Rob Archer wrote:I've recently re-read the book that got me into 'proper' cycle touring: 'Adventure Cycling in Britain', by Tim Hughes (Blandford Press 1978). In the very useful section on gearing, he recommends (on page 35) that gears lower than 30 inches (about 1:1.1) are less desirable, and explains several reasons why - not least the risk of lifting the front wheel on a very steep hill.
I liked Tim Hughes' descriptive writing, but I disagree with him on this technical point.
In a pure steady state (exactly uniform pedalling speed over each rotation of the pedals) the gradient at which the front wheel lifts off the ground is a function of geometry only and is totally independent of gear ratio. For a given bike/rider/load weight distribution, it is a function solely of when the vertical through the centre of gravity first falls behind the rear wheel contact point. You can shift the CofG forward by using front panniers, or by getting out of the saddle and putting more weight on the handlebars, but once you've done that, and established a new weight distribution, the critical gradient again becomes a function of the position of the CofG.
However, in practice, you do not pedal at an exactly even speed. We all (especially, I suggest, uphill) shift the pedal (and hence the bicycle) faster between about 10'0'clock and 4'o'clock than when going over top centre or bottom centre. This means the whole bicycle is accelerating (and then deccelerating) twice each crank revolution. The extra force required to accelerate the bike exerts a turning moment that tends to lift the front wheel. (Imagine that the back wheel were fixed rigid to the ground - tramping on the pedals pulls harder on the top run of the chain, which tends to lift the front of the bike up over the rear wheel.) So under these circumstances, the gradient that the front wheel lifts is less than the gradient set purely by geometry.
So the more smoothly we can pedal, the closer we can approach the gradient limit set by geometry (centre of gravity) alone. And the lower the gear (for a given gradient and speed), the easier it is to pedal more smoothly.
So, if you want to maximise the gradient you can pedal up without lifting the front wheel:
(1) get a bike with long chainstays or other geometric features that move the CofG forward of the rear wheel (you don't see mant tandems lifting front wheels!)
(2) put luggage at the front of the bike rather than the back
(3) get out of the saddle and put more of your weight on the front wheel if that suits your cycling style
but having done all that
(4) fit a lower gear.