I realize this will be different for every motor, but is there not a rule of thumb.....oh boy...for calculating HP? If you have a motor geared for 38mph and need to slow down you will not get the full HP of the motor, IE: a 6 to 1 reduction ratio with a 12" wheel and a 3000rpm motor at 24volts will probably give you only1/4 hp at 19mph. But is there a way to get close with math?

You have to approach the problem from two directions, with luck you meet in the middle Side one, How much power does the motor generate? Motor maker will provide Hp vs rpm graph. Using your gear ratios and wheel diameter you can create a graph of motor hp vs vehicle speed. Side two, How much hp is required to move the bicycle? There are 3 sources of losses that occur when a wheeled vehicle moves. 1. rolling resistance, function mostly of mass tire type and air pressure 2. Wind resistance, function of velocity and cross section area and shape. 3. Grade resistance, function of slope being climbed (or descended) and mass. You must make measurements or calculated estimates of those three items. Make a family of curves, one for flat ground and then a series of 1%, 2 % up to about 6 or 8%. Where the hp curve crosses a given load curve is the max speed the vehicle will travel. Vary the gearing to move the HP generated curve around to maximize vehicle performance for the desired operating conditions. Piece o'cake

For a motor (anything that rotates really), power = torque * speed. Gearing down the motor will not necessarily reduce the power of the motor. The speed of the motor goes down but the torque output goes up, since power is the product of torque and speed, the power can remain the same. It's not enough to just know the speed of the motor, you can buy a $3 motor from radio shack that will do 9000rpm with 3 volts, but there's no way it is going to ever push a human sized vehicle at 57mph (19mph x 3). You also need to know what torque it can produce at the various speeds. With just two values at a given voltage (the no-load speed and the stall torque), you can estimate how the motor will behave at all speeds, since motors typically have a straight torque-speed curve. Do you have the no-load speed and stall-torque (or alternatively, the torque-speed curve) for your motor?

Yes there is a method to calculate HP. HP = V x I x Eff/746 HP = Horse power. We normally use Watts V = Voltage I = Current eff = efficiency of the motor Efficiency = Output Power/Input power I obviously cannot advise you what the efficiency of your motor is, but as an example; Eff = 60/75 eff = 0.8 per unit, so 0.8 x 100 = 80% Feed this data into the above; HP = 240 x 5 x 80/746 HP = 129 I trust this will start you off to working out your solution. David