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    power, torque

    Do i understand it correctly that higher power engine will have higher torque, and lower power one will have lower torque; when torque is not enough we should shift to lower gear combination where it would be enough, however speed of bicycle would be slower. What happens when torque is not enough to turn the wheel - do engines have any protection from overload, will engine's parts be damaged when it works in that mode when it hardly turns the wheel or it doesn't matter? How much bigger should the torque be (compared to the counterreacting) to move the bike and give it acceleration?
    I need an engine for a bike to be able to go up long (10 -15 km), moderately steep ascends (10-15 deg), with allowed rider weight (110 kg or so). Speed is not important; i do not want it to be greater than 25 kmh on flat portions and priority is slow, smooth riding with the longest battery life. Would lets say 250 w cope with the task at the lowest gear combination without overheating or breaking down or a higher power should be chosen?

    Originally posted by miken View Post
    Do i understand it correctly that higher power engine will have higher torque, and lower power one will have lower torque; when torque is not enough we should shift to lower gear combination where it would be enough, however speed of bicycle would be slower. What happens when torque is not enough to turn the wheel - do engines have any protection from overload, will engine's parts be damaged when it works in that mode when it hardly turns the wheel or it doesn't matter? How much bigger should the torque be (compared to the counterreacting) to move the bike and give it acceleration?
    I need an engine for a bike to be able to go up long (10 -15 km), moderately steep ascends (10-15 deg), with allowed rider weight (110 kg or so). Speed is not important; i do not want it to be greater than 25 kmh on flat portions and priority is slow, smooth riding with the longest battery life. Would lets say 250 w cope with the task at the lowest gear combination without overheating or breaking down or a higher power should be chosen?
    I think a clarification of terms might help.

    To get a measurement of "Power" you'll need three different elements, and they're all important:

    1: Force. This refers to the amount of energy applied -- measured for our purposes usually in pounds or kilograms.

    2: Distance. This refers to how far something has been pushed.

    3: Time. How long it took to accomplish both 1 and 2.

    Torque is a combination of 1 and 2. Force multiplied by distance = torque

    Power is a calculated by multiplying torque, by the measure of time...

    So--here we go:

    Story goes, way back when, somebody just wanted to figure out a standard way to measure power. They dropped a 1000 pound weight down a well, with a pulley at the top, and harnessed up a horse to try to pull like heck and lift that weight.

    Well--according to the story, that (average or not?) horse was able to struggle that weight a whopping 33 feet over the course of one minute...

    So--go back to the formula: 1000 pounds force, x 33 feet, x 1 (for 1 minute). And so, 33,000 foot-pounds per minute--is our common measurement used today--for one "horsepower" (for our e-bike world, it's worth noting that 746 watts is equal to one horsepower).

    The calculation for torque in Newton Meters is less of a story, but the same basic deal. Force x Distance.

    Unfortunately, it's not always a "given" that the correct terms will actually be used by everyone--so there remains some room for confusion.

    However--to your questions as best I can:

    While we can assume the one-minute time-frame is a constant in the formula, it's not too hard to imagine how two motors with identical "Power Output Ratings" could still have radically different "Torque Output Ratings". A good example of this, would be to compare direct-drive hub motors to geared hub-motors.

    Electric motors like to spin fast. They're most efficient when they do. The faster an electric motor is spinning, the greater its torque, (and its power). DC electric motors can be geared for more torque at low-speeds, but they can also be wired internally in different ways, for either more torque, or more top speed. So, if you are climbing hills, at a max of 25 kilometers per hour, I think a geared-motor is definitely the way to go.

    How much power? That's a difficult thing for anyone but you to decide. But to help you begin to make comparisons, it can be helpful to know a baseline: A good strong healthy bicyclist should be able to put out around 250W of power. So--if you choose a 250W motor, you're basically adding another strong person's power to your bike. If you choose for a motor with a high gear-ratio (in the neighborhood of 1 to 10 would be good), you will end up with a lower top-speed (like your desired 25 KPH), but your motor will be under a lot less stress, because it can spin much faster inside.

    Now--as far as acceleration characteristics, geared motors, with their higher initial torque, usually provide much greater amounts of "pull" at lower speeds, when compared with a direct-drive motor. You'll see sharp acceleration with a high-torque geared motor. They produce actually pretty good power across their operating range, but once they reach their preset "max speed" that's all you're gonna get from a geared motor--while the direct-drives are more like steam-engine locomotives. The faster they go, the more powerful they get--and they sometimes seem to want to keep speeding up until you've just flat run out of juice to feed them, or the self-generated headwind is just too great... But this difference is especially helpful if you will be using your bike frequently on hills. For example, if you should stop on a hill, and must pedal uphill from a stop in order to get going again, this situation will be far less stressful on your system, the greater the gear-ratio of your motors is. Direct-drive motors wouldn't like that situation so much. It wouldn't hurt them in any way, but from a standstill, they wouldn't have the torque available to help you very much. Direct-drive motors don't want to climb steep hills, they want to set land-speed records!

    I've read that many motors (internally, or through their controllers) do have overload and overheat protection, but I'm sure there are also many which do not. I'd ask your vendor once you're ready to start choosing products.

    As far as gear-combinations, that depends on whether you go mid-motor, or hub-motor. For hub-motor projects, I'd say it doesn't matter a lot--you'll just shift into whatever gear feels right for the circumstance--same as you always have.

    For a mid-motor design, I would opt for a large rear-sprocket, and a smaller front (crank-set) sprocket. This will give you much more power at lower speeds. It will of course reduce your top speed, but you said you want that to be slow anyway--so yeah. Go for the low-end torque, and get the big sprocket in back with a mid-drive. Set it up with some "soft start" or the like, and it'll still be gentle enough on your chains and other components.

    I hope this is helpful to you, and that if I've said something incorrect that a more knowledgeable poster will correct me!

    Best of luck in your adventures!

    Take care,

    Last edited by tklop; 05-19-2018, 06:16 AM. Reason: to fix a typo and for clarity


    • JPLabs
      JPLabs commented
      Editing a comment
      Sure, generally stating efficiency as you did seems perfectly accurate to me. For the specific questions:

      It is more difficult to explain these things in comments, as we do not have formatting features to bold and underline for emphasis. So I used ALL CAPS. I do not mean to yell at you, nor express any frustration, only to emphasize words for understanding.

      1) Torque vs Work:

      Consider this: For work to occur, you need force applied over a DISTANCE, so motion of the 'object under study' is a requirement, or no work was done. The thing being pushed on needs to move. No moving, no work.

      Pushing a mass one meter with one Newton force does some work, since force was applied over distance, moving it. Pulling on a bolt with a wrench, without motion, does not, no mater how much torque is applied.

      With torque, it is simply a STATIC force. No motion occurs, if for example you apply 100 Nm with a wrench, to a stuck nut. BUT, once that nut moves, you have started to do work.

      Perhaps this can better illustrate that rotational force (Nm torque) is not work


      2): Current effect on torque:

      For a GIVEN MOTOR DESIGN, torque will be roughly proportional to current. But between DIFFERENT motor design, sure, other things matter, too. Number of windings, diameter, magnet gap, practically everything about design effects it, too. But for trends on a particular example, torque is proportional to current. Double current, within the linear range of motor operation, and you double torque. That's the simple, first order relationship. Magnetic saturation and a whole lot of really complex things make this generally untrue in reality, once 'high current' is reached, especially. But, for a simplified understanding, it is a good guiding principal.

      I hope maybe that makes it more clear.
      Last edited by JPLabs; 07-03-2018, 05:41 AM.

    • tklop
      tklop commented
      Editing a comment
      It has been a lot of years since I was learning all the Newtonian stuff.

      You explained that quite well. If I followed correctly, force applied at a distance--static--will give us a "moment" type of measurement, while once movement has occurred (the actual motion--the bending of the arm, the twist of the wrench, the turning of the motor)--then we're talking about a "work" measurement.

      I appreciate the clarification on the motors too. Motor design does plays a role; if we're comparing torque characteristics between different kinds of motors, things won't be so straightforward. But for any given single type of motor, operating in its normal range, the relationship between current and torque remains (pretty much) proportional. Okay!

      And also, I all too often get stuck using caps when I'd rather italicize. I hate to SHOUT--but as you say, we're not always given the formatting choices! No offense taken. I like seeing the words you "highlighted" with all caps. I appreciate it for the sake of clarity!

      Thanks a lot!


    • JPLabs
      JPLabs commented
      Editing a comment
      Well, apparently I explained OK enough, at least. You got it!

      Fun little dialog.

    Still Im not sure what power to choose - 250 or 350 W? (Im considering bafang middrive geared motor). I want the lowest characteristics possible. My requirement is for a bike of bike + rider weight 100 kg to be able to climb 6% uphills at speed of at least 10 kmh. (I found out that greater power gives greater speed, but w/km number becomes slightly higher, so with higher power it'll travel a smaller distance on one charge.)

    According to this model 200w gives 10.5 kmh on 6% grade. Based on your practical experience, putting you data what can you say about this model, is it close to reality? I changed only mass, grade and drivetrain loss, all other coefficients left as they are.

    Then it's a matter of gear combination (for torque at bottom bracket axle to be less then max torque of motor's outside wheel, with some margin). According to my calculation for this case torque at the rear wheel hub will be 21.3 Nm at 89 rpm, after going through max rear sprocket 34/48 - the motors chain ring it becomes 29.6 with 64 rpm at the bb axle; 29.6< max torque 80 Nm, ok; operational w = 80 rpm, if we wanted to increase w to 80, torque will also have to increase and so the power (because the resistance force F goes up with speed, and increasing rotational speed at bb will increase speed of bike); lower torque would result in lower w and lower speed of bike with this gear combination; is it normal for outer ring of motor to rotate at lower speed (64), which is outside of its stated range 78-83 rpm?
    Acceleration mode from 0 to 10 kmh. Here i chose desired acceleration so that bike would gain 10 kmh in 10 sec, got resisting force, and found that torque at the wheel would have to be 30, which translates through 34/48 to 42 at the bb, with angular velocity reaching at time 10 sec w = 64 rpm. 42<80, so it suits, w is again smaller.

    Both 250 and 350 W motors have max torque 80 Nm, but lower power engine should have lower torque, how is it possible that hey have the same torque? Where can i find detailed specifications on bafang and other motors and conversion kits (because what i read is from an internet store)?

    Here on paper everything looks wonderful, but after having read some info it seems that it's not quite so. I need to find out where the error is. If 250 W is equivalent to a strong cyclist why some people complain it cant pull uphill?
    Last edited by miken; 07-01-2018, 04:27 PM.


    • miken
      miken commented
      Editing a comment
      Check if my calculations are correct:
      for a mass of rider + bike m = 80+20 = 100 kg, to go up 6% uphill at speed 7 kmh = 1.9 ms, power needed is P = 132 W (according to that calculator)
      Force that motor must apply to bike in order to overcome the opposite force is F = P/v = 132/1.9 = 69.5 N
      ( angular velocity of wheel w = v/r = 1.9/ 0.31 = 6.09 rad/s = 58 rpm )

      acceleration corresponding to F is a = F/m = 69.5/100 = 0.69 m/s2
      since a is const, angular acceleration of wheel would be α = a/r = 0.69/0.31 = 2.24

      torque that needs to be applied to wheel equivalent to F is T = I α
      moment of inertia I = r^2 m = 0.31^2 * 100 = 9.6
      T = 9.6*2.24 = 21.5 Nm at velocity w = 58 rpm - rear wheel
      or T = F*r = 69.5*0.31 = 21.5 Nm

      find torque and ang speed at the chainring:

      w1/w2 = N2/N1 = T2/T1
      N number of teeth on cogs, N1= 34 the biggest rear cog, N2 = 48 - chainring of motor,

      48/34 = T2/21.5 = 58/ w2 , T2 = 30.1 Nm, w2 = 41 rpm
      operational torque of bbs 01 250W is T >=30, max 80, so T2 is ok; operational w = 73-83,

      assume w2 does not suit; change chainring to make w2 = 80:

      N2/34 = 58/ 80 = T2/ 21.5 , N2 = 24 , T2 = 15, now W2 is ok, but T is below the lower limit for T

      P(v) and F(v) are almost linear functions for low v.
      So if priority is power (we do not want engine to overheat), for each v there'll be a certain T and w, which could be changed through gear train, but we need to know what is better for engine - higher T and lower w, or lower T and higher w?

    Gosh, miken.

    I admire the heck out of your precision!

    But I'm not up to checking your math, sorry.

    A couple things:

    First, the motor: I know you want the smallest motor that will still function for you. But a motor that is "too powerful" for your needs, when operated at lower power settings, can still give you what you are seeking. A motor with capacity above what you need, also won't have to be running close to its operating limits, and will (probably) last a lot longer. Also, your numbers up there (unless I missed something) were assuming you're not pedaling along--just the motors are doing the work, correct? I mean, if you're willing to supplement a little 250W motor with your own energy--from your leg muscles--it'd take a lot less electrical energy to climb that hill. To figure out how much energy you might expect to contribute, you could go to a gym, and get on one of the electric stationary exercise bikes. Then, you can play with the settings, study the readouts, determine just how much human-power you can add to the mix, at what RPM is comfortable for you to sustain for the amount of time your planned journey will take. It might be wise too, to consider those numbers as something less than concrete--maybe one day you'll feel particularly tired or maybe you'll get sick, or suffer an injury, so you just haven't the energy to pedal. Perhaps allowing for this might require you to step up to the next-level motor--and just adjust your pedal-assist to meet your situations as they arise... Or maybe all this over-analysis will complicate your math to the point of uselessness! If so, sorry about that...

    Second, the battery: It sounds to me as if you want to get by with the teeniest battery you can find, that can meet your minimum requirements. This would also be strong motivation for finding also the lowest-possible powered kit that'll get you up the hill--so I do understand. But in practical use, battery capacity isn't something which works all that well at the minimum end of the scale. Battery capacity also diminishes over time. So, if you buy the "bare minimum" battery, you'll soon find it has transitioned from "bare minimum" into "inadequate". I have seen many e-bikers pushing their "assisted" bikes down the bike-paths. These fine men and women were clearly disappointed in their batteries, and it's evident as hell they wished they could go further on a charge. But I have never heard anyone complaining about having too much battery capacity.

    It's your call, your dough, your project--I'm not here to tell you what to do. But I believe that seeking to buy the "bare minimums" when it comes to your choices of battery and motor--will probably leave you disappointed.

    Is it possible to provide some flexibility in your figures? Can you plan to set aside some capacity for "alternate routes" perhaps? What if you needed to haul something heavy up that 6% grade one day? Would an extra 10% or 15% of pulling power help you out? Will considering "a little bit extra" in terms of motor power and battery capacity allow you to make your decision a little more easily?

    For myself, I planned from the very beginning, on spending about 2/3 or my project's total projected costs on the battery. For my project, any less battery capacity would have been a disappointment. Costs and prices vary for the different kinds of kits and batteries available, of course, but I think keeping that cost-ratio in mind, can help.

    In any case,

    Best of luck!

    Last edited by tklop; 07-03-2018, 03:57 AM. Reason: for clarity


      I understand that I can run 750w engine at 200w, and in that case I'll have that spare power, but if I run 250w at 750w it'll overheat and get destroyed. What I'm trying to figure out is whether it's possible to climb a moderately steep hill at 200w of power; because according to calculations it should be possible with the right gear combination. Max battery capacity Im considering is 13Ah 36V = 470 Wh; it should be enough for 24 km of such climbing. If calculations are incorrect and it'll take let's say 400w then this battery will last only 12 km and it's not suitable. In that case I will not be considering an e bike at all because it makes no sense. Even if technologies in the future improved and allowed to carry 3-5 times more energy in the same battery, it would be a potentially very dangerous, explosive thing. Could you do a test, climb a moderately steep hill at 200 w?
      Last edited by miken; 07-03-2018, 04:15 AM.


      • tklop
        tklop commented
        Editing a comment
        I think you could climb a moderately steep hill with 200W of power, yes. You could also do it with 100 watts--or even with 50--if you got the gear-ratios low enough. You can make it work. But just as your calculations indicated, the smaller the amount of available power you have, the slower you'll have to go, to sustain the climb. But theoretically, as long as you keep slowing the gearing down, and providing more and more leverage to the motor, there's no real limit on how weak a motor you can get by with... Well, after a point you'll be going so slowly you'll tip over--so the spindle motor from that old Walkman might not be the best choice!

        I suggest a double-approach: Go ahead and shoot for efficiency. The best way, is to pedal along--nothing will extend your range better than your own legs can. But also, go ahead and select a motor with a stronger rating than you need, and then turn the settings down to where you want them to be. And do the same with your battery--get more battery than you think you will need, and then work to conserve it--by pedaling along. The capacity you mention sounds a little on the weak-side to me--but it might be adequate. If you opted for 48V instead of 36V you could also get some extra watt-hours squeezed into similar battery dimensions--so, yeah... Perhaps that's another option to consider.

        Now--as far as running a test... I am an American, but live in The Netherlands. Here, we ain't got a lot in the way of hills. To scale, this nation is actually flatter than a pancake--as was shown by students from the University of Leiden. So, that'd be hard for me to do. To further complicate things, my project is a bakfiets, which weighs in (with rider, battery, toolbox, heavy-ass chain-locks) closer to--if not more than 200KG! So I don't think my numbers would really help you all that much anyway. Maybe somebody else can do some experimenting, and get you that data, but I'm afraid I won't be that guy.

        I've not conducted any surveys, but many people discovering e-bikes, wind up so happy with the experience, that they end up using their e-bikes much more than they had originally planned to. That has also proved to be true in my case. This is another good reason, to consider allowing yourself a certain amount of range and hauling capacity beyond that which falls within your current expectations for use. Try not to unnecessarily limit yourself.

        Anyways, look: I'm not trying to sell you anything, miken, I just want to see you be happy with your project! Being frugal is good, but if you try to skimp too much, I'm afraid you'll be setting yourself up for a disappointing result.

        Take care,

        Last edited by tklop; 07-03-2018, 04:48 AM.

      Consider, also, that a 250W motor will most likely deliver more than 250W power. Need to look at motor current and voltage to better understand. Motor ratings are extreme generalizations, and not accurate enough for design work to see what a bike will really do. OK for general planning.
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