Science can be fun!

I nearly took a trip to Spillsville this morning.  35miles into a 40mile ride with 800m of climbing - any self respecting roadie will look to cheat the elements in this situation.  So I'm tramming through Havercroft, slightly downhill at ~25mph... Transit van up ahead which has slowed down for a traffic calming chicane so I managed to jump into the slipstream and draft for a while.  Now my experience of Transit van drivers is they don't slow down or stop for anyone.  Right?  Well I came across the jumpiest, most courteous Transit van driver this side of Watford.

Anyway at 30mph, he hits the anchors and stoops in between two parked cars to let opposing traffic through.  Yours truly also hits the anchors and manages to slow down.  However, the back tyre loses traction and consequently the wheel which it shrouds steps out to the side.  I'm skidding and fearing the worst, but luckily I kept everything in the correct orientation.

This had me thinking about vehicle stopping distances...

The Highway Code stopping distances are derived from a combination of driver thinking-perception time and the subsequent vehicle braking and stopping distance.  Braking systems on ‘modern’ cars allow them to decelerate at approximately 1.0g; indeed the Highway Code stopping distances are based on 6.57m/s/s or 0.67g.

Driver thinking-perception time will vary from subject to subject, but a conservative average value is taken for the purpose of the calculations.  The Highway Code stopping distances are based on a thinking-perception time of 0.7s.

Assuming a vehicle’s braking system is operating properly, the minimum stopping distance for the vehicle will be determined by the coefficient of friction between the tyres and carriageway surface.  According to the work-energy principle, the friction force must do enough work to reduce the vehicle’s kinetic energy to zero.

Braking and stopping distance

 µ = coefficient of friction

d = distance (m)

v = initial velocity (m/s)

m = vehicle mass (kg)

g = acceleration due to gravity (m/s2)

t = thinking-perception time (s)

Workfriction = -Fd = -mad = - mµgd = -½mvv so braking distance db = v2/2µg

Thinking distance dt = vt

Total stopping distance, d = vt + v2/2µg

If we consider a car travelling along the M62 at 70mph in clear and dry conditions; using these first principles, we can see how the Highway Code braking and stopping distances are derived.

v = 33.3m/s (70mph)

t = 0.7s

µ = 0.67

g = 9.81m/s2

Braking and stopping distance, d = 107m

Thanks for reading and not falling asleep!