One of the important facts about a cycling course is the gradient of a big climb, customarily expressed, as on highway signs, as a percent. For example, the Col de la Madeleine, which the Tour de France goes over in stage 17 this year, has an average gradient of 8% for 19.5 km. I’ve seen it written in a few places (e.g., CyclingNews) that this is the percentage that the elevation gain is of the horizontal distance, in other words, the tangent of the angle that the road is pitched up from horizontal expressed as a percent. While that may be true, I doubt it for two reasons. First, the distance that the race travels is measured along the road surface, which is most certainly not horizontal or the elevation gain would be zero. So, the horizontal distance would have to be calculated. Second, the ratio of the directly measured quantites, elevation gain to distance along the road, the sine, is exactly the ratio of the force pulling the rider backwards (down the hill) to his weight, a very good way of assessing the relative difficulty of various climbs.
Be that as it may, it all amounts to a mere quibble, since the difference between the tangent and sine is insignificant for the size of the angles involved. For example, sine(6°) = 0.1045, tangent(6°) = 0.1051; about six in a thousand.
posted @ 01:15 AM EDT