Human Power Available For Flight
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Human Power Available For Flight

by Chris Roper

Most of the early data is in the form of graphs showing power against time. These are graphs of constant-power v duration. (They are not, as one might imagine at first glance an indication of how your power drops off as you get tired.) The subject was usually a fit male of, unfortunately, unspecified weight. Each graph is the results of several tests. For each test, the subject would pedal at a specified constant power output for as long as he could. Then this constant power and this time would be recorded as one point on the graph. So, what we learn is that some guy, many years ago, could pedal at a constant 300 watts for such a time and that he could pedal at a constant 200 watts for some known, longer time.

Power against time for various athletes. D R Wilkie

Reproduced From “Man as an aero engine” D.R Wilkie Journal RAeS, August 1960. See Library. Click on image for larger picture.

Now, suppose we want to answer the questions :-

  • "Am I fit enough to fly that plane?" or
  • "Which of our group is the most appropriate pilot-engine?" or
  • "For our project, what can we assume will be the power available?" or
  • "Will I be able to complete this course in this plane?"

First, appreciate that it is not watts that is the significant parameter. It is watts per kilogram. Or, in British units, (foot pounds per second) per (pound weight). Since both the "pounds" in this expression are forces, and since the "foot" implies a foot vertically against gravity, we can express this as feet per second, vertically. In other words, how fast you can run upstairs.

Alternatively, you can measure your output on a dynamometer, and then weigh yourself. Either way you arrive at Watts per Kilogram or feet per second.

3 watts/kg = 1 ft/sec. 1.356 watts = 1 ft lb/sec.

If you can run upstairs fastest, you are the most appropriate pilot. It’s not who can turn out the most watts.

It is obvious that a heavier person will have to output more effort to raise their own weight. But, compare a heavy pilot and a light pilot, one after the other, in the same aeroplane. You might think that since both have to counter the weight of the empty plane as well as their own weight that any comparison should include the weight of the plane. It might appear that whichever of them can run upstairs carrying that weight the fastest would be the champion. Or, that the relationship between power, weight and suitability follows some other, possibly more subtle law. Well, in practice, it doesn't. It can be shown that assuming a reasonably conventional HPA, and a person whose weight is within a reasonable range that, to a close approximation, the required power is a constant times the weight of the pilot. To be strict, the function of power against all-up-weight is a curve. However, the tangent to this curve which passes through the origin will be close to the curve over the range of weights that occur in practice. Any discrepancy will be masked by the variation in fitness from day to day that we all experience.

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