your partner in efficiency

As an undergrad I developed a serious bicycling habit.  Our club would take longish sixty to one hundred mile rides on weekends. These were tours rather than anything approaching racing so we talked along the way.   One of the members was obsessed with the idea of human powered flight.  His spirt was contagious and several of us volunteered labor and calculations helping to build the first prototype in quest of the Kremer Prize.  It was one of those rare challenges where the goal was just barely possible. 

 

My involvement wasn't that deep, but I quickly learned to appreciate the efficiencies required. Questions arose.  What sort of athlete would be required?  How would power move from muscles to where it could be useful?  What kind of aerodynamic design would be most efficient and what was the flight envelope?    

We knew bicycles were efficient.  A good chain drive was almost 99% efficient and you could match the power output curve of the pilot to the requirements of a propeller. That's when I learned only the pilot's legs would be used... using arms and legs wouldn't work for a couple of reasons.  And what about the nature of the leg motion?  Lots of interesting issues and answers.

 

A bit earlier an article on the cost of transportation appeared in Scientific American.  This is the famous piece that Steve Jobs loved to refer to when he pointed out a person by themselves isn't incredibly efficient, but on a bike they're spectacular.  But why?

 

There are a number of ways to approach the problem, but I'll ask a slightly different question and hopefully cover a bit more ground.  

"Why can you go faster on a bicycle than you can run?"

We have two basic models of bipedal motion: walking and running.  When you walk you straighten your knee which lifts you just a bit as your heel comes up shifting weight to the front of the foot. The other leg swings forward, staying close to the ground most of the time.  One foot doesn't lift completely until the other has landed. You don't move up and down much and most of the work is done by muscles in the upper part of your leg.

 

Running is very different.  Your body lifts further and lower leg muscles become important as the motion makes you rise up on the forward part of your foot.  Runners will go into great detail on what's happening, but basically you're launching yourself with quite a bit of force using more muscles and force than when you walk.  When a foot lands some of the energy used to break the fall is stored in tendons for release during the next launch -  a mechanical battery. Optimizing efficiency is the work of training and genetics. [ An odd thing about the efficiency of running and walking is that walking is most efficient over a very narrow speed range, while running has a much flatter efficiency curve.¹ ]

 

You can go faster running by increasing the length of your strides (or leaps), but there are limits. Your leg is a kind of double pendulum.   It takes energy to accelerate it forward and some energy to brake that motion as it starts to reach its forward limit.  It's worse if your leg is heavy.²

 

Rather than swinging legs a cyclist spins a crank.  The crank's motion is a circle about a third of a meter in diameter. A much smaller distance than walking or running strides.   Circular motion means the cyclist isn't having to waste the kinetic energy of their moving lower leg by slowing it (it does waste a some energy, but not nearly as much). The knees and thighs still need to be stopped and started, but the motion is much smaller.  The end result is less wasted energy from leg motion.³

 

Like running there's an upper limit to how fast a cyclist can move their legs and still generate their greatest power.  That's where gears come into play.  The gears and large rear wheel allow the bike to move a longer distance forward than the distance your feet travel in one revolution of the crank.  And different gear ratios allow you tailor your effort to the conditions - speed, head wind, hills ...

 

On a smooth flat road your speed is usually limited by wind resistance and the power your muscles can develop.  It's amazingly efficient.  With very little effort you can sustain a pace that no marathon runner can keep pace with.   

 

note:  I've skipped over a lot.  Human motion is a rich and not completely understood science, but hopefully this is good enough.

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¹ without going into great detail I show a chart here.

² To think about this consider the leg's moment of inertia and the fact that all parts of the leg aren't moving at the same speed. The upper leg moves slower - this is why fast running animals have their muscle concentrated in the upper leg.  Carbon fiber lower legs can make partial amputees faster than an otherwise similar runner with an intact leg.

Note the power your muscles generate increases as cross sectional area, while the weight increases as the volume.  Larger muscles increase in power more slowly than their weight increases.  This is why most competitive distance runners are of average height and very lean. 

³ The cyclist's center of gravity isn't moving as much either and that saves energy.

 

Comments

[funnmtb.co.uk]

Almost an engineering comparison study of cycling vs animals ahah