- Measure the average steepness of the worst hill that you cannot avoid climbing. Use a level and a ruler (metric or decimal), then divide rise into the span to get the grade percentage.
- Total combined weight, plan for at least 400-500lbs (181-226 kg). If you have a cycle-truck or a velomobile that can hold two people, think about at least 600-800lbs (272-362 kg).
Before going ahead and getting the power you’d like consider the legalities in your country. (see post “which are legal”)
There are 2 types of e-bike motors. (See post “electric bicycle motors”). E-bikes, and conversions, can have motor power from 250 watts to 1000 watts.
The higher power 1000w motors should (sometimes must) have 48v battery.
When talking about watts of power you need to distinguish between input power and output power. The suppliers of the bike motors and bikes with motors usually talk about input power. The motors will at best be about 80% efficient (and less at high or low speeds) so 250 watt motor produces about 200 watts of output. It is usually output that determines legality on the road.
Doubling power to 500 watts does not give proportionally higher maximum speed (approx 32-35 kmh) but it does mean bigger increase in uphill speed or ability to climb steeper hills. As you travel the three main forces you have to overcome are wind resistance, rolling resistance and gravity. The first varies with (approx) the square of your speed, and the others vary in proportion to the speed. You can estimate the wind + rolling resistance, at any speed, as being the downhill gradient at which that steady speed is just maintained when rolling down that hill.
How much power do you need for a hill? You can work out approximately how much power you need for a hill :
Watts = (total) weight (kg) x 9.81 x speed (M/sec) x gradient (%/100)
For instance 100kg at 20kmh at 4% (3% hill + 1% w+r) = 100 x 9.81 x 20000 x 0.04/3600 = 218 Watts and
100kg at 28kmh at 5.5% (3.5% hill + 2% w+r) = 420 Watts
That is approximately what you can expect from 250w (200w) and 500w (400w) motors.
Many people confuse torque with power. They are different terms. Motors can have high torque and low speed, or low torque and high speed and yet have similar power output. For instance the two different types of e-bike hub motors, the ungeared and internally geared motors have quite similar power, although the former is a high torque low speed motor and the latter is a low torque high speed motor. Its internal reduction gears reduce the speed of the axle and increase torque in same proportion so that the output of the two is quite similar.
Torque is the force that “wants” to turn the motor. Power is the rate at which work is done. The conversion between power and torque is :
Torque (NewtonMetres)= Watts/radians per second = Watts x 0.5 x diameter)/(kmh/3.6)
You may have seen a Tour de France cyclist going up a 14% slope at about 30kmh. That cyclist is putting out about 1300 watts! You won’t do as well with any bicycle motor. (But if you do have 500 watt motor and do overtake a cyclist training on a hill be considerate – he or she is working hard, but you are not).
Just as with a car’s motor in any gear there is a speed range where the motor performs most efficiently, while at much lower or higher speeds the motor will either struggle or max out. Electric motors have various performances, just as fueled motors do. An electric bike motor can struggle, or stall, just as car motor in the wrong gear will.
You may find a “performance curve” for an electric motor. Usually there will be several variables (power in, power out, rpm or torque, efficiency, current, voltage) plotted against motor rpm or torque. Efficiency will generally be a maximum in the middle range of motor speeds, and be very low at low speeds. The power out will flatten off and not increase much with increasing motor speed despite the input power increasing. This is because the motor loses efficiency at faster speeds and increasing input power has less effect.
For going up steep hills a motor that has high torque at low speed is better. If the speed going uphill is within the high efficiency range the motor will stable and the bike will go up the hill steadily. The speed going uphill will usually be less than the motor’s most efficient speed. In this case the motor will slow, lose efficiency, and struggle…but if you make enough assistance to the motor you can go up any hill at a steady speed.
Wheel speed calculation:
52 sprockets / 12 sprockets on the rear= 4.333 ratio? X 60rpm crank speed x (20” x pi=62.8inch circumference) = 16327.987 inch min. / 12 inch = 1360.6655ft/min. x 5280ft x 60min/hr= 15.45 mi/hr
Gear reduction: Calculate wheel speed needed then find ratio of gears:
Wheel diameter x pi x motors peak efficiency RPM ÷ 12”per foot x 60min. ÷ 5280ft per mile = wheel speed without gear reduction ÷ 15mph = ? to 1( gear reduction needed.)
Low voltage = low speed = high torque. However a huge gear reduction could have advantages, like a smaller motor:
/ how to motorize a big heavy vehicle/ Hub Motors / How much power do you really need?