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Planning a long drive

Forces and motion · level 4, lesson 6 of 6

A question to start

The team wants their rover to reach a hill 4 km away. The rover's top speed is 152 m an hour. Will it get there in a day? In a week? How would you plan it?

The idea

A rover never drives all day at top speed. A plan has to use the average speed over whole sols, counting every stop:

\[\text{average speed} = \frac{\text{total distance}}{\text{total time, stops included}}.\]

On a typical driving sol, a rover might:

  • wait for the morning's commands from Earth and warm up;
  • drive for about 2 hours, stopping every few metres to look ahead;
  • spend the afternoon taking pictures and sending them home;
  • sleep through the cold night to save power.
Mars: rover Earth: a person walking
Top speed 152 m an hour about 5 km an hour
Length of a day 24 h 39 min (a sol) 24 h
Typical distance in a driving day 100 to 200 m 20 to 30 km on a long hike
asleepwarm updrivepictures, scienceasleepone sol: 24 h 39 min

Many sols are not driving sols at all: the rover stops for days to drill a rock or study a place. So the long-run average is lower still.

Worked examples

1. Pure driving. 4 km at 152 m an hour is \(4000 \div 152 = 26\) hours of driving, more than a whole sol of non-stop driving.

2. Two hours a sol. At 152 m an hour for 2 hours: 304 m a sol at best. \(4000 \div 304 = 13\) sols, if nothing went wrong.

3. With stops to look. Stopping often to check the path cuts the rate to about 150 m a sol: \(4000 \div 150 = 27\) sols. Add one science sol for every two driving sols, and it becomes about 40 sols, nearly six weeks.

Try it

  1. Why is a rover's average speed much lower than its top speed?
  2. A rover drives 120 m a sol. How many driving sols for 3 km?
  3. If it also stops one sol in every three for science, about how many sols does the 3 km take altogether?
  4. A sol is 24 h 39 min. Is 40 sols more or less than 40 Earth days?
Answers
  1. Most of the time it is stopped: night, warming up, looking ahead, doing science.
  2. \(3000 \div 120 = 25\) sols.
  3. 25 driving sols are two-thirds of the total, so about \(25 \times 3 \div 2 \approx 38\) sols.
  4. More: \(40 \times 39\) min is about 26 hours extra, so 40 sols is about 41 Earth days.

Common mistake

Using the top speed for a long trip. For any long journey, on Mars or on Earth, the stops matter more than the top speed. A plan must use the average over whole days.

Where it leads