Wind Gradient & Correction Factors
Readers who have found this article having read
Yaw, Drag & Component Choice
may be wondering if we at CPL aren't a little obsessed with the subleties of wind.
The truth is, we have to be, because when a rider is spending the majority of his power output moving through the air, the relative speed and direction of that air matters - a lot.
It matters in terms of his speed over the ground and it matters whenever we want to accurately model that speed or the power required to produce it.
This article appears in response to an important question...What is the best or correct wind input to a model of cycling power?
Is it forecast wind, is it something that should
be measured locally, or can we use forecast wind tempered by some correction factor that suits our purposes?
We recently did some field testing on quite a windy (read "typically windy" if you're in the UK) winters morning and found that the metorological wind implied by our validated power
model was significantly different than the number we read from an airport weather station just a few miles away. An initial conclusion was that we might achieve better results measuring
the wind with a hand held anemometer, at rider height, but what when that isn't possible? We then worked through a number of the criteria that may affect wind and eventually came up
with a model based correction factor.
- Wind speed in particular is affected by surface friction attributed to the local terrain. This means that the closer we get to the ground, the slower the wind. Have you ever stood on a roof
terrace and noted that the wind feels significantly stronger than it did in the street? Pilots are familiar with this concept of
wind gradient because it means they have to apply different
wind correction factors to their navigation plans, depending on crusing altitude, and because they have to be very aware of extreme wind gradients close to the ground, aka "windshear".
It also means that the use of the surrounding ground can have a real impact on surface windspeed. Ride through a field of sunflowers on the
Tour de France and the wind gradient may be
steeper than were you to ride across the desert in the Tour of Qatar.
- Perhaps obviously, wind speed is affected by nearby obstructions such as buildings and trees. In fact wind gradients differ between urban and rural environments - a town centre
prologue time trial is not the same as a longer, more windswept test through the fields of Normandy. International norms for the siting of weather station equipment state that wind
speed and direction sensors should be located 10 metres above any obstructions (usually the ground) and clear of obstacles.
- The speed of the wind itself, as measured at a "surface" weather station, affects the magnitude of wind gradient, greater speeds being associated with steeper gradients. As does
the stability of the air, in some way related to the amount of solar radiation it receives - the wind gradient genuinely differs between day and night.
A Model for Wind Gradient
To find a model for wind gradient we have to look to an unusual field...smoke dispersion models used in the regulatory control of chimney stack siting! In this domain it is normal
to use a model of wind gradient to relate wind speed at the top of a chimney (height X) to speed at a nearby weather station (height 10 metres). There is a standardised model
of wind gradient, applicable to other engineering applications, that is said to hold at all heights AGL (above ground level) and we can apply it to the problem of calculating a
reasonable wind at rider height, say 1 metre from the ground. Really interested? Really?! There is an outline of this
particular model here
We are now offering this method of wind gradient correction in our
main power models. Simply input the wind speed from a local weather station, as normal, check the "Gradient"
option next to the wind speed input box and the model will convert what is assumed to be a windspeed observed at 10 metres AGL into a slightly lower speed more like that experienced
by a rider moving 1 metre from the ground. You can try this simple model here: