Power Considerations

Because each LiPo cell has a nominal voltage of 3.7 volts, to achieve our 35 watts of power we would need to discharge at (35/3.7 = ~9.5 amps) continuously. During start up, against wind, or up a hill the required power will be much higher. In fact, for a motor rated at 1500 watts max we would be drawing 400 amps! At these currents even the wires that deliver power to the motor start to look like resistors.

Because of these losses, it turns out that motors (and a lot of things) are generally more efficient at higher voltages and lower currents. This is a big part of why power line transmission is done at such high voltages when your phone only really wants a little over 4 volts to charge.

It can be extremely difficult to balance the wide variety of cells available against cost. So I wrote a quick script to scrape a website's catalogue and make suggestions for me. It did a better job than I did initially, and so for this project we'll start with a 6-series (6s) battery pack. This will range based on its wear level and state-of-charge from between (3.7*6)= 22.2 volts and (4.2*6)= 25.2 volts. At our average 35 W, we will be near 1.5 amps discharge. This lower discharge rate has the added benefit of helping the cells age much better.

Motor Selection

Brushless DC motors are usually given a rating called Kv. This can be read as their "voltage konstant" and specifies, generally, how many RPM a motor needs to turn to generate 1 volt. It's usually interpreted the opposite of that, though: how many RPM a motor will turn per volt of potential. This can be confusing at first— doesn't the frequency generated by the controller determine the rotation speed? Well, yes, but only by controlling how "hard" it throws the rotor forward to the next pole; a motor will never spin faster than its Kv rating.

So how fast do we want to spin? Earlier we specified that we need to move at a 4:30/km pace. The test stroller has 20" wheels with a circumference of approximately 1.6 meters. That means it needs to spin 625 times per kilometre over those four-and-a-half minutes. 625/4.5 = ~138 RPM. If we want to do tempo runs at a 20min 5k pace, it's closer to 158 RPM.

The aircraft hobby scene has developed a ton over the years, and good compact brushless motors are available relatively inexpensively. However, with a 20" pneumatic drive tire nothing will have the torque required to start from a stop without some gearing. This is actually great, though, because the most powerful motors have a low Kv rating. At ~23 volts we will need a rating less than (23 * 138) = ~3200. 23:1 gearing would be challenging as well.

Power Application

Now might be a good time to think about how a spinning motor can effect a spinning wheel. There are a few specific aspects to this and they're mostly related to one fact: running strollers do not have a swivel wheel. Steering is performed as seldom as possible, and made possible by an intention location of centre of gravity near the rear axle. This prevents mishaps where a swivel wheel meets unpredictable ground, self-turns, and the stroller self-topples. Kids can present certain attitude-oriented challenges while running, but violence is never the answer.

Taking this idea further it becomes clear that driving one of the rear wheels will cause yaw-slip and make straight travel a challenge. Counter-acting this by driving both wheels may be feasible, but separate driving wheels doubles costs and seems inappropriate for an application that primarily will go straight. Using one motor (and thus locking both wheels to the same speed) will either prevent turning entirely or require the fabrication of a limited-slip differential. For a stroller.

Driving the front wheel, however, will have the added benefit of allowing the parent to lift the powered wheel off the ground if an immediate stop is required. Generally, as a rule, I strive to put as few bugs as possible into my code, but when children and cars are potentially involved a safe mode of failure is required.

Gearing

The most forgiving, low-cost, and light-weight method of power transmission for this application is probably a toothed belt. This also allows us to arbitrarily vary the wheel RPM making for a wider range of acceptable motors. So what RPM will the motor be at, typically? Well, for larger motors a typical Kv specification is ~250 (RPM/V) +/- 75. Given our 6S battery pack we will typically be running at ~23 volts. The top rotational speed of our theoretical motor would be (250 Kv * 23 V) = 5750 RPM. Recall that wheel RPM at our specified pace of 4:30/km is 138RPM. This is a 41.6:1 reduction! The smallest pulleys listed on SDP/SI with a 3mm pitch have 14 teeth. This would necessitate a 582-tooth wheel pulley, which, at a 3mm pitch, would be 556mm in diameter (a couple inches short of 1ft).

I don't know where to buy a pulley that large, and my 3D printer can reasonably do 190mm at most, so the top speed might end up being a tad faster. Colin Furze: we're coming for you.

3D printing a pulley is appealing. All that's needed is a means of attaching it to the wheel. Most running strollers use a spoked wheel like a bicycle, and at our power levels transmitting power through the spokes will likely be acceptable. If we use a little trigonometry to determine the angle of the spoke relative to the axle, bolts with a slot down them lengthwise allow a robust attachment to the wheel.

As mentioned, the bed of my 3D printer is, practically speaking, 190mm square. A 195-tooth HTD3 pulley has an outsize diameter of 185mm, which is perfect for fit. Coupled with the 14-tooth drive pulley that gives us a ratio of 13.92:1.

• At 138 wheel RPM, our 4:30/km pace, the motor will spin 1922 RPM. This is somewhat low in terms of motor efficiency, but we should have motor commutations quickly enough to satisfy the speed controller.
• With an 80% efficiency on a 6S battery pack, 4600 motor RPM = 330 wheel RPM, or 8.8m/s = 31km/h top speed. Excessive, but technically this satisfies our requirement, which is the best kind of satisfaction.

Cost is a significant factor in this project. While there are several motors that would fit our requirements, the Propdrive V2 50-60 is $53, ships from the U.S., and claims a maximum power capability of 2400 watts. Good luck getting a data sheet, but this should enable us to 1) start, and 2) climb hills, of which Phoenix has several formidable examples.