Wheel size vs. speed for electric soapbox

Not directly Arduino related but hoping to pick the brains of you electric motor experts on this a bit.

For a school project that I'm teaching we're going to build electric cars - soapboxes is a better word I think. Two 775 type motors rated 35W geared down to 200 rpm are to propel a car made out of a 2x4' (62x124 cm) piece of plywood with one student on top. Each motor drives one of the rear wheels; two smaller wheels on the front that take care of the steering, and a simple PWM power controller for the speed. The wheels are directly driven by the motors.

The question I have is related to the effect of wheel size on total speed. I have built a prototype with wheels of some 25 cm diameter, and with my 90-something kg on top it reaches a firm walking speed, about 6 km/h. I'm quite happy with that. Fast enough to be fun, slow enough to be safe (no brakes).

Now (unfortunately no chance yet to do testing) I'd like to know what to expect from changing the wheel size, and why. My guesses:

Smaller wheels: more torque to the ground, giving faster acceleration. At full speed the motors will be running at higher rpm, enough to compensate for the smaller wheels? Higher rpm means lower current through the motors and less overall power.

Larger wheels: less torque to the ground, slower acceleration. However at full speed motors are running a bit slower, more current, more overall power, resulting in a higher top speed.

Too small wheels: motors run easily at (near) full 200 rpm but the small wheels mean low speed.

Too large wheels: motors don't have enough torque to get the vehicle in motion (something I experienced with my wheels already on a not so flat surface, and getting stuck behind a small bump, needed a little push to get started).

There must be a sweet spot somewhere in there, maximum acceleration (for a drag race across a basketball court) and maximum speed (for a race of a few laps around this court).

You need to do some experiments to see - I’d also measure motor current using an analog ammeter .

If you pull your loaded cart via a spring balance at various speeds you can work out the power required to achieve that speed , and your likely maximum with the power output of your motors .

Look up equations of motion for calculations for acceleration too.
You are correct about the effect of diameter , but your limiting factor for speed is power - to overcome the rolling resistance of your cart .

You only have 75watts , that’s not a lot of power ( electric pushbikes with assistance motors start at 250w)

You need to do some experiments to see - I’d also measure motor current using an analog ammeter .

Why analog? I measured with a digital one and free running I got a surprisingly low 1.5A. I don't have an analog multimeter that does that range unfortunately. Stall current is supposed to be 10-12A (seller's info).

You only have 75watts , that’s not a lot of power ( electric pushbikes with assistance motors start at 250w)

I know, it's not much. I just don't want the kids to zip around at highway speeds :slight_smile: As said I got to about 6 km/h on my first quick build which is good enough for this project.

So when a motor is loaded, the speed goes down, and the current goes up. P = I * V so the electrical power input goes up. How does that relate to a motor's output power? Does that go up as well? Of course at the extreme, when stalled, the output is at zero as there's no motion while the current and input power is at its maximum. Assuming the battery can handle it (LiFePO4 10 AH 12V) that's some 120-140W per motor.

As you are using PWM a digital multimeter may not read the current correctly .

You are looking for “ best performance “ fastest speed , lowest power - the motor will run at its best efficiency at a certain speed /load and you don’t want to overload the motor , but you want max speed. The motors output and efficiency will vary with its rotational speed too .
Bigger diameter wheels increase speed ( to a point) but reduce acceleration .
As you load the motor the current rises and its power output rises and the speed reduces . Lots of variables and learning opportunities in this project - experiment, but research and do the maths too

I measured the current without the motor controller. Straight connection to the battery, no motor controller in between.

A DC motor driven at a constant voltage should be able to present the following performance curve.
Available from most motor manufacturers.
(Of course, you need that matches the model of the your used motor.)

If you want to run the longest time, use the points that maximize efficiency.
If you want to run the fastest, use the point where you have the most power.

Apply the required load to the motor and measure the current.

A 16cm diameter wheel would give you 6.032km/h @ 200 RPM, do you know the motors' full load torque?

Ratings by seller (I can't measure to confirm): 12V, 200 rpm; 2.9A; 35W; 4 kg.cm torque.

Free running I measured about 1.5A. From the image in #5 (thanks for that, karma++) the current at rated point would be roughly double that, so that makes sense. I'm nowhere nearly strong enough to seriously slow down the motor by holding its axle, so couldn't really load it much. I have to attach a wheel and then can probably get it to stall by grabbing it with my hand.

Just looking at the specs it seems the 24V motor simply has double the current double the power. Makes me wonder what the difference between the two really is. It's definitely worth trying to connect two batteries in series :slight_smile:

We're definitely going for most power. 10 Ah batteries, if they last for half an hour to an hour that's quite certainly enough. So drawing some 5A per motor - which the graph suggests is probably where its maximum output power is - will be a good target.

Now going from pulling force (as suggested as measurement) to torque to motor power... that's way out of scope for a typical G8 student (~14yo).

You are doing things in the wrong order:

  1. Choose wheel size that's correct for the vehicle, for handling and stability etc.

  2. Determine the parameters (max speed, torque requirements), given that wheel size

  3. Size the motor(s) and gearing, select a gearmotor.

  4. Choose a suitable motor driver.

In otherwords tune the motor and gears to the transmission, not the other way around.

Starting with choosing a motor is likely to end up grossly underpowered or overpowered.

If you are constrained in choice of motor then the only variable you have left is
the gear ratio - that's what you can tune to optimize performance relative to the ideal.

You are doing things in the wrong order:

I would if I were to develop a commercial vehicle with optimal performance. This is a school project. After all our prep work there will be two mornings of building, after which we'll do a race and beauty contest, and when done it's all taken apart so we can do it all again next year.
Picking a suitable size, and then cutting the wheels out of plywood, is part of the student's work.

Some very helpful tutorials and calculators for simple wheeled robot design can be found at www.societyofrobots.com

The RMF calculator covers wheel size, vehicle mass, speed, acceleration and motor characteristics.

Thanks! I'm going to look into those.

Plenty of time for that... school is closed AGAIN due to COVID :frowning: The whole project had to be postponed by a few months.