Limits on Human Performance
What is the ultimate strength of the Achilles Tendon
Find or calculate the cross-sectional area of the Achilles Tendon. Cite any sources.
Based on your answer, what force can the typical Achilles Tendon supply before rupture?
In order to transfer the the force on the balls of the feet directly to the lower legs during the jump, the force on the Achilles needs to be roughly twice the force on the balls of the feet. Given the maximum force the Achilles can handle, how large of a force can be applied to the balls of the feet during the jump without rupture?
If you apply that force to the floor, what force is supplied back on your feet (Newton’s 3rd Law)?
If that peak force were supplied during launch phase, what would be the peak net force? (Don’t forget about gravity cancelling out some of the upward force supplied by the floor).
If the peak net force was what you found above, what would be the average net force (assuming the force curve peak-to-average force ratio as your own jump).
If that average net force were supplied over the same launch time as your jump, what would be the impulse?
What would be the change momentum during the launch?
What would be the final velocity at the end of launch phase?
How long would it take for your velocity to become zero at the peak of the jump?
What is the maximum hang time possible given the limitations of the strength of the Achilles tendon?
Determine the maximum kinetic energy a person can gain during the launch phase.
Determine the maximum height that a person can jump based on that kinetic energy (Use conservation of Energy).
Additional Limits on Human Performance
Having already found the maximum kinetic energy a person can gain during the launch phase, what is net work that would be done during the launch phase. (Work-Energy Theorem)
Using the distance the center of mass traveled during your own launch phase, calculate the work done by gravity during launch (Work equation).
Determine the work that would be done by the jumper during launch.
If the work was done over the same time interval as your launch phase, what would be the power output of the person.
Convert your answer to horsepower.