When I started looking into the workings of e-bikes, I was taken by the number of different drive systems on the market. When I tried to make some comparisons between them, it got difficult. I often found 250 watt models, 350 watt models, 500 watt models, 750 watt models and even 1000 watt models, but what does it all mean to the rider? The problem with trying to get a clear picture of what the ratings of e-bike drive systems mean is that there is no “carved in stone” standard that all of the manufacturers use to tell you about their systems. They just don’t give enough information in their “sales literature” to get very specific about the actual horsepower that the e-bike is actually going to be able to deliver to the drive wheel. Let’s take, for example, a combination that has a 350 watt “rated” motor, a battery pack that is rated at 14 amp hours (Ah) and a controller that isn’t rated in the sales literature at all (as they usually aren’t).
The fact that the motor is rated at 350 watts leads us to believe that if we hooked the motor directly up to the battery pack (no controller in the circuit at all) and loaded the motor down with whatever it took to match the load that it is rated for (whatever that is, it isn’t stated either), then it could deliver 350 watts of power for some length of time. How long? Well, in theory, in order to put out 350 watts of power, when connected to 36 volts, it would have to draw 9.7 amps of current. That’s because watts = the volts driving the current in a circuit multiplied by the amount of current supplied. So, 36 volts X 9.7 amps = 350 watts. Incidentally, one horse power (HP) is equal to roughly 746 watts, so our motor would be delivering about .47 HP. We also know that our 36 volt battery pack is rated for 14 amp hours (Ah), so that means it should be able to handle the load (for a while). 14 Ah could represent 14 amps for one hour or 7 amps for 2 hours or 3.5 amps for 4 hours etc. Note that the rating of the battery pack is in Ah, not just amps, so that gives a reference to time. Talking about e-bikes, we always look at the battery pack’s supply in terms of how many watts it can supply and for how long. Since watts = volts x amps, in this case we get 504 watts and because the rating is in Ah, we are talking about 504 watt hours (Wh) that the supply has available (14 Ah x 36 volts). So, if our motor requires 350 watts, we can divide the 504 Wh by 350 watts and we come up with 1.44 hours that the motor should run under the rated load (whatever that is). Now remember, we are talking NO CONTROLLER in this part of this exercise. Putting it all together, our supply has 504 Wh and our demand with the loaded motor is 350 watts so, everything should work fine for 1.44 hours (504 divided by 350). If we reduced the load of the motor so that it only is putting out 175 watts, the motor should work for twice as long or 2.88 hours. If we cut the load in half again to 87.5 watts, the motor should now run 5.76 hours, etc. Life would be so simple, but then we throw in that darned controller. The controller’s job is to “ration” the power to the motor proportionally to the needs of the rider and his circumstances. So, it doesn’t ALWAYS offer the entire 36 volts and 14 amps to the motor. In fact, it hardly ever does and if it does, it would only be in very short “bursts”.
The way that the controller rations the power of the battery pack to the motor is quite complex. First, the controller looks at sensor inputs. These sensors can be mounted to the frame, the bottom bracket (pedal assembly), the spokes, etc. There could be what are called “cadence counters” to see how fast the spokes (or pedals) are going by or there could be “torque sensors” to see how hard the rider is pushing on the pedals. There is also an input from the display that the rider has set to tell the controller what level of assistance he desires. Most e-bikes seem to have about 5 different selections available. There is also an input that comes from the position of the throttle, if it has one and is being used. The number of sensor inputs depends on the system (model of e-bike) that we are talking about and how it is being operated.
The motor is driven by the controller by sending it pulses of energy through a process called Pulse Width Modulation (PWM). PWM is a method of controlling the speed of the motor that has been used for many years and is commonly used on golf carts. However, the golf cart industry is tending toward the use of AC motors and controllers which offer some distinct advantages over DC, but it will be a while before that technology works its way down to e-bikes (I think). You could think of PWM as switching pulses of energy to the motor in bursts that are proportional to that required to do what is needed at any phase of the “ride”. If the motor needs to operate at a higher level of power, it provides longer bursts of energy. If the motor needs less energy, it supplies smaller bursts. We could talk all day about PWM. There is a much deeper discussion about PWM over in the golf cart section here: If you could only see what is really happening at M- Welcome to Golf Cart Stuff Hodgepodge. In the golf cart industry, one of the most important ratings of the entire system is the maximum current (in amps) that the motor speed controller can supply without doing damage to itself. In the e-bike advertisements that I have seen, such a limit has never even been mentioned. That’s an important issue, because no matter how large the battery pack is or what the rating of the motor, if the controller can’t (or won’t) supply enough current to fulfill the current required, the rating of the motor makes little difference. You could have a 750 Watt motor and a 48 volt battery, but if the controller won’t supply 16 amps of current, then you will never get the motor to operate at its full potential of 750 watts.
The controller is constantly changing its output to match the rider’s requests and the riding conditions. As I already mentioned, it doesn’t just send 350 watts of energy to the motor all of the time. Of course, in addition to performance, another thing that most riders want to know, is what is the “range” of the e-bike that they have. In order to do so, it seems logical that the best way to do that is to break up the “type” of riding circumstances that might be experienced and give them a “label”. The label is best expressed in the amount of Wh that are being used in each circumstance.
In order to discuss the energy used from the battery pack by e-bikes (or golf carts) it’s important to understand the term watt hour (Wh). A watt is defined as the amount of electrical energy used when 1 amp of current is supplied under the pressure of 1 volt to a load. A watt hour (Wh) is the energy used when that happens for 1 hour. So, an amp of current supplied to a load for 1 hour by 1 volt of pressure equals 1 Wh. Now, the same amount of energy would be used if ½ of an amp of current was supplied under a pressure of 1 volt for 2 hours. The same amount of energy would be used if 2 amps of current were supplied for ½ of an hour. So, a Wh is just a measure of energy, but it is related to time. If you lighted a 60 watt light bulb with 110 volts AC for 1 hour, it would consume 60 Wh of energy. It doesn’t matter what the source of the energy is. It could be 12 volts DC supplying 5 amps (12 X 5 = 60), 110 Volts AC supplying .545 amps (110 X .545 = 60), or 36 volts DC supplying 1.67 amps (36 X 1.67 = 60). As long as it is 60 watts of power and occurs for 1 hour in time, it equals 60 Wh of energy.
Once again, in this discussion of Wh (watt hours), it’s important to keep in mind that if someone says, for instance, they are using 100 Wh at any given time, it really means that if they continued what they are doing for an hour straight, then (and only then) they would consume 100 Wh. It would seem more appropriate to say they were using 100 Wh per hour (Wh/h) They probably won’t do exactly 100 Wh for anywhere near an hour because circumstances will change as the rider goes up and down hills or speeds up or slows down. He might even spend half of the next hour sitting at a stop sign, using no energy at all. But the Wh is more of a projection of what how much energy would be used at the current rate if continued for an hour. The Wh is a way to evaluate energy consumption so that we can compare one situation during the ride to others. If the rider continued the 100 Wh circumstance for half an hour, he would consume 100 W x ½ h = 50 Wh. That way, the Wh for different parts of the ride can be “totaled up” to calculate the energy used from the battery pack.
The range of the battery pack is dependent on the Wh being consumed. Let’s say, for example, that your e-bike had a 36 volt battery pack rated at 13.88 Ah. (I’m just making up numbers that make it a little easier to work with). That would mean that your battery pack had a capacity of about 500 Wh (13.88 Ah multiplied by 36 volts). Let’s say that you discovered that the range of the e-bike, under “average” circumstances turns out to be about 50 miles. If it took 5 hours to do that 50 miles, (assuming that you were riding the whole time and not stopping) then you would have averaged 10 miles per hour (MPH). That would mean that you were using 100 Wh per hour (5 hours times 100 Wh/hour equals 500 Wh). It would follow that you were using 10 Wh per mile (500 Wh divided by 50 miles). If the same e-bike only had a range of about 25 miles in the same 5 hours, it would still be using the 500 Wh, but would only be averaging 5 MPH and would be using 20 Wh per mile.
It ends up that the general estimate that I found in popular e-bike literature and internet postings seem to support an “average” of about 20 Wh per mile, under “average” circumstances.
So, one of the best ways that you could get a “very general” idea about how far an e-bike that you are thinking about buying would have for a range, would be to look at the battery pack’s rating. Just multiply the voltage of the battery pack (36 or 48, whichever it has) times the rated Ah and that gives you the total Wh. Divide that number by 20 (20 Wh per mile average) and you’ve got the approximate range.
There are several ways that you could extend the range. One would be for the rider to lose some weight (the weight of the rider is definitely a factor). Another would be to select an easier course (less hilly) and yet another would be to play with the gear ratios that were used in the ride (sprocket gearing with mid drive e-bikes and hub gear selection with hub drive models). But, by far and away the easiest way to increase the range is to increase the number of Wh available. As mentioned above, the amount of Wh available is a product of the voltage of the battery pack multiplied by the Ah rating of the pack. So obviously a pack with 48 volts rated at 14 Ah would provide 672 Ah instead of 504 Ah provided by a 36 volt 14 Ah pack. However, you generally can’t just go to a 48 volt pack with a 36 volt system. The voltage has to match the limitations of the controller and the motor. But you could go to a 36 volt pack with a higher Ah rating (if there was one available) and that would increase the capacity and therefore the range. I think that is one reason that manufacturers seem to be headed more toward the 48 volt systems. As far as power is concerned, there is no reason you couldn’t build a 500 watt or 750 watt motor that works on 36 volts just as easy as designing it for 48 volts, but you wouldn’t be able to use the 48 volt battery pack. You’d be stuck with a 36 volt battery pack, so there goes the higher capacity of the 48 pack.
Most of the e-bikes that I could find on the internet seem to have about 5 different levels of assistance that they offer. Once again, just how many Wh get used at any one time will depend on the level of assistance requested by the rider and the inputs that the controller receives from the various sensors.
Below, are some typical circumstances and estimates of range and Wh being used at the time:
150 lb. rider
Flat surface
Low Demand, rider is pedaling and only requesting minimum assistance (probably 2 or 3 on the system)
Estimated range = 31 Miles (per internet source)
31 miles divided into 504 Wh = 16.25 Wh per mile
So, if you can get an idea of how many Wh are being consumed in a certain circumstance, you can just multiply Wh for the circumstance times the time (in fractions of an hour) and you can calculate how many Wh you have used (or are using). Let’s look at another circumstance.
Let’s say that the rider now hits a very hilly area (same rider and same level of assistance). Now it is estimated that the rider’s range will drop to around 22 Miles. That means that the system is now consuming about 23 Wh per mile.
There are many good internet websites that have that type of information. One that I have looked at many times is ebike-escapes.com. Check it out. They base their numbers on their “expertise“ and from rider’s experiences. They have put some great information together. Be sure to look for their e-bike range calculator.
Now, back to our original issue of trying to figure out which system is best (250 watt, 350 watt, 500 watt or 750 watt). Obviously the bigger the number, the more power the motor is able to deliver, but who knows if the additional power will ever be used anyway. The controller dictates the amount of “drive” power that goes to the motor with its interpretation of the circumstances. The most “requiring” circumstance is of course, when the rider decides to let the e-bike do all of the work and just supplies throttle information to the controller (no pedaling at all). In that case, the more powerful motor systems would definitely offer more performance. The price to be paid, of course, is how long the system will go before it depletes the battery pack (and the price that you pay for the upgraded e-bike when you buy it). In this case, the thing that would be of the most importance, would be the rating of the battery pack. In studying the systems, I’ve discovered that some manufacturers even use the same exact motor on different models with different voltage ratings. To get more power out of the motor, they just use a higher voltage battery pack. As discussed already, the wattage is determined by both the Ah and the voltage, so it’s easy to see that when you multiply the Ah by 48 volts (for instance) instead of 36 volts, you come up with a lot higher wattage. And most DC motors can run at different voltages, they just perform better with the higher voltages (to some limit). Also, as previously mentioned, when calculating the Wh of the battery pack, the 48 volt value means more Wh available. Instead of multiplying 36 volts times 14 Ah and coming up with 504 Wh, if you multiply 48 volts times 14 Ah you come up with 672 Wh. For that very reason, most newer models of e-bikes seem to be going toward 48 volt systems. If you plotted on a graph the voltage supplied to the motor, the RPM that the motor is spinning at, and the current supplied by the controller, you would get a “curve” that indicated the motor’s power output with different amounts of a load applied to it. The output of the motor is affected by all of these things. As the voltage is increased, the entire curve changes. Likewise, if the controller “limits” the amount of current (which it does) to the motor in order to protect itself as well as the motor, then that changes everything also. Since the e-bike manufacturers don’t give you details about all of these things that affect the motor’s performance, it’s impossible to get very precise in estimating exactly what the performance is going to be. Especially without more information about the controller and its limitations. I think, in general, it has become a good sales pitch to put as big a number in the descriptions used for the e-bikes as possible, but whether the additional power would even get used is a mystery. As the ratings of the systems seriously affect the price being asked for the e-bikes, I think I would want to ride the bike (or one about like it) before I bought one. I would put it through its paces under a variety of circumstances and “see how it feels” before I made a commitment. Keep on riding, Ron.
For information about books written by Ron Staley about both electric and gas driven golf carts and their repair, visit the following links.
Electric Golf Cart Repair, both as an eBook and in Hardcopy:
Book: Ronald L Staley: 9780578560557: Amazon.com: Books
Gas Golf Cart Repair, both as an eBook and in Hardcopy:Gas Golf Cart Repair Book: Ron Staley: 9798987911303: Amazon.com: Books