Rear wheel diameter; torque vs acceleration

[E-HP]

I see posts frequently that state that a smaller diameter wheel develops more torque. Now that my 24" rim arrived, and since looks pretty good sitting next to my new Leaf hub, I'm going to go ahead with relacing the wheel. Playing with the simulator before made me hesitate, since the gains were not major going from 26" to 24", but since it's less than 2mph loss speed-wise, the small advantages would still be nice to have.

Here's what seems odd. I have the Grin simulator set up for my bike, comparing both wheels, all else being equal. At full throttle, at every speed up to top speed, the 26" has more torque, by a small margin around 5%-6%. However, also at full throttle, the acceleration of the 24" wheel is quicker, by the same margin (leaving throttle auto unchecked, then moving the sliders for each to the same speeds).

To me, it makes sense that the smaller diameter wheel will accelerate faster, but I didn't expect the torque to change in the opposite direction.

The 24" wheel has 5%-6% quicker acceleration all the way up to 34mph, where the torque curve drops off, so not a whole lot, but for most of its range. Still, people put tons of money into cars just to get another 5% back in performance, so I'm doing the swap once I decide on a tire and get it ordered. Any explanations or theories about the effect on torque and acceleration from changing wheel diameter that the simulator is displaying?

https://ebikes.ca/tools/simulator.html?motor=Leaf%205T&batt=cust_72_0.05_24&cont=cust_70_200_0.03_V&hp=0&axis=mph&frame=mountain&autothrot=false&throt=100&grade=0&bopen=true&cont_b=cust_70_200_0.03_V&motor_b=Leaf%205T&batt_b=cust_72_0.05_24&hp_b=0&wheel_b=24i&grade_b=0&autothrot_b=false&throt_b=100

 

[Chalo]

Wheel diameter has no effect on torque. Torque is force times radius, so enlarging the radius reduces the force, and the reverse is also true. But the torque from any given motor at the same voltage and current will be the same.

A smaller diameter wheel will mean lower free speed, and perhaps lower top speed. Acceleration will be quicker and the motor will be able to reach equilibrium at a more efficient maximum road speed.

 

[E-HP]

Wheel diameter has no effect on torque. Torque is force times radius, so enlarging the radius reduces the force, and the reverse is also true. But the torque from any given motor at the same voltage and current will be the same.

I think it likely doesn't impact the motor's torque, but the simulator describes it as wheel torq(ue), which I assume mean applied to the ground. Several motors display the same behavior.

 

[john61ct]

The smaller wheel requires less torque to get the same acceleration

or same torque delivers more acceleration.

"wheel torque" meaning at the hub rather than on the contact patch?

 

[afzal]

Wheel diameter has no effect on torque. Torque is force times radius, so enlarging the radius reduces the force, and the reverse is also true. But the torque from any given motor at the same voltage and current will be the same.

I think it likely doesn't impact the motor's torque, but the simulator describes it as wheel torq(ue), which I assume mean applied to the ground. Several motors display the same behavior.

For a certain motor power, neglecting losses, power at the wheel is same irrespective of the wheel dia.
And power = torque * angular speed, angular speed being proportional to wheel dia.

T(26") * w(26") = T(24") * w(24") = P
=>
T(24") = T(26") * w(26") / w(24")
=>
T(24") =T(26") * 26/24

[ T - torque, w - angular speed ]

Per the reasoning above, shouldn't lower wheel dia give higher torque at the wheel for the same motor power ? or am I wrong ?

EDIT: Above considers the case at same motor rpm

 

[AHicks]

Regarding "torque" looking at that chart, it would appear to me that all else being equal, the lower rpm torque values are always higher than when measured at higher rpm. So from there its safe to assume I think that the larger wheel will produce (require?) the most torque.

My GUESS is, the reduced efficiency and power shown in the graph may be related to the number of turns of wire. For instance, if there were a 4 turn (speed) version of this same motor, I wonder how it would compare to the graphs shown here?

 

[DogDipstick]

Hmmm whats the difference in this example setup?:

Identical except for o9ne variable....

My setup is similar. Then look at the lower model. The lower model has two variables changed. What happened?

One variable between them: Result being, one is alot faster, one is alot tork-y-er



Two variable; Now, all of the sudden, we peak power, much closer to each other. Again, What happened? Why does a kV change and a Wheel Dia make so much difference? Just two variables, the rest being the same? Why such different top speeds? All around? Huh.


Ok So now we are back to the OP question.

Only thing in this example, is, the variable is the wheel dia ( same kV)...

Much closer together. Top speeds AND accelerations.

Why does current drop with back EMF? Why does the back EMF has such a great effect on current and power? Questions I have.

Same except the dia:

Random quoted definition ( superfluous)...
Ok Im done.

"This voltage is in series with and opposes the original applied voltage and is called "back-electromotive force" (by Lenz's law). With a lower overall voltage across the motor's internal resistance as the motor turns faster, the current flowing into the motor decreases. One practical application of this phenomenon is to indirectly measure motor speed and position, as the back-EMF is proportional to the rotational speed of the armature"

 

[Comrade]

To me, it makes sense that the smaller diameter wheel will accelerate faster, but I didn't expect the torque to change in the opposite direction.

But torque didn't change. It just shifted. You get same torque, just at different speed relative to ground.

 

[E-HP]

To me, it makes sense that the smaller diameter wheel will accelerate faster, but I didn't expect the torque to change in the opposite direction.

But torque didn't change. It just shifted. You get same torque, just at different speed relative to ground.

The wheel torque is different depending on diameter, only a small amount in my example, but you can see the 24" wheel torque curve is lower in torque than the 26" wheel. Here's an example of 26" vs 16", which displays a much larger difference, but still, the smaller wheel has much less wheel torque through the entire range:
https://ebikes.ca/tools/simulator.html?motor=Leaf%205T&batt=cust_72_0.05_24&cont=cust_70_200_0.03_V&hp=0&axis=mph&frame=mountain&autothrot=false&throt=100&grade=0&bopen=true&cont_b=cust_70_200_0.03_V&motor_b=Leaf%205T&batt_b=cust_72_0.05_24&hp_b=0&wheel_b=16i&grade_b=0&autothrot_b=false&throt_b=100

At 20mph, in this example, the smaller wheel displays 22% less wheel torque, but 31% quicker acceleration:

 

[neptronix]

The torque and continuous power handling potential of a smaller wheel running at a higher RPM is higher. When you take advantage of that extra capacity, you will see the extra power shine through.

You can see this extra power show on the ebikes.ca simulator with many high kV windings in 20" wheels versus an equivalent winding in a 26" wheel, it makes the difference between the 45mm MXUS "3kW" being rated at 3000w in a 20" wheel but only giving ~2250w continuous in a 26".

ZombieSS showed us long ago how we could hit 50mph on crappy 0.5mm lam 9C motor clones. He did it with a small wheel and a lot of volts. Can't achieve that kind of power density with the 26" version because you can't get the motor's RPM per mph as high.

About 5-7% higher power potential is roughly correct for a 24" wheel versus a 26". Great way to go if your geometry allows it and you want more power. Low negative impact on your upright bike's geometry, too.

 

[detraquez]

Hi all !

I have spent a lot of time of the simulator wrapping around all this and with different setups in the real world to compare. If you want acceleration, you need more thrust or force which a function of torque and wheel radius. The motor simulator can be configured to display thrust instead of torque, thus taking wheel diameter in account in the graph. Just swith the blue curve to display thrust.

The equation for torque

τ = LFsinθ [Nm]

τ = axle torque Torque [Nm] (function of motor Kv and phase current, not described here)
L = lever length, in our case wheel radius (half of the diameter, tire included) [m]
θ = angle at which the force is applied, in our case 90° as the ground is always perpendicular to radius of the wheel. sin90° = 1, this term can be simplified. [°]
F = force applied to ground to propel vehicle [N]

The acceleration is proportional to the force applied to the ground, so we can rearrange the equation to :

F = τ/(Lsin90°) = τ/L

Just divide the torque [Nm] by the wheel radius [m] converted in meters. At equivalent torque, a 24-inch wheel delivers more thrust.

Here are two identical simulations, one displayed in Torque and one in Thrust

First one (torque) :
https://ebikes.ca/tools/simulator.html?bopen=true&wheel_b=24i&batt=B7208_DT&batt_b=B7208_DT&cont=C40&cont_b=C40&motor_b=M3525_SA&motor=M3525_SA&blue=Nm

Overall torque is lower throughout entire range with 24 inch vs 26 inch.

Second one (thrust) :
https://ebikes.ca/tools/simulator.html?bopen=true&wheel_b=24i&batt=B7208_DT&batt_b=B7208_DT&cont=C40&cont_b=C40&motor_b=M3525_SA&motor=M3525_SA&blue=Lbs

Thrust, or acceleration is higher for 24 inch until back emf kicks in and power drops, where the 26 inch keeps pushing a little longer, due to slightly lower rpm and same travel speed.

Hopes this helps.

 

[Comrade]

Thrust, or acceleration is higher for 24 inch until back emf kicks in and power drops, where the 26 inch keeps pushing a little longer, due to slightly lower rpm and same travel speed.

So, when the wheel RPM is the same, in 24" or 26" or any other size, the hub is providing the same torque, but obviously different thrust due to different wheel size. Is that an accurate statement?

 

[neptronix]

What most people tend to do is not adjust for the differential in speed.

Here is what the scenario looks like with the speed adjusted to be equivalent in a 24 vs 26" comparison:

https://ebikes.ca/tools/simulator.h...l_b=26i&bopen=true&throt_b=95&hp_b=100&hp=100



There's the extra torque.. as well as some extra efficiency.


Let's try this on a 20 vs a 26".. and thankfully, the 9C has windings for each, so we can make a near perfect comparison:

https://ebikes.ca/tools/simulator.h..._b=26i&bopen=true&throt_b=100&hp_b=100&hp=100



And look at the 26 inch motor.. it over heated a long time ago..

Put more like 80A into the simulator and 250 phase amps and put these two motors under saturation and you'll see that a 23% smaller wheel spinning at the same speed per mph can produce up to 23% more torque.

 

[amberwolf]

Why does current drop with back EMF? Why does the back EMF has such a great effect on current and power?

Because the back EMF (BEMF) is the voltage generated witin the motor windings as it rotates. This gets higher with faster motor speeds. The higher the BEMF is, the more voltage it takes to create the same voltage *difference* across the windings, and thus the same current thru them.

So the more BEMF, the less current, all other factors the same.