Re:Switzerland bores underground
by jcranmer on Thursday August 04, 2016 @01:40PM
(#12227201)
If you want some hard numbers on why high grade is so problematic:
When you're pulling something along a road or a railtrack on level ground, the primary force you need to overcome is rolling friction, which is proportional to µ×N, where µ is in the range of 0.001 (rail) to 0.01 (road) and N is the normal force against the surface. For a 10 kN car (that's about 1000 kilos), this means that you need a force of about 10 N for a railcar. When you go up an incline, the rolling friction decreases according to the cosine of the angle, but now you need to overcome gravity--and this amount goes up by the sine of the angle. A measly 2% grade requires pulling a force of about 210 N, a factor of 21×.
Basically, grade really kills because you actually have to counteract gravity as opposed to friction.
When you're pulling something along a road or a railtrack on level ground, the primary force you need to overcome is rolling friction, which is proportional to µ×N, where µ is in the range of 0.001 (rail) to 0.01 (road) and N is the normal force against the surface. For a 10 kN car (that's about 1000 kilos), this means that you need a force of about 10 N for a railcar. When you go up an incline, the rolling friction decreases according to the cosine of the angle, but now you need to overcome gravity--and this amount goes up by the sine of the angle. A measly 2% grade requires pulling a force of about 210 N, a factor of 21×.
Basically, grade really kills because you actually have to counteract gravity as opposed to friction.