It is quite easy to calculate the power PHill needed for climbing a steep hill. If there
would be no air or rolling resistance, all we need to know would be the mass m of the
rider plus bicycle, the acceleration due to gravity g (9.81 m/s²), the
difference h of the climb, and the time t.
The work WHill (in Joule) to climb the hill is
Then the power is simply the work divided by the time:
g×h / t
Since we are still fighting the air resistance and rolling resistance (but at
low speeds...), we have to add this contribution PAir and
It depends on the effective frontal area cwA and the rolling coefficient
Look at my motion of a cyclist page for details.
But this contribution is (at low speed) small compared to the power needed for the climb, so
we can use a rough guess for the values for cwA (0.4) and cr
(0.005). Therefore we also need the length
of the climb (an not just the elevation difference) to calculate the speed. Finally
we need the efficiency of the chain, which is roughly 98%.
One can change these values in the table below to see how they affect the final result: