Human Power Generation In an analysis of sustainable sources of energy, an engineer wants to estimate the amount of power that a person can produce. In particular, can a person who is riding an exercise bike power a television (or similar appliance or product) during the workout? Treat the

Question

Human Power Generation

In an analysis of sustainable sources of energy, an engineer wants to estimate the amount of power that a person can produce. In particular, can a person who is riding an exercise bike power a television (or similar appliance or product) during the workout? Treat the following information as given when making the order-of-magnitude estimate: (1) An average LCD television consumes 110 W of electrical power. (2) A generator converts about 80% of the supplied mechanical power into electricity. (3) A mathematical expression for power P is

[latex] P=\frac{Fd}{\Delta t} [/latex]

where F is the magnitude of a force, d is the distance over which it acts, and Δt is the time interval during which the force is applied.

Approach
We are tasked with estimating whether it is feasible for a person exercising to independently power a product that requires approximately 110 W. We first make some assumptions to make this estimation:
• To estimate a person’s power output while exercising, we will make a comparison with the rate at which a person can climb a flight of stairs with the same level of effort
• We will assume that a flight of stairs has a 3-m rise and that it can be
climbed by a 700-N person in under 10 s

We will calculate the power generated by a person climbing stairs and then compare it to the power required.

Accepted Answer

The stair climbing analogy provides the estimate of power output as

[latex] P=\frac{(700N)(3m)}{10 s} \longleftarrow \left[p=\frac{Fd}{\Delta t} \right] [/latex]
[latex]=210\frac{N.m}{s} = 210 W[/latex]

where we have used the definition of the watt from Table 3.2.

Table 3.2 .Certain Derived Units in the SI

Quantity	SI Derived Unit	Abbreviation	Definition
Length	micrometer or micron	[latex]\mu m[/latex]	[latex]1\mu m = 10^{-6} m[/latex]
Volume	liter	L	[latex]1 L = 0.001 m^{3}[/latex]
Force	newton	N	[latex]1 N = 1 (kg . m)/s^{2}[/latex]
Torque, or moment of a force	newton-meter	N . m	—
Pressure or stress	pascal	Pa	[latex]1 Pa = 1 N/m^{2}[/latex]
Energy, work, or heat	joule	J	1 J = 1 N . m
Power	watt	W	1 W = 1 J/s
Temperature	degree Celsius	°C	°C = K – 273.15
Although a change in temperature of 1 Kelvin equals a change of 1 degree Celsius, numerical values are converted using the formula.

The useful work that a person can produce is therefore approximately 200 W. However, the generator that would be used to convert mechanical power into electricity is not perfectly efficient. With the stated efficiency of 80%, about (210W)(0.80) = 168 W of electricity can be produced.

Discussion
First, we evaluate the order of magnitude of the solution. This amount of power seems reasonable, because some nonelectric exercise bikes generate enough power to run their own displays and resistance. Second, we revisit our assumptions to make sure they are reasonable. While the stair-climbing analogy may not be perfect, it provides an effective estimate of the amount of power someone could generate over a sustained time. Third, given the uncertainty in our estimates and the range of exertion while exercising, we conclude that a person can generate 100–200 W over an extended period of time. This would be sufficient for a wide range of LCD televisions.

approximately [latex]100 – 200 W[/latex]

Question 3.9: Human Power Generation In an analysis of sustainable sources...

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