Originally Posted by
subgrade
There is one other nuance: if the climb is short and you speed up before it, the momentum will make more difference than the gear you are in - i.e., the effort you will put in using, say, 48/16 or 38/16 will be very similar, but the speed in the latter case will be lower.
Spending energy on a climb itself will always be faster than trying to carry speed into it.
Speed up a climb is almost linear with power. Pedal 20% harder, go 20% faster. 90% of your energy goes into hauling your carcass up to the summit.
Speed on flat ground is almost proportional to its cube root. Pedal 20% harder, go 6% faster. Even at low speed the overwhelming majority of your effort goes into overcoming aerodynamic drag.
Most of the energy you put in will be lost overcoming aerodynamic drag. Assuming a good position on the drops - 15 MPH on flat ground 74% of your power is wasted on aerodynamic drag, 83% at 20 MPH, 89% at 25 MPH, 92% at 30 MPH.
You might have more fun accelerating before a hill, but won't be faster than using your energy more efficiently.