Maths to how to work out gearing

[moT]

This has been troubleing me for some time. Assumeing no other vairables such as fricton or wind how would you work out your top speed for different gearing ratios? Also asumeing your engine redlines at 14000rpm you have a gearing ratio of 15 drive and 40 wheel, the wheel has a diamiter of 60cm. useing pie you can work out the cicumfrence of the wheel and with the graring figue out how many times the wheel spins per min at 16000rpm then use that to figure out top speed. Anyone got an answer?

[rat biker 08]

I put that in the to hard basket :(

[Grub]

Oh Tom, you MUST go to the Gearing Commander site (http://www.gearingcommander.com/) ... it's just plain brilliant.

Ratios, tyre sizes, front & rear sprockets ... change any of them and see the results!

There's a huge library of common bikes in there already so you don't even have to know your bike gear ratios.

[merv]

Yep you sure can work it out, but you need to know the gearbox ratios and the primary drive ratio between the crankshaft and the clutch basket too to get your overall ratios sorted.

I've posted this before sometime but here's the spreadsheet I use to do the calcs and this one has my VFRs ratios loaded on sheet 2 so just overtype them with your own numbers.

[moT]

i need to know the formula to work it out! i have tried and it doesnt make sence ahhhhh too many numbers for my brain

[Grub]

i need to know the formula to work it out! i have tried and it doesnt make sence ahhhhh too many numbers for my brain

No, it's ok ... don't thank us, it's ok ... really it is. Sorry we couldn't meet your "needs".

[merv]

Use my spreadheet, does it all for you, but you have to know the bikes gear ratios, sprocket sizes, wheel and tyre sizes. In other words you've got to be able to fill in the numbers in the pink column yourself.

Grubs link is a Yankee site I suppose and they don't have the numbers for the 400 so you'll have to look them up. Do you have a book or manual for the bike? Otherwise do a search for gear ratios for your bike.

[moT]

Use my spreadheet, does it all for you, but you have to know the bikes gear ratios, sprocket sizes, wheel and tyre sizes.

wow now thats cool

cheers

[merv]

wow now thats cool

cheers

Remember just touch the pink column, don't go deleting formulas in the other columns coz they aint idiot protected.

Then again if you want to know the formulas you can look at them, but just don't overtype those cells or delete them eh.

[moT]

I wld still like to know how to work it out

[McJim]

I find the easiest way is to take the bike out for a spin and choose a rev bench mark for each gear. e.g. 5,000 rpm.

Ride along in 1st until you hit 5,000rpm and note your speed.
Change to 2nd and bring the revs to 5,000 and note your speed
Change to 3rd (spot the pattern?) etc.

Do this for all your gears and you will know approximately the size of each gear. Armed with this information you can calculate notional speeds (roughly) for each gear at redline (if redline is 14,000 and you can achieve 100kph in top at 5,000 then 100kph divided by 5,000 multiplied by 14,000 = 280kph)

Does that help?

[McJim]

Additionally once you have all of that data (you now have a good idea of what is happening inside your gearbox) you can then apply this to the front and rear sprockets and to the circumference of your rear wheel to find out what sort of changes can be made to the external ratios for other notional top speeds. This should also allow you to calculate your gearbox ratios, insert them into the pink area (mmmm sounds nice) on Merv's spreadsheet.

[merv]

Well here's the explanation - for whatever gear you want to do the calc for you've got to know the gear ratios. (Or do it the way Jim has just explained which you can do if you can't find the numbers though it is based on your speedo and rev counter accuracy - no biggie there though.)

e.g. in 6th gear my VFR has a 1.939 primary ratio (that's crank to clutch basket) while the gearbox ratio is 1.035 and the final drive ratio being the sprocket size difference is 16:43 which is a ratio of 2.688.

Multiply them all together 1.939 x 1.035 x 2.688 = 5.393, so the engine turns 5.393 times for every time the back wheel goes around once.

Now if the engine is doing 11,500rpm at redline ( I don't worry about it reaching limiter at 12,500) then the back wheel is turning 11,500/5.393 times = 2,132.39 times every minute.

Now you love the backwheel sizes in inches but the tyre in mm and I guess most accurate calc would be to actually measure your tyre diameter. Let's say it 17 inches being 431.8 mm and the tyre is 170mm with a 60% profile i.e. 102 mm and two tyre thickness add to the diameter, so add 204mm, then the wheel must be about 635.8mm diameter.

You know the circumference is diam times pi don't you?

So that is 1997.42mm or 1.99742m. Turn that 2,132.39 times and you've gone 2,132.39 x 1.99742 = 4,259.29 metres or 4.25929 kilometres and that's in a minute. An hour is 60 minutes so multiply by 60.
i.e. 60 x 4.25929 = 255.557 kilometres in the hour. The spreadsheet says 256 as we've probably both done a bit of rounding.

Does that all make sense to you now? Simple huh. That is what the spreadsheet has built into its formulas.

[merv]

Did I put you all to sleep with that maths lesson?

[Grub]

Google is your friend VFR400 raatios and speed at RSM Real Speed Calcualtor (http://www.racingsm.org/vel.php#). The VFR400 ratios are in the database, bottom left.

[merv]

OK if the ratios Grub has pointed you to are correct for your model (and there are zillions of 400s) your spreadsheet looks like this as attached.

There are still some variables we don't have from you or that website like true wheel and tyre size and what maximum rpm are you getting - is 16,000 it coz stock those motors do about 14,000 don't they, which you mentioned as redline, so have you warmed yours up? If it only does 14,000 enter that in the spreadsheet.

I've taken your sprocket combo as 15/40 as mentioned above and put 16,000 into the spreadsheet and guessed the other useful rpm figures. I left it as a 17 inch wheel but some VFR400s had 18 inch.

[jrandom]

useing pie you can work out...

I find that combining pie and working out tends to leave me back at square one.

[merv]

I find that combining pie and working out tends to leave me back at square one.

Is that something to do with square pies? When I was at Uni in ChCh back in the 70's there used to be these Stevenson's Famous square pies, not sure if that place is still going. Sound like they woulda suited someone kinda random eh!

[jrandom]

Is that something to do with square pies?

<img src="http://mathworld.wolfram.com/images/equations/PiSquared/Inline3.gif"/><img src="http://mathworld.wolfram.com/images/equations/PiSquared/Inline4.gif"/><img src="http://mathworld.wolfram.com/images/equations/PiSquared/Inline5.gif"/>?

Ahem.

Sorry...

[Cajun]

http://www.gearingcommander.com/ <-- is the one i use got a bunch of build in bikes, but more american based bikes, for vfr400 isn't there, but in turn if you know the raw information you can install it and save it

blah see grub already recommended this one.