Torque of rear axle from static condition ?

Say the effective raduius of your foot from the bottom bracket centre is 100mm and you're standing out of the saddle and using a bit of arm power so the load is maybe 1.1 times your body weight. Say your body weight is 65kg (a medium sized human or quite a heavy competetive cyclist!). You might generate a moment at the bottom bracket therefore of 70Nm. An old fashioned bicycle had a chain wheel:rear sprocket ratio of about 1:3 so you'd have about 23Nm at the rear wheel.

Now suppose you aren't Eddie Mercks, you'll probably have 12-15Nm at the rear wheel.

Usual Disclaimer:: this could of course be totally incorrect and should under no circumstances be used for any purpose what so ever, excepting myrth.

i design transportation like vellotaxi (total 3 people, 1 driver at front and 2 passanger at the back) using pedal assist. i use hub motor, the average power is 200 W, max 400 W. Because it' pedal assist i must pedalling first to move the vehicle from static condition. I calculate the free body diagram at one rear wheel. i design this vehicle to move 10 km/hr constant (average use) and to reach thet constant velocity i got 8,2 second from static condition. so a = 0.339 m/s. And the result is :

Torque at rear wheel is almost 10000 kgmm (98.1 Nm) and the power is 0,9 kW

and for strart moving at climb position with the road angle 8 degree T=23000 kgmm (225.63 N/m) and the power increase become 1,9 kW.

So i got the force to push pedal (pedal force)=25 kg for the lightest force from the tansmision ratio with n pedal is 201.32 rpm.

Is my calculation is ok ? or is it to heavy? especially for the torque at rear wheel. If you have suggestion to calculate rear axle, please let me know.

How degree of road surface (to climb position) this vellotaxi can go in the relity ?

Thanks

I'm confused, are you trying to predict the velotaxi's performance from a given torque input or work out how much torque you need to achieve a given performance?? A couple of fundamental parameters you haven't mentioned are the mass/weight and the radius of the driven wheel. From these you can work out acceleration and how it will climb gradients for a given torque and power.

From a stop condition, the linear force to move the vellotaxi is essentially the force required to accelerate the mass of three people plus the vellotaxi. Say the taxi weighs 110lbs (i.e. ~ 50Kg) and each person weighs 165lb (i.e. ~ 75Kg) then you have a total mass to accelerate of 3*75 + 50 = 275Kg.

1mile/h = 63360 inch/h or ~1610m/h or ~0.45m/s; say 0.5m/s

v = at [v = velocity; a = acceleration; t = time]
For initial start, goal speed is 1mph (0.5m/s) in 0.5sec => a = 1m/s2

For total mass of ~275Kg
f = ma [f = force; m = mass; a = acceleration]
f = 0.5 * 275 ~= 140N

This force can be considered to act horizontally on the rear axle, and torque about a lever arm measures the same at both ends - so it is also the linear force the week applies to the road and can therefore be used to calculate the torque required to accelerate the vehicle. For rear wheels of diameter 24 inches == 60cm; radius = 30cm.

Torque = force * radius = 140N * 0.3m = 42Nm

You'll lose a little power - i.e. need some extra torque - to overcome the compressibility of the tires and the interaction between the tire and the road; say + 10%:

Torque at the rear axle ~= 46Nm

At the pedal: given the ~ 3:1 gear ratio that Wrenched mentions, the torque must be 3 * 46 ~= 140Nm (to accelerate to 0.5mph in 0.5sec)

A 75Kg human weighs ~10m/s2 * 75Kg = 750N

Given a pedal with a crank length of 100mm (from Wrenched) - or 0.1m - a 750N human standing on the pedal can exert 75Nm torque on the pedal axle.

Conclusion: a 75Kg (165Lb) human, standing on the pedals (but not pulling on the handlebars, and not using toeclips to pull up on the other pedal) will be able to accelerate a fully loaded vellotaxi to 1mph in about 1 second. GIVEN ALL THE ASSUMPTIONS ABOUT MASS, GEAR RATIO, PEDAL CRANK LENGTH AND WHEEL DIAMETER MADE ABOVE. And given the 10% factor for tire losses.

Concisely put Odyssey. Would we need to allow something for cranking the engine over, as I suspect it's a direct drive affair?