250W RC belt drive - how to pick voltage/gearing for best efficiency

[PKM]

I'd like to build a Tom Stanton-style rear wheel belt drive for my road bike. One of the requirements for this project is to keep it UK road legal which means 250W and no assist over 25kph, so I'm wondering how to pick gear ratio and voltage to get the peak efficiency out of an RC style small brushless motor to make the most of my limited watts.

I believe the highest efficiency comes near the unloaded RPM of the motor - if there's a formula to calculate it I'd be interested, or just use something like the Aerodrive SK3 as an example. I'll use the maximum motor assist speed as my target speed for peak efficiency, because it's quite flat where I live and 25kph isn't very fast

For some initial numbers, a 149kv motor (the lowest I can find most places) on a 6S battery would need a 15:1 reduction to hit 25kph at 80% of no-load speed. All else being equal, I get the idea higher voltages and lower currents give better efficiency, but is the gain in switching to a 12S battery at half the current enough to outweigh needing a second reduction stage to get to 30:1?

Secondly, while I'm sure I need to overrate the motor if I want to run 250W through a small brushless for long periods, is there a major advantage in eg. a 2000W rated motor over a 1000W? Are motors with larger rotor diameters likely to give better torque under load?

 

[E-HP]

One of the requirements for this project is to keep it UK road legal which means 250W and no assist over 25kph.

I believe the highest efficiency comes near the unloaded RPM of the motor - if there's a formula to calculate it I'd be interested, or just use something like the Aerodrive SK3 as an example. I'll use the maximum motor assist speed as my target speed for peak efficiency, because it's quite flat where I live and 25kph isn't very fast

For some initial numbers, a 149kv motor (the lowest I can find most places) on a 6S battery would need a 15:1 reduction to hit 25kph at 80% of no-load speed. All else being equal, I get the idea higher voltages and lower currents give better efficiency, but is the gain in switching to a 12S battery at half the current enough to outweigh needing a second reduction stage to get to 30:1?

I would use the Grin simulator to test assumptions and relationships, even if the specific motor isn't listed. It's really handy. Using the BBS02 mid drive for an example, comparing two scenarios is easy. In the link below, all things are equal (weight, gearing, etc.), except the controller and battery. For the batteries, the configurations have the same total energy (but voltage and amp hours differ proportionally). For the controllers, the current is limited so that the battery voltage times the current equals 250W.

https://www.ebikes.ca/tools/simulator.html?motor=MBBS02&hp=0&axis=kph&cont=cust_4.8_9.6_0.03_V&batt=cust_52_0.2_11.07&cont_b=cust_10.41_20.82_0.03_V&motor_b=MBBS02&batt_b=cust_24_0.2_24&hp_b=0&wheel=700c&wheel_b=700c&mid=true&gear=1&tr=11&bopen=true&mid_b=true&gear_b=1&tr_b=11

I'd vote for system B.

Not sure how they measure/test the current or how they check the bikes, but if it's based on the rating of the battery voltage and controller, the simulator could help.

 

[PKM]

Thanks for the tip - I see why people rave about the famous simulator.j

I've tweaked one thing from your comparison - my point was that to have the motor operating in its ideal efficiency range at a specific speed, for the same kV motor I'd have to halve the gear ratio when doubling the voltage. That results in this comparison which looks more realistic.

If that's true, it tells me that a higher voltage system would have better efficiency and more torque through much of its mid range, so is probably a better system overall, with comparable top speed performance - but the low voltage version isn't a disaster so I can start with the 6S batts I have now and change the gearing/pack later on.

My other question was whether running a way over-specced motor at low wattage is going to be bad for efficiency: this set of torque/efficiency curves seems to imply that for the biggest SK3 motor, at 38V peak efficiency is reached at something like 1000W and that 6.5A is only barely above the no-load current. Again, I might be interpreting these curves all wrong - there's enough variables here that I'm a bit swamped trying to find something that fits my two fixed requirements.

 

[SlowCo]

If you want to keep it road legal at 250W continuous (peak can be higher) and would like to get the most assistance out of it, don't use Tom's direct drive on the rear wheel version. Make it a mid drive that assists your pedaling at the crank. That way all the gears get the full torque and power.
This thread has a lot of good info:https://endless-sphere.com/forums/viewtopic.php?t=96769

If it will be an on road bike you could change the chain set up to belt drive. Please update this thread with progress and photo's when you start building

 

[PKM]

I think you're right, a mid drive would be the most efficient option, but I'm steering away from it because I'd like to keep the bike relatively easy to revert to stock, and it's a lot harder to DIY than a simple belt drive. The building is the point more than the end result for me (otherwise I'd buy a second hand commercial ebike, which is an option)

 

[BalorNG]

Why exactly 'RC crank drive' is harder than belt wheel drive?

I daresay they are equivalent, though you have 'virtual fixed gear' with former. I don't think that's bad though - I think that might actually be beneficial for biomechanics (like oval rings, for instance - you legs get 'pulled through' dead spots).

 

[PKM]

Direct drive to the wheel is easy to do and doesn't require too much messing about with the bikes existing drivetrain: 3d print or machine a motor mount that clamps on the seat tube, print or laser cut a belt pulley that zip ties to the spokes, belt between.

Driving the cranks would need me to either give up one of two chainrings to the motor drive, add another sprocket in a fairly cramped location or replace the entire BB with a mid drive unit, all of which I'm hoping to avoid. It also needs more gearing because at cruising speed the back wheel does about 200rpm, the cranks 60rpm so it's the difference between a 12.5:1 reduction and a 40:1

 

[SlowCo]

It also needs more gearing because at cruising speed the back wheel does about 200rpm, the cranks 60rpm so it's the difference between a 12.5:1 reduction and a 40:1

You obviously haven't read the thread I linked to completely. They use a potentially 2kW motor with a 1:10 gearing on the crank. That means that it can only deliver roughly 200W continuous an around 400W peak power. But in every gear. Much more useful then the 250W continuous directly to the wheel you're planning to use. It would be a different story if you would "secretly" use the full potential of the 2kW RC motor directly to the wheel... :wink:

 

[BalorNG]

They use a potentially 2kW motor with a 1:10 gearing on the crank. That means that it can only deliver roughly 200W continuous an around 400W peak power.

It means nothing of the sort. Watts is torque times RPM. Reduction decreases RPM while increasing torque. Provided you have enough volts and amperes, power will stay the same.

Also, motors indeed have a certain efficiency curve and spinning at no load they are 100% INefficient, because it draws current but produces no work, and 99% of losses are iron losses btw.
By halfing rotational speed you reduce iron losses by half, and copper losses depend on current.
So, if you intend to put overpowered motor and want to use it to 1/4 of it's capacity, you should undervolt it accordingly.

 

[PKM]

Also, motors indeed have a certain efficiency curve and spinning at no load they are 100% INefficient, because it draws current but produces no work, and 99% of losses are iron losses btw.

Makes sense - I know the motor won't be providing any torque when turning at the no-load speed, so while cruising it would be turning slower than kV * voltage, but I don't know by how much.

By halfing rotational speed you reduce iron losses by half, and copper losses depend on current.
So, if you intend to put overpowered motor and want to use it to 1/4 of it's capacity, you should undervolt it accordingly.

As I understand it, resistive losses are I^2R, so doubling current quadruples resistive loss. This is why I'm a bit lost trying to work out the most efficient configuration, so many variables! I also don't know whether a 24V battery with the controller at 50% throttle is effectively the same as a 48V battery at 25% - with the controller limited to 250W it will be limiting the power pretty much all the time.

Maybe I'll avoid premature optimization and just get a motor that looks sensible to see how it performs.

 

[BalorNG]

As I understand it, resistive losses are I^2R, so doubling current quadruples resistive loss.

Indeed, resistive (copper) losses are not unlike aerodynamic losses - they start off small, but ramp up quickly.
Iron losses is not unlike rolling resistance - they rise linearly with speed (also producing heat), and the more powerful your motor is, the higher 'no load current' it will have at a given RPM (everything else being equal, like lamination thickness)

That is why, if you want highest efficiency, you should not use a motor that is rated for much more than you require, because you'll forever stay outside of efficiency curve peak. Halving the volts will proportionally decrease iron losses, while copper losses depend on current, like I said. Just don't use too much .

There is thread here somewhere about relationship of KV, volts and amperes, very good read.

I also don't know whether a 24V battery with the controller at 50% throttle is effectively the same as a 48V battery at 25%

No: 24v controller at 50% throttle for a given wattage will push half the current each PWM pulse than 48v controller at 25%, at least that's how I understand it (I'm still pretty new - and already did my share of wrong assumptions so you better recheck my advice to be sure). That imply you'll get same iron losses, but double (or, actually, qudruple, right) copper losses.

Our muscles are pretty much exactly the same, btw. Spin too fast - and there are greatly increasing losses due to intermuscular friction ("iron" losses), push too hard - and switch to anaerobic metabolism that is 10 times less efficient.

Since both our our legs and motors are at their most efficient when they spin in the certain goldilocks zone of RPM and torque, it makes total sense to use the motor (with reduction) to spin cranks, and than use transmission to vary RPM/load at the wheel.

 

[SlowCo]

They use a potentially 2kW motor with a 1:10 gearing on the crank. That means that it can only deliver roughly 200W continuous an around 400W peak power.

It means nothing of the sort. Watts is torque times RPM. Reduction decreases RPM while increasing torque. Provided you have enough volts and amperes, power will stay the same.

Apparently you didn't read the thread ( https://endless-sphere.com/forums/viewtopic.php?f=28&t=96769 ) either although you did promote a plastic chain in that thread...
By using a small light weight 2kW peak power RC motor rated for a 12S battery at just 4S with a 1:10 gear reduction on the crank the motor can only help roughly between 200W and 400W as the cadence of pedaling would be <100rpm. Read the first post (and other posts) bij FZBob. So it's not about what the motor could potentially deliver but what it can (and does) add to the pedaling of the rider.

 

[BalorNG]

By using a small light weight 2kW peak power RC motor rated for a 12S battery at just 4S

Yup, like I said in the post above, undervolting the motor shifts it's efficiency band towards the wattage range (and RPMs) OP is striving for. And yes, I did read entire thread, it was very educational (and OP should rear an other thread of his, about his belt drive woes).

Your post, however, rather unambiguously imply that reducing gearing by 10 decrease watts by 10 as well:

They use a potentially 2kW motor with a 1:10 gearing on the crank. That means that it can only deliver roughly 200W continuous an around 400W peak power.

Please be more clear.

 

[SlowCo]

Please be more clear.

I was only trying to help and advise this OP to use the motor on the crank and not directly to the wheel as aiding the pedaling through the gears seems more efficient. And makes the most of the road legal 250W he is aiming for. I wasn't trying to get in a discussion about the motor itself. Apologies if I wasn't clear enough.

 

[PKM]

Well I'm glad to see I'm not the only one who finds this a bit of a minefield...

To the people telling me to use mid drive: I'm not ignoring your suggestions, I'm on board with why it's more efficient - as BalorNG writes, consistent RPM range is a good thing. My problem with it comes back to the mechanics:

- a 125kv motor on a 6S batt would need something like 40:1 gearing to the cranks to get into what I assume is a reasonable RPM range for the motor
- I have to dick about with the cranks which I'm cautious about doing on a bike I'd like to be able to return to stock
- No possibility of drive without pedaling, unless I have some crazy freewheel arrangement

Ultimately though, this is a DIY project first and an attempt at making a real practical vehicle second. A family member has a couple of essentially brand new (mid drive, already guaranteed road legal) ebikes I could probably buy from him, which I might do at some point if I get serious about using it. The purpose of this project is to scratch build something because it's always been an ambition of mine and because building stuff is my hobby. I'd like to attempt it with a belt drive in the interests of "built not bought" (and maybe once I've made those mistakes for myself I'll cave and build a mid drive).

 

[BalorNG]

Well, that's reasonable... though you can 3d print a 'belt chainring' too, which will be easily removable. Btw, I've actually used PLA+ to 3d print a 10T cog, put on 180w (actually more like 150w, as it turns out) motor AFTER 10x reduction gearbox, and it held up just fine.
If you don't want a middrive after all, than you are indeed better off with with higher voltage battery for sure, if motor simulator is of any indication.
Using lower voltage indeed a bit more effective at close to max RPM, but the band is extremely narrow - good for middrive, not exactly for wheel drive.

 

[Grantmac]

Rather than driving the cranks via a separate chain and chainwheel you could look at a "chain puller" style. Depending on wattage you might still need a freewheel. Also you'd need a gearbox but at that wattage they are easily found in the robotics field for reasonable prices or could be done with multiple belt stages. 25:1 would be about right.

 

[BalorNG]

After playing about with reduction, it seems I can use this motor with pretty damn good efficiency (85% after all the reductions!) at 150 watts if I use *less* reduction and run it at about half of duty cycle.

That's a 115 kv copter motor rated for 3kw at 12s. 18 pole pairs, half kg weight.

 

[PKM]

Your chain setup looks good - if I can manage something like that I'd prefer it over belt because I get the idea the tension needed for good belt drive saps power.

What RPM and voltage are you getting your best efficiency at? I'm still interested in the relationship between theoretical freewheeling RPM (50% duty cycle * 12S * 3.7 V/cell * 115kv = 2553rpm?), loaded RPM and efficiency.

I'm still likely to go direct rear wheel drive because I just got some sprag bearings that could form a freewheel setup, and have access to a commercial mid drive ebike if/when I want it so direct drive would be a good comparison.