What makes a slow day?

We’re into hot day season, with a heatwave arriving in the UK it feels like a good time to talk about density. The density of the air is essentially “how many air particles exist in each metre cubed of air”. This is the cause of a day feeling slower than it should be. It’s usually the culprit of a windless, perfectly temperatured and otherwise faultless evening time trial being unreasonably slow for no reason.

Pressure and density are related, and if you’ve ever been on a trip away to the mountains, you might notice it on your weather trends plot…

As you can see, the density of air on my rides dropped off a cliff, right about the time I went to Andorra where I was staying at 1800m above sea level.

The maths

Density, pressure and temperature are all related to one another (and impact the power required to ride at a given speed). We’ll start with the relationship between the three…

Density is proportional to pressure and inversely proportional to temperature. Density drops when pressure drops and density drops when temperature rises.

The way to think of the difference between pressure and density is that pressure is the weight of the air above you (this changes with different weather systems and altitude) and density is the amount of air you need to push out of the way.

How does density impact our speed?

This the aerodynamic equation which explains how much power a rider needs to maintain a speed, v.

The power needed to ride at a given speed is directly proportional to the density (and thus pressure) of the air. On those days where you find your power numbers are high but speed is low for no reason, you can often blame the density. One thing you notice when you go up a mountain is how fast you start riding for low power which got me thinking, as density changes with altitude, is there a perfect altitude to maximise every speed?

Air density drops linearly as you go up a hill, which means the power needed to ride at a given speed does exactly the same…

It’s not that simple though

You’d think this was an argument for doing an hour record attempt on the moon (in fact, if you had a velodrome on the moon travelling at 60kph would only need about 9W) but obviously as the density of air decreases so does the oxygen available to our muscles to produce power. VO2 max doesn’t drop linearly though, it starts off decreasing slowly before a slightly faster drop (but the point at which the decrease in VO2 max breaks linearity varies from athlete to athlete).

An hour record is typically raced at around a riders’ LT2, so we’ll use that as a reference point.

The ideal altitude sits at where the gap between an athlete’s LT2 power and the air density is biggest, which will usually be just before their power drop becomes non linear. If I was preparing for an hour record (which I’m not), I would acclimatise myself to around 2500m in training and do a lactate ramp at progressively lower altitudes (or maybe just a straight up 60 minute TT effort on the turbo).

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