## [Bike] Estimating Power On Climbs

From: andrew cooke <andrew@...>

Date: Thu, 20 Jan 2022 19:31:49 -0300

I was slowly pedaling up a hill today, staring at my cycle computer
to avoid looking at the endless climb in front of me, when I realized
that you can easily estimate your power from the grade and speed
(km/h).

Me + my bike weight about 72kg.  Actually a bit more (I need to lose a
kilo or two), but 72 turns out to be a nice number in what follows.

72kg ascending vertically at 1m/s requires a power of 720W (because
g=10, more or less).

A speed of 1km/h is 1000m/3600s or 1/3.6 m/s.

Small angle approx means that if you are riding at a speed S(km/h) on
a gradient of G then your vertical speed is SG/100 km/h or SG/360 m/s.

So the power required (at 72kg) is SGx720/360 W or 2SG W.

For example, at 10km/h on a 5% grade your power is 2x10x5 = 100W.

Now this is incorrect if you're moving fast enough, or riding up a
shallow enough slope, that air resistance is important.  But for
climbing it's fine.

Obviously if you+bike weighs more or less than 72kg you need to
Andrew