This Wednesday (3/19/2014) we’ll be joined by Jim Reardon to talk about his paper about the optimal way to run 400 and 800 meter races. Here are some questions you can use to get your students thinking about this:
 Should you always run your hardest?
 Should you try to go the same speed the whole time?
 Should you be exhausted by the end?
 For how long should you accelerate?
 Jim says that entropy is the key, what does that mean to you?
Here are some ideas about the three models propose:
 You provide propulsion, friction slows you down, let’s keep track of the energy.

 v is velocity
 is the friction coefficient
 f is the propulsive force (per unit mass)

 E is the runner’s energy supply
 is the replenishment rate
 you get all the values by fitting to the races we have data for
 predicts that you should run your second half of the race faster

 Energy comes both aerobically and anaerobically
 aerobic is constant
 anaerobic decays
 max power is used
 energy goes into kinetic energy, drag losses, and heat

 S is the effective area
 rho is the air density
 the rest are fit parameters
 predicts deceleration in the 100m race
 still gets 400 and 800 meter elite races wrong
 X factor
 entropy is key!
 calculus of variations
 maximize distance in given time
 similar to Brachistochrone approach
 matches data very well!