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Dealers Primer on Voltage. Amps, Watts
What is VOLTAGE and which Voltage is best?
Voltage can be thought of as the pressure or strength of electric power. All things being equal (see AMPS below), the higher the voltage the better, because high voltages pass more efficiently through wires and motors. Very high voltages (100+ volts) can give you a nasty shock because they also travel through people rather well, but the sort of voltages found on electric bicycles (12 - 48 volts) are quite safe.
What are AMPS?
Amps can be thought of as the volume or quantity of electric power. To aid this analogy, the flow of amps is called the current, as in the flow of a river. Unlike a river, though, the speed of the current is fixed - only the volume varies. This is controlled by the Electronic controller of your electric bike.
The maximum flow of amps in a bicycle drive system can vary from 10 to 30 or more. A current of 30 amps requires thick wiring and quite substantial switchgear.
What are WATTS?
Once we know the voltage (or pressure) and current (or volume), we can calculate the power, or wattage by multiplying the two figures together. The number of watts in a system is the most important figure of all, because it defines the power output. A few examples:
The 418 Street Bike motor draws 15 Amps x 36 Volts = 540 Watts
The 098 City Bike draws 15 Amps x 48 Volts = 720 Watts
The 441 Folding Bike draws 12 Amps x 24 Volts = 288 Watts
The TRIKE draws 15 Amps x 36 Volts = 540 Watts
The 443 Mtb draws 15 Amps x 36 Volts = 540 Watts
Th 415 Stealth Climber draws 20 Amps x 36 Volts = 720 Watts
The 643 Town and Country Cruiser draws 26 Amps x 48 Volts = 1248 Watts x
It's impossible to calculate the power without knowing both the number of amps and volts. Large machines, like cars, trains and trucks have their power measured in the same way - usually as kilowatts, or units of 1,000 watts. The old-fashioned 'horsepower' unit is the equivalent of about 750 watts.
What about the legal limit of 750 Watts in the USA?
The legal limit refers to the continuous power output, whereas the figures above are for absolute maximum power. Most motors can give maximum output for a minute or two, but they'd melt if asked to do it all day - just like a cyclist. Obviously, maximum power is more useful than continuous power as a guide to the way a bicycle will climb a hill. Look at the spec of bikes on sale and you may see 200 watts, 350 watts or (illegally) 1250 watts. These figures are only a rough guide to the true maximum power output, and are the continuous power. Most batteries can give a PEAK Amps for a few seconds, and most electronic controllers can give a shorter time of peak Amps as well.
How to figure continuous Watts listed with the bikes? This is not so easy, because this should actually be calculated with the motor, controller, battery working in sync with each other. To build an electric bike, you need to match up each of these as good as possible for maximum efficiency.
Continuous Watts gets close by multiplying the efficiency of the motor (about 75%)by the Watts calculated above.
A motor is listed as a 350 watt motor, a 1250 watt motor, a 200 watt motor, etc. What does this mean? This is the wattage that the motor runs most efficiently. So the 643 would have the following calculations:
Maximum power: 1248 watts x .75(efficiency) = 936 continuous watts available power to motor However, when you figure all this together, there is continuous rating that puts it at about 750 watts from actual useage. Thus, we can just slip under the legal continuous limit of 750 continuous watts when you figure heat loss, road friction, and line loss, and any other factors. Frankly, speaking this is the most powerful motor controllerbattery configuration that we can have and get under the legal limit. Again this is average. When our 48 volt batteries are fully charged we will actually be at around 52 volts. So you will be cruising much above this, especially when bike is not hot. However, when the battery is cold around freezing your battery will only work at about 80 85% efficient with the Lead Acid. So you understand there are a lot of factors and across manufacturers you cant always compare numbers with numbers and get the real power comparisons.
How many watts do I need?
As a general rule, a cyclist can produce several hundred watts briefly, and one hundred watts for a reasonable length of time. To be really useful, a motor needs to produce another 100 Watts on a continuous basis, with peak power of at least 350 watts. Just to confuse things, our measurements are of power consumption - losses in the motor and drive system mean that the power output to the wheel can be much lower.
If you expect the motor to do most of the work, especially in a hilly area, you'll want a peak consumption of 600 watts or more. On the other hand, if you prefer gentle assistance, a peak of 200 watts similar to the 441 folding bike may be enough.
Bicycles, scooters, and even automobiles are all governed by the same fundamental power requirements. At constant speed, the power required to move the vehicle and the passenger goes to three places:
1. The power required to overcome the rolling resistance of the wheels on the pavement.
2. The power required to overcome the wind resistance associated with moving the vehicle/passenger through the air.
3. The power required/provided to move the vehicle and passenger up/down any incline (if not traveling on flat pavement).
(NOTE: If you liked high-school physics, see the Physics of ebikes at the end.)
How big a battery do I need?
The capacity of the battery is usually measured as the amount of current it can supply over time (defined as amp/hours). However, this is useless on its own, because you'll need to know the voltage too. By multiplying the two figures together, we get watt/hours - a measure of the energy content of the battery.
It's best to choose a package that will provide twice your normal daily mileage. It's difficult to guess the mileage from the watt/hour capacity, because actual performance depends on the bicycle and motor efficiency, battery type, road conditions, and your weight and level of fitness.
How can I measure the efficiency of an electric bike?
We measure overall efficiency by dividing the watt/hours used by the battery charger by the mileage achieved, giving a figure of watt/hours per mile. This varies according to the terrain, the weight and riding style of the rider and the type of battery and charger, typically, an electric bicycle will consume 10 - 20 watt/hours per mile. So a big battery like the 643 Town & country Cruiser will give the longest range. This is fine for most uses, although it's a big, heavy battery. As a general rule, medium-sized NiMH, Lithium, or the new LiFePO4 batteries on lightweight bikes give the best results for those who want to pedal more like a bicycle.
Do electric bicycles recharge when you coast downhill?
With the exception of the Canadian BionX, the answer is NO. Taking into account wind-resistance, road friction and so on, there's surprisingly little energy left over for recharging the battery, even before generator and battery losses are taken into account. In most systems the motor coasts when you ride downhill, but those that don't (mainly electric scooters) are capable of putting back only 15% of the power absorbed climbing the hill. Regenerative systems do have their advantages though - mainly in reducing brake wear and over-heating.
Which battery type is best?
Lead-acid batteries are cheap and easily recycled, but they are sensitive to maltreatment and have a limited life. Weight for weight, NiMH gives more capacity, but it's expensive. Ni-MH is available as the only battery option for the 441, and as s choice on the 443 MTB. Our Trike and 415 Stealth Climber bikes come with Lithium-ion (Li-ion) batteries. These are more weight-efficient than the other types, and are supposed to have a longer life, but can do some odd things. Charging and discharging must be carefully controlled to prevent the cells going into terminal meltdown, so chargers are packed with electronics, as are the batteries. Costs are coming down rapidly and now effective battery management circuits are built in on the Lithium-ion, so they are much safer. Lithium-iron-phosphate (LiFePO4) is the newcomer to batteries (usually called Life-Po) is a bit heavier than the Lithium Ion (LiMN), but has the advantage of 1500 2000 recharges, is safer, and promises to become even cheaper once the technology becomes mainstream. Very few bikes offer these batteries yet. Liberty is working hard to incorporate this into their newest bikes.
Should I choose a brushless motor?
Broadly speaking, there are two types of electric motors:
Direct Current motors - simple but comparatively heavy and inefficient, and
Alternating Current motors - smaller, lighter and more efficient over a broader speed range
Generally speaking, Direct Current motors have brushes to transfer power into the rotating bit and Alternating Current motors do not. However, most of the brushless motors fitted to electric bicycles are a hybrid of the two types, often called 'Hall Effect'. These are not quite as clever as a full Alternating Current motor, but do away with the brushes, so they should be more efficient and more reliable than the straight Direct Current type. Hall Effect motors the brushless motors on Liberty electric bikes. Direct Current brushed motors may have mechanical brushes, but they're mercifully short of complex electronics. The 441 Folding Bike has brushed motor
Physics of Electric Bikes
We can write this as an equation:
Total Power =Power-rolling-resistance +Power-wind-resistance +Power-hill-climbing
(Note that Total-power is the power delivered to the driving wheel of the vehicle net of any friction in the transmission and inefficiencies in the power system.)
To a first approximation, power-rolling-resistance is in turn determined by the weight of the vehicle/passenger (W), the speed of the vehicle (S), and a coefficient that characterizes the rolling resistance of the wheel (a).
Power-rolling-resistance = aWS
To a first approximation, Power-wind-resistance is determined by the "frontal area" (F) of the vehicle/passenger (the area of the outline of the vehicle/passenger when viewed from the front), a coefficient (b) that characterizes the shape of the vehicle/passenger, and the CUBE of the speed (S x S x S).
Power-wind-resistance = bFS^3
Power-hill-climbing is determined by the grade of the hill (G), the weight of the vehicle/passenger (W), the speed (S) of the vehicle/passenger.
Power-hill-climbing = GWS
So, the entire equation is:
Total-Power = aWS + bFS^3 + GWS = (a+G)WS + bFS^3
Before we do some calculations, we can make some interesting observations:
1. Total power required is strongly influenced by speed.
2. At high speeds, the effect of wind resistance will be very large (because it depends on S cubed).
3. Light vehicles/passengers have an overall advantage. In fact, although W does not appear in the expression for wind resistance, frontal area (F) is highly correlated with W, so overall size/weight pretty much influences all three categories of power consumption.
Now, some approximate numbers. (This uses metric units, but provide some examples and conversion factors for those of you who think in English units.)
a = coefficient of rolling resistance
0.008 for high-pressure 700mm road bike tire
0.020 for a mountain bike tire
0.040 for a typical (e.g., 9 inch) pneumatic scooter tire
W is weight in Newtons (1 pound = 4.45 Newtons)
S is speed in Meters/Second (1 mph = 0.45 meters/second)
b = drag factor in kg/m^3 (This includes air density factor for sea-level air. Picky engineers: see note below.)
0.6 for a square-edged box
0.4 for most human-like shapes
0.2 for a egg-shaped object
F = frontal area in square meters
0.4 for a crouched racing cyclist and bicycle
0.6 for an upright cyclist and bicycle
0.8 for a standing scooter rider
G = height of climb/distance of climb (e.g., % grade)
Typical maximum railroad grade = 0.02
Typical maximum bike path grade = 0.05
Typical maximum overpass grade = 0.08
Maximum grade on Pike's Peak mountain road = 0.10
Powell St. in San Francisco (cable cars) = 0.17
Examples:
1. How much power is consumed to propel a medium-sized (165 lb.) adult standing on a scooter with 9 inch pneumatic tires traveling at 12 mph?
W = 165 lb. = 734 Newtons
S = 12 mph = 5.4 Meters/second
a = 0.040
b = 0.4
F = 0.8 square meters
G = 0
Total-Power = (a+G)WS + bFS^3 = (0.04+0)734 x 5.4 + 0.4 x 0.8 x 5.4 x 5.4 x 5.4 = 159 + 49 = 208 watts
2. How much power is consumed in the same situation except traveling up a 2% grade at 12 mph?
now G = 0.02
Total-Power = (a+G)WS + bFS^3 = (0.04+0.02)734 x 5.4 + 0.4 x 0.8 x 5.4 x 5.4 x 5.4 = 238 + 49 = 287 watts
3. What happens if the scooter is going 20 mph on the flat?
now S = 20 mph = 9 meters/second
Total-Power = (a+G)WS + bFS^3 = (0.04+0)734 x 9 + 0.4 x 0.8 x 9 x 9 x 9 =
264 + 233 = 497 watts
Some notes:
Note that climbing a 2% grade (G=0.02) consumes the same power as rolling on tires with a rolling resistance of 2% (a=0.02).
Note that the power required to propel a vehicle does not depend on the power source. In other words, a scooter powered by kicking requires the same power for the same speed, weight, etc. as a scooter powered by an electric motor.
Finally, let me note that the vast majority of small electric vehicle manufacturers do not appear to know these basic laws of physics. I see a lot of scooters with advertised top speeds of 15-17 mph, yet with 9 inch pneumatic tires, and with motors and transmissions that can deliver only about 150 watts to the wheels. You can calculate for yourself that the specs must be highly exaggerated (or the manufacturers must assume that a small child is riding the scooter down a big hill...). Caveat emptor.
NOTE TO THE PICKY ENGINEERS (you know who you are): The expression for wind resistance is actually rho/2 * Cd * F * S^3, where rho is the density of air and Cd is a non-dimensional drag coefficient. Since rho is around 1.2 kg/m^3, the rho/2 term is around 0.6. To simplify these calculations, I included this factor of 0.6 in computing the "coefficient" b.
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