## Wednesday, July 20, 2011

### l'Alpe d'Huez - one for the mortals

About this time last year I posted this item about ascent times of leading professional riders up l'Alpe d'Huez and what power to body mass ratio would be required to do that.

There's a chart which shows the relationship between ascent time and power to body mass ratio (watts per kg - W/kg). It also provides an indication the impact of wind can have on climbing speeds.

Times for leading riders since 2001 are shown on the chart.

The guys over at the Science of Sport blog referenced it in a post here, after seeing it on a cycling chat forum I posted to recently.

Well for a bit of fun (and considering the Tour de France is heading up the Alpe in a few days), I thought I'd post a follow up chart which covers the power to body mass ratio for the rest of us mere mortals.

Here it is (click to embiggen):

It's not a hard chart to read.

Want to ride up l'Alpe d'Huez in 1 hour dead? Then you'll need to be able to sustain around 3.75 W/kg, give or take depending on the wind. If you are 70kg, then that's around 260-265 watts.

If you know your sustainable power is 3.4W/kg, then you can expect to get up the Alpe in around 66 minutes.

In calculating these values, I've made a few assumptions (listed on the chart), although the relationship between speed and W/kg on steep climbs is not particularly sensitive to those assumptions.

After power and mass, wind has the biggest impact on speeds when climbing. Hence the two extra lines for head and tailwinds.

At my best form*, I would expect to climb it in around 56 minutes.

How fast have you been up l'Alpe?

* My power to body mass ratio for 1-hour at best is ~ 4.2W/kg (based on my racing power at the UCI World Cup this year), but I have to allow a bit of extra mass for my prosthetic leg. I'll get to do it one day.

## Friday, July 15, 2011

### Aero Profiling

Earlier this week I posted this item about power to aerodynamic drag ratio for the individual pursuit.

I mentioned in that item a table prepared some time back by Andy Coggan, which was similar to his power profiling table (which lists typical power to body mass of riders - W/kg for various time ), except it showed Functional Threshold Power (FTP) relative to aerodynamic drag (CdA) - W/m^2, instead of as per the original power profiling table.

The top end of the table would represent what's required to set a World Best Hour record.

In this way, a rider's power to aero drag ratio can be compared against the world's best.

Andy has kindly sent me the data, so here is the table for reference. Thanks Andy.

Enjoy!
(click on the pic to superaeronate)

## Wednesday, July 13, 2011

### Individual Pursuit - What Makes us Faster?

A long time ago, in a galaxy far away, a Jedi Knight called Andy Coggan developed an insightful (but often misunderstood) table of numbers known as Power Profiling. Power junkie cyclists have been (mis)using the table to psych out their mates for years now.

The Power Profiling table lists power to body mass ratios for four key durations: 1-hour, 5-minutes, 1-minute and 5-seconds, chosen to reasonably represent the energy systems/physiology that predominantly underpin performance over these duration, i.e. (respectively): lactate threshold, maximal oxygen uptake (VO2max), anaerobic work capacity & neuromuscular power.

Power to body mass ratio is an excellent overall predictor of performance potential. It is especially good for determining performance when climbing hills.

However, performance in flatter time trials and individual pursuits is much more a function of power and aerodynamics than it is of power and body mass. Body mass of course impacts aerodynamics, however the relationship between them is variable, with overall morphology and position on a bike far more influential than body mass per se.

So, when choosing the one performance factor most important for flatter time trials and pursuits, one needs to focus on improving a different ratio – the Power to Aerodynamic Drag* ratio (power to CdA ratio - W/m^2).

The higher the W/m^2, the faster we go. Pretty simple really.

In 2009 Jedi Knight Coggan, being somewhat prescient, developed a draft version of his power profiling table, this time expressing performance in terms of the ratio of 1-hour power to CdA . I’d love to share a link to it, but I’m not sure I have a public location I can point you to (it was originally posted on a discussion forum about two years ago which has suckerific search function). I’m sure either Andy will provide a link, or post up a new blog item about it at some stage.

In any case, I thought at the time it might also be of interest to develop a similar table for the Individual Pursuit, so Andy whipped up one for me, and I then took that data and created a chart and table. Now that was nearly two years ago and I've been meaning to do a blog post about it ever since! Okay, so it's a little late but here it is.

The table show times for 2km, 3km and 4km individual pursuits and the corresponding W/m^2 required to attain that performance (click / right click to show full sized version):

So, for example, if you want to ride a 3km pursuit in 3:35, you will need a power to aero drag ratio of about 1900 W/m^2.

Alternatively, if you know your power and pursuit time (on a fast track), then you can back calculate an estimate of your CdA. e.g. a rider who completes a 4km pursuit in 4:30 requires a power to aero drag ratio of ~ 2200W/m^2.

If we know their power output we can then estimate their CdA. Let’s say they averaged 480W.
CdA = (480W) / (2200W/m^2) = ~ 0.218 m^2

It’s not perfect of course, just a guide and there are many factors to consider. Besides, if you have a power meter on your track bike, there are better ways to determine your CdA.

The chart below plots the same data, as well as show where on the chart the current world record holders appear for the following categories:

Elite Men & Women
Junior Men & Women
Masters Women

Hence, these world records represent the current upper limit of W/m^2 for each category:

The records are from the UCI website here: Track World Records

With the exception of Sarah Hammer’s WR in Aguascalientes, all of the others were set at sea level and in indoor velodromes (and so the assumptions used for the table data will be closer to the mark).

In the case of Sarah Hammer, due to the significantly reduced air density at altitude, it is probable her W/m^2 is overstated and is a little less than previous world record holder Sarah Ulmer whose record was set at sea level. The Power/CdA estimate for Ulmer’s 3:24.537 ride is 2200 W/m^2.

One thing the chart emphasises is just how much one needs to improve W/m^2 in order just to go even just a few seconds faster. When you are near your physiological performance (power) limit, we can see how important aerodynamics are to overall performance.

And just how freakin good those world record rides are.

Now of course there are some assumptions used to make up the data for the tables (assumption are shown on the table and chart). For example, it does assume a pretty fast track/tyres at a typical sea level air density, but really it’s just a guide, and serves to emphasise the importance of aerodynamics and thinking in terms of W/m^2 when working out what to focus on to improve your pursuit and time trial performance.

If your track and/or tyres are slower than the best, then it’s likely the performance suggested as attainable from a given power to aero drag ratio is overstated (or the W/m^2 required for a given performance is understated). Also, the rate of change in kinetic energy and associated variable power demands will also have some impact on these estimates. These data have used typical assumptions for that, but of course everyone’s initial acceleration, mass and fade in speed during their pursuit rides are different.

I’ll look into doing a similar chart for the hour record at some stage.

Where do you fall on the table?

For those interested in more discussion on factors impacting pursuit performance, then these items by Andy Coggan are a great place to start:

Demands of the individual pursuit, part 1
Demands of the individual pursuit, part 2

* Aerodynamic Drag is expressed as the combination of our two factors:

- Coefficient of Drag (Cd), a unit-less measure which is related to the shape of an object and how that affects air flow around it (e.g. think of a brick vs a bullet shape, the bullet shape has a lower Cd); and

- Effective Frontal Area (A), measured in square metres (m^2) which is how much area we present to the air (e.g . compare a van and a Mack truck – the truck has a larger frontal area and has to push more air).

These two factors are multiplied together to determine how "slippery" we are through the air.

Some example typical CdA values:
Commuter cyclist: 0.4 – 0.7 m^2
Road racing cyclist: 0.26 - 0.38 m^2
Time trial/pursuit rider: 0.2 – 0.3 m^2
Sports car: 0.5 - 0.6 m^2