Oh mother... 
Depends basically on what are your input, what's your wanted output, and which units you prefer. As I'm an engineer and (long time ago) scientist, I like to use SI units , which means time > t [sec] frequency > [1/s] length > L [m] angle > alpha [rad] or at least derivatives of SI units , e.g. t [min] or [h] , alpha [°] , L [mm] etc Lets play with kinda example, say you've an engine going 6000 rpm {in engineering language: n1 = 6000 [1/min] or omega = 628 [rad/s]} , and you like to get 55 mph wheel speed {engineering world: v = 88 [km/h] or v = 24.4 [m/s]} Then you've to assume somehow the given tire circumference, lets say you're using a pair of old 30.5-32 firestone 23° pullers, which have roughly a static diam of appr D=1665[mm] , which should end up with appr. L=5.03[m] circumference {floored 1.6[m] x pi}. Divide the wanted speed of 24.4[m/s] by the dynamic tire circumference of 5.03[m] gives you a wheel rotational speed of 4.85[1/s] or n2 = 291[1/min]. So the overall gear ratio from crank to wheel shall be i = n1/n2 = 6000[1/min] / 291 [1/min] = 20.62[-] A tailored equation for that purpose can look alike overall gear ratio i = (engine speed [1/min] / 60) / (wanted wheel speed [mph] x (1.6/3.6) / tire circ [m]) The above used constant of (1.6/3.6) is necessary to convert [mph] into [m/s]. For tire circ in [m] look in the available catalogues, brochures etc or take a tape and convert the units by yourself. |
