Friday, 10 August, 2001
Are Human Powered Vehicles Practical?
Somebody at work a while back postulated that it was possible to design a human powered vehicle in which a person could, with moderate effort, achieve and maintain 60 MPH. It's a nice dream, until you sit down and do the math. You can imagine that a lot of people have spent considerable time crunching these particular numbers. It didn't take me long to find the International Human Powered Vehicle Association on the Internet. Using the spreadsheets from their tools page, I came up with some representative numbers.
The primary impediments to motion are rolling friction and air resistance, so I selected the vehicle that has the least air resistance (a streamlined recumbent bicycle), and a tire with very low coefficient of rolling friction (0.002). Finally, I assumed that the combined weight of rider and vehicle is 200 pounds. To maintain a speed of 60 MPH with that combination would require a sustained power output of 0.825 HP. Fine. But even elite athletes (think Lance Armstrong) can achieve a sustained power output of only 0.4 horsepower (about 300 watts) for long periods. A reasonably fit person can expect to maintain between 0.1 and 0.15 HP for a 4-hour period. Obviously, we can't expect human powered vehicles to travel at 60 MPH.
The interesting thing is that the power requirement doesn't increase linearly with weight. If you double the weight of the bike and riders to 400 pounds (say, a dual bicycle with two people pedaling), the required output power only increases to 0.892 HP. Two elite athletes working together could come very close to a sustained 60 MPH.
If you reduce the speed requirement to 30 MPH for a single-person vehicle, you reduce the power requirement to 0.13 HP--something that a reasonably fit person could achieve with some effort. You'd want a shower when you got to where you were going, though. And that's on flat ground with no wind. If you add a 10 MPH wind and a 1% grade, you triple the power requirement. Ouch. Before you argue that better gearing would solve the problem, remember that gears don't increase power, but rather allow you to apply it more efficiently.
So how to overcome friction and air resistance? Overcoming friction requires better materials. Certainly there are less resistive materials than rubber, but using them would reduce braking and cornering ability, so they're probably not very practical. Air resistance is more complicated, but in general is a function of the area exposed to the wind. A faired, streamlined recumbent bicycle has an effective area of about of a square foot. It's hard to imagine that you could build a modern sized vehicle that has an effective area less than that.
Friction and air resistance are limiting factors for all types of vehicles. We don't worry too much about it in our gasoline powered cars simply because we literally have horsepower to burn. Solar powered vehicles, though, have problems similar to human powered vehicles: there's not enough solar energy hitting a typical car--even if it could be converted 100% efficiently--to propel the car at 60 MPH. Solar and human power may be good alternatives for short or slow trips, but we still need a separate energy source for speed or heavy loads. I'm not saying that we need to stick to burning fossil fuels, but we need something. Gasoline-electric hybrid cars are a step in the right direction for personal transport. For larger transport (ships) and local power plants, pebble bed nuclear reactors look promising.