Subject: Re: Gear Ratios To: Mark Panos References: <32C66844.2EDC@ozemail.com.au> From: Cameron Simpson Reply-to: cameron@research.canon.com.au Errors-to: cameron@research.canon.com.au Return-receipt-to: cameron@research.canon.com.au Organization: Canon Information Systems Research Australia, Sydney, Oz Mark Panos writes: | Do you have a formula to work out theoretical top speed for motorbikes. | I know its got something to do with final drive ratios, transmission | ratios (top gear) and drive wheel circumference, but I don'y know what | order and whether to divide multiply or what? Hmm. Not to hand. It should be ascertainable by solving: engine_torque * mechanical_advantage = wind_resistance These terms all vary with revs and speed - wind resistance goes up with speed faster than linearly (and the bike shape will affect the exact rate, due to basic drag and turbulence, hence that UGLY UGLY ducktail in the new GSXRs) and engine_torque is the _available_ torque at the output shaft (i.e. after internal engine resistance has been subtracted, otherwise these factors would have to appear at the other side with the wind resistance). The easiest thing is the mechanical advantage. You'll want to compute this for all gears (well, probably only the top two) as it's conceivable that the higher mechanical advantage in 5th is enough to do better than the 6th gear. Usually not, though. Since engine_torque is non-linear (witness those peaky curves in dyno charts) and wind drag is easier to measure in a wind tunnel than by computer modelling you want to have a graph of drag-vs-speed to hand. This will let you make a function to map speed to drag, and speed is a function of (revs,mech_adv). Engine torque is also a function of revs. Thus you get: e_t [f(revs)] * mech_adv = drag [f(revs, mech_adv)] you will see that you only have to search the revs and mech_adv spaces. Since you'll only have two mech_adv values (or perhaps a few more if you're investigating changing wheel radii and sprocket tooth counts) you can just vary the revs until equality is reached (for low revs you'll have LHS > RHS and thus the bike will accellerate and for high revs you'll have the reverse, slowing the bike due to drag - in between is the top speed). In the back of the the owner's manual is normally a table of ratios for the various gears - this should get you revs:rear_wheel rotation; I forget whether it accounts for the drive chain - it may just be gearbox ratios, in which case you'll have to multiply by front_sprocket_teeth -------------------- rear_sprocket_teeth Multiply that by the moment arm (rear wheel radius) and the engine_torque and you have the LHS of the equation (force to the road through the tyre). A table of measuremeants gets you the RHS. Solve for top speed. - Cameron Simpson cameron@research.canon.com.au, DoD#743 http://www.zip.com.au/~cs/ -- EMACS: Escape Meta Alt Control Shift