I’ve been talking on and off about how we don’t use our own human energy anymore – everything is electric or hydrocarbon powered. In the spirit of
hybridding, it’d be nice to harness human power where appropriate. There are better studies of this topic than what I’m about to write, but this one is compact and pretty!(?) When I bicycle (bicycles are a great way to get our energy out – see my prev. blogs:
1,
2,
3). I can push the pedals with about 200 pounds of force (~900 N), I can bike continuously for 30 min. (1800 sec), and I can move my feet about 10 rev per second (10 m/s). If I plot these limits in a figure (Figure 1). I can multiply the three values together to get an energy output. I can provide 4.5 kWH! my house eats 15 kWH a day – I could reduce my electric bill by a third.
Not quite. It’d be impossible to do all three at once. For one reason, that’s almost 4000 (nutritional) calories. I only take in half that in a whole day. In any half hour exercise session, one would like expend up to 500 calories. That scoops out a major portion of our graph (see Figure 2).
Finally, just like an electric motor’s Torque-Speed curve, I wouldn’t be able to provide the max force at the max speed. Let’s assume a linear relationship between max force and max speed. As you see in Figure 3, this removes a triangle off of the back wall. That backwall (force x speed) is actually power in watts – more on this in a moment. Furthermore, the floor of the plot is distance (speed x time). You have to
pace yourself, right? So, I wouldn’t be able to sprint for the full 30 minutes. Let’s carve out unreasonable distances as well. Lastly, the left plane of the figure is momentum (force x time). This is the least physically intuitive of the six, but we can guess that one would be able to provide the max force for the full 30 min. So, we carve out some of that too. The result is a an plot that shows what one can provide – roughly a maximum at that 500 calories, or ½ a kWH – and rest assured, you’ll be pooped after that.
Many tasks though have a power requirement. Power is not conserved, though. And you can store energy slowly (low power input) and expend quickly (high power, but over short time). If we look at the power vs. time curve we can see what one could provide with the view provide in Figure 3. This is shown in the final figure (Figure 4) and indicates that my assessment is a little on the high side. But it’s something like 1 kW for 15 minutes that we grown adults are good for.
That’s not too bad is it? One can probably do quite a bit with that.
(P.S. all these graphs were made in the new Microsoft excel 2007 beta version)
Finally, just like an electric motor’s Torque-Speed curve, I wouldn’t be able to provide the max force at the max speed. Let’s assume a linear relationship between max force and max speed. As you see in Figure 3, this removes a triangle off of the back wall. That backwall (force x speed) is actually power in watts – more on this in a moment. Furthermore, the floor of the plot is distance (speed x time). You have to pace yourself, right? So, I wouldn’t be able to sprint for the full 30 minutes. Let’s carve out unreasonable distances as well. Lastly, the left plane of the figure is momentum (force x time). This is the least physically intuitive of the six, but we can guess that one would be able to provide the max force for the full 30 min. So, we carve out some of that too. The result is a an plot that shows what one can provide – roughly a maximum at that 500 calories, or ½ a kWH – and rest assured, you’ll be pooped after that.
3 comments:
The graph is interesting, but I would like to challenge the outcome (1kw x 15mins). Record-breaking cyclist Sam Whittingham (rides recumbent bikes with full fairings) achieves 450W (ish) for 5 minutes during record attempts. Through strenuous training for a year, he aimed to increase that to 465W for the same period.
Having done a little more research, it appears that his power output must either a) be wrong, or b) be measured differently, as other data backs you up quite neatly. Sorry for the lack of links; I'm new at this.
thanks for the post. I've been feeling a little squeamish about my values, so I was glad to see that someone fact-checked me. If I get the time to re-do this, I will likely reduce the numbers a bit. Researching this Wittingham fellow, it appears that he did 275 kWh, and I said an average fit adult could do 250 kWh. Of course, mine was determined with a 100% efficient machine. His recumbant is probably pretty efficient but likely somewhere less than 85%. This points out an important caveat: even though you could produce 250 kWh, you still have to convert that to useful energy!
Post a Comment