Originally Posted by
asgelle
Just so you know, if you now want to claim air resistance is proportional to velocity, which is not the same as equal air resistance, the 0 drag result still holds since rolling resistance is already proportional to velocity. Therefore, the analyticcycling calculation considers one resistance proportional to velocity and another which goes as velocity times the grade of the road. That sounds exactly like what you're proposing.
You're right. The reason that the example you gave in that post didn't work out is because the total resistance was so insignificant compared to the potential energy gain while climbing - which resulted in the uphill speed being way below half of the flat speed. That's why I increased the rolling resistance coefficient in the analyticcycling example I gave a ways up this thread, to arrive at a more reasonable flat speed.