## [Cycling, Computing] Power Calculation and Brakes

From: andrew cooke <andrew@...>

Date: Sat, 24 Apr 2021 16:20:34 -0400

It's common (eg Strava) to estimate a cyclist's power output from their GPS
and elevation (barometric) data.

The basic idea is fairly simple: we can calculate the power required for the
bicycle to behave as recorded at each point in time using mass / gravity /
height, CdA / speed, and rolling resistance / speed.

This ignores wind, which makes the effective speed for wind resistance (CdA)
different from the measured speed, and so introduces errors.

Also ignored, but not commonly discussed, is braking.

If the cyclist does not use the brakes then all we have discussed so far is
correct.

If the cyclist brakes *and* pedals then we will underestimate their power
output because they are expending additional energy we do not "see" in the
data (assuming that there is no power meter data).

If the cyclist brakes when not pedalling then we *should* (if we have
sufficient resolution, perfect parameters, etc) see a negative input power.

In practice, when you estimate power, you do see negative spikes.  I had
assumed that these were noise, but the above suggests that it is also
reasonable to interpret them as braking.

In conclusion, then, braking may be visible in the output from modelling and
is not inherently a source of uncertainty *unless* the cyclist brakes when
also pedalling.  That exception is more likely than it sounds since "when
also" does not, in practice, mean (only) concurrently, but also at any time
within the "time step" used in the calculation (eg 10s).

Andrew