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Calculating the power needed to complete a ride with BBSHD motor

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    Calculating the power needed to complete a ride with BBSHD motor

    Does my Ebike have enough power to complete a ride, including total battery life to finish the ride, and enough power to tackle the steepest climbs on the ride?

    I have been researching this for an upcoming excursion. The trick for me is that my bike is being built and is going to be delivered about 1 week before a bike / camping trip. So, I’m trying to do the best I can to predict how it will behave. After I get the bike and test it, I will post findings, and compare to my predictions here.

    To analyze this, I considered the following questions:
    1. What is the length, altitude, and elevation gain for the ride?
    2. How many watts are required to complete the ride?
    3. How much power is required from the battery to deliver the required watt hours to the pedals?
    4. Will my battery produce the required total watt hours to complete the ride?
    5. Will my motor produce enough power to climb the steepest hills?
    6. Do I have the right gear?
    7. Will my motor overheat during the process?

    Step 1: What is the length, altitude, and elevation gain for the ride?

    For my ride, I went to and found that the ride consists of the following data:
    • Length: 5 miles
    • Ascent: 2040 feet
    • Elevation – 7000 to 9000 feet
    • Average Grade: 8%
    • Max Grade: 15% has this same information for lots of road bike rides.

    Step 2: How many watts are required to complete the ride.

    I went to Kreuzotter to calculate the total watts in power required to complete the ride.

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    Step 2(a): Enter data about the ride and my bike

    I entered the data about my bike, as best I could. In this case, I will be riding a mountain bike and pulling a trailer with a heavy load. To be conservative, I figured my bike and trailer will total 150 pounds, and I added my fat ass at 182 pounds. That’s a heavy load!

    For rolling resistance, I used in 1.75” off road tires on a trike. I will actually have 4 tires rolling (two for the bike and two for the trailer). I input the bike that resulted in the highest rolling resistance available, but I believe the calculated rolling resistance that the website used will be lower than my actual rolling resistance. This doesn’t affect the calculation too much though, as a I found when playing with the various bike/ tire options.

    I entered the average grade of 8%. Altitude, temperature, and wind speed are not major factors for this ride, because it’s a long slow climb. I entered a 7 mph average speed, which is what I would hope to do hauling a trailer up a two-track road.

    I didn’t change the standard elevation or wind speed – I don’t think these variables matter in a 7 mph climb.

    Step 2(b): Convert instantaneous Watts to total Watts.

    The website gave me a result of 436 watts required to go 7 mph on an 8% grade.

    So, if I do 436 watts for 42 minutes, the total watt hours would be 436 watts x 42 minutes / 60 min per hour = 305 watt hours.

    Step 3: How much power is required from the battery to deliver 305 watt hours to the pedals?

    The 305 watt hours above is the power required to be supplied to the pedals to move the bike. I don’t have a way of measuring watts delivered to the crank from the motor. But, I can calculate the amount of electric power being delivered into the motor from the battery. The motor’s efficiency will tell me how much of the input power will be converted to watts delivered to the pedals.

    The specs for the Bafang BBSHD say that it is capable of achieving over 85% efficiency:

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    What I don’t know, however, is how that efficiency changes as the RPMs of the motor change.

    I found a bike motor efficiency graph on

    Because I have a mid-drive motor, the relevant graph from that article looks like this:

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    This chart shows that the motor being analyzed is most efficient at between 75 and 90 RPM. The Bafang specs show the RPM as 130-150, however, and I think that it is logical to assume that the specs for the motor (power, torque, etc.) are relevant in the stated RPM range.

    I’m making as assumption that the shape of the efficiency curve for the Bafang BBSHD resembles the curve shown in the chart above, but that the efficiency zone (i.e., the zone between the two vertical yellow lines) is found between 130-150 RPM, rather than 62-92 RPMs as shown in the chart. This is just a guess, but it is supported by numerous anecdotal references I have seen where people have said the BBSHD likes to spin fast. I learned a new term too: “clown pedaling.” More on that later. . .

    I’m going to assume that I will be able to stay in the efficiency range of 130-150 RPM for the bulk of the ride, but not all of it. So I’m going fudge a little and predict an 80% efficiency overall. This is still probably a best case scenario . . . or is it?

    With 80% efficiency, my motor will need to pull 381 watt hours from the battery in order to generate 305 watt hours of power to the pedals. (305 / 80%).

    Step 4: Will my battery produce 381 watt hours?

    My battery is a 48v and 14 AH (or amp hours). To get to watt hours, I multiply 48 x 14 and get 672 watt hours.

    I know there are some limitations on battery power that may affect this calculation. The only reference I’ve seen to the useable watt hours from a battery was a reference to an 80% useable ratio, but I can’t remember where I saw it. I’m going with it though, so I’ll say that my 672 watt hour battery has 537.6 watt hours of useable power. (672 x 80%).

    So my first question is answered . . . sort of. If I can keep my bike in the maximum efficiency zone of 130-150 RPM at 7 mph for the entire ride, then I should need 381 watt hours of power, and my batter should produce 537 watt hours of power -- enough to go the distance.

    But, the assumption about keeping a constant RPMs is a big one. Can I maintain that? How? More on this later. . .

    Step 5: Will my motor produce enough power to climb the steepest hills?

    For this, I went back to the Kreuzotter website. I used the same data as before, but I changed the grade from the average slope of 8% for my ride to the maximum slope of 15%. This now showed that a whopping 781 watts are required to maintain a 7 MPH pace. Using the 80% efficiency factor, I calculated that the battery will need to deliver 976 watts of power from the battery to the motor (781 / 80%).

    In order to determine the max power available for my motor, I multiplied the voltage of my battery (48v) times the maximum throughput in amps that my controller will allow (in my case, 30 amps). For my bike, I can get a maximum of 1440 watts of power from the battery, well over the 976 watts needed to climb a 15% grade on my bike. I don’t need it for this calculation, but I noted that my bike should be capable of producing 1152 watts of power at the pedals (1440 * 80%). At some point I may fool around on Kreuzotter to find out what this may mean in terms of maximum speed on my bike, and then I’ll compare it to the actual field results and see if it’s close.

    Step 6: Do I have the right gear?

    In order to hit the 80% efficiency factor, I know I have to have an RPM of 130-150. I want to go 7 mph. The question then is whether I have a gear that will result in the bike traveling 5 mph at between 130-150 RPM.

    For this, I go to

    I input my tire size, wheel size, front chain ring size (30), and size of rear cogs.
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    From this chart, I can see that I will be going 7.27 MPH at 130 RPM in the lowest gear. I thought I had maybe gotten a chain ring that is too small, but this tells me that I could actually be better off with an even smaller chain ring (or larger rear cassette). These motors like to spin fast!

    I think 7.27 MPH is going to be fine on some parts of the ride, but there are some switchbacks and there may be bumpy and rocky parts. I may have to slow down, bringing the RPM out of the efficiency zone of 130-150 RPM. I don’t know what this does to my calculations, because I don’t know what the efficiency of the motor is at lower RPMs.

    This is a major wild card in the entire analysis.

    Step 7: How do I keep the motor in the efficiency zone?

    Whether or not the analysis above properly estimates the power needed for this ride, I know that I want to be able to ride the bike in the efficiency zone - as much as possible. How do I do this?

    Basically, I want the bike to act like a cruise control. Regardless of the slope of the road, I want to maintain exactly, say, 135 RPM. This would be the equivalent of maintaining an exact speed, in miles per hour, of the bike, assuming I’m staying in the same gear. Ideally, the motor should maintain this RPM regardless of how much I’m pedaling (or not pedaling). I realize that I would only be pedaling to start going, because once it hits about 120 RPM I will just be spinning as fast as my legs will turn.

    What I’d like to do is program a PAS mode to do the following:
    • Bring in power slowly, once the pedals start moving.
    • Add as much power as necessary to reach 135 RPM
    • Keep adding / subtracting power to maintain 135 RPM, so long as the pedals are moving
    • Stop all power when the pedals stop

    I think this is where “clown pedaling” is going to come into play. The motor will be sensing whether the pedals are turning, and then will add power up to the RPM limit. But as noted above, the pedaling wouldn’t be adding any actual power, because I’d be pedaling way slower than the 135 RPM of the motor.

    A better option would be to program a throttle-only mode, where I would replace the clown pedaling with depressing the throttle. I’d be hoping for a throttle mode that would say: “add power slowly until you reach 135 RPM, then add / remove power as necessary to stay there.”

    I am going to post a separate question about programming the BBHSD on this.

    Step 8: Will my motor overheat?

    One problem with this plan could be the heat generated by the motor. Here is where the efficiency chart comes back into play. If the motor generates 80% of power to the pedals, what happens to the other 20% of power from the battery? The answer: heat! So when the motor is operating a very low efficiency, all that wasted power results in excess heat. This is why the worst situation for an ebike is described as being at a standstill, on a steep incline, in a high gear, and then mashing the throttle to full power. The low RPMs mean that almost all of the power from the batter will result in heat – very little power will get to the pedals, and the steep incline means that a ton of power to the pedals is required to get the bike moving. I have not seen many reports of overheating a BBSHD, but if there was a case for it, my planned ride would qualify. Long, steep, slow, heavy.

    I have purchased an aquarian thermometer, but not sure if I’ll have the guts to open up my controller and try to install it.

    Therefore, I need to be able to get the bike as close to the desired RPMs as possible before bringing in the power from the motor. If these wattages correspond to the watts I regularly see while training on my spin bike, I believe I can generate 300 watts at the pedals with a good hard push. I can do that for a minute or more if necessary. 500 watts is almost a flat out 100% sprint for me. So if I’m going to plan to stop for any reason, the key is to do it on a flatter section (hopefully at less than 8% grade).

    I will test all this eventually, but unfortunately for me I have almost no time to test this before I undertake the trip.

    I would love to know if this matches what people are seeing on their bikes – especially if anyone has a PAS or throttle programmed to perform in the way I describe above.

    Has anyone seen an efficiency vs RPM chart for a Bafang BBSHD?

    Let me know what you think.


    Last edited by Blbrand16; 08-16-2018, 11:00 AM.

    Is this a serious post??

    A 5 mile ride? Really? You`re going through all this over a FIVE mile ride??

    "My battery is a 48v and 14 AH"

    Chuck the battery on the bike and get out into the fresh air and throw those calculations and docs in the bin!


      Ha yeah, I guess it sounds silly when you say it like that, but it is a serious post.

      Maybe the piece you didn't see is that this is a 5 mile straight up hill climb up a ski mountain, pulling a 150 pound cargo trailer. So that's why I'm trying to understand if my bike will help / make it / melt.


        Please let us know how your trip turns out. This is very interesting. Granted its only a 5 mile trip but with the added conditions I completely understand your concern. Make sure you have adequate brakes for the decent as well. The knowledge and scientific method you applied to tackle your questions is quite impressive. Even though you only have a 5 mile Ride as tommie put it, the knowledge and methods you've shown us here could be applied to others that have more lengthy rides in various conditions and I thank you for sharing it. I look forward to hearing and seeing some pics??? of your upcoming trip and your setup. Have a Great Time!
        2018 Motobecane Boris Fat Bike BBSHD Build


          I can only offer course data reference snippets along the lines of, my 52V bike needs over 1200 watts to pull 400lbs up a steep grade at approx. 12-14 MPH.

          Have you seen the following online range / consumption calculators? They're limited, but may be useful to audit portions of your own calculations:

 (plot route / elevation changes via map)


          The very rough but quick estimator I use with my 13.6AH shark packs is 1 mile per battery amp/hour, which presumes no pedal assist, full throttle / max speed across mildly hilly terrain, with a few miles of reserve and ~25% remaining battery capacity. I use this (again, very rough) calculation mostly when making a groceries run - how fast / far can I go and still get the frozen foods home ok ;-)
          Last edited by ncmired; 08-14-2018, 07:23 AM.
          BBSHD/BBS02B builds: IGH 1 2 3 4 5 6


            I like this because I am thinking about it now. My theory is just test to destruction, or in this case ride till it dies so maybe someone else can add the math.

            You are missing the most important factor: voltage sag. I can be as high as 48 volts, on a 52 volt battery, blip the throttle, and trigger the BMS because it sagged to 41 volts. However I can PAS for miles down to a resting voltage of 43 volts. If the end of your route is flat you can do well, but if up hill you can't suck the last bit of life out of it because of voltage sag.
            Last edited by xcnick; 08-14-2018, 07:43 AM.


            • ncmired
              ncmired commented
              Editing a comment
              Yep - very true!

            • xcnick
              xcnick commented
              Editing a comment
              When I said hill, you did understand load. I actually do the PAS uphill last, just no throttle blips. So imagine a loop going up and downhill. I am most comfortable starting from the top and then PAS back to the car. At first there is anxiety of going up hill to the car. However if you go uphill first you save all you can on assist 1. If you save the hill to the end you might find enough battery left to PAS uphill with assist 4 which is really nice! If you screw up and even 1 won't get you to the car there are plenty of gravity bikers driving to the top you can catch a ride with. There is some irony in that I peddle more than they do.

            I question RPM efficiency as gospel. Certainly throttle only operation works best with these RPMs. However I think Bafang is pretty smart and designed PAS to work best below max efficiency RPM. Do this. Go up something that loads up to the max at a RPM you can pedal until it reads 1500 watts then start pedaling. It helps alot! But why? adding 100 watts to 1500 watts shouldn't even be noticeable.


              PAS is going to be much more efficient than throttle in terms of burning watts. And fewer burned watts will mean less generated heat which I am going to guess will become a serious issue. The BBSHD essentially has a fuse inside that safely terminates motor operation when the motor gets too hot: The nylon center gear melts and turns to peanut butter. I'm only half kidding. You had best not find out the hard way where your limit in this regard is.

              Here are two PAS programming levels I have used in the past. Both share the speed% settings. the 'Economy' settings came from a BBSHD driver who had analyzed output results vs. watts expended and came up with a range-extending profile as a result. I found it to require settings of PAS6+ before i felt any reall assistance and wanted to spread it out some, so I came up with the 'econ+' profile which let me shift down a bit.

              Economy Econ+ Speed % PAS
              1 1 10 0
              7 9 25 1
              11 17 30 2
              15 24 35 3
              22 31 40 4
              33 38 45 5
              47 47 50 6
              69 69 60 7
              85 85 80 8
              100 100 100 9
              In the end, I developed an entirely new profile. As follows:

              Current Speed PAS
              4 10 0
              11 20 1
              19 30 2
              28 40 3
              38 50 4
              49 60 5
              61 70 6
              74 80 7
              87 90 8
              100 100 9
              Note that PAS0 is a mild boost. Speed settings are even increments and the current differentials increase by one point between each step for what is meant to be as smooth of a top-to-bottom curve as possible, with mildly increasing increments of boost in between each level (the theory being when you want more you want *more* especially at the upper end of the scale and this curve helps deliver that).

              So, this curve satisfies my desire for performance that utilizes 10 distinct assist levels rather than an effective three or four. But still retains economy. Your programming needs to be somewhere in this realm.. .certainly not left at default which will pour out watts that will translate into heat.

              Also, look into heat sinks on the exterior of the motor. You should be able to reduce casing temps by up to 15 degrees fahrenheit which will help mitigate what you're going to be doing to this motor.


                Remember to downshift to get to more efficient range of motor, you will know when the motor is not operating efficiently as it will struggle.

                The most important factor from your battery in this case is if it can provide the power for a sustained run. Voltage will sag badly if it cannot. In this case you will want it to be able to sustain 10 A continuous or so to deliver about half a kW of power at 48 V (nominal).

                Also consider your potential energy change. In order to lift 150 kg up 650 m at 80% efficiency will take about 1/3 kWh. This is included in your nifty calculator, but I felt it useful to pull it out to show how much energy is going to the elevation change. This is in addition to the energy you need to overcome rolling resistance and air drag. 1/2 kWh would probably be enough, but again, make sure it meets the current/power requirements you need. Most 1/2 kWh batteries should handle 1C discharge, which would be able to produce 500 watts continuously. If you want to go faster you might need a larger battery capacity for the added power delivery or use a chemistry that can handle greater than 1C discharge. Many go to 2-5C or even higher.
                Last edited by Viking79; 08-20-2018, 09:44 AM.


                  Many thanks for the thoughtful replies. My bike is en route to me now, and I should be able to start testing and playing with the programming by next week. My trip starts Sept 7, so I dont have a lot of time.

                  BTW, my bike is a custom build from High Power Cycles. It's a BBSHD built on a KHS six fifty 680+, with a 30 T chain ring, 48v 14 Ah battery. Supposed to be good for 2000 watts. I can't wait to see what this sucker can do.

                  I will report back with results.


                    Hi Bibrand. Just like to chime in with my own two bobs worth. I'm frequently amazed by the level of knowledge and innovation I discover on this forum. That's a serious Phd type hypothesis right there. I'm intrigued to hear how the ride actually pans out now. My other hobby is paragliding and the boffins in that sport employ the latest gadgets, equations and trickery to elicit the best possible glide angles out of our wings. From experience when theoretical science collides with reality, reality wins. Love your commitment and dedication to the cause though. All the best with the ride.


                      RESULTS ARE IN:

                      Well the bikes performed like champs. I almost made it to the top. The battery failed about 300 yards from the top. Here are my observations:

                      - These motors kick ass. We put them through a serious torture test and they performed beautifully.

                      - What I learned was that the terrain mattered a great deal. We anticipated a fairly smooth dirt road but what we found was in many places the road had turned to a rocky single track. The rocky terrain took way more power than a smooth road. Honestly, had I known the road would be that rocky, I wouldn’t have attempted it!

                      - The bikes had PLENTY of raw power to pull the load up even the steepest and rockiest parts.

                      - My bike did not have a display that indicates Watts being used, so I cant report on the actual watts I was using, but based on feel (and having ridden lots of stationary bikes with watt meters) I think the calculation of watts needed felt about right.

                      - Karls Special Sauce worked great. I experimented before the trip with some different programming options, but I found Karl’s to give plenty of good options when combined with my bikes gears

                      - Neither the motor nor the battery ever showed any signs of overheating. They remained just barely warm throughout the ride.

                      All in all, I was really impressed with the Bafang HD. I am looking forward to using it on future excursions.

                      Click image for larger version

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                      Last edited by Blbrand16; 09-24-2018, 11:33 AM.


                        That's great! Glad it worked out for you. Thank you for letting us know how your trip went. I saw you mention you have a 30T front cog, can I ask what the rear gearing range is on your bike and which gears did you use?
                        2018 Motobecane Boris Fat Bike BBSHD Build


                          Congratulations! Now... since you are carrying along a trailer ... go get a second battery and toss it in with the rest of your gear :-)