## Monday, December 04, 2006

### A Ratio Question

I went for a ride on my bicycle yesterday on a gravelled path beside the new `fast track’ line leading towards the Channel Tunnel. On the way back I passed the point where the `Lady in White’ has sometimes glided out onto the road. The point is near the lovely village of Cobham. Many years ago Mr. Pickwick was moved to exclaim that this was 'one of the prettiest and desirable places of residence' he had ever met.

The `Lady in White’, or so the story goes appears just as cars round a bend. As she is, apparently, dressed in a diaphanous white outfit it is no wonder that she is regarded favorably by the locals.

If I had been riding a horse I wonder if the horse would have shied at the sight of her. As it was my bicycle became much heavier. It is possible that my heart beat went up because I was riding up a steep little hill. I do know that I suddenly thought of how the gears on a bicycle would make a wonderful 11+ question.

I have bicycle wheels that are 26 inches in diameter. When I changed to the lowest gear, because the hill was steep, and I wanted to see the `Lady’, I went much slower. There are 22 teeth on the lowest front chain wheel and 30 teeth on the rear gear. This means that I was traveling at about three miles an hour. (For each time the pedal goes round the rear wheel turned about 0.7 times.) I know that at three miles an hour I should have jumped off and walked but I thought that a moving object would have been harder for the `Lady’ to catch.

If we raise the number of teeth on the front chain wheel and reduce the number of teeth on the rear wheel to have a new gear ratio of 3:1 how fast will I be going downhill?

I am sorry that questions like this do not come up in the practice papers from reputable 11+ sources. Questions on gear ratios and speed certainly have some relevance to all cyclists.

An ancillary 11+ question could have been around the number of times my heart beat would have risen if I had increased my speed going up the hill – and if I had seen the `Lady in White’.