Wilbur Bud

Ignoring the rightness or wrongness of stopping for a stop sign, the periodic debates made me wonder about how long I’m spending each day stopped at stop signs, so I tried to calculate the time.

Considering at a minimum it’s the time to stop plus the time to speed back up to the cyclist’s normal speed, I come up with approximately 6 seconds for myself, including about one second to actually look at the intersection while stopped before proceeding. That based on myself and bike weighing 200 pounds, commuting at a speed of 15 mph, that my maximum sprint power output is constant at 1,000 Watts for the few seconds of startup, and that I can stop my loaded bike at a specified rate consistent with full stop within 15 feet from 10 mph.

I counted my stop signs on the way home last night, looks to be about 20 of them (not including traffic lights – 8 of those). So, my minimum total delay due to stop signs is probably in the range of 2 minutes of my nominal 60 minute commute, for a overall average loss of 3 percent. Probably more than that due to other traffic in the intersections, but that would seem kind of normal to me and not part of any delay induced just by stopping.

Time to stop depends on initial speed and also braking ability. While many State laws still define adequate braking as those that are able to skid the wheels, a few States have laws like “Must be able to stop within X feet from a speed of Y mph.” A brief search says Florida requires 25 feet from 10 mph and Massachusetts requires 30 feet from 15 mph, plus a model State law text requires 15 feet from 10 mph. Using 15 feet from 10 mph as a model I calculate a braking acceleration of -7.174 feet per second squared. But, assuming many cyclists may travel much faster than me, I had a look at the stopping times from typical speeds using that calculated acceleration value (thinking most cyclists could stop more quickly than that if they wanted to do it).Time to speed back up gets a little trickier, because it depends on the weight of the cyclist and bike plus how much power the cyclist can generate, along with what speed is desired. While cycling forums generally talk about “dialing up to 400 Watts” that value is really more of a steady state sustainable output for a top cyclist over a long distance, and getting up to speed from a stop sign is more of a short duration peak or sprinting power output. Given that, the information I found stated that a non-athlete sprinting in 30 second increments on a cycle can generate more like 900 Watts for the short duration, and professional cyclists can generate more like 2,000 Watts peak. For myself, based on that information, I’m going to say I can sustain 1,000 Watts for the 5 seconds or so it takes me to get up to speed.

First step is to calculate how much energy it takes to arrive at my desired speed (ignoring nuisances like friction and wind resistance). Kinetic energy equals one-half the mass times the square of the speed, so ˝ (200 pounds/32.2)*22*22 = 1,512 lb-ft. The unit correction constant of 32.2 is due to the USA system of units (feet, pounds, etc.).

Second step is to calculate how fast I can get up to speed knowing my power output. If I weighed less I’d need less energy. The energy is a constant once you ignore wind and other friction effects, but I’m going to assume my full power capability of 1,000 Watts is constantly applied. 1,000 Watts = 738 lb-ft per second once I make the conversion to the US customary system of units. So, when I divide Energy by Power I get (1,512 lb-ft) / (738 lb-ft per second) = 2.05 seconds to get up to a speed of 15 mph when bike and rider weigh 200 pounds and the rider can put out 1,000 Watts for a few seconds.
Those are all calculated values with loads of assumptions, and while they generally match my personal experience on the road, I’d be curious if anyone has ever taken any measurements?