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Motors on Mars

Electricity and magnetism · level 7, lesson 6 of 6

A question to start

Perseverance's top speed is about 152 metres an hour. Ingenuity's rotors spun at about 2,400 turns a minute. Both were driven by electric motors. How can motors work so slowly and so fast?

The idea

The rover. Each of Perseverance's six wheels has its own motor, and the four corner wheels have steering motors too. An electric motor runs best spinning fast, so each wheel motor drives the wheel through a gearbox that trades speed for torque: the wheel turns slowly but pushes hard.

The helicopter. Ingenuity's two rotors spun in opposite directions, driven by electric motors. Its batteries, charged by a solar panel, gave about 350 W on average during a flight of up to about 90 seconds.

The thin air. A working motor warms up and sheds heat to the air around it. Mars air is so thin that it carries heat away far more slowly, so motors there shed more of their heat in other ways, mostly by conducting it into the parts they are fixed to.

Air around a motor Mars Earth
Density at the surface about 0.016 kg/m³ 1.217 kg/m³
fast motorgearsslow, strong wheel

Worked examples

1. The wheel. The wheels are 52.5 cm across, so each turn rolls \(\pi \times 0.525 = 1.65\) m. At 152 m an hour, a wheel turns \(152/1.65 = 92\) times an hour: about 1.5 turns a minute.

2. The gearbox. Suppose the motor spins at 5,000 turns a minute. The gears must slow it by \(5000/1.5 \approx 3{,}300\) times.

3. The rotor. 2,400 turns a minute is 40 a second: \(\omega = 40 \times 2\pi = 251\) rad/s. Suppose one rotor's motor gives 175 W, half the total: its torque is \(\tau = P/\omega = 175/251 = 0.70\) N m.

Try it

  1. How many motors does Perseverance use to drive and steer?
  2. Why does a wheel motor need a gearbox?
  3. How much energy did Ingenuity use in a 90-second flight at 350 W? Give it in joules and in watt-hours.
  4. Why is cooling a motor harder on Mars?
Answers
  1. Ten: six to drive, four to steer.
  2. Motors run best fast; the gears turn that into a slow, strong turn of the wheel.
  3. \(350 \times 90 = 31{,}500\) J, which is \(31{,}500/3600 = 8.75\) Wh.
  4. The air is about 75 times less dense, so it carries heat away far more slowly.

Common mistake

"Gears give extra power." Gears trade speed for torque. Apart from a little friction, the power into the gearbox equals the power out.

Where it leads