Bike Physics

About your ride across Pennsylvania, I got curious about the hills and how much power you had to produce to climb them. If I remember correctly, you said they were 10% grade and you rode 4 mph. So, trying to remember back to physics class...

  Pitch of the hill = 10% = 1 ft rise over 10ft of run
  Speed = 4 mph
  Weight 200 lbs. (my guesstimate)

  force = mass * acceleration = 20# (10% of 200#) = 88.9 kg-m/s/s
          20 lb * .454 kg/lb * 9.8 m/s/s (acceleration of gravity)
  distance per sec = 4 miles/hr * 1609 m/mile / 3600 s/hr = 1.79 m/s
  watts = force * distance/sec = 88.9 * 1.8 = 160

  1 horsepower = 745.7 watts, so you produced .21 hp
(Note: I weigh 185, carried 20 lbs. tools and gear + 20 lb. bike 5mph is the upper limit of these uphill climbs, some were 11% This yields .33 hp as an upper limit.)

Also, I researched the Gossamer Condor and Gossamer Albatross, the human powered aircraft that won the Kremer prizes for flying a figure-eight and crossing the English channel. The first required a minimum of .33 hp for a few minutes to fly about 5 mph with 6 lbs of drag. The second required a minimum of .25 hp to fly at 12 mph, the trip took 169 minutes, and the pilot nearly collapsed from exhaustion at the end. The pilot, Bryan Allen, was a bicycle racer.

Paul Macready, the engineer who designed those aircraft, talked about .33 hp being anaerobic while .25 hp was aerobic and sustainable for the two hours they expected the channel crossing to take. Unfortunately, they had a head wind... aint that how it goes! It would be interesting to know more about the anaerobic threshold in relation to power. I assume that the aerobic power maximum increases with body weight and conditioning.