## Friday, June 11, 2010

### Crr - roller vs. field test results

by Andrew R. Coggan, Ph.D.

One of the "perks" that comes with owning a power meter is the ability to quantify two of the most important physical factors determining our speed at a given power, i.e., our aerodynamic drag characteristics (i.e., CdA) and our coefficient of rolling resistance (i.e., Crr). (Our "all up" mass, of course, is also an important factor, especially when climbing or accelerating, but obviously you don't need a power meter to know how much you and your bicycle weigh.) Various methods for estimating these parameters are outlined on pages 249-252 of our book, and I have provided more detail about my specific approach in prior posts, e.g.:

Here, I would like to share the results of a compilation of such tests that I have done over the last 7 y, in particular focussing on how well the Crr values that I have obtained for various tires compare to the well-known roller tests performed by Al Morrison. The results of this comparison are shown in the figure below:

Figure 1. Comparison of field vs. roller data for Crr for five pairs of tires.

The data shown in the figure represent the average values (n=3-5 per pair of tires) of a subset of all such experiments I have performed, including only those where the temperature was between 15 and 25 deg C (ambient temperature for the experiments shown was 19.9 +/- 2.1 deg C). When mismatched pairs of tires were tested, I used the average value obtained during Al's roller tests, i.e., I assumed that my weight was equally distributed on the front and rear wheels of my TT bike. Finally, since I tested the Continental Ultra 2000 clincher tires using butyl tubes, whereas Al tested these (my) tires using latex tubes, I have adjusted the value he obtained upward by 0.00038, i.e., the average difference he has obtained in his roller tests when comparing butyl vs. latex tubes.

As can be seen in the figure, the roller and field test data agree quite closely, even though they have been performed by different individuals using different equipment and procedures. As might be expected, however, the Crr values I have obtained on an asphalt road are higher than what Al has measured using plastic rollers. Part of this difference, of course, is almost certainly due to differences in the two surfaces, and in fact when testing on aluminum rollers I have consistently obtained Crr values that are 18% lower than those found by Al, even when using identical procedures. It is also possible, however, that other factors contribute to the difference between the field-test and roller data, e.g., differences in the calibrations of our power meters (or scales), small biases in the values assumed for chain friction (field tests) or bearing friction (roller tests), etc.

The most important "take home" message, however, is the high correlation found between the roller and field test data (over a wide range of Crr values), which strongly supports the validity of the former as an approach for differentiating between the Crr of different tires. Indeed, the precision of roller testing is so much greater (i.e., by a factor of ~10x, in my experience) that it should be considered the method of choice for anyone who owns a power meter (and rollers).

(Note: I have previously posted the above plot to various web fora. If it differs from such prior versions, it is the result of more meticulously examining the data to spot errors, make certain that the brand, model, and width of tire that I tested was exactly the same as that tested by Al, etc.)

## Tuesday, June 8, 2010

### How to estimate VO2max using a power meter

by Andrew R. Coggan, Ph.D.

Unlike sports such as running or swimming, cycling entails the use of a machine (i.e., a bicycle) that greatly restricts the athlete's freedom of movement. That is, a cyclist's legs move in a circle the diameter of which is dictated by the length of the crank arms, the degree of leg flexion/extension is essentially fixed as a result of the chosen saddle height and crank arm length, almost all motion occurs in the sagital plane, etc. As a consequence, the economy (i.e., O2 cost) of movement during cycling varies less between individuals than in most other sports. Indeed, it is possible to predict someone's rate of oxygen uptake (i.e., VO2) during cycling with reasonable accuracy just by knowing their power output. For example, the American College of Sports Medicine provides the following formula:

VO2 (L/min) = 0.0108 x power (W) + 0.007 x body mass (kg)

It should be noted that this formula is based on data from untrained individuals exercising at relatively low power outputs. In my experience, however, on average it appears to apply just as well to trained cyclists. Thus, for the present purposes there seems little reason to use another formula unless data are specifically available regarding a given individual’s economy, i.e., their actual VO2 vs. power relationship is known.

Different approaches to estimating power at VO2max

Assuming that a person’s VO2 can in fact be accurately predicted using the above formula, the question becomes, what is the best way of estimating the minimal power that will elicit their maximal oxygen uptake, i.e., their VO2max? There are at least three different approaches that can be used, as discussed below:

1) Estimating VO2max from power data collected during an incremental exercise test

VO2max sets the upper limit to aerobic ATP production, so quite logically there is generally a very good correlation between a person’s VO2max and the highest power they produce during an incremental exercise test continued to fatigue. Indeed, such testing is usually conducted specifically to determine VO2max (via direct measurement of respiratory gas exchange), and the highest power maintained for 1 min during such a test is sometimes referred to as maximal aerobic power, or MAP (especially in the UK and Canada). In reality, however, due to the contribution of anaerobic metabolism sufficiently-motivated individuals typically achieve a power output during such tests that is significantly (i.e., 10-15%) higher than the minimal power that would elicit VO2max. In fact, this must be the case for the classic plateau in VO2 that defines VO2max to occur. Unfortunately, however, the precise contribution of anaerobic energy production varies not only between individuals, but also with rate of increase in power during such tests. As a result, the precise relationship between MAP and the minimal power required to elicit VO2max also varies, which tends to undermine the accuracy of any estimates of VO2max based on such testing.

2) Estimating VO2max from a steady effort of appropriate duration

As an alternative to the above, one could use the average power during a maximal, steady effort lasting approximately 5 min as an estimate of the minimal power elicting someone’s VO2max. The assumption in this case, obviously, is that the duration chosen (whatever it happens to be) represents the maximal duration that individuals can be expected to exercise at precisely 100% of VO2max. As with the approach described above, however, differences between individuals in their ability to generate energy anaerobically complicate selection of the appropriate duration. Specifically, while a cyclist with a low anaerobic capacity might only be able to maintain this intensity for much less than 4 min, another with a high anaerobic capacity could sustain it for well over 6 min. Again, the variable contribution from anaerobic energy metabolism tends to restrict the accuracy with which VO2max can be estimated using this method.

3) Estimating VO2max from a well-paced pursuit-style effort

When faced with the task of minimizing the time required to ride just a handful of kilometers from a standing start, e.g., when racing a short, flat prologue TT or a pursuit on a track, experienced cyclists will typically start out at a significantly higher intensity than they can sustain for the entire distance, especially during the initial acceleration phase. After they have “burned through” their anaerobic energy reserves, however, they then typically settle into a steadier, “pay as you go” pace calculated to result in essentially complete exhaustion just as they cross the finish line. The resultant power profile therefore shows an initial spike followed by a more gradual decay to a plateau or quasi-plateau in power after 1.5-2.5 min (depending on the individual’s anaerobic capacity). As would expected based on physiological knowledge, in my experience this quasi-plateau in power typically corresponds quite closely with that individual’s power at VO2max. Two examples supporting this contention are shown in Figure 12.8 on page 247 of the 2nd edition of our book, with two more examples shown below.

Figure 1. Estimated VO2 demand versus actual VO2max in two cyclists racing 3 km pursuits

The advantage of this approach, then, is that it works regardless of the individual’s anaerobic abilities, as everyone, no matter how gifted/highly-trained in this regard, must eventually reduce their power to a level that can be generated fully aerobically. It does, however, require that the cyclist be capable of pacing themselves appropriately so as to minimize their time (maximize their average speed) for the distance. If they don’t start out hard enough, they may not fully deplete their anaerobic capacity before the end of the test, leading to an overestimation of their power at VO2max. On the other hand, if they start out too hard, which is a far more common mistake to make, the greater muscle fatigue will result in their power decaying steadily throughout the test, resulting in the power at the end of the effort underestimating their power at VO2max.

Estimating VO2max from power data: why bother?

Since it is the actual power that a cyclist produces that propels them forward, regardless of how it is generated (i.e., aerobically or anaerobically), the above discussion begs the question, why bother attempting to estimate VO2max from power data in the first place? Indeed, in many cases knowing a person’s actual VO2max (versus, say, the power they can produce for 5 min) merely serves to satisfy innate curiousity. There can be situations, however, that quantifying (or at least estimating using the above method) VO2max can be useful. For example, comparison of a rider’s VO2 at functional threshold power to their VO2max (especially across time/seasons) can provide insight into the extent to which the former ability has been maximized, and thus help guide training decisions. As well, an estimate of VO2max may be useful in adjusting training or racing (pacing) strategies when traveling to altitude (or from altitude to sea level). While such decisions can be made based simply on “raw” power data, being able to differentiate the aerobic and anaerobic contributions to, e.g., a maximal 5 min effort means that they can be made more confidently.