## Hill Climbing

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/sý), the elevation difference h of the climb, and the time t. The work WHill (in Joule) to climb the hill is
WHill= mæ gæh
Then the power is simply the work divided by the time:
PHill= mæ gæh / t
Since we are still fighting the air resistance and rolling resistance (but at low speeds...), we have to add this contribution PAir and PRoll. It depends on the effective frontal area cwA and the rolling coefficient cr. 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:

 cwa (effective frontal area) cr (rolling coefficient) Chain efficiency

Now let's calculate the power!  Insert your own values and click on button "Calculate Power"

 length of the climb (m) elevation difference (m) total weight (bike + rider) (kg) time (sec)

Result:
 power due to hill climbing power due to air resistance power due to rolling resistance power (hill + air + roll) total power (due to 98% efficiency)