WORK – A Physics Primer for Cyclists

What is Work?

Work-- Gottfried Wilhelm von Leibniz
Leibniz (pictured immediately above) and Newton pioneered the math and science behind cycling physics
This entry is part of 3 in the series Physics for Cyclists

In my previous installment of this series, I wrote about watts. That from a strict educational and physics perspective is backwards, but because cyclists obsess on watts it works. However, we do need to understand the physics behind WORK in order to fully understand how watts are computed.

WORK – A Physics Primer for Cyclists — What Qualifies as Work?

In the previous example I gave an example of work using a boat lift. Regardless of how long it takes two different people to lift a boat out of the water the same distance, the work is the same. In order to get to power quickly, I left out some key considerations of what qualifies as work.

In order for something to be work it must meet the following qualifications (limiting the discussion to mechanical concepts such as we experience while cycling):
1. You must cause a change in the objects position or movement
2. You must use force to cause the change

Point 1 is not so obvious as to what qualifies. According to Newton, an object at rest remains at rest and objects in motion stay in motion unless acted upon by an external force. Just because you are moving on your bike does not mean you are applying force to it, even on the flats. Turning your bike is a change in motion requiring force as well as starting to move your bike again.

WORK – A Physics Primer for Cyclists — An Immovable Object

Imagine a big strong brick wall. You walk up to it and with all of your strength you push on it. You push so hard and so long you start to sweat. How much work did you do? The answer is none, you moved nothing so no work is done. Imagine again you have just crested a big climb and begin to descend, your speed changes from 11 mph to 35 mph. How much work did you do? Little if any, because gravity is working on you and the bike to increase the speed.

In both cases above intuition may lead you to believe you expended great power, but the fact is you expended little if any power.

WORK – A Physics Primer for Cyclists — Newton’s First and Second Laws

Work -- a pack of cyclists producng work
Work work work work work!
So how is it a ride on the flats registers power when we are not working against gravity? Again, going back to what is usually a pre-cursor lesson we need to think of force. In Newton’s ideal world there is no wind resistance no friction. However, when are in the real world we have to constantly fight to overcome wind resistance, mechanical resistance in our drive train and components, and road friction. The faster we are moving the greater those forces become and the more force we must generate and apply to overcome.

Even though the net result is that the speed is not changed, the motion is still affected. If we were not pedalling we slow down, so the affect of pedalling is changing your motion! So you still qualify for doing work.

So now, we have all the ingredients for performing work. We have to apply force to our pedals to keep moving and we are changing our position. Once we are working we are generating power!

WORK – A Physics Primer for Cyclists — Calculating Work

How can we calculate how much work we are doing on the bike? That for the most part is tricky on the flats (or any horizontal component of our movement) because the amount of force needed to overcome wind resistance and the frictional forces present is hard to know. However, we can easily calculate the vertical component of work accomplished by climbing a hill or mountain. That formula is:

Work -- formula for work due to liftng an object
Use this formula to determine the work you need to do to climb a hill!

  • M is your “weight” (technically speaking, it is mass not weight) in kilograms (add in your bike’s mass)
  • Y is the change in altitude (in meters) you climbed.
  • 9.8 m/sec2 is the acceleration due to gravity which is a constant and fixed.

Very simple! There is additional work to keep you and your bike moving horizontally, but we know when climbing that work is small in comparison to the vertical component.

WORK – A Physics Primer for Cyclists — In conclusion

  1. Without you applying force you accomplish no work
  2. Without that force affecting movement (speeding up, slowing down, turning, cancelling out other forces) you accomplish no work
  3. Vertical work is easy to compute
  4. Horizontal work is hard to figure out and requires fancy gauges and computers

Now go and turn out some work!

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