#### This paper by CTC Technical Officer Chris Juden shows the energy costs of stopping in terms of distance lost.

The whole point is that cyclists like to keep going. For a skilled rider that means the most convenient and continuous route gets them to where they want to go for the least effort.

Cycle tracks beside the highway that require a rider to give way at every entrance are a real discouragement to cycling for beginners and experienced riders alike.

When one rides a bike, one soon learns that stop-go cycling is whole lot harder work than keeping on rolling at a steady speed. However it's clear that the people who design British cycling facilities do not share this tacit knowledge - unlike in other countries! So I thought it might help if I investigated the engineering principles that discourage us from using the brakes and explained the wasted energy in simple terms of extra distance ridden.

#### Why cyclists won't stop

Everyone likes to keep moving, but cyclists have more reason than most for conserving their momentum. Riding a bike at a steady speed takes only about as much energy as to walk at one quarter that speed. Twelve mph cycling equates to 3mph walking and these are typical speeds for purposeful cycling and walking. Each requires about 75W of power from the "human engine" and people are as happy to cycle four miles to work as they are to walk one mile. Each should take from 20 minutes up to half an hour, including stops, at a total energy expenditure of some 100kJ.

Every time a cyclist or pedestrian stops, they lose kinetic energy and have to work harder upon starting off in order to accelerate and restore that kinetic energy. Kinetic energy is proportional to mass times speed squared, so to reach a steady cycling speed, four times that of walking, makes a 16-fold increase, plus a bit more (say 25%) for the extra mass of the bicycle, means that a cyclist has to expend about 20 times as much energy as a pedestrian in order to reach his normal journey speed. And because that speed is four times faster, that energy would have carried the cyclist 80 times further than the pedestrian, had neither been required to stop. It is interesting to see just how far a cyclist could go, at a given speed, for the same amount of energy as may be required to reach that speed. This gives a direct measure of the energy cost of stopping. For typical cycling speeds, of 10 to 12mph, on a middling kind of bicycle, it can be calculated that one stop-start is equivalent to cycling an additional 100m. Compare this with the pedestrian, who can stop and start again with no more energy than it takes to make a couple of steps!

This explains why cyclists, when riding on the footway, are extremely disinclined to give way at side roads. Compared to a pedestrian, it adds a considerable extra distance to their journey. Of course a cyclist's journey is likely to be four times as long, so any given stop doesn't add such a big percentage to it (we're back to 20 rather than 80 times the trouble caused to a pedestrian), but by the same token, this means the cyclist will cross four times as many side roads in the course of such a journey. It also explains why cyclists sometimes find it easier to take a longer route without so many junctions.

Just as a cyclist's higher speed and (slightly) greater mass inflate the energy demands of stopping and starting, the acceleration of a car requires a huge expenditure of energy compared to that which keeps it moving. However the cyclist feels it directly in his legs, whereas the motorist is hardly conscious of the energy expended when he presses the accelerator. A cyclist caught in stop-start traffic becomes acutely aware of this difference in perception. The drivers will rush to close any gap that appears ahead of them ñ then brake ñ whereas the canny cyclist will try to conserve his energy and just keep rolling at a steady speed.

My simple equation of cycling distance to the energy cost of stopping, on the other hand, assumes that the cyclist brakes and accelerates very suddenly. If he were instead to cease pedalling some distance before the stop and let his kinetic energy decay naturally, and then accelerate very gradually away, spreading the process over an appreciable distance, the cost of stopping would largely be absorbed in that distance. It would instead cost a great deal of time. In practice there is a trade-off between extra time and extra distance or energy. The cyclist chooses his own compromise, braking and accelerating hard if he is short of time, going easy if he is short of energy. In any event, the comparison with distance holds true, since that gives a valid and convenient estimate of the additional time a journey may take if it involves a stop.

The calculation is also affected by assumptions about the type of bicycle used and the effort expended by the rider. Fast cyclists have good reason to be more averse to stopping, since an energetic rider on a racing bike (200W, 22mph) would find it easier to add 200m onto his journey, rather than interrupt it. But even slow cyclists suffer significant penalties from stopping. For a leisurely rider on soggy tyres (40W, 8mph), each give-way costs at least 60m. And since such a person would be unlikely to walk faster than 2mph, the 80 to one comparison still holds true.

Let anyone ride a bike, and they'll soon discover that compared to walking, stopping is a waste of hard-earned momentum. They'll all just want to keep rolling!.

I haven't even touched upon balance and control. Bicycles are like the Sundance Kid: better when they move! Upon starting and stopping a bicyclist manages a complex transition between static and dynamic stability. With practice this becomes automatic, but it is something which less experienced cyclists may still find quite difficult ñ even risky ñ and naturally seek to avoid. So children and less confident adults have a further reason to keep on rolling.

Well I hope you all find that useful and are able to persuade the planners sometimes to make the cars stop instead. They can do it without falling over!

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- Created: 12 September 2002