A Definitive and Graphical Guide to Human Energy/Power

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)

Fantastic Island Game

Here's another thing, I couldn't find anything about online. It's a little puzzle called the Fantastic Island Game - obviously some mangled translation from Chinese, but it's no simple or cheap puzzle. The peices have a nice feel and a lot of thought has been put into its design.
As you can see from the pics, you get 7 pieces (ala Tetris) that can be assembled into, get this, 124 different simplex pyramids (like the one I solved at the bottom). The mind's activity during this 'puzzling' is quite refreshing to me. I know a little bit about how puzzles can be solved computationally, so sometimes I get bored with such things because I know the best way to solve some puzzles is to follow a rote set of actions. But, in general, we need to keep pushing ourselves to solve such puzzles if we wanna keep our wits about us (what I mean is, as we get older, we need to exercise that ol' wetware).
Part of the freshness offered by this puzzle, is the 3-nature that the pieces congeal in. From my previous posts, one can see my fascination with ternary systems, and this is a great example. As you build the pyramid, pieces aren't to the left/right of or above/below one another (as in the binary way of things we usually consider) but the interactions are harder to define.

Anyway, a lot of fun and getting good at this is good for ya - my humble opinion.

a random walk

In some of the computational research I do, one often talks about taking a “random walk through the space.” This is to get a feel of how messy a design problem is, or how much things changed by making the same size small changes.To me (and probably no one else), there’s an interesting tie-in with music. I’ve been taking bass lessons again and working with a teacher on walking bass lines. In jazz the bass players have adopted this walking thing – taking small steps to transition between chords in a song. It takes some talent to choose notes that are not completely obvious and yet not completely random. One can’t be too interesting otherwise it’ll distract from the melodic, and not too boring otherwise the whole tune will suffer.

Looking at design and the decisions we make in design, I can see an analogy. In engineering, we don’t always want the most creative solution (especially if there’s no precedent that it’ll work or if you have to go to great lengths to make it by retooling your manufacturing), and we don’t want something to boring or predictable (else no one will buy it, and we won’t be truly innovative).

Don’t worry about me. This depresses me a little as well. I’d like to think we are always best with the crazy ideas even if it means no one else will understand :).

an uncomfortable truth about air power

In my last post, I wrote about a mythical approach to transportation - one that relies on charged air. I still very much like this idea, but there are two big problems with it to be frank:

1) Pressured air (pneumatics) is much more dangerous than pressured liquid (hydraulics) – i.e. things can explode.
2) The control system for using compressed air as an energy storage medium is difficult to design.

The latter is going to be a big challenge for my air-powered bike idea. This is because as you pedal the bike and charge up your pressurized air tank that will be used to drive the wheel(s), the pedaling will constantly get harder and harder. One will require some gearing that will hopefully shift for you so that you can keep pedaling with a fairly even force imposed. Here’s a simple two-gear idea. It doesn’t require pedaling in the traditional sense, but rather an up and down motion like a stair-climber. The mechanism would require the shifting to simply lock one of the cylinders (while unlocking the other).

Air Power

Rarely do internet searches disappoint. But yesterday, I was disappointed twice by two related searches. I overheard two colleagues of mine talking about a vehicle, car if you will, that can transverse the continental US on a single tank of compressed air. This turned up nothing. Perhaps they were sharing a joke and I was naïve to the punchline. Ahh well. At any result, I did find an air-powered car that reportedly can travel 185 miles.

This relates back to a previous post I made about the nature of energy. Vehicles are particularly tricky because of what I called the discrepancy in space (i.e. they need to be portable). A windmill or a nuclear reactor are hardly portable, are they. And countless alternatives fail to meet the demands (battery powered car?).

I’m also a big fan of bicycles. Not that I’m much of a star on a bike, but I love the fact that it has long evolved as an efficient way to get energy out of humans. So, I was really excited to read in Wired magazine about an air-powered bicycle with a picture of what I thought was one. Again an internet search of air-powered bicycle didn’t get me to what I thought was a bike driven by human generated air-power. But rather, like the car, one charged by more conventional means.

Why I am disappointed about this. Well, energy and power are not the same. Energy is conserved, not power. We humans can’t produce a whole lot of power, but energy we get a lot of, some more than we need. We tend not to use the kilocalories we store up as soon as we’d like. In fact, FDA says you take in 2000 calories (kcal) a day. With a good workout, you can expend a quarter of that, or about 0.6 kilowatt-hours. So, the instructables site let me down with my future air powered bike. But poking around that sight I also saw someone state how it’d be impossible to charge a 2HP air tank. That’s just not true. One person may not be able to create that much power. But that’s the great thing, we don’t store power, we store energy! Air is an untapped storage media of excess energy.

Sooo, the bike I wanted to see (which I guess I’ll have to design someday) uses your pedaling to store energy in the bike and outputs to the wheels when you want and at what rate (i.e. what power).