Originally Posted by
TomD77
Run is not the hypotenuse. In simple terms, % grade is rise/run X 100 where run is the horizontal distance (level). This is the same as the tangent of the angle X 100.
Until the slope starts getting very steep there is very little difference between level distance and traveled distance (hypotenuse). The relationship between travel distance and level distance is the cosine of the angle. So an 11% slope is a 6.28 degree angle, the cosine of which is .994. So the difference is in the third decimal place, roughly 30 feet per mile for 11%. Pretty much nothing in biking terms. For your example above, the cosine is .997 (rounded) or around 17 feet error per mile, undetectable by odometer.
OK Tom - thanks. I was confused because I did not think you could have a grade over 100%, i.e. if you have an incline angle greater than 45degrees. That just intuitively did not seem righ to me. Some disciplines use the same term but have different meanings. Although I must confess I too have degrees in Engineering but they lack "Civility". So I should have stuck with my first answer.