Windbags

There seem to be a lot of windbags lately.

Once again people in the twitter/forum sphere are ignoring just how much wind affects speed for the same power output, even on steep climbs where overcoming gravity is the major energy demand factor.

Let me give you a basic example.

Let's take a rider with Pro Tour level power to body mass capability as follows:

400W Functional Threshold Power
69kg body mass
and allow 8kg for bike + kit

So that's a rider with an FTP of 5.80W/kg

A few assumptions about a point along a typical climb:
Gradient: 8%
Air Density: 1.065kg/m^3 (e.g. 1010hPa, 20C, 50% humidity @ 1000m altitude)
Rolling resistance: 0.0045
CdA: 0.350m^2
Wind: none

At that point on the climb, at 400W their speed would be 20.6km/h. But that of course assumes there is zero wind.

Conversely, if we have a rider climbing an 8% gradient at 20.6km/h with those air density, mass and rolling resistance values, then they will be required to output 5.80W/kg.

Pretty straightforward so far.

So what happens to our estimated power based on speed and gradient etc if there is some wind but we don't account for it? In other words we measure their speed as 20.6km/h, but we do not know the actual wind conditions?

Well let's assume we know precisely the mass (body and the bike + kit), rolling resistance, air density and rider's coefficient of aero drag (CdA). I'll get to errors in those later.

If there was an overall tailwind, then for the same power output the rider will climb faster. But if we don't account for that tailwind when estimating power output for that faster speed, then we will over estimate the rider's power output. And conversely, if we don't account for any headwind, we will under estimate the rider's power output.

So just how wrong can we get power estimates if we rely on climbing speed alone and do not account for the wind? Well to save you the trouble, I've plotted the W/kg actually required to climb at 20.6km/h with wind speeds ranging from a tailwind of 5m/s to a headwind of 5m/s.

Just so it's clear, this chart shows the power to body mass required to ride at 20.6km/h on that 8% gradient and with the other assumptions earlier listed. We can see just how much the wind conditions impacts the power required to maintain a given speed.

Hence, if you do not know the wind speed, then you have quite a sizeable potential error in any estimate of power from the rider's speed.

I've colour coded the Beaufort Wind Scale ratings on the chart. Of those shown on chart for instance, a Gentle Breeze is when light flags are extended. Even riding into a light breeze of 2.5m/s (that's not enough to extend light flags) means an error in calculating W/kg of over 9%! If the wind were a gentle head breeze of 4.2m/s, then the error in power estimated from speed increases to over 17%!!

Let's put that into perspective. A 10% power variation about the variation in power output for a trained rider from out of form / off-season to their peak fitness levels. That's the level of potential error in power estimates from a light breeze we can just start to feel on our skin.

Of course the actual wind speed and direction relative to a rider changes during a climb, some climbs have more shelter than others, the amount of shelter varies (trees, vans, people, other vehicles in race convoy etc), the wind does change direction due to the shape of the mountain itself, and of course the road itself changes its direction relative to the prevailing wind. Then there is the impact of drafting other riders, which is more of a factor with increasing headwinds.

So no doubt there are some swings and roundabouts, but who can really tell what the actual wind is? Answer: No-one.

If you can see flags flapping, then forget about making sensible estimations of riders' power to mass values. And if you can't see them flapping, then at least include some error bars in the estimate, unless you know exactly what the wind was doing.

What about the other assumptions, such as CdA, Crr, mass of bike + kit?

OK, well let's examine the impact of getting each one of those assumptions wrong by say adding 10% to each. What does that do to the power required to ride at that same speed?

CdA @ 0.385m^2
Power for same speed = 404W (+0.9% error)

Crr @ 0.00495
Power for same speed = 402W (+0.5% error)

Bike+kit mass @ 8.8kg
Power for same speed = 406W (+1.4% error)

We can see that error in estimates of power from climbing speed are less sensitive to errors in CdA, Crr and bike/kit mass*, and are dwarfed by the error introduced by wind, and wind is rarely, if ever, measured with any accuracy on these mountain ascents.

* even so, it helps to get them as correct as we can

Wind matters a lot when determining cycling power from speed, no matter the gradient.