Calculating/estimating top speed

Hi

I'm thinking about buying a bike with a Bofeili crank drive and a 36V 8,8 Ah battery (bottle with samsung cells).

How do I calculate/estimate the top speed without pedalling, light pedalling and heavy pedalling? Wheel size is 26 inch and I weigh 78 kg / 171 pounds. The supplier tells me it can reech speeds of up to 40km/h with light pedalling... that seems fast for a 36v bike...

I've recieved the following motor scheme from the supplier:

davy1010 said:

How do I calculate/estimate the top speed without pedalling, light pedalling and heavy pedalling?

Wheel size is 26 inch and I weigh 78 kg / 171 pounds. The supplier tells me it can reech speeds of up to 40km/h with light pedalling... that seems fast for a 36v bike...

Click to expand...

You can get pretty good estimates from the ebikes.ca simulator even though it doesn't have your particular motor setup. This uses the simulator to do all the heavy lifting to compute more complicated considerations like aero drag, etc that vary with speed. We are left with a few simple arithmetic additions...

The simulator has two parts:

1. A section that computes a "Load Line" that indicates the power necessary to propel the bike to any desired speed
2. A section that estimates a curve showing the power the motor can develop at different speeds

The speed at which the motor power curve intersects the Load Line is the speed the bike will achieve. Simple.

In this case the simulator isn't configured to handle either this motor/drive or the idea of simultaneous rider pedaling, so we just use the first part of the simulator and apply some good guesses about the motor and rider power.

• STEP 1 - Determine motor and rider power
  
  Bike: The specs from the vendor are a little difficult to make out because of the language issue, but it appears that at 90rpm (generally assumed to be an upper limit for comfortable sustainable pedal cadence) the motor/drive will develop 321W. The drive alone may develop more power at rpms higher than are comfortable to pedal, but we'll just use this 321W figure in all cases as a lower 'max' limit in which we have reasonable confidence. (The table seems to indicate a 72% motor/drive efficiency at this point - which is mildly interesting, but not something we are going to use...)
  
  Motor/drive Watts = 321W
  
  
  Rider: Using the estimate that an amateur racing bicyclist can sustain 3W/kg for an hour, we figure he could provide 234W if he weighed 78kg like you. Riders can produce far more in bursts, but we are looking at sustainable power. You may not be at this skill and conditioning level, so we can also use a second rider (you) that is de-rated to 80% or
  
  Racer Watts = 234W
  Your Watts = 234W * 0.8 = 187W
  
  
• STEP 2 - configure simulator for bike + rider + grade
  
  The idea is to turn off the unwanted plots leaving only the Load Line and configure only enough of the simulator to generate that curve properly. This will show how much power is required to propel the bike - this has nothing to do with motor, etc - it's based on just the aero drag, rolling resistance, weight, and grade.
  
  1. Using the radio buttons at the top, turn off all the unwanted (motor) plots leaving the single Load Line plot
  2. Assuming your bike weighs about 65lbs/30kg and you weigh 78kg, set the simulator 'custom weight' for 108kg.
  3. Set it for 'Mountain Bike' which is an okay guess for any bike with a forward-leaning posture and semi-fat ebike tires.
  4. Set the Grade as appropriate (e.g. 0%)
     
     Things will look as shown below - yellow are things you can adjust for your bike, the green ones are fixed, and just ignore the red fields (which deal with the motor or are computational outputs - not inputs).
     
     
  5. Press "Simulate". You will get a plot that has a custom Load Line for your parameters that shows how fast the bike will go for any combined rider+motor Wattage.
  
  
  
• STEP 3 - Apply Power estimates to Load Line to determine speeds
  
  So - now we can use the simulator as a tool to get some answers:
  
  • Determine the "No-Pedal" speed
    
    Place your cursor on the plot just above the horizontal Speed axis, left-click, and drag the cursor left/right until the 'Load' field in the left table under the plot reads 321W. Screen resolution may not let you hit it exactly, but close enough. The speed displayed is how fast the bike will be propelled by that wattage. Here we see the bike will go a bit over 31kph without pedaling. Easy!
    
    
    It's worth noting that 31+kph is 19+mph - just about the US legal limit (20mph) for sale of ebikes. This might suggest that our estimate is fairly accurate...
    
    
  • Determine maximum speed for "Amateur Racer" pedaling + motor assist
    
    Here we just add the rider power contribution to the motor power and get: 234W + 321W = 555W.
    Repeat the 'drag cursor' operation and we see the max speed is about 39kph which is not far off the vendor estimate of 40kph.
    
    
  • Determine maximum speed for your 'perhaps-no-quite-so-fit' pedaling + motor assist
    
    We repeat the calculation for total power using your 'everyday guy' power and get: 187W + 321W = 508W
    Repeat the 'drag cursor' operation and we see the max speed is about 37kph - not much different - it takes increasing amounts of power to go faster at higher speeds so all that extra 'fitness' only bought about 2 kph.
  As mentioned above, these estimates take into account weight, aero drag, rolling resistance, and grade. The motor/drive efficiency is out of the picture because the manufacturer gave us a rated power. The drive line (chain, etc) loss isn't going to make a huge difference so we can ignore it for these purposes. We don't have all the detailed power curve estimations that the simulator normally uses, but for a pretty fair estimate only at the maximum output, this technique works okay.
  
  To summarize:
  • your No-pedal speed is about 31kph,
  • your sustained 'pedaling hard' speed + motor is about 37kph,
  • everything in between comes of just pedaling less vigorously, and
  • a very fit individual can sustain 39kph (vendor claimed 40kph)

This estimation procedure 'reads' a lot more complicated than it is - once you get the hang of what is going on, this only takes a few dozen clicks to work a calculator and the simulator to get similar results.

Hope this helped!

• EDIT - A note about the generality of this solution: We are relying on 'the power to propel the bike' being equal to 'the actual power developed by the motor' - not the battery power consumed to produce the motor power. So - the simple volt-ampere product of battery power cannot be used. Normally the simulator does complicated modelling stuff for us and draws the curved red 'motor power' line which takes many factors into account - it actually computes efficiency after the fact from battery power and simulated motor power.
  
  So in general - for unsupported motors/controllers/batteries, it's best to use options in the motor half of the simulator and just let it do its work.
  
  However, this particular estimation situation is a little unique in that the vendor gave us a final motor power figure of 321W for the complete motor/controller/battery system (which if you examine the table is Volts * Amps * Efficiency). So for the case at hand, we take advantage of that pre-computed motor power instead of the conventional approach of using the simulator for all facets of the estimate.

Thanks very much. Great explanation!

40 kph sounds spot on to me. More roughly estimated, looks like your setup's maximum wattage is about 500w. That will get you into the 22 mph ballpark, on a normal bike.

That's about 35 kph, then you might be getting about 5kph more speed by pedaling another 100w worth. I could see 40 kph easily with some moderate pedaling on the flat.

This is based not on a simulator, but a rough idea of what I needed to go those speeds, on thousands of miles of riding. It's not better than the simulator, but you tell me watts, and I can pretty much tell you what speed could be done with that wattage.

But out in the world, you will have this barely noticeable wind, or grade, that will often mean your max speed pedaling is 30-35 kph. Or if the wind is at your back, the opposite, and you could easily hit 45 kph pedaling in the right gear.

Great explanation teklektik!

Yes. Grade and wind speed and direction are v.important. Note to self: Next time trying off a cliff, must try wings, kite, etc...

I have bought the Bofeili. Read my experiences here.

I love all the explanations and calculations above. Well done.

However, in real life, the 36V Bofeili gets you to 25kmh max without pedalling. And only when the battery is completely charged. No way will you get anywhere near 30kmh without light pedalling, at least on my version. With light pedalling, you easily get the 30kmh, but you really have to put in a lot of effort to get to 40kmh. With untrained me pedalling like crazy and the Bofeili in highest power mode, I still get passed by fast lycras on the flat.

The real advantage is going uphill. Here the additional ~250W really make a difference, and instead of pedaling 5kmh up a 10% hill, you are going 8kmh. Even with pedaling, battery is empty after 20-25km in highest power mode.

So you are saying it's max power is 250w? Then 25kph would be about what I would expect too. 30-35 kph is in the 400w ballpark. 40 kph is about 600w or more. 50 kph is about 1000w, 55kph is about 1500w. See how much the ante increases as you get faster?

I was looking at that chart, and thinking you had up to 500w, and would not be limited to below speeds typical for 48-14 gearing. But even in the highest possible gear, 250w doesn't generally get you much more than 25 kph. Unless just slightly downhill.

That's a good speed for efficiency though, and you can easily pedal up to 30 kph IMO. 40 would be sprinting I bet. Once moving 35 kph, adding 5 kph more takes a lot more watts than going from 25 kph to 30.

If you had 500w, then the gearing would still limit your speed. 44-14 would be tough to push much past 35 kph.

hjns said:

However, in real life, the 36V Bofeili gets you to 25kmh max without pedalling. And only when the battery is completely charged. No way will you get anywhere near 30kmh without light pedalling, at least on my version. With light pedalling, you easily get the 30kmh, but you really have to put in a lot of effort to get to 40kmh. With untrained me pedalling like crazy and the Bofeili in highest power mode, I still get passed by fast lycras on the flat.

The real advantage is going uphill. Here the additional ~250W really make a difference,

Click to expand...

Thanks for the post - very interesting. I followed the link trail through your post - the retailer advertising is confusing at best - particularly the whole business about 'unplugging the controller' to get a power boost - although that may just have been the Google translation at work....

ricardo.ch said:

It is according to EU standard EN 15194 (throttled to 25kmh pedelec). By simply unplug the controller, the motor, the bike support to 45 km / h !

Click to expand...

I'm certain that some of the discrepancy you point out is misunderstanding the Chinese vendor plots and table (beyond any optimism there that we might expect) - I'm now wondering now if the two different (W) lines are for the limited and unlimited operation(?)... a Chinese translator would be good . I'm also unsure what the plots are trying to present and the bad coloring doesn't help.

Anyhow - using your information and playing 250W (instead of 321W) against the Load Line above brings things much closer to your experiences - 28kph no-pedal, 35kph 'everyday guy' assisted, and 37kph for 'fit' - a controller override to ensure the 25kph limit w/o pedaling would bring this to the expected 25kph at the bottom end. At 30kph the simulator shows about 300W (rider adds ~50W) so your 'light pedaling' description at that speed seems to work out as well. Looks like the 321W figure was clearly a poor choice to drive the estimates above.

So - I'm hoping you could fill in some details - what's up with the 'unplug the controller' remarks by ricardo.ch? Also - am I correct that you normally running it in the EU-compliant mode with limiting engaged?

Hi Dogman and Teklektik,

Yes, I think your remarks are spot on, and prove again the low variability (=high accuracy) of the estimates of Ebike.ca's simulator. Furthermore, I was informed that there is a higher-power (350W?) version of the crankmotor, but at least that is not the model that I have.

On my bike, the controller has a break out wire with a simple plug. Plugged-in, the controller detects the 25kmh limit, and abruptly ceases providing support completely when going faster than 25kmh. This may make the model EU (and Swiss) complient, but it is a terrible experience and really makes the rider completely loosing interest in pedaling along. Unplugged, the controller keeps assisting. Here max speed is as mentioned giving a much more satisfying experience.

Pedaling lightly and unplugged, I have biked past many Swiss cops at a speed around 25-30kmh, and none of them took any notice. Note that the Bofeili does not have a speedo, and the only way I could find out my speed was using the Navigon and/or OziExplorer on my Mobile.

hjns said:

On my bike, the controller has a break out wire with a simple plug. Plugged-in, the controller detects the 25kmh limit, and abruptly ceases providing support completely when going faster than 25kmh. This may make the model EU (and Swiss) complient...

Click to expand...

This is interesting - particularly since the limiting is switchable - a member in another thread had made a point that being able to disable limiting by switch was not allowed under EU reg - but could not substantiate it.

BTW (returning to earlier thoughts): the simulator indicates 600W necessary to push the bike to 40kph, so with the new 250W figure, the rider would need to supply 350W - which is in keeping with your 'a lot of effort' (sprint) experience. Again, an encouraging correspondence...

hjns said:

Furthermore, I was informed that there is a higher-power (350W?) version of the crankmotor, but at least that is not the model that I have.

Click to expand...

Interesting - so the original estimates above may actually be valid but apply to a different model that yours. Sort of a confusing sales situation.

Thanks for getting back - lots of good info to help clear up my confusion about this bike...