72 Powering the Body


In the previous chapters we learned that the body uses chemical potential energy to do useful work. In addition to being limited in efficiency, that biochemical process is also limited in how quickly it can proceed. Therefore, your body is limited in how quickly it can do work. The rate at which work can be done to convert energy from one form to another is known as the power. We can calculate the power as the work done divided by the time required to do the work (\Delta t).

(1)   \begin{equation*} P = \frac{work}{\Delta t} \end{equation*}

We can see now that power has units of J/s, also known as Watts (W). Another common unit for power is horsepower (hp). There are 746 W per hp.  The rate at which the body does work to convert chemical potential energy to to thermal energy is know as the thermal power. The rate at which useful work is done to convert chemical potential energy to mechanical energy is know as the mechanical power.

Reinforcement Exercises

Everyday Example: Jumping

Jumping requires that muscles lengthen (lowering phase) and then quickly contract to do the work of converting chemical potential energy to kinetic energy. Jumping launch speed, and therefore height, is limited by the power of skeletal muscle.

For example, a jump that raises the center of mass of 65 kg person by 0.5 m, would require an amount of useful work equal to the gain in gravitational potential energy:

    \begin{equation*} \Delta PE_g = mg(\Delta h)= 319\,\bold{J} \end{equation*}

At 20% efficient, the muscle would need to actually convert 1620 J of chemical potential energy:

    \begin{equation*} \Delta PE_c =  \frac{324\,\bold{J}}{0.2} = 1620 \,\bold{J} \end{equation*}

Even if the muscle contraction of the launch phase occurred over a full half-second then the power output would be:

    \begin{equation*} P=  \frac{1620 \,\bold{J}}{0.5\,\bold{s}} = 3420 \,\bold{W} \end{equation*}

Multiplying our result by 746 hp/W we find that power output to be about 4.3 hp, which is much higher than the maximum short-burst power output of humans[1].

However, storing elastic potential energy in the strain of the Achilles tendon and releasing that energy to do work at the same time as the muscles can significantly increase the power output. In the next chapter we will estimate how much this strategy can improve jump height.

Everyday Examples: Energy Billing

Standard power convert energy from one form to another. The most common type convert chemical potential energy into thermal energy via combustion and then convert thermal energy into kinetic energy via turbines. A large power plant might have an output of 500 million Watts, or 500 MW.

When you receive a power bill in the U.S. the typical unit you are billed for is kiloWatt-hours (kW-hr). These units can be confusing because we see Watt and think power, but this is actually a unit of energy. This makes sense because you should be billed based on the energy you used, but let’s break down the confusing units.

Power is energy divided by time, so a power multiplied by a time is an energy:

    \begin{equation*} Power \times \Delta t = \frac{energy\,converted}{\Delta t}\times \Delta t \end{equation*}

The issue here is we a mixing time units, specifically hours and the seconds that are inside Watts. The reason might be that customers can better relate to kW-hr than joules when thinking about their energy usage. For example, leaving ten 100 W light bulbs on for one hour would be one kW-hr of energy:

    \begin{equation*} (10\, bulbs)\frac{100\, \bold{W}}{bulb}(1\, \bold{hr}) = 1000\, \bold{W\dot hr} = 1\, \bold{kW\dot hr} \end{equation*}

  1. C. T. M. DAVIES (1971) Human Power Output in Exercise of Short Duration in Relation to Body Size and Composition, Ergonomics, 14:2, 245-256, DOI: 10.1080/00140137108931241


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