### The Physics recap

### And the Physiological impact...

So the gain in speed from the physics side of the equation is somewhat negated by the reduction in physiological capacity. But by how much, and what might be the optimal or "sweet spot" altitude for a cyclist seeking to set a new record?

The physics side of the equation is easier to predict than the physiological, since the physics applies equally to all, however individual physiological response to altitude is quite variable, both from person to person, but also depending on how well a rider has acclimated to altitude. There are even differences in how altitude affects elite versus non-elite riders.

There have been a few published papers examining the impact of altitude on aerobic athletic performance and from these formulas to estimate the loss of power as a function of altitude have been developed. There was one from the 1989 paper by Peronnet et al, two from the 1999 paper by Bassett et al, one each for acclimated and non-acclimated athletes. Adding to those, I have generated a fourth formula, based on the 2007 study by Clark et al. The relevant papers are:

Péronnet F, Bouissou P, Perrault H, Ricci J.:

A comparison of cyclists' time records according to altitude and materials used.

Bassett DR Jr, Kyle CR, Passfield L, Broker JP, Burke ER.:

Comparing cycling world hour records, 1967-1996: modelling with empirical data.

The effect of acute simulated moderate altitude on power, performance and pacing strategies in well-trained cyclists.

Peronnet et al used empirical data from actual world cycling hour records to estimate the impact of altitude on an elite cyclist's power output. The assumptions used in estimating altitude induced power loss may have some error; in particular due to methods used to estimate the power for each rider as neither the power nor coefficient of aerodynamic drag was actually measured.

According to the old Wattage forum FAQ item by Dr David Bassett, Jr, the two Bassett et al formula were derived from earlier papers examining altitude impact on aerobic performance of four groups of highly trained or elite runners. So while these formulas were not derived from cyclists we can still generalise from those to the loss of aerobic capacity for cyclists.

Finally, the study by Clark et al measured the impact on peak oxygen utilisation (VO2), gross efficiency and cycling power output on ten well trained but non-altitude acclimated cyclists and triathletes by testing riders at simulated altitudes of 200, 1200, 2200 and 3200 metres. They examined a number of factors, including maximal 5-minute power output, VO2 and gross efficiency relative to performance at 200 metres, as well as sub-maximal VO2 and gross efficiency.

I used these data to generate a formula similar to those from Peronnet et al and Bassett et al. Of course there is an assumption of an equivalent reduction in 1-hour power as for 5-minute power. Clark et al noted slightly greater reductions in VO2 peak than for 5-minute maximal power, and no change in gross efficiency at 5-min max power with altitude. So there is some anaerobic metabolic contribution presumably making up the difference. There was some loss of sub-maximal efficiency noted at a simulated 3200 metres.

I chose in this instance to use the reduction in 5-minute power rather than fall in VO2 peak as the base data for the formula, and applied an adjustment to offset the formula for sea-level equivalency to bring it into line with the formula by Peronnet et al and Bassett et al. Of course when you look at the reported data there are of course sizeable variations within the test group at each simulated altitude, so the formula is based on group averages for each simulated altitude.

Here are the formulas:

**x = kilometres above sea level:**

**Peronnet et al:**

Proportion of sea level power = -0.003x

^{3}+ 0.0081x

^{2}- 0.0381x + 1

**Bassett et al**

**Altitude-acclimatised athletes**(several weeks at altitude):

Proportion of sea level power = -0.0112 x

^{2}– 0.0190x + 1

R

^{2}= 0.973

**Bassett et al**

**Non altitude-acclimatised athletes**(1-7 days at altitude):

Proportion of sea level power = 0.00178x

^{3}– 0.0143x

^{2}– 0.0407x + 1

R

^{2}= 0.974

**Simmons’ formula based on Clark et al:**

Proportion of sea level power = -0.0092x

^{2}– 0.0323x + 1

R

^{2}= 0.993

There is some variance between each formula's estimates, although the gap between the Non-acclimatised athlete estimates by Bassett et al and by Simmons based on Clarke et al is not all that large, ranging up to a ~2% variance.

The formula by Peronnet et al is the least aggressive at reducing the estimate of a cyclist’s power at higher altitudes, and that may be due to various not insignificant assumptions used in calculating each rider’s power outputs.

### OK, so now we have estimates of both the physics upside and the physiological downside of altitude, What happens when we merge the two?

Well if I recreate the chart showing the physics, and overlay on that the curve showing power output as a function of altitude, this is what we get if we examine a rider capable of sustaining 51km/h at sea level:

Let me explain how to interpret the chart.

First of all, the vertical axis scale has been changed for clarity – the slightly curved coloured lines still represent the power to drag ratio required to attain a given speed at various altitudes.

So let's examine the case for a rider capable of sustaining 51km/h at sea level.

The thick orange line represents the power to drag required to sustain 51km/h. At sea level that's ~1,800 W/m^2 (Red circle 1). The exact value depends on a few other assumptions of course, so let's just use that as our "baseline" W/m^2 value.

Now if we apply the Bassett et al formula for power reduction for an altitude-acclimatised athlete, then their baseline sea level power (and with it their power to aero drag ratio) falls with increasing altitude. This drop in sustainable power with increasing altitude is indicated by the black dotted line.

If you trace the black dotted line from left to right, we can see that at Red Circle 2, the power to drag ratio crosses the line marked 52km/h at an altitude of ~700 metres. Then as you trace the dotted line further to the right, we can see it cross the 53km/h line at ~1,500 metres. Tracing the line to the right hand edge of the chart out to 3,000 metres altitude, we can see it doesn't quite reach the 54km/h line, falling a little short at 53.9km/h. So for this altitude-acclimatised athlete, they can gain an extra 2km on their hour record simply by choosing to ride at an altitude of 1,500 metres.

### OK, so what happens if the athlete is not acclimatised to altitude?

This time the non altitude-acclimatised power line is indicated by the lower black dashed line. It starts at 1,800 W/m^2 at sea level indicated at Blue circle 1, but as we trace that line to the right, it falls away more quickly than for the altitude-acclimatised athlete, crossing the 52km/h line at ~1,000 metres altitude (Blue circle 2) and not reaching the 53km/h line by the time the athlete is at 3,000 metres, where in this case the athlete would be estimated to achieve a speed of ~ 52.9km/h (Blue circle 3).

So while the acclimated athlete can improve their speed by 1km/h by going from sea level to 700 metres, and increase speed by 2km/h by going up to 1,500 metres, to achieve the same speed gains the non-acclimated athlete would need to ride at an altitude of 1,000 metres and would not be able to attain a 2km/h speed gain even at 3,000 metres.

We can see that as the altitude increases, the extra speed gains begin to diminish, and there are risks in going too high, especially if you are not acclimated, or experience an above average decline in power with altitude.

Any rider considering an hour record would do well to consider the opportunity presented by tracks located at altitude. Of course costs, logistics, regulations all factor into the choice of venue, and how much time a rider may need to acclimate to altitude, and their individual response to altitude.

### So what tracks are there at altitude?

- Aguascalientes, Mexico: 1,887 metres above sea level
- Guadalajara, Mexico: 1,550 metres above sea level
- Aigle, Switzerland: 415 metres above sea level
- Astana, Kazakstan: 349 metres above sea level
- Grenchen, Switzerland: 340 metres above sea level

- La Paz, Bolivia: 3,340m
- Cochabamba, Bolivia: 2,571m
- Arequipa, Peri: 2,295m
- Mexico City, Mexico: 2,260m