ME 577/BME 595 – Human Motion Kinetics Homework #6

Sensitivity Analysis and Dimensional Analysis 1. Shown below is a famous example of a weightlifter who injured himself in Olympic competition.

Figure 8-1: Initiation and progression of a patellar tendon rupture by a weightlifter in Olympic competition. From Sports Biomechanics by Roger Bartlett (E&FN Spon, New York, 1999).

The weightlifter shown above was in the process of starting the second phase of a clean-and-jerk maneuver when his patellar tendon ruptured. Assume that he weighs 980 N and, when combined, the lower legs and feet account for 13% of his total weight. If the lower leg is approximately 40 cm long, what are the reactions at the knee? What is the force in the patellar tendon?

Figure: A schematic of a weightlifter just before he attempts to press the weight above his head. Realistically, this problem requires a dynamic analysis, but we can learn a lot by starting with a static representation. Perform a sensitivity analysis on the force in the patellar tendon. Your parameters should be the angle of the lower leg (50-75o), the length of the tibia (variation in your immediate family – please ask permission before taking measurements of individuals), and the angle the patellar tendon makes with the tibia (8-13o). Which parameter exhibits the most sensitivity? 2. Using the data obtained by G.I. Taylor (paper 2, table 1), use dimensional analysis to estimate the energy in the atomic bomb blast. While, strictly speaking, this is not a biomechanics problem, it will be good to tell people that you know how to determine the energy in an atomic bomb blast. You may assume that the relevant parameters are the initial energy in the weapon, E0, air density, blast radius, and time.