^{rd}place, 55 seconds down on Sagan. Let’s have a look at this amazing power file from the World Championships.

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## Thursday, January 14, 2016

###
Ben King Richmond Race Analysis 2015

Read More
## Thursday, October 13, 2011

###
Great interview about Training and Racing with Power meter from Kona Ironman Pros

## Wednesday, August 31, 2011

###
Top 10 things I've learned using a power meter (an oldie but a goodie)

**by Andrew R. Coggan, Ph.D.**

I just stumbled upon this Lettermanesque top 10 list that I first posted to the web in 1999 (after my 1st season using a PowerTap):

Top 10 things I’ve learned using a power meter

10) I shouldn’t lose weight

9) I need big gears

8) I need small gears

7) Strength is irrelevant

6) Don’t start too hard in TTs

5) Train less, rest more

4) Heat acclimatization is critical

3) Specificity

2) SPECIFICITY

1) SPECIFICITY!

Interestingly, even after all this time I'm not sure I would change anything on the list (except perhaps the "train less, rest more" conclusion, as I don't train or, especially, race as much as I used to).
## Monday, April 18, 2011

###
Estimation of CdA from anthropometric data

**by Andrew R. Coggan, Ph.D.**

The popularity of wind tunnel testing to determine a cyclist's aerodynamic drag characteristics (i.e., their CdA, which is the product of their frontal area, A, and a dimensionless "shape factor", Cd) has grown considerably in recent years. A number of field tests for estimating CdA have also been developed and, in at least some cases, carefully validated/evaluated (e.g., http://www.trainingandracingwithapowermeter.com/2010/10/challenge-to-cycling-aerodynamicists.html). Nonetheless, there are times when a simple, "quick-and-dirty" estimate of someone's CdA is all that is needed/desired. For example, a cyclist or triathlete lacking a powermeter on their bike may still wish to estimate how much power they need to produce to achieve a particular performance, e.g., a certain average speed in a flat TT or triathlon bike leg. A convenient way of obtaining a ballpark estimate of CdA based upon easily-obtained measurements can also be used as a "smell test" to see whether other data (e.g., CdA values presented by others) make sense, and/or to place a given athlete's CdA in better context (i.e., are they more or less aero than typically found?). In such situations, it is possible to estimate A based on various anthropometric data, which can then be combined with an estimate of Cd to arrive at a final value for CdA. While this approach is rather crude, in my experience it works well enough to occasionally still be useful.

As indicated above, the first step is to estimate an individual's projected frontal area when in the aero position on their TT or triathlon bicycle. I am aware of at least five different formulae for making this calculation, as listed below. The first was originally related to me by Sam Callan, Director of Coaching Education for USA Cycling, whereas the other four are from the listed scientific papers. In the case of Heil's equations, STA = seat tube angle, TA = torso angle, and SW = shoulder width (readers of this blog are encouraged to consult the original paper to see precisely how these were defined/determined).

**1. Australian Institute of Sport**

**2. Bassett et al. (Med Sci Sports Exerc 1999; 31:1665-1676):**

**3. Heil DP. (Eur J Appl Physiol 2001; 85:358-366):**

Once a value for frontal area is obtained, this must be multiplied by an appropriate value for Cd. Contrary to the assertions of many, cyclists are not "bluff bodies", i.e., the Cd of a cyclist upon a bicycle (even sitting upright on a mountain bike) is significantly less than that of, say, a flat plate, and perhaps more importantly, can vary as a function of yaw angle. Nonetheless, reasonable estimates of CdA (at 0 deg of yaw) can still usually be obtained by multiplying the above-derived frontal area(s) by 0.707, which is the average value for n=8 cyclists of varying stature and build tested by Dr. Chet Kyle in the Texas A&M wind tunnel (cf.*Cycling Science* 1991; Sept/Dec: 51-56 - Cd values ranged from 0.652 to 0.793). Alternatively, Cd can be estimated from body mass using an equation derived by Heil based on a meta-analysis of the literature:

So just how precisely can CdA be estimated using the approach described above? This question can be addressed two ways, i.e., via standard propogation-of-error analysis and also by example.

1) Propogation-of-error analysis: The standard errors of the estimate (S.E.E.) provided by each equation for estimating frontal area range range from 0.009 to 0.017 m^2. Frontal area, however, only accounts for ~60% of CdA, i.e., Cd can and does vary between individuals and thus accounts for the other ~40%. The S.E.E. values listed therefore do not tell the whole story, i.e., one must also take into consideration the variability in estimating Cd. Based on the data of Kyle and using standard propogation-of-error methods, the overall imprecision in estimating CdA would be 0.016-0.019 m^2, or plus/minus somewhere between 5 and 10% of a typical value.

2) Some examples: The table below lists anthropometric data along with estimates of A, Cd, and CdA obtained using the equations discussed above for two individuals, both of whom have been tested in the Texas A&M wind tunnel. Due in part to chance alone, the values obtained by using the third equation developed by Heil combined with either method of estimating Cd agree almost exactly with those determined in wind tunnel testing. While this outcome cannot be expected in all cases, the table below does serve to illustrate the range of values the various equations provide, and in fact it is often useful to "bracket" such estimates by calculating all possible outcomes (as shown), rather than relying upon just one single estimate.

**Table 1. Estimates of A, Cd, and CdA using the various equations.**

## Monday, March 7, 2011

###
Prediction of muscle fiber type from powermeter data, part 4

## Friday, January 7, 2011

###
Prediction of muscle fiber type from powermeter data, part 3

**by Andrew R. Coggan, Ph.D.**

In this previous blog entry:

http://www.trainingandracingwithapowermeter.com/2010/12/prediction-of-muscle-fiber-type-from_07.html

I described a way of predicting muscle fiber type distribution based on force-velocity (or power-velocity) data collected using an SRM. Because each individual's situation is different, I had not intended to go into detail regarding how to actually collect such data. My previous post generated more interest than I anticipated, however, so in this post I will attempt to at least provide some general guidelines. Nonetheless, I anticipate that anyone attempting to perform such testing themselves will likely have to go through a bit of trial-and-error to perfect their own approach.

**Force-velocity testing using the inertial load method**

As described previously, the force-velocity relationship during cycling is essentially linear (such that the power-velocity relationship is parabolic in nature). This has been demonstrated in various studies, either via use of a specially-constructed isokinetic ergometer (1) or by simply having subjects perform multiple, maximal efforts against varying resistances on a standard friction-braked (Monark) ergometer (2). However, the simplest and hence most elegant approach of all is the inertial load method devised by Dr. Jim Martin (3). Dr. Martin's method utilizes a standard Monark ergometer that has been modified such that 1) the only source of resistance is the inertia of the flywheel and 2) the position of the flywheel can be measured with high temporal (i.e., 1 microsecond) resolution (cf. Fig. 1).

**Figure 1. Inertial load ergometer developed by Dr. Jim Martin.**

With this ergometer, near-instantaneous power can be measured every 3 deg of crank revolution based on the rate of acceleration of the flywheel. Alternatively, power can be averaged over a complete pedal revolution, thus reflecting the combined extension/flexion of both legs. In either case, judicious choice of the inertial load (which depends upon the moment of inertia of the flywheel and the gearing) enables the subject to reach their optimal pedaling rate in just 2 s, and to complete 6.5 revolutions in just 4 s. This makes it possible to determine an individual's force-velocity (or power-velocity) relationship during a single, brief test in which significant fatigue does not occur.

Few readers of this blog are likely to have access to an ergometer like the one developed by Dr. Martin. However, it is possible to obtain similar data using an SRM by 1) recording data at a sufficiently high frequency, and 2) selecting an appropriate resistance. The "how" and "why" of this approach are described below.

**Force-velocity testing using an SRM**

*Sampling frequency*

Although a standard SRM system cannot match the very high temporal/spatial resolution of Dr. Martin's ergometer, it is possible to capture the average data for each individual pedal stroke, which is all that is needed to determine the force-velocity relationship. This can be achieved by selecting the highest possible recording frequency/shortest possible time interval (e.g., 10 Hz, or every 0.1 s, when using a PowerControl IV). This will cause the SRM to "stutter", i.e., to repeatedly report the same values for power and cadence for individual pedal strokes, as shown in Table 1 below:

In this particular example, the SRM began recording data upon completion of (presumably) the first crank revolution, which was performed at an average of 444 W/55 rpm. These same values were then repeated until completion of the second crank revolution, which occurred between 1.1 and 1.2 s after the first and was performed at an average of 668 W/88 rpm. The third crank revolution was then completed between 1.7 and 1.8 s at an average of 721 W/105 rpm, etc. In other words, as long as the time required for a single crank revolution is shorter than the sampling interval, the results obtained are actually event-based (i.e., are averages over individual pedal revolutions) rather than time-based. Indeed, even with a newer PowerContol (i.e., version V and above) that can only record data at a maximum of 2 Hz (i.e., every 0.5 s), an individual must be pedaling at >120 rpm before multiple pedal strokes will be averaged together. Consequently, essentially identical results are obtained regardless of whether data are recorded at 10 Hz (every 0.1 s), 5 Hz (every 0.2 s), or 2 Hz (every 0.1 s), as shown in Figure 2 below:

**Figure 2. Effect of different sampling frequencies on data obtained during force-velocity testing.**

*Appropriate resistance*

The other key aspect when performing force-velocity testing using an SRM is selection of an appropriate resistance. If the resistance is too low, then the individual will be able to accelerate the cranks too rapidly, and only a few point(s) far to the right/down the force-velocity relationship will be obtained, and/or force will fall off excessivly due to the difficulty in coordinating muscular actions at very high pedaling rates. On the other hand, if the resistance is too great, the subject will not be able to accelerate the cranks rapidly enough, and only a few data points at the upper left end of the line will be obtained before fatigue begins to occur. If the resistance is just right, however, data will be obtained across a broad span of velocities (and hence forces) before fatigue develops.

These points are illustrated in Figure 3 below, which displays data from force-velocity tests performed with different inertial loads. With the high and medium inertial loads, I was not able to accelerate the cranks rapidly enough, and hence "fell off" my force-velocity line after 4 s (denoted by the arrows) at very low and moderate velocities, respectively. Conversely, with a lower inertial load, comparable to that of Dr. Martin's ergometer, data were obtained over a broader range of velocities before fatigue ensued.

**Figure 3. Effect of inertial load on data obtained during force-velocity testing.**

Note that the regression line was calculated by excluding all data collected after 4 s then pooling the results from all three tests. The SRM was set to record data at 2 Hz.

The data shown above were obtained by mounting my bicycle in a Velodyne trainer and then varying the inertial load provided by the Velodyne's flywheel by simply using different gear ratios. While it would be possible to provide guidelines for appropriate inertial loads to for others to try, the wide variety of conditions under which such testing may be performed as well as uncertainty regarding the exact mass/moment of inertia of particular trainers, rollers, etc., means that this would be much less helpful than it might at first appear. As a general rule, however, individuals attempting such testing using the typical low-inertia magnetic or fluid trainer are likely to find that they need to use moderate-to-large gears to obtain good data. On the other hand, those attempting such testing outdoors will need to use very low gears - lower, in fact, than usually found on a road racing bicycle. In any case, the key point is that the cyclist must be able to accelerate the pedals rapidly, but not too rapidly, something that is readily determined via preliminary tests.

*Reproducibility*

When adhering to the above guidelines, excellent reproducibility can be obtained, with both within-day and between-day coefficient of variations generally being 2% or less as shown in Table 2 below:

In particular, the circumferential pedal velocity at which maximal power is produced (i.e., CPVopt)which is the basis for prediction of muscle fiber type distribution using the data of Hautier et al. (2), is highly reproducible.

*Standing vs. sitting*

By recruiting additional upper-body musculature, standing out of the saddle increases the maximal power that an individual can produce by roughly 10%. With the exception of experienced BMX riders, however, few cyclists are well-practiced at pedaling both rapidly and powerfully while standing. As well, the need to support 100% of body mass means that fatigue may develop more rapidly. In any case, the usual effect of standing is to increase the Y interecept but also to steepen the slope of the force-velocity relationship, as shown in Figure 4:

**Figure 4. Effect of standing on the force-velocity relationship.**

As a consequence, the circumferential pedal velocity associated with maximal power output will generally be shifted to a lower value, which will lead to underestimation of the percentage of type II fibers than an individual possess when using the equation presented previously (which is based data collected while seated). This would therefore seemingly preclude use of data from, e.g., standing start efforts performed using typical gears as part of normal training or racing to predict an individual's muscle fiber type.

**What about other powermeters?**

Unfortunately, as indicated at the outset of this series of blog entries, at least in my hands powermeters other than the SRM do not appear to be able to provide data of sufficient quality to permit accurate (or at least easy) determination of an individual's force-velocity relationship while cycling. I will discuss these issues and provide some examples in the next entry.

**References**

1. McCartney N, Heigenhauser GJF, Jones NL. Power output and fatigue of human muscle in maximal cycling exercise. 1983; 55:218-224.

2. Hautier CA, Linossier MT, Belli A, Lacour JR, Arsac LM. Optimal velocity for maximal power production in non-isokinetic cycling is related to muscle fiber type composition. Eur J Appl Physiol 1996; 74:114-118.

3. Martin JC, Wagner BM, Coyle EF. Inertial-load method determines maximal cycling power in a single exercise bout. Med Sci Sports Exerc 1997; 29:1505-1512.
## Tuesday, December 7, 2010

###
Prediction of muscle fiber type from powermeter data, part 2

**by Andrew R. Coggan, Ph.D.**

**Figure 4. Power-velocity relationship during cycling.**** ****Cool! But how do I measure my own force-velocity or power-velocity relationship?**

**References**

1. Gasser HS, Hill AV. The dynamics of muscular contraction. Proc Royal Soc B 1924; 96:398-427.

2. Gilliver SF, Degens H, Rittweger J, Sargeant AJ, Jones DA. Variation n the determinants of power of chemically-skinned human muscle fibers. Exp Physiol 2009; 94:1070-1078.

3. McCartney N, Heigenhauser GJF, Jones NL. Power output and fatigue of human muscle in maximal cycling exercise. 1983; 55:218-224.

4. Hautier CA, Linossier MT, Belli A, Lacour JR, Arsac LM. Optimal velocity for maximal power production in non-isokinetic cycling is related to muscle fiber type composition. Eur J Appl Physiol 1996; 74:114-118.

5. Gardner AS, Martin JC, Martin DT, Barras M, Jenkins DG. Maximal torque- and power-pedaling rate relationships for elite sprint cyclists in laboratory and field tests. Eur J Appl Physiol 2007; 101:287-292.
## Archive by Subject

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Worlds. Amazing. You had to be there. Thousands of people, incredible course, the
best riders in the world and stellar bike racing. Richmond Virginia shined and really laid out
the red carpet for everyone and it was heart warming and reassuring to have
drivers honking at you with “Thumbs up” and taking pictures of cyclists as they
rode around the outskirts of town for the week, instead of giving you the other
finger. Ben King, local boy makes
good. Ben not only rode in the
breakaway for 90+ miles, but not was he only one from the breakaway to finish
the race, but he in the front group at the base of Libby Hill on the last
lap. Only then, did he lose contact with
the front group, finishing in 53^{rd} place, 55 seconds down on
Sagan. Let’s have a look at this
amazing power file from the World Championships.

First off, one of the differences between the World Tour
level and all the rest is the sheer amount of work that has to be done in the
race, just to complete it. Work is
kiloJoules and 1 Joule is a watt per second, so 1kJ is 1000 Joules. Ben did 6,402 kiloJoules of work in the 6
hour and 24 minute race. For those of
you that regularly get crushed after doing 3000 kJ of work, can you imagine
doubling that? This is equal to over
7000 kCalories burned and that’s a lot of burritos. A normal Continental pro race here in the US,
is between 2500-3000kJ, and this is a
critical difference between abilities of the Continental pros and the World
Tour pros. Translate this into Training
Stress Score and reminder that 100 TSS equals the same amount of training
stress as 1 hour at FTP and Ben did 418 TSS for the race, so the equivalent of
4 hours back to back at FTP. Some
other highlights include 7,838’ of climbing, an Intensity Factor of .81(81% of
FTP for 6 hours 24minutes), an average
power of 276watts and normalized power of 323 watts. Yes, 323 watts for 6 hours 24 minutes. Three. Hundred. Twenty. Four. 6 hours. 24 minutes. Can you do 323watts for 20 minutes? An
hour? How about 6 hours? Oh yeah,
he weighs 148lbs. So that’s 4.88
watts per kilogram for the entire race.
Those are the statistical highlights of an epic world championship
race. Let’s dig into some of the finer
points.

Read More

I was really fortunate to be able to interview some of the top pros from Ironman 2011 in Hawaii this year. SRAM/Quarq was the sponsor of the event and Luke McKenzie(2nd on the bike!), Kate Bevilaqua, and Rasmus Henning all talked about how they use their power meter in training and racing. Look for a pretty cool article on Ironman power files coming soon!

here are the video interviews.

and more here http://me.lt/9e5JO

Hunter

here are the video interviews.

and more here http://me.lt/9e5JO

Hunter

I just stumbled upon this Lettermanesque top 10 list that I first posted to the web in 1999 (after my 1st season using a PowerTap):

Top 10 things I’ve learned using a power meter

10) I shouldn’t lose weight

9) I need big gears

8) I need small gears

7) Strength is irrelevant

6) Don’t start too hard in TTs

5) Train less, rest more

4) Heat acclimatization is critical

3) Specificity

2) SPECIFICITY

1) SPECIFICITY!

Interestingly, even after all this time I'm not sure I would change anything on the list (except perhaps the "train less, rest more" conclusion, as I don't train or, especially, race as much as I used to).

The popularity of wind tunnel testing to determine a cyclist's aerodynamic drag characteristics (i.e., their CdA, which is the product of their frontal area, A, and a dimensionless "shape factor", Cd) has grown considerably in recent years. A number of field tests for estimating CdA have also been developed and, in at least some cases, carefully validated/evaluated (e.g., http://www.trainingandracingwithapowermeter.com/2010/10/challenge-to-cycling-aerodynamicists.html). Nonetheless, there are times when a simple, "quick-and-dirty" estimate of someone's CdA is all that is needed/desired. For example, a cyclist or triathlete lacking a powermeter on their bike may still wish to estimate how much power they need to produce to achieve a particular performance, e.g., a certain average speed in a flat TT or triathlon bike leg. A convenient way of obtaining a ballpark estimate of CdA based upon easily-obtained measurements can also be used as a "smell test" to see whether other data (e.g., CdA values presented by others) make sense, and/or to place a given athlete's CdA in better context (i.e., are they more or less aero than typically found?). In such situations, it is possible to estimate A based on various anthropometric data, which can then be combined with an estimate of Cd to arrive at a final value for CdA. While this approach is rather crude, in my experience it works well enough to occasionally still be useful.

As indicated above, the first step is to estimate an individual's projected frontal area when in the aero position on their TT or triathlon bicycle. I am aware of at least five different formulae for making this calculation, as listed below. The first was originally related to me by Sam Callan, Director of Coaching Education for USA Cycling, whereas the other four are from the listed scientific papers. In the case of Heil's equations, STA = seat tube angle, TA = torso angle, and SW = shoulder width (readers of this blog are encouraged to consult the original paper to see precisely how these were defined/determined).

Frontal area (m^2) = 0.18964 x height (m) + 0.00215 x mass (kg) - 0.07861

n = ?; R^2 = ?.??; P = ?.??; S.E.E. = ?.??? m^2

n = ?; R^2 = ?.??; P = ?.??; S.E.E. = ?.??? m^2

Frontal area (m^2) = 0.0293 x height (m) x mass (kg)^0.425 + 0.0604

n=8; R^2 = 0.76; P = 0.05; S.E.E. = 0.009 m^2

n=8; R^2 = 0.76; P = 0.05; S.E.E. = 0.009 m^2

Frontal area (m^2) = [0.00433 x STA (deg)^0.172 x TA (deg)^0.096 x mass (kg)^0.762] + 0.066

n=21; R^2 = 0.54; P less than 0.001; S.E.E. = 0.017 m^2

n=21; R^2 = 0.54; P less than 0.001; S.E.E. = 0.017 m^2

Frontal area (m^2) = [0.00653 x STA (deg)^0.183 x TA (deg)^0.099 x mass (kg)^0.493 x height (m)^1.163] + 0.066

n=21; R^2 = 0.56; P less than 0.001; S.E.E. = 0.014 m^2

n=21; R^2 = 0.56; P less than 0.001; S.E.E. = 0.014 m^2

Frontal area (m^2) = [0.0148 x STA (deg)^0.184 x TA (deg)^0.099 x mass (kg)^0.408 x height (m)^0.925 x SW (m)^0.426] + 0.066

n=21; R^2 = 0.69; P less than 0.001; S.E.E. = 0.013 m^2

n=21; R^2 = 0.69; P less than 0.001; S.E.E. = 0.013 m^2

Once a value for frontal area is obtained, this must be multiplied by an appropriate value for Cd. Contrary to the assertions of many, cyclists are not "bluff bodies", i.e., the Cd of a cyclist upon a bicycle (even sitting upright on a mountain bike) is significantly less than that of, say, a flat plate, and perhaps more importantly, can vary as a function of yaw angle. Nonetheless, reasonable estimates of CdA (at 0 deg of yaw) can still usually be obtained by multiplying the above-derived frontal area(s) by 0.707, which is the average value for n=8 cyclists of varying stature and build tested by Dr. Chet Kyle in the Texas A&M wind tunnel (cf.

Cd (unitless) = 4.45 x mass (kg)^-0.45

Given, however, the unknown precision of this equation and the fact that Kyle found no significant relationship between Cd and mass, there seems to be little reason to recommend it over simply using a fixed value of ~0.7.

So just how precisely can CdA be estimated using the approach described above? This question can be addressed two ways, i.e., via standard propogation-of-error analysis and also by example.

1) Propogation-of-error analysis: The standard errors of the estimate (S.E.E.) provided by each equation for estimating frontal area range range from 0.009 to 0.017 m^2. Frontal area, however, only accounts for ~60% of CdA, i.e., Cd can and does vary between individuals and thus accounts for the other ~40%. The S.E.E. values listed therefore do not tell the whole story, i.e., one must also take into consideration the variability in estimating Cd. Based on the data of Kyle and using standard propogation-of-error methods, the overall imprecision in estimating CdA would be 0.016-0.019 m^2, or plus/minus somewhere between 5 and 10% of a typical value.

2) Some examples: The table below lists anthropometric data along with estimates of A, Cd, and CdA obtained using the equations discussed above for two individuals, both of whom have been tested in the Texas A&M wind tunnel. Due in part to chance alone, the values obtained by using the third equation developed by Heil combined with either method of estimating Cd agree almost exactly with those determined in wind tunnel testing. While this outcome cannot be expected in all cases, the table below does serve to illustrate the range of values the various equations provide, and in fact it is often useful to "bracket" such estimates by calculating all possible outcomes (as shown), rather than relying upon just one single estimate.

**by Andrew R. Coggan, Ph.D.**

In previous blog entries in this series:

http://www.trainingandracingwithapowermeter.com/2010/12/prediction-of-muscle-fiber-type-from.html

http://www.trainingandracingwithapowermeter.com/2010/12/prediction-of-muscle-fiber-type-from_07.html

http://www.trainingandracingwithapowermeter.com/2010/12/prediction-of-muscle-fiber-type-from_20.html

I described a method for predicting muscle fiber type distribution from force-velocity (or power-velocity) data collected using an SRM. Unfortunately, as I have mentioned several times before other powermeters appear to be incapable of providing data with sufficient accuracy and/or temporal resolution to enable such calculations. For example, the original PowerTap recorded data only once every 1.26 s, which is generally insufficient for this sort of testing. Furthermore, data from a PowerTap are inherently "noisier" due to aliasing effects - that is, since the calculations are time- instead of event-based, each data point represents the average over a non-integer number of pedal revolutions, leading to values that tend to alternately high and low relative to the true value. Although more recent versions of the PowerTap can now record data at 1 s intervals (i.e., the current ANT+ standard), this aliasing problem still exists.

Unlike Saris's PowerTap, the Quarq CinQo is event-based, i.e., like the SRM it averages data over complete revolutions before broadcasting it as ANT+ messages. Unfortunately, however, the CinQo (or at least the one I had use of) seems prone to grossly overestimating power/grossly underestimating cadence when power and cadence are changing rapidly, e.g., when resuming pedaling after a brief pause. This is evident in Fig. 1 below, which shows the sort of abnormal power "spike" than can occur under such conditions:

**Figure 1. Abnormal "spike" in power generated by Quarq CinQo when resuming pedaling after a brief pause. **

**Figure 2. Quadrant analysis of the data file containing the abnormal power "spike" shown in Figure 1.**

As shown in this figure, a number of data points were recorded in which the *average* effective pedal force calculated from the power and cadence exceeded ~1500 N, with a maximum value of ~2500 N. Since the peak force on the pedals is usually about twice the average force, this would imply peak forces of ~3000 to ~5000 N, or **approximately 4-7x my body mass**. Given that I can only lift ~1x my body mass when performing two-legged squats, such values are clearly artifactual in nature.

When performing force-velocity (or power-velocity) testing, the result of this tendency of the Quarq to overestimate power/underestimate cadence when resuming pedaling is a non-linear AEPF-CPV relationship, as shown in Figure 3 below:

**Figure 3. Non-linear AEPF-CPV relationship generated by Quarq CinQo during force-velocity testing.**

In theory it might be possible to avoid this issue by sampling the "raw" ANT+ data stream (which is broadcast at 4 Hz) and/or by judicious editing of the collected data. However, without access to additional equipment (in the first case) or more trustworthy data collected using another device (in the second case), such solutions seems to be markedly less-than-ideal.

The above data were recorded using an iBike iAero as the ANT+ receiving device, so it is possible that they reflect limitations in how the data are handled by it rather than limitations in how the data are originally generated by the Quarq. It is difficult to envision, however, how this might be possible and still obtain close agreement between Quarq/iBike and, e.g., PowerTap data under less challenging conditions. Furthermore, I have recently been successful in using a Lemond Fitness Revolution trainer paired with their Power Pilot to generate linear force-velocity data that closely match that provided by an SRM, even though, like the iBike, the Power Pilot uses the ANT+ protocol to record data once per second. This suggests (although certainly does not prove) that the non-linear nature of the Quarq/iBike force-velocity curve reflects the behavior of the former, and not the latter.

**Method #2: Estimation of muscle fiber type from fatigability**

Given that powermeters other than the SRM appear incapable of generating robust force-velocity cuves, how can somebody who doesn't own one estimate their muscle fiber type? One possibility is to rely on some other fiber type-specific property of muscle, e.g., fatigue resistance.

Compared with fast-twitch (type II) muscle fibers, type I muscle fibers contain more mitochondria, are surrounded by more capillaries, etc., making them better adapted for sustained, aerobic energy production. Conversely, type I fibers have a lower maximal ATPase activity, have lower activities of glycolytic and glycogenolytic enzymes, etc., meaning that they rely tend to rely less upon production of ATP from anaerobic sources, i.e., ATP/PCr breakdown and lactate production. For these and other reasons, type I muscle fibers are more fatigue resistant, even during short-duration, high intensity activities such as a 30 s Wingate-test type effort as shown in Fig. 4:

**Figure 4. Relationship between muscle fiber type and fatigue index during a 30 s maximal effort.**

The data in the above figure are drawn from a study that I conducted at Ball State University under the direction of Dr. Dave Costill, which eventually came to serve as my master's thesis (1). Compared to the regression relating optimal CPV to fiber type provided in the 2nd article of this series, the correlation between the fatigue index (i.e., the percentage decline in power during the test) and muscle fiber type is not as high. Given, however, that it is based upon a secondary characteristic of muscle fibers (i.e., fatigue resistance vs. contractile properties), this is perhaps not unexpected. The strength of the correlation is also comparable to that reported in the scientific literature in similar experiments. In any case, these data can be used to predict muscle fiber type using the equation below:

% type I area = 139.3 - 1.931 * fatigue index

R^2 = 0.596

P<0.05

S.E.E. = 9.7%

**Final thoughts**

In some regards, the formula presented above - and indeed, this entire series of blog entries - can be considered to be "navel gazing" of limited practical value. After all, when racing a bicycle it is the actual power you can produce over relevant durations (along with, e.g., tactics) that determine the outcome of a race, not your muscle fiber type *per se*. Furthermore, I strongly believe that "if it walks (sprints) like a duck (slow-twitcher) and talks (resists fatigue) like a duck (slow-twitcher), then it is a duck (slow-twitcher)", regardless of what a muscle biopsy might reveal or what formal tests/predictions I have described might suggest. Nonetheless, I do think that being able to "pin a single number on things" may help at least some people understand their own physiology just a little bit better, with this deeper insight hopefully helping them prepare better for/perform better in competition.

**References**

1. Coggan AR, Costill DL. Biological and technological variability of three anaerobic ergometer tests. *Int J Sports Med* 1984; 5:142-145.

http://www.trainingandracingwithapowermeter.com/2010/12/prediction-of-muscle-fiber-type-from_07.html

I described a way of predicting muscle fiber type distribution based on force-velocity (or power-velocity) data collected using an SRM. Because each individual's situation is different, I had not intended to go into detail regarding how to actually collect such data. My previous post generated more interest than I anticipated, however, so in this post I will attempt to at least provide some general guidelines. Nonetheless, I anticipate that anyone attempting to perform such testing themselves will likely have to go through a bit of trial-and-error to perfect their own approach.

As described previously, the force-velocity relationship during cycling is essentially linear (such that the power-velocity relationship is parabolic in nature). This has been demonstrated in various studies, either via use of a specially-constructed isokinetic ergometer (1) or by simply having subjects perform multiple, maximal efforts against varying resistances on a standard friction-braked (Monark) ergometer (2). However, the simplest and hence most elegant approach of all is the inertial load method devised by Dr. Jim Martin (3). Dr. Martin's method utilizes a standard Monark ergometer that has been modified such that 1) the only source of resistance is the inertia of the flywheel and 2) the position of the flywheel can be measured with high temporal (i.e., 1 microsecond) resolution (cf. Fig. 1).

With this ergometer, near-instantaneous power can be measured every 3 deg of crank revolution based on the rate of acceleration of the flywheel. Alternatively, power can be averaged over a complete pedal revolution, thus reflecting the combined extension/flexion of both legs. In either case, judicious choice of the inertial load (which depends upon the moment of inertia of the flywheel and the gearing) enables the subject to reach their optimal pedaling rate in just 2 s, and to complete 6.5 revolutions in just 4 s. This makes it possible to determine an individual's force-velocity (or power-velocity) relationship during a single, brief test in which significant fatigue does not occur.

Few readers of this blog are likely to have access to an ergometer like the one developed by Dr. Martin. However, it is possible to obtain similar data using an SRM by 1) recording data at a sufficiently high frequency, and 2) selecting an appropriate resistance. The "how" and "why" of this approach are described below.

Although a standard SRM system cannot match the very high temporal/spatial resolution of Dr. Martin's ergometer, it is possible to capture the average data for each individual pedal stroke, which is all that is needed to determine the force-velocity relationship. This can be achieved by selecting the highest possible recording frequency/shortest possible time interval (e.g., 10 Hz, or every 0.1 s, when using a PowerControl IV). This will cause the SRM to "stutter", i.e., to repeatedly report the same values for power and cadence for individual pedal strokes, as shown in Table 1 below:

In this particular example, the SRM began recording data upon completion of (presumably) the first crank revolution, which was performed at an average of 444 W/55 rpm. These same values were then repeated until completion of the second crank revolution, which occurred between 1.1 and 1.2 s after the first and was performed at an average of 668 W/88 rpm. The third crank revolution was then completed between 1.7 and 1.8 s at an average of 721 W/105 rpm, etc. In other words, as long as the time required for a single crank revolution is shorter than the sampling interval, the results obtained are actually event-based (i.e., are averages over individual pedal revolutions) rather than time-based. Indeed, even with a newer PowerContol (i.e., version V and above) that can only record data at a maximum of 2 Hz (i.e., every 0.5 s), an individual must be pedaling at >120 rpm before multiple pedal strokes will be averaged together. Consequently, essentially identical results are obtained regardless of whether data are recorded at 10 Hz (every 0.1 s), 5 Hz (every 0.2 s), or 2 Hz (every 0.1 s), as shown in Figure 2 below:

The other key aspect when performing force-velocity testing using an SRM is selection of an appropriate resistance. If the resistance is too low, then the individual will be able to accelerate the cranks too rapidly, and only a few point(s) far to the right/down the force-velocity relationship will be obtained, and/or force will fall off excessivly due to the difficulty in coordinating muscular actions at very high pedaling rates. On the other hand, if the resistance is too great, the subject will not be able to accelerate the cranks rapidly enough, and only a few data points at the upper left end of the line will be obtained before fatigue begins to occur. If the resistance is just right, however, data will be obtained across a broad span of velocities (and hence forces) before fatigue develops.

These points are illustrated in Figure 3 below, which displays data from force-velocity tests performed with different inertial loads. With the high and medium inertial loads, I was not able to accelerate the cranks rapidly enough, and hence "fell off" my force-velocity line after 4 s (denoted by the arrows) at very low and moderate velocities, respectively. Conversely, with a lower inertial load, comparable to that of Dr. Martin's ergometer, data were obtained over a broader range of velocities before fatigue ensued.

Note that the regression line was calculated by excluding all data collected after 4 s then pooling the results from all three tests. The SRM was set to record data at 2 Hz.

The data shown above were obtained by mounting my bicycle in a Velodyne trainer and then varying the inertial load provided by the Velodyne's flywheel by simply using different gear ratios. While it would be possible to provide guidelines for appropriate inertial loads to for others to try, the wide variety of conditions under which such testing may be performed as well as uncertainty regarding the exact mass/moment of inertia of particular trainers, rollers, etc., means that this would be much less helpful than it might at first appear. As a general rule, however, individuals attempting such testing using the typical low-inertia magnetic or fluid trainer are likely to find that they need to use moderate-to-large gears to obtain good data. On the other hand, those attempting such testing outdoors will need to use very low gears - lower, in fact, than usually found on a road racing bicycle. In any case, the key point is that the cyclist must be able to accelerate the pedals rapidly, but not too rapidly, something that is readily determined via preliminary tests.

When adhering to the above guidelines, excellent reproducibility can be obtained, with both within-day and between-day coefficient of variations generally being 2% or less as shown in Table 2 below:

In particular, the circumferential pedal velocity at which maximal power is produced (i.e., CPVopt)which is the basis for prediction of muscle fiber type distribution using the data of Hautier et al. (2), is highly reproducible.

By recruiting additional upper-body musculature, standing out of the saddle increases the maximal power that an individual can produce by roughly 10%. With the exception of experienced BMX riders, however, few cyclists are well-practiced at pedaling both rapidly and powerfully while standing. As well, the need to support 100% of body mass means that fatigue may develop more rapidly. In any case, the usual effect of standing is to increase the Y interecept but also to steepen the slope of the force-velocity relationship, as shown in Figure 4:

As a consequence, the circumferential pedal velocity associated with maximal power output will generally be shifted to a lower value, which will lead to underestimation of the percentage of type II fibers than an individual possess when using the equation presented previously (which is based data collected while seated). This would therefore seemingly preclude use of data from, e.g., standing start efforts performed using typical gears as part of normal training or racing to predict an individual's muscle fiber type.

Unfortunately, as indicated at the outset of this series of blog entries, at least in my hands powermeters other than the SRM do not appear to be able to provide data of sufficient quality to permit accurate (or at least easy) determination of an individual's force-velocity relationship while cycling. I will discuss these issues and provide some examples in the next entry.

1. McCartney N, Heigenhauser GJF, Jones NL. Power output and fatigue of human muscle in maximal cycling exercise. 1983; 55:218-224.

2. Hautier CA, Linossier MT, Belli A, Lacour JR, Arsac LM. Optimal velocity for maximal power production in non-isokinetic cycling is related to muscle fiber type composition. Eur J Appl Physiol 1996; 74:114-118.

3. Martin JC, Wagner BM, Coyle EF. Inertial-load method determines maximal cycling power in a single exercise bout. Med Sci Sports Exerc 1997; 29:1505-1512.

In this prior blog entry:

http://www.trainingandracingwithapowermeter.com/2010/12/prediction-of-muscle-fiber-type-from.html

I briefly discussed some of the differences between the two major muscle fiber types found in human skeletal muscle (i.e., slow-twitch, or type I, and fast-twitch, or type II), and also indicated some ways in which knowledge of an athlete’s muscle fiber type distribution could, at least in theory, be helpful in optimizing their approach to training and racing. Continuing on from that introduction, in this entry I will describe one of two ways of estimating an individual’s fiber type based on data obtained using a powermeter.

**Method #1: Estimation of muscle fiber type from muscle contractile properties**

As first demonstrated by Gasser and Hill in 1924 (1), the force-velocity relationship of isolated muscle is non-linear – that is, as the speed of muscle shortening increases, force falls off quite rapidly at first, then more slowly thereafter. On a molecular basis, this is because it takes a finite amount of time for the head of the myosin protein to attach to the actin filament, generate force, and then detach before reattaching again at another binding site. Consequently, fewer and fewer such force-generating bonds can be formed as the myosin and actin filaments slide past each other at higher and higher speeds. However, because the myosin found in type II fibers can complete this cycle (and hydrolyze ATP) more rapidly than that found in type I fibers, force declines less rapidly as a function of contraction speed in type II than in type I fibers. The result is not only a higher maximal speed of shortening, but also a higher maximal power output. As well, the speed of shortening at which maximal power is developed is also higher in type II than in type I fibers. These functional differences are readily apparent in Figures 1 and 2 below, which are based on the data Gilliver et al. (2).

I briefly discussed some of the differences between the two major muscle fiber types found in human skeletal muscle (i.e., slow-twitch, or type I, and fast-twitch, or type II), and also indicated some ways in which knowledge of an athlete’s muscle fiber type distribution could, at least in theory, be helpful in optimizing their approach to training and racing. Continuing on from that introduction, in this entry I will describe one of two ways of estimating an individual’s fiber type based on data obtained using a powermeter.

As first demonstrated by Gasser and Hill in 1924 (1), the force-velocity relationship of isolated muscle is non-linear – that is, as the speed of muscle shortening increases, force falls off quite rapidly at first, then more slowly thereafter. On a molecular basis, this is because it takes a finite amount of time for the head of the myosin protein to attach to the actin filament, generate force, and then detach before reattaching again at another binding site. Consequently, fewer and fewer such force-generating bonds can be formed as the myosin and actin filaments slide past each other at higher and higher speeds. However, because the myosin found in type II fibers can complete this cycle (and hydrolyze ATP) more rapidly than that found in type I fibers, force declines less rapidly as a function of contraction speed in type II than in type I fibers. The result is not only a higher maximal speed of shortening, but also a higher maximal power output. As well, the speed of shortening at which maximal power is developed is also higher in type II than in type I fibers. These functional differences are readily apparent in Figures 1 and 2 below, which are based on the data Gilliver et al. (2).

**Figure 1. Force-velocity relationship of isolated type I and type II human muscle fibers.**

**Figure 2. Power-velocity relationship of isolated type I and type II human muscle fibers.**

Unlike the force-velocity relationship found in isolated muscle, during cycling the relationship between force and velocity is essentially linear, as first shown by McCartney et al. (3) and as illustrated in Figure 3 below. This is apparently due to the complex interaction of multiple muscle groups, each having their own unique force-velocity relationship, acting over multiple joints. Consequently, rather than the positively-skewed curve found for isolated muscle, the power-velocity relationship is well-described by a parabolic function, as shown in Figure 4. (Note that the constants of the two equations differ slightly due to the way individual data points are weighted somewhat differently while calculating the linear and non-linear regressions.)

**Figure 3. Force-velocity relationship during cycling.**

Despite these differences, the same general principles described above apply, i.e., the higher the percentage of type II fibers (especially when expressed as a fraction of total muscle area or volume) an individual has, the less of a decline in force they would be expected to exhibit as velocity (cadence) increases. Consequently, all else being equal they would be expected to have a higher maximal neuromuscular power and a higher optimal pedaling velocity. Indeed, this is precisely what both McCartney et al. (3) and Hautier et al. (4) found for n=2 and n=10 subjects of varying fiber type, respectively. Furthermore, Gardner et al. (5) have demonstrated that field-based tests performed using an SRM can provide force-velocity data comparable to that obtained under more controlled conditions, i.e., on an ergometer in a laboratory setting. Thus, at least in theory it should be possible predict someone's muscle fiber type distribution with reasonable accuracy from such field tests.

To derive an equation for doing so, I converted the cadence data of Hautier et al. (4) to circumferential pedal velocity (CPV in m/s; which is equal to (cadence * 2 * Pi * crank length in m)/60) and then calculated the regression of the % type I fiber area on the optimal pedal velocity (CPVopt, the pedal velocity at which maximal power is produced) (instead of the reverse as originally presented by Hautier et al. (4)). The result was:

% type I fiber area = 242.7 - 89.5 * CPVopt (m/s)

R^2 = 0.784

P = 0.001

S.E.E. = 2.8%

For the subject whose data are shown in Figures 3 and 4, this equation would predict a % type I area of just 26% (therefore 74% type II). This is consistent with their extremely high maximal power output as shown in Figure 4, as well as their extremely high maximal theoretical CPV (CPVmax), i.e., 4.84 m/s or 280 rpm on 175 mm cranks. (In fact, provided the relationship between force and velocity is truly linear, CPVopt will always be one-half of CPVmax.)

A detailed answer to this question is beyond the scope of this blog. In essence, however, doing so requires measuring power and cadence with high temporal resolution while performing a maximal effort against just the right amount of external resistance. If the resistance is too great, then significant fatigue may develop before a sufficient number of data points are obtained out/down the force-velocity line or up-and-over the peak of the power-velocity curve. Conversely, if the resistance is too small, then too few (or even no) data points will be obtained on the right-most half of the force-velocity line or on the ascending portion of the power-velocity curve. Perhaps the best suggestion I can make, then, is that people simply experiment, e.g., by performing maximal accelerations from a dead-stop using various gear ratios. Depending upon the conditions (e.g., outdoors vs. upon some form of trainer), this may entail the use of either very small gears (e.g., 39 x 23) or very large gears (e.g., 53 x 12). Regardless, the SRM should be set to record data as frequently as possible, to try to "capture" as many individual pedal strokes as possible. If an insufficient number of data points are obtained during a single effort to permit reliable determination of the force-velocity or power-velocity relationship, data from several short efforts can be combined. For example, the data shown in Figs. 3 and 4 were drawn from five different "gate starts" performed by an elite BMX cyclist, each one of which provided data for just 1-3 pedal strokes (recorded at 0.1 s intervals).

1. Gasser HS, Hill AV. The dynamics of muscular contraction. Proc Royal Soc B 1924; 96:398-427.

2. Gilliver SF, Degens H, Rittweger J, Sargeant AJ, Jones DA. Variation n the determinants of power of chemically-skinned human muscle fibers. Exp Physiol 2009; 94:1070-1078.

3. McCartney N, Heigenhauser GJF, Jones NL. Power output and fatigue of human muscle in maximal cycling exercise. 1983; 55:218-224.

4. Hautier CA, Linossier MT, Belli A, Lacour JR, Arsac LM. Optimal velocity for maximal power production in non-isokinetic cycling is related to muscle fiber type composition. Eur J Appl Physiol 1996; 74:114-118.

5. Gardner AS, Martin JC, Martin DT, Barras M, Jenkins DG. Maximal torque- and power-pedaling rate relationships for elite sprint cyclists in laboratory and field tests. Eur J Appl Physiol 2007; 101:287-292.

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