Worn Tyres and Circumnavigating the World

Cars and the three ages of man.

When I was quite young we boys would discuss how fast our cars would go but as we got more savvy we would boast about their acceleration, or as one 1970's racing driver called it, their "squirt".  But now I am aged, just like malt whiskey, and now we discuss consumption. 

"My new VW Touran 2litre diesel is doing over 50 mpg" I announced to my fellow senior citizens. "Probably because you have new tyres, it will go down when they are worn" was one repost. So let's look into this.

BUT Are all all things equal.

The axle spins the wheel, and the friction of the tyre upon the road pushes the car forward. The torque (i.e. circular force) to propel this is proportional to the distance of the force from the centre of revolution, i.e. the radius. So as the tyre wears the radius reduces and so the required torque is less. Does this mean the engine works at a lower effort and probably more efficient.  I suspect this is so.

QI, Stephen Fry and Circumnavigation.

What reminded me of the original conversation was a question on the BBC QI when Stephen Fry asked 

Imagine a belt is placed tightly around the earth which we will assume is perfectly spherical. Now if a belt was placed around the same globe, only everywhere 1 meter high, how much longer would this belt be?

It is basically the same question as for the tyre. The answer is 

Assume radius of earth is R, then extra length is 2π(R+1)- 2πR = 2π meters 

So it is just 6.28 meters longer. Seems ridiculous but remember the radius of earth is 6,371,000 meters so an extra meter is proportionally very small.