Ebike Design: How much power is enough?

Electric bicycles (ebikes) are legally limited to using motors having an output of 750 watts in the USA. Is this too little or too much power? Ebikes in Asia, in their millions, commonly have 250 watt motors, which matches the European limit of 250 watts continuous output.  Australia and the UK, however, mandate 200 watts as the legal limit in power. Schwinn is coming out with a line of ebikes for 2007, based on their existing European line, that have 175 watt motors. So is 175 watts enough? Well, that depends on how fast you want to go and what bike you plan to ride.

In the USA, ebikes are limited by federal law to a maximum of 20 mph, yet ebike kit motors having 350 watt motors are considered small.  Most Americans seem to be opting for at least 500 watt motors, and many are encouraged to think they need 600-750 watt motors. What was not long ago a generous maximum (of 750 watts) is becoming perceived as a bare minimum. But how much power is needed (as distinct from desired) if we choose to limit ourselves to going the legal 20 mph? Is 20 mph even a reasonable speed for a bicycle?

A fit human able to put out 200 watts, riding a quality bike on flat ground, can go about 20 mph, and can maintain this speed for an hour or so. Such fit humans have to work to achieve and maintain such cycling performance. They tend to take cycling seriously, and workout regularly. Elite competitive racing cyclists can go even faster and farther, of course, but average folks are only good for about 40-60 watts of effort, and then for only a relatively short time. Average not-so-fit adults can ride the cheap bikes they tend to own (and hardly ever ride) about 7-10 mph, and it doesn't take much of a headwind or a hill to slow them to a crawl. So if an average human, by riding an ebike, could cruise at 20 mph, they would be more than doubling their human-power-only speed as well as greatly extending their range.

Fit humans tend to enjoy cycling because they can go reasonably far and fast, while average people may choose not to cycle because they cannot comfortably go very fast or far. Perhaps if most humans could go as fast as those who enjoy cycling, then they too would enjoy ebike riding enough to use an ebike instead of a car for short trips. Even if a person contributes only 50 watts of human power toward getting somewhere, that's better than 0 watts sitting in a car that uses 20,000 watts to get them to the store when 200 watts would suffice sufficiently. By starting out at 50 watts, a person might reasonably aspire to put out 75-100 watts after a few months of riding an ebike.

While the following chart shows that 150 watts of electric power, when combined with a modest human contribution, is enough to go 20 mph on flat land, it also shows how power requirements drastically increase with increasing headwinds and increasing slope. Note that highway engineers rarely design roads with slopes greater than six percent. Alluvial slopes at the foot of mountains and forming valley floors, on which most urban areas are built, are rarely more than 2-3% in slope, so higher slopes would be uncommonly encountered.

Watts required to maintain a speed of 20 mph

(150 lb rider, 30 lb emotor/batteries; at sea level)

Notice that on a steep slope it doesn't matter much whether you're riding the world's most expensive bike or something you picked up for $10 at a yard sale. Aerodynamics, however, on flat land really does matter. A light fairing, even a partial one, can produce big payoffs in performance. For a practical vehicle, a short wheelbase recumbent with fairing would be hard to beat.

So let's see, assuming a through-the-gears motor and a modest 50 watt contribution from the human, a bike would need about 170 watts at the wheel to go 20 mph on flat land and about 350 watts on a 2% slope. Above that lower gears would have to be used. A 250 watt motor, maybe 75% efficient, would be adequate under most conditions (0-2% slope, head wind <10 mph).

The problem with “more is better” is that a motor that could go anywhere, up any hill, into any wind at 20 mph would be seriously overpowered and operate inefficiently 99% of the time. Unless the motor (or motors?) could operate efficiently at both 170 watts output and 1400 watts (which would not be legal anyway), speeds of less than 20 mph would have to be accepted. Still, being able to take a hill at 5-10 mph that most riders would otherwise have to get off and push the bike up is not a bad deal.

What would be the performance of a SWB recumbent without a fairing (about as fast as a diamond frame racing bike but far more comfortable) be for varying amounts of power applied to the wheel?

Short Wheelbase Recumbent Speed (mph)	10 mph wind	25 mph wind		0% slope	1% slope	2% slope	3% slope	4% slope	6% slope	10 % slope	15% slope
50 Watts total	6.2	2.9		10.0	6.0	4.0	3.0	2.4	1.7	1.0	0.7
100 Watts total	5.0	9.7		14.4	10.4	7.6	5.8	4.7	3.3	2.1	1.4
150 Watts total	6.8	12.2		17.3	13.6	10.6	8.4	6.9	4.9	3.1	2.2
200 Watts total	14.3	8.4		19.6	16.1	13.1	10.7	8.9	6.5	4.2	2.9
250 Watts total	19.1	12.5		21.5	20.4	16.8	13.8	11.5	8.5	5.4	3.7
350 Watts total	22.4	15.4		28.1	24.3	20.9	17.8	15.3	11.6	7.6	5.2
500 Watts total	26.4	19.0		32.3	28.9	25.7	22.7	20.1	15.8	10.6	7.4
750 Watts total	31.6	23.8		37.6	34.6	31.7	29.0	26.4	21.8	15.5	11.0

If the rider and assist motor could apply 750 watts to the wheel, then and ebike could legally operate only on roads having a slope greater than 7% or into headwinds greater than 35 mph, conditions that would almost never be encountered. The above data assumes that power is applied efficiently at any speed, which requires multiple gears to allow the motor to operate in its “sweet spot” at all times.

A 250 watt hub motor would be adequate and efficient on flat ground, but because hub motors tend to be only single speed motors, it would bog down and eventually stall as slope or headwinds increased. Using a more powerful hub motor would allow steeper hills to be climbed, but such a motor would never operate efficiently, but would be overpowered at the optimal motor rpm on flat land and would operate with increasing inefficiency as motor rpm dropped with decreasing bicycle velocity.

Just as a single-speed bike cannot be pedaled efficiently under all conditions, a single-speed motor cannot operate efficiently either over varying terrain. Because motors are more powerful than most humans and can operate efficiently over a wider range of rpm, they do not require as many gears as a human, but 5-8 would be required for effective hill climbing.

So, general conclusions: Those living where it is relatively flat and with only occasional high winds can get by adequately with a 250 watt or less motor. Those living in moderate hill country could use a 350 watt motor. If the only flat land is a few short stretches between steep hills, then 500 watts may be the ticket to ebike happiness. If the only way to get anywhere is to go up extremely steep hills, then a 750 watt motor and some really good brakes should be considered, but otherwise, less is more (efficient).

Related articles:

The Case for Power-Assisted HPVs

The eTrek: A practical eHPV

Ebikes as Exercise Bikes

Power vs Slope

Related links:

Ebike Touring Association

A bicycle velocity calculator is available at: http://www.kreuzotter.de/english/espeed.htm

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