Ken Roberts - - Skating

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where does the power get "wasted"?

first written: April  2008

I keep reading posts on various forums about "efficiency", which makes me think about how to analyze it.

Here's a try:

aerobic power is generated mainly from carbohydrate fuel and oxygen.

about 75% of the energy in the chemical bonds in the carbohydrate fuel is lost in this process -- the resulting work of the muscle fibers contracting is only 25% of the energy available. (Also carbon dioxide is released).

Therefore if "not wasting energy" is the goal, just stay home and watch TV. Active life is inefficient.

  • A significant percentage of the carbohydrate energy goes to non-muscular processes -- especially for operating the brain.

  • Another portion goes to muscles which can never deliver propulsive work -- especially for operating the heart.

What's "left over" after that is available for power from "skeletal" or "peripheral" muscles. Here's some of the things it gets used for:

  • posture: maintaining the basic configuration of the bones and joints, mostly against gravity.

Unlike some machines, we don't just "lock" our bones and joints into a desired configuration -- just holding a stable "isometric" configuration requires muscular effort. It burns calories and uses up some oxygen.

Different motion patterns for propulsion might require more or less energy to be used to maintain the "posture" configurations which are appropriate for that motion. Typically motions in which the posture is more "bent over" require more energy to hold that posture stable.

Some postural configurations which require more energy to sustain, also offer more effective leverage or "gearing" of key muscles or a higher percentage of direct transmission of muscular moves into propulsive work -- (so there are trade-offs)

Some people use more muscular tension than necessary to maintain posture.

Some energy to maintain postural configuration is required for the desire propulsive motion, other energy might be avoidable.

  • balance: small adjustments to keep from falling over.

People with well-practiced specific balance use smaller more accurate corrective moves, which take less work.

Also sometimes a person with better specific balance can sustain a configuration which offers more effective leverage or "gearing" of key muscles or a higher percentage of direct transmission of muscular moves into propulsive work.

Some energy to maintain balance is required for the desire propulsive motion, other energy might be avoidable.

  • recovery moves: needed to complete the stroke-cycle, to bring body parts into a configuration where they can make the same push again.

Some recovery moves themselves add positive propulsive work. Often this depends on timing and other tricky points, since often the attempted propulsive work in a recovery move is self-cancelling. For example, recovering the leg forward is partly propulsive in running, but not in normal walking (with continual ground contact).

Some propulsive muscle moves are "self-recovering". For example pelvis - lower spine rotation in walking and running. If pushing with the Right leg, the rotation of the pelvis about the spinal axis to bring the non-pushing Left hip forward to add propulsive work to the push thru the Right leg also finishes with the Right hip backward. Which is exactly the configuration needed to make a propulsive pelvis - lower spine rotation move for the push of the Left leg.

  • static friction to enable transmitting propulsive work to ground: In some situations, downward force in addition to body weight is needed to have sufficient static friction to transmit a forward-backward force to the ground.

An example might be classic striding in cross-country skiing, especially when climbing a steep hill. Extra downward pushing force is needed at the same time forward-backward force is being applied -- in order to prevent the ski from losing grip and slipping back. This extra force causes the mass of the upper body to move upward in reaction, and can sometimes it has so much upward momentum that both feet are lifted off the ground simultaneously after the leg-push finishes -- so the next leg-push cannot start until time has elapsed for the mass of the upper body to fall down again.

In most situations for most propulsive motions, body weight and the propulsive forces themselves are sufficient to provide sufficient static friction.

Some performers might apply more downward force than necessary, while other more skillful performers might take it closer to the "edge" of only the minimum required.

  • transmit work thru body parts: Sometimes some joints and muscles are held static ("isometric") to transmit the propulsive work from another muscle move to the ground. Or transmit it to the mass of the remainder of the body.

Human muscles and joints are useful in this static transmission role. Especially smaller muscles can sometimes make a larger contribution to overall power by statically transmitting the work from larger muscles, rather than attempting to add active work of their own. This function of "isometric" static transmission does not do propulsive work, but it does consume fuel and oxygen.

  • wasted muscle moves that are unrelated to any propulsive goal.

I guess this is what lots of people mean by "wasted energy" or "inefficient" motion. But it's only one way in which the power generated from fuel and oxygen is not available to add to propulsion work.

Also moves with lots of people think are just "wasted" actually do make a contribution to propulsion (thru a less obvious exploitation of the physics of propulsion), or are necessary to support propulsive contribution of other muscles (in one of the ways described above).

What remains after those uses can be applied to propulsive work. But it's not so simple . . .

mainly because the moves are not in exactly the right direction for propulsion. The ideal propulsive force pushes straight backward against the ground and straight forward against the mass of the body.

But most actual propulsive moves by the human body push diagonally. Either a combination of backward and downward against the ground (as in striding or pole-pushing). Or a combination of backward and sideways against the ground (as in skating) -- well actually the skating leg-push is a diagonal combination of three directions: backward and sideways and downward against the ground.

Only the directional "component" of force which is in the forward-backward direction is directly + immediately added to propulsive work.

Other directional components (downward and sideways) of the pushing force can also contribute to propulsion, but only indirectly, deferred to a later phase of the stroke-cycle, or to the next stroke-cycle.

These deferred forces may result in additional losses of power:

  • they need to be transmitted (again) thru body parts.

If some of these muscles are used in static "isometric" mode, that's a loss, as described above under "transmit".

  • after the force has been transmitted, it's still not in exactly in the ideal  foreward-backward direction. So again only a portion of the force is applied directly and immediately to propulsive work. The remainder must be transmitted again, with further losses as described here.

Again and again and again.

  • may result in time delays in the stroke-cycle.

Since one of the three main drivers of propulsive power is stroke-cycle time, delay means loss of power.

  • may result in other moves being pushed into a less favorable power point on the "muscle force intensity versus muscle speed". curve.

Or some other moves could be pushed into a more favorable power point on their curve.

So even the muscle moves and forces which are not "wasted" still have power losses.

Why does power matter so much?

Because the goal of human propulsion is to move some distance in some amount of time -- so some positive speed is required. The rate of speed is determined by this equation:

[Resistance Force] * [Foreward Speed]  =  [Direct Propulsive Power from muscles]

where [Resistance Force] is the sum of the forces opposing forward motion: like air resistance, or friction against the ground, or if climbing up a hill then gravity is included. Especially for air resistance, the intensity of resistance depends on the overall body posture and to some extent which muscle moves are being used - (so a change to postural configuration which takes less energy to maintain might also increase air resistance -- there are trade-offs.)

Actually it's more complicated, since each of those quantities varies at different times in the stroke-cycle, so the equation has to be sort of "integrated" over the whole stroke-cycle.

It gets more complicated, because

[Resistance Force] depends on [Foreward Speed]

because air resistance gets disproportionately larger at higher speeds.

[Direct Propulsive Power from muscles] depends on [Foreward Speed]

because muscles produce different power levels depending on the speed, sometimes higher, sometimes lower -- but above some speed (different for each muscle move) the power capability only declines with speed.

Yet another complication is that how much power each muscles can deliver depends on the duration of time it needs to sustain that power level.

At higher speeds, as the performer tries to raise the speed rise even higher, [Resistance Force] tends to only rise and [Direct Propulsive Power] tends only to fall. So there's an upper limit.

But despite all that complexity, more Power generally means higher speed -- in getting from one place to another.

 

Chasing efficiency is a complicated game.

Trying to use "efficiency" to increase speed is a very complicated game.

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