Physical Work

Mechanical Tasks

It is one thing to understand how objects move. But what about the things that make it move? Mechanics is interested in quantifying the effort it involved in activities moving objects. For a cyclist, it is one thing to understand how the cycle moves, and another to understand the effort needed to make it move. Suppose you are making a one mile ascent up a 5% grade slope. How would that compare to making it up a 10% slope.

These are examples of mechanical tasks, and the first step in analyzing them is to determine how much effort is required to complete them. Notice, we are interested in the effort and not how quickly we can accomplish it. That is something we can estimate once we know the total effort.

What is physical work?

Physics quantifies effort as work and it is independent of the time needed to perform the work. It is like the cost of an item and is not concerned with whether you make the payment at the sale or pay for over time.

How is work computed?

If we are looking to complete a task that involves motion against opposing forces, it would seem a reasonable measure to calculate  how far the object needed to be moved and the magnitude of the forces opposing the motion.

Total Work = Force * Distance

You may ask why it is computed as f*d and not f * d² or f/d? The answer is it “works” and and we should feel comfortable accepting it for that reason.

Work is usually computed in Joules which equate to Newton-Joules. You may wonder why the metric system is used. The reason is when we move on to discuss power, power is measured in Watts which are joules per unit time. Since Watts is used throughout the World including the United States, it is easiest to use these units.

A Simple Work Calculation

You are weightlifting  and looking to lift 125 lbs moving the weight from your shoulders up two feet. How much effort will this take? The only tricky part is converting to MKS units. Otherwise, it is a simple multiplication.

Force = 125 lbs * 4.44 Nwts/lbs = 556.02 Nwts

Distance = 2 ft * 0.30 Meters/ft = 0.60 Meters

Work = 338.95 Newton• Meters = 338.954 Joules

Suppose you wanted to double the weight, how does the work change? The answer is it is doubled or 667.909 Joules.

What happens when the path and forces vary?

When the path and the forces over that path have variation, the actual mathematics requires work to be computed in small increments where we can assume the line is reasonably straight and the force reasonable constant. Then all of these pieces are added up to get the total work.

Total Work = Sum( Segment Force * Segment Distance)

As the segments get smaller, this technique is called Integral Calculus, and fortunately for us, we do not need to worry about it when dealing with many aspects of Physical Cycling.

How difficult is it to compute cycling work?

Cycling provides key simplifications that make work computations nearly trivial. Cycling forces are constant in many scenarios of interest. Both Rolling Resistance and Gravity are constant over the path. Aerodynamic Drag remains constant as long as the cyclist is looking to maintain their speed.

When you are looking to compute the effort and you are dealing with constant forces, the total work can be computed as the force times the total path length whether straight or curved. And in the case of Gravity, the total effort is even simpler. It is the CyclistCycle Weight multiplied by the ElevationGain.

Cyclist Work Scenarios

In cycling, we will find we are dealing with two types of work:

  • Work required to move the CyclistCycle forward a given distance.
  • Work performed by the cyclist in pedaling determined by multiplying the pedal force times the distance the pedal moves.


Next Topic:   Physical Power



Cycling as seen through the eyes of elite cyclists.