45 Dataset 2: The forces involved in running

Brokk Toggerson

What is involved in running?

This dataset is really for those interested in biomechanics/kinesiology. The fundamental question is, “What forces are involved in a person running, and how do these forces impact the way someone runs?” For these data, we will be exploring Dr. Toggerson’s run shown below. He is running on a series of devices called force plates which measure the forces on Dr. Toggerson in the parallel \parallel (x-direction) and perpendicular \perp (y-direction). While there are several plates (to make a smooth running surface!), there is only one which is taking measurements: the third plate from the left in the back row.


Some data you will find useful

The force data from the force plates can be seen at this spreadsheet.

We will define Dr. Toggerson’s height at landing to be y =0 and the point he lands on the plate to be x=0.

Quantity Value
Dr. Toggerson’s mass 70 kg
Dr. Toggerson’s height 1.68 m
Dr. Toggerson’s width shoulder-to-shoulder 50 cm
Dr. Toggerson’s depth front-to-back 24 cm
Vertical Speed at contact with the plate -0.47 m/s
Horizontal Speed at contact with the plate 5.018 m/s
Density of air \rho[1] 1.204 kg/m3
Viscosity of air \eta[2] 1.73×10-5 N·s/m2
From https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/shape-effects-on-drag/

What you need to figure out

Begin by building your simulation without considering any effects of air resistance.


Key Questions

  1. Draw two free body diagrams, one while he is in contact with the force plate and one at the top of the “arc” of his stride.
  2. At what time does Dr. Toggerson leave the plate?
  3. Using our categories of forces, what types of forces are F_\perp and F_\parallel (Weight, tension, …)?
  4. The total force from the ground on Dr. Toggerson is called the ground reaction force in kinesiology/biomechanics circles. What is the maximum ground reaction force?
  5. Is ignoring air resistance reasonable? Hint: Since both forms of air resistance depend on velocity, you may want to find the point where he is moving the fastest.


Key Questions

  1. When is Dr. Toggerson:
    1. Moving down and speeding up
    2. Moving down and slowing down.
    3. Moving up and slowing down.
    4. Moving up and speeding up.


Key Questions

  1. What is the maximum fraction of Dr. Toggerson’s initial kinetic energy is converted to gravitational potential energy over the course of the stride.


  1. https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/properties-of-air-text-version/
  2. https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/properties-of-air-text-version/


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