6.3 Hans and Franz compete at the muscle Olympics

Muscles Hans and Franz have both entered the prestigious Muscle Olympics (leaving their pesky tendons at home). They will each compete in three events in an attempt to bring home the coveted Golden Sarcomere. Being the poor student that you are, you’re hoping to make a little extra cash by placing some bets on the competition. The Olympic program with the competitor’s vital stats has just arrived in the mail and your bookie is on the phone – what bets do you want to place?

(a) For each event, predict whether Hans or Franz will win. Defend your choice using muscle mechanics principles and equations we’ve discussed in class. (You get credit for your reasons, not for just correctly guessing the winner). If there is a muscle property that you think is important that isn’t listed, assume that it is the same for both Hans and Franz. Assume both muscles have linear force-length properties and moment arms that are constant with joint angle. For all events, the muscles are loaded into a revolute joint with the given moment arm.

“Clean and Jerk”: The joint moves through a range of motion at a constant angular velocity of 100°/sec. The winning muscle is the one that produces the most force at the instant that it reaches optimal fiber length.

“60° Torque-off”: Each joint is fixed at 60°. The winning muscle is the one that produces the largest torque during an isometric contraction. Assume that each muscle is at optimal fiber length when the joint is at 60°.

“110° Torque-off”: Each joint is fixed at 110°. The winning muscle is the one that produces the largest torque during an isometric contraction. Assume again that each muscle is at optimal fiber length when the joint is at 60°.

(b) Hans and Franz were not both satisfied with their performance in the Torque-off competitions—they each thought they should be able to win both the 60° and 110° categories. They convince the Olympic officials to let them have a rematch. Over the weekend, both muscles worked hard to try to improve their odds. Franz went to the local Gold’s Gym and bulked up. Hans went to the local yoga studio and stayed in downward-facing dog all weekend. After this intense conditioning, their vital stats had changed, but each muscle still reaches its optimal fiber length at 60°—get your bookie back on the phone and predict who will win the two Torque-off competitions now.

(c) Using what you learned in this problem, comment on why we may have redundant muscles in our bodies.

Disclaimer: Don’t take Hans’s and Franz’s experiences literally. Only a chronic stretch and a sustained weight training program could actually change the properties of your muscles – but you already knew that.