Suppose: I want to cycle up a mountain with a speed of 9 km/h, an altitude difference of 1400m, a distance of 17Km. Can you explain to me how I can calculate this using this example?

Answer

Dear Marc,

In what follows, a general formula will be drawn up, so that you can easily use it in the future when you drive up a mountain.

To begin with, we have a mass m. If we increase this mass m in the Earth’s gravitational field, we have to do work. The work done is equal to the increase in potential energy, which can be calculated as:
W = m * g * h ,
with W : work in J (Joule),
m : mass in kg,
g : gravitational acceleration = 9.81 m/s²,
h : conquered height in m.

The power is equal to the work divided by the time that this work is performed:
P = W/t,
with P : power in W (Watt),
t : duration in s.

We do not know the duration directly, but we do know the average speed and the length of the route. From this we can determine the duration:
t = l / v,
with l : route length in m,
v : average speed in m/s.
If we know the average speed in km per hour we can also write the formula as:
t = 3.6 * l / v_kmph,
with v_kmph : average speed in km per hour.

The combination of the above formulas gives us:
P = m * g * h * v_kmph / ( 3.6 * l )

All data at a glance:
m = 80 kg (mass of adult person + bicycle)
g = 9.81 m/s²

h = 1400m
v_kmph = 9 km/h
l = 17000m.

We then find:
P=162W,
which is a very realistic value for a human performance on a bicycle.

Note that the power calculated here is only for overcoming the height. In reality there are additional losses, such as rolling resistance and air friction. These will ensure that the actual power output is higher. However, given the relatively low speed (9 km/h), rolling and air resistance will remain limited.

With best regards,