Roundabouts: the speed factor

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Did somebody ask why one must drive slowly in a roundabout? Two reasons: safety and curvature. Safety is complicated in detail but intuitively clear. Hardly any crashes occur at a speed of 0 mph and the ones that do are minor. :-)

Curvature is simple. High school physics experts and rocket scientists know about centripetal force: it is the force that must be provided to cause (any) body to turn. Centrifugal "force" is the feeling you get when your car is turning and your own body wants to go straight. Most drivers are guided to a safe cornering speed by experiencing the magnitude of this force ("flying by the seat of your pants").

The size of the centripetal force is    
   
where m is the mass, v is the speed, and r is the radius of curvature. It's useful to drop the mass and think in terms of the centripital acceleration, which is one-size-fits-all (bodies):
   

It's handy to express the acceleration in terms of the acceleration of gravity (g = 32 ft/sec/sec). Going from 0 to 60 mph in 6 seconds, for example, requires an acceleration of 0.46 g.

What does this mean for a "typical" roundabout, vehicle, and driver under good driving conditions? A"typical" turning radius of 40' at a "typical" speed of 15 mph requires a centripetal acceleration of 0.4 g. The v-squared dependence limits a vehicle's speed pretty well. Most drivers, I think, would consider a centripetal acceleration of 0.6 g as a reasonable (typical!) upper limit. This acceleration would occur for a vehicle speed of 18 mph. A factor of 1.5 range of "acceptable" centripital acceleration corresponds with a narrower range of 1.2 in acceptable speed.

The v-squared dependence is also important in the inverse case. If you want to design a roundabout where it is comfortable to travel twice as fast, 30-36 mph, the radius must be increased by a factor of 4, to 160' turning radius or 320' diameter. Whoa! Getting up towards a freeway entrance in size. At the price of urban real-estate, this is rarely going to happen in town.

I sometimes think of a roundabout as a horizontal speed bump with a few added hazards (other vehicles) to strengthen the effect!


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