"At a soirée of the Royal Society conducted by Hill in 1952 two subjects mounted a specially built tandem stationary bicycle. While one subject pedaled the other subject resisted him through directly coupled pedals. At a speed of 35 revolutions per minute, the subject pedaling forwards used 3.7 times as much oxygen as the one pedaling backwards. It was demonstrated that a small woman, pedaling backwards, could rapidly exhaust a large man pedaling forwards against her resistance. Since oxygen consumption and heat production are closely tied, the muscles of the woman were presumably generating far less heat, even though the coupling of the pedals guarantees that the forces and displacements experienced by the woman's feet were the same as those for the man's."
Thomas A. McMahon, from chapter 2 of Muscles, Reflexes and Locomotion, Princeton Univ Press (1984).

Background:
The lecture notes tell you about Hill's equation for muscle velocity-tension

with the figure below from McMahon's Muscles Reflexes and Locomotion

note the greater tension/fiber for negative velocity. The graph has been normalized

where we use in the Matlab code described below, and you have control of constant k.
Note that α and β have the units of tension and velocity, respectively.

Muscle details:
1. Recruitment. To increase tension (or velocity of contraction) muscle fibers are recruited, from the weakest cells with the most endurance up to the strongest fibers, which are most easily fatigued. Yes is it true that individual fibers can be stimulated at increasing rates by their motoneuron axons, up to tetanus tension, but once one fiber is pulling to the max, another fiber is recruited as necessary. In the simulation below we have it that the "strong biker" has 100 fibers involved in pedaling, with the maximum tension of the fibers from 1 to 100 force units. In exercising the simulation (Tandem04.m) you choose the number of "weak biker" fibers, an integer less than 100.
2. Velocity-dependent tension. Hill's equation shows the hyperbolic relationship between muscle velocity and muscle tension. Note that when an active muscle is pulled by an external load in the opposite direction of its intended contraction the muscle is "doing a negative" (as weightlifters say) and its velocity is less than zero. The tension per fiber is much greater in muscle fibers doing negatives than tension in a fiber going the same speed in the opposite (positive) direction.
3. Muscle fatigue. The FG (fast glycolytic) muscle fibers (white meat) that can exert the greatest maximum tension are the most easily fatigued. In Tandem04.m we model the fatigue as a first-order time constant that increases in duration as the maximum tension per fiber decreases.

Requirements:
(1) On each of the computers in the lab, in the Work folder of Matlab, is a folder Tandem that has a read-only file Tandem04.m function and its subroutines TanFly04, FatigueCalc.m and recruit_fiber.m. The call is
Tandem04(Wcnt, frce_thet, del_frce0, vmax, drg, fatigue_fac, k)
where the input arguments are
Wcnt: the number of weak muscle fibers;
frce_thet: the threshold force (torque) the strong biker must meet in the recruitment function;
del_frce0: the approx difference between strong and weak muscle torque used by the matlab ODE solver;
vmax: the zero-force velocity derived from Hill's equation:
drg: the drag term from the model for the bicycle load;
fatigue_fac: increases time constant of fatigue onset: if less than 1.00 (but greater than 0) it means the rate of fatigue is increased;
k: the term noted above, from Hill's formula for normalizing velocity or tension.

Tandem04.m is linked to colored notations for its various sections.

If you open Matlab and type at the command window
>> Tandem04(94, 2400, 90, 900, 14, 1.00, 0.2)
you will be asking for 94 weak fibers, with a pedal tension of 2400 units, a strong-weak force difference of 90 units, a vmax of 900 velocity units, a mechanical drag or friction of 14 units, a fatigue factor of 1.00 and constant k = 0.2 for Hill's equation normalization. When you run Tandem04.m with those conditions you will see that the strong muscle fatigues in 35 seconds, and a final fiber number vs tension plot looks like:

Your challenge: by adjusting the simulation parameters available to you (except for pedal tension), arrange that the "strong" biker fatigues at a number of seconds to be given by JD or TA. For example: 45 seconds. play around with the fatigue and other factors and become comfortable with their effects on time when the strong biker is stopped by the weak biker.

(2) Forward pedaling vs weak resistance on the tandem bike.
Inspect the stationary tandem bike. Note that the gear ratios for the two sets of chains connecting pedals to the rear flywheel are the same. Notice the mechanisms for tightening the chains.

Note:
The Machine Shop modified a 50 year-old Schwinn tandem bicycle formerly owned by Profs Blume and Bower.

2007: The tandem bike has fallen into disrepair: For 2007 etc skip to section (3) below.

(3) PART 3 MUST BE ADMINISTERED BY THE PROFESSOR, WHO WILL THEN SIGN OFF YOUR LAB.

We have not yet outfitted the tandem bike or biker with sensors. Answer one of the following questions, [selected by JD] in the following way: in your IP folder, in a Word file:
i: find a specific sensor for the question, and reference with a website and particular part number, and price.
ii: describe how the specificed sensor output could reach a nearby 6024E DAQ card in a computer.
iii. draw out or describe how the parts would be mounted on or near the stationary tandem in the lab.

Money is no object here. You can specify the most exotic parts you like. Surgery is not prohibited either: see below.

You are also allowed to modify the bike itself in your design...

a. How could you monitor the rotation speed of the bike pedals? The cycles/second speed may be rather slow so you cannot just monitor when one of the pedals passes by once or twice per cycle.
b. How could you monitor the bending moment in the arms of the pedals during rotation? To avoid symantic difficulties, let's say you will want to measure the strain in one of the arms, and have the measurement come off the arm. Are there optical ways this can be done? Translate strain(s) to bending moment.
c. How could the oxygen use of a biker be sensed? Look up what a spirometer does...you may have seen O2-CO2 sensing in Bio 80. We will want to know how the sensor will be mounted, near the "rider".
d. How could the temperature of the quadriceps muscle be monitored? Let yourself imagine that a rider might agree to a modest surgical implant... Keep in mind the leg is moving...
e. How could nerve and muscle activity of the quad be monitored? Again, suppose a subject agreed to a modest surgical--electrode implant...

What we are looking for here is about a half hour of effort online or otherwise, resulting in a "prototype" design to be shown; the result of the prototype may be feedback from the Prof that may take another half hour to implement for a final answer...

Possible FTQ's: Will the time for fatigue of the strong biker in the simulation increase, decrease or stay the same, given a change to a parameter selected by JD? What other muscles, besides quadriceps, participate in pedaling a bicycle? See
http://orgs.jmu.edu/strength/KIN_425/kin_425_muscles_quadriceps.htm
otherwise the modification of design for part 3 may stand in for your FTQ here...

mathematical FTQ: What (nonlinear first-order) differential equation can account for the hyperbolic form of the velocity-force curve? Reading: pages 11-16, 30-35, from T. A. McMahon, Muscles, Reflexes and Locomotion.