How good is my memory?

And I just used the chart on the back of the rule book they sent each year :blink:

Brian d marge

17th March 2006, 23:15

I bet your wife doesn't agree with that theory?

I ll direct your attention to the * I * at the begining of the sentence.:gob:

Stephen

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