Trailer power

After the ride Sunday where I pulled Laura up a number of hills, I was curious how much extra power hauling a trailer actually required. Both last week, on mostly flat surfaces, as well as Sunday I found it difficult to sustain more than about 18 MPH, and hauling the trailer up the hills just killed me. The last 20 miles of the Daffodil Classic was flat to a gentle uphill – a route I would normally cover easily between 15 and 20 MPH, but I was so tired I was closer to 10 MPH.

A fellow Wino clued me in to Analytic Cycling, which includes some nice force calculators that included pretty much everything I could ask for, saving me hours of remembering high school physics. Some basics… assuming me + bike = 100kg (about 220 lb, which should be close), flat, a cadence of 80 rpm, and a crank length of 175, going 15 MPH (which is 6.71 meters per second), and using most of the defaults on the ForcesPower page, requires a power output of 72.6 watts. Go up a slight incline (say 3%), and the power required to sustain 15 MPH goes to 270.0 watts. Here are two power curves (power vs speed):

power_100kg_0pct.gif

power_100kg_3pct.gif


Notice that it’s a quadratic relationship!

Now, let’s add that trailer. I’ll call it an extra 25kg, or 55 pounds. About 20 for the trailer, 35 for Laura, give or take. I’ll add some additional space to the effective frontal area: 0.2 m^2, which is about a square foot. I’m sure the trailer is more, so good enough for a lower bound. As it turns out, there isn’t a huge increase on a flat road – 97.7 watts, or about 25 watts difference. Not a huge deal in absolute terms, but still about a 33% increase in required power. On that incline, again a minor 3% climb, it goes to 344.5 watts, or nearly 75 watts more. Again, about a 30% increase in power. As the incline raises, power required for 15 MPH converges to requiring about 25% more power with that trailer.

power_125kg_0pct_7eff.gif

power_125kg_3pct_7eff.gif


Put another way, climbing a 3% incline weighing 125 kg at 15 MPH requires 344.5 watts. What is an equivalent for 100 kg and 344.5 watts? At 15 MPH, it only takes 335.8 watts for a 4% incline. Or, at a 3% incline, the speed can be increased to about 18 MPH.

Granted, these are just rough estimates… I gotta get a power meter and find out what the actual power required really is. But roughly, I’d imagine a reasonably loaded trailer is basically a 3 MPH or 1% grade tax, which feels about right.

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