# Two wheel drive electric motorcycle speed calculation problem



## cds3302 (Oct 14, 2021)

I've built a electric motorcycle with two hub motors (no gear ratio) which are directly drive by two independent but same controllers and same throttle.
If throttle is turned, two wheels will be drive at the same time with same throttle signal but a little different speed due to the difference of the radius.
The front RPM and rear RPM are approximate but I don't know how to calculate the vehicle's speed by these two RPM since they are both driving.

Assume the front RPM is 246, radius is 0.24 meter, which the wheel's speed is equals to 22.25km/hr.
The rear RPM is 250, radius is 0.25 meter, which the wheel's speed is equals to 23.56km/hr.
Can the velocity of the electric motorcycle be 22.905km/hr?
If not, how can it be calculated?

Thanks for your reply!


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## Watsonpj (Jul 4, 2019)

Once the wheels are on the ground they will travel at the same surface speed, as friction will synchronise them, unless you have so much power that they lose traction but as they are fairly closely matched i think that's unlikely.
As the previous contributor said just use one as the input and go with that most likely the rear will give the best indication as its a fixed angle.
Best of luck Pete


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## cricketo (Oct 4, 2018)

My hunch is that is a bad design. A better (though probably still not ideal) design would be to have two motor controllers getting input from the same throttle, but having a bit of a translation to account for the difference in RPM to speed mapping. Even with cheap non-programmable motor controllers that will be easy to accomplish by having a microcontroller taking the throttle input, then splitting it into two outputs with slight amplitude adjustment for the smaller wheel.


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## brian_ (Feb 7, 2017)

The speed values may be different because of small errors in one or both (due to tire rolling radius not being exactly as expected, for instance). The speeds will also be different whenever the bike is turning a corner - the front goes further than the rear unless the rear is slipping significantly.

I agree that for the purpose of a speedometer, just use one of the two speeds. Is there some other reason to reconcile the speed calculations?


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## brian_ (Feb 7, 2017)

cricketo said:


> My hunch is that is a bad design. A better (though probably still not ideal) design would be to have two motor controllers getting input from the same throttle, but having a bit of a translation to account for the difference in RPM to speed mapping. Even with cheap non-programmable motor controllers that will be easy to accomplish by having a microcontroller taking the throttle input, then splitting it into two outputs with slight amplitude adjustment for the smaller wheel.


I don't think there's any problem with the design. The "throttle" input is normally interpreted as a torque request; in any road vehicle it is not a speed request, so there's no conflict between front and rear controllers taking the same request, even though their rotational speeds are different (as they would be in nearly any motorcycle). You don't need a translation of the throttle signal because it is not related to speed.

I think cds3302's only issue is determining the actual speed of the vehicle, not controlling it.


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## remy_martian (Feb 4, 2019)

The two wheels can't be turning at different speeds unless one is slipping.

On a street motorcycle, if the front wheel is slipping you are in deep doodoo.

One or both are slipping and if traction is regained, the rider gets to taunt death with "high siding" off the bike (think of the bike as a catapult).

So, no, you don't average speeds...you pick one.

On motorcycles, OEMs use the _front_ (not the rear as suggested) wheel for the speedometer.

As an aside, I'm curious about the make and model of hub motors you're using, and the power rating of each.

I suspect you have an electric bicycle you've overpowered legally to fall into motorcycle regulations, but it's not a motorcycle per se.


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## brian_ (Feb 7, 2017)

remy_martian said:


> The two wheels can't be turning at different speeds unless one is slipping.


Maybe try reading this again:


brian_ said:


> The speed values may be different because of small errors in one or both (due to tire rolling radius not being exactly as expected, for instance). The speeds will also be different whenever the bike is turning a corner - the front goes further than the rear unless the rear is slipping significantly.


The will be turning at different _rotational_ speeds if they are not identically sized (and they're not in most motorcycles, and not in this case). They will be running at slightly different _road_ speeds (which can be ignored for speedometer purposes) if turning a corner or if either driven wheel (two in this case, which is not normal for a motorcycle) is slipping.



remy_martian said:


> On motorcycles, OEMs use the _front_ (not the rear as suggested) wheel for the speedometer.


But in cars, OEM's use whatever wheels are driven for a mechanically driven speedometer, regardless of whether they are front or rear, although I'm sure there were some weird antique things with a speedo gear on a non-driven front hub and a long cable to the speedometer. The difference in speeds is negligible for the purpose of a speedometer. With all new cars now having ABS they have a speed sensor for each wheel, and it's anyone's guess what speed is used for display on the instrument panel.


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## remy_martian (Feb 4, 2019)

^ Maybe you should reread - rotational rate is not rotational speed. You can't change the context of your post, or mine. I was answering OP, not you.

Speed is distance over time. Rotational rate is either radians, or revolutions, per unit time. Tires are rated at max speed, not RPM....one of the main reasons for speed limiters on production vehicles.

We're also talking about motorcycles, not cars, in this topic. The treatise on different rotational SPEED of the front/rear wheel are irrelevant. Averaging the two, as proposed, is unnecessary, given the mice-nuts difference (zero if no slip)...let alone your going around corners, lol.

One tire, of known circumference, and its rotational rate can be used to derive a speedometer. In a motorcycle, every one I've seen is off the front wheel - whether electronic or mechanical.


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## brian_ (Feb 7, 2017)

remy_martian said:


> ^ Maybe you should reread - rotational rate is not rotational speed.


Yes it is: rate of position change is speed; the rotational rate of an engine or a motor is routinely referred to - correctly - as speed. Rotational rate or speed is of course not linear rate or speed.



remy_martian said:


> We're also talking about motorcycles, not cars, in this topic.


True, which doesn't matter even slightly.



remy_martian said:


> Averaging the two, as proposed, is unnecessary, given the mice-nuts difference...
> 
> One tire, of known circumference, and its rotational rate can be used to derive a speedometer. In a motorcycle, every one I've seen is off the front wheel - whether electronic or mechanical.


I agree.



remy_martian said:


> In a motorcycle, every one I've seen is off the front wheel - whether electronic or mechanical.


Again, that may be true but it it unimportant. Every motorcycle I've seen is only rear-wheel-drive, and almost all have gas engines; neither of those apply to this motorcycle, and that's okay, so why insist on using the front wheel speed? It really doesn't matter.

Cars use the driven wheel speed because the transmission was traditionally the easiest place to hook up a gear to drive a mechanical speedo cable. I don't know why motorcycles traditionally use the front hub... perhaps because the speedo is traditionally mounted on top of the front forks. All completely irrelevant to this electric motorcycle and its determination of speed from electronic signals from drive motors (or controllers).


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## cricketo (Oct 4, 2018)

brian_ said:


> Yes it is: rate of position change is speed; the rotational rate of an engine or a motor is routinely referred to - correctly - as speed. Rotational rate or speed is of course not linear rate or speed.
> 
> 
> True, which doesn't matter even slightly.
> ...


I don't know if there is any benefit to the reading the actual ground speed when dirt biking, but that's one case where reading the speed from a non-driven wheel may be more accurate than from the driven wheel which is likely to lose traction and slip.


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