The Extended Critical Power Model
Old and new
Suppose we impose a constant work rate Plim and we measure the time the test person can sustain this power until complete exhaustion Tlim . If we do this for a number of different work rates we obtain a data set [Plim, Tlim]
In the old CP or Critical Power model it is accepted that the sustained power
Plim is proportional to the inverse of the sustainable duration Tlim. In other words the harder you work, the shorter you can sustain it.
Plim = CP + W'/Tlim
CP is the Critical Power, and W’ is called the Anaerobic Capacity
This simple hyperbolic relation is still used in many texts and computations, but it has to be treated with caution. First we will show that it may be correct in some cases such as short distance swimming, but that we need a more precise description for the medium-long exercises such as running and cycling.
For the purpose of graphical presentations the awkward hyperbolic relation is reformatted into a linear relation when we put the inverse of the sustainable time 1/Tlim on the x-axis, and the corresponding power Plim on the y-axis. The resulting graph should be a straight line that intersects the y-axis at the value CP, and that has a slope equal to W'
Unfortunately In the case of running and swimming direct power measurements are not possible and the velocity has to be used instead of power, in which case the basic relation can be written as
Vlim = CV + D/Tlim
Where Vlim is the measured velocity, CV is the critical velocity and D is the anaerobic distance.
For running and swimming we can use the PR (personal records) of the athlete
Here we see the graph of the personal best swimming speed versus inverse time of Katie Ledecki.
The intersection with the y-axis is at her critical velocity CV of 1,577 m/s or 5,68 km/h.
The slope of the fitted line is her anaerobic distance D = 21,53 m
How do we interpret these data ? It is as if D is a free or give-away distance that can be subtracted from the total distance, and that the resulting rest distance is then swum at critical velocity CV
It is possible to predict her best performance on e.g. 300 m in following way
Time over 300 meter T(300m) = (300 – 21,53)/1,577 = 176,58” or 2’56.56’
and hence her speed over 300 meter
V(300) = 300/176,58 = 1,699 m/s or 6,1164 km/h
However it is not possible to predict her performance at distances much shorter than 400 m or distances much longer than 1500 m
In short, the swimming performances of Katie Ledecki are well described by the simple critical power (velocity) model for swimming performances of duration between approximately 4 and 15 minutes.
Things get complicated when we consider performance durations in a much wider range, such as the running records in the mid-long distance running. Let us have a look at the personal records of Haile Gebrselassie.
We see that the simple CP model does not account for all his results and we are forced to consider 2 performance zones corresponding to the black and the red data points.
His conventional critical velocity is the zero-intersection of the upper (red) line at CV = 6,43 m/s
His anaerobic distance is D = 118 m
However these data are not suitable to predict his performances in the longer runs such as the 20 k or the marathon distances.
Let us try to predict his best marathon by using only these data from the red points
T(marathon) = (42195 - 118)/6,43 = 6544 s or 01:49:04 , which is an absolutely impossible result.
The black data points identify his personal records in races on 10 km and 20 km
Here the zero intersection is a new threshold that will be called Recovery Threshold RT = 5,54 m/s and the slope is much higher than his anaerobic distance D. This slope is indicated for now as D” = 1226 m. Although D” behaves as if it were some “anaerobic distance capacity” it certainly is not and we will have to discover its real meaning in proper time.
In any way we can model the performance in the long distance runs as ;
Vlim = RT + D”/Tlim
Now we can predict his best marathon as T(marathon) = (42195 - 1226)/5,54 = 7395 s or 02:03:15
In real life Gebrselassie established a Marathon world record in 2008 at 02:03:59 , only 44 s or 0,6 % slower than predicted from his 10 k and 20 k record times.
The intersection between the straight black and red segments corresponding to the middle and the long distances identifies a new important threshold.. It lies at the point V = 6,53 m/s and at sustainable time T = 1234 s. Its meaning is that at the velocity 6,53 m/s there is a clear transition in the use of muscle power and of energy systems.
Cycling
In cycling with a powermeter [Plim, tlim] data can be obtained from 2 testing protocols or power data sources.
1) From MEX or Multiple EXhaustive testing in the laboratory or in the field for at least 5 or more well-chosen power or duration settings.
2) From the Mean Maximal Power MMP - curve. It is understood that the MMP curve must be constructed with enough representative data such as at least 3 months of daily training and racing.
In the next example we use the MMP curves of international WT cyclists. We select 16 representative data points between 2’ minimum and 1 hour maximum. The data were collected from the subjects power files for a complete year of training and competition.
The standard MMP graphics with its logarithmic x-axis scale is not easily interpreted but we can present the same data as before with the inverse of duration on the x-axis.
Here is such a plot for a male (upper) and a female (lower) grand WT champion. Let us name then John and Jane. Similar to the running speed plot of Gebrselassie we discover now the characteristic two-segments which for the moment we will call the Hard and the Severe exercise zones
In this plots the right hand points are for durations 3 minutes, the leftmost points are for 1 hour.
Logically the best performances of John are higher than Jane’s.
The zero-intercepts of the hard exercise (red and orange) segments are the resp. recovery thresholds RT.
The slope of the hard segments are W". We will call this the aerobic fitness.
The zero-intercepts of the severe exercise segments (blue and black )are the resp. critical power CP, of which we will show to be identical to the Maximal Aerobic Power MAP.
The slope in the severe segments are the anaerobic capacity W’
The intersection between the hard and the severe segments is called Super Critical Power SCP. The name SCP was used first in 2014 by Mike Puchowicz from Veloclinic.com
The next table shows the relevant numerical parameters for these two particular cyclists.
In order to fully understand the meaning of these thresholds and parameters we need insight into the management of the aerobic and the anaerobic energy systems and the distinction of zones of work intensity.
Zones of work intensity and training load indexes
All physical work is produced from 3 possible metabolic energy sources, the Aerobic, the Lactic Anaerobic and the Alactic Anaerobic systems. The aerobic system uses oxidation of carbohydrates (sugars) and fats (lipids). The necessary oxygen for this process is provided by the intake of oxygen by the lungs and by its cardiovascular transport to the muscle fibres. The CO2 resulting from this oxidation is transported to and is exhaled by the lungs.
This aerobic power and energy production can go on until depletion of the stored fats and sugars. A standard human body has a storage of fats that theoretically enables it to run multiple marathons at low pace. Unfortunately the sugar storage is much less but it can be replenished even during an effort at low intensity through the intake of glucose and other nutrients..
The lactic anaerobic system does not "burn" fat or sugars but uses stored glycogen through a complicated 10-step bio chemical reaction called glycolysis. In glycolysis some lactate is produced and recycled which results in an increase of the blood lactate concentration. This lactate is by no means a waste product because it is essential to the power production and it is recycled into new glycogen. This is the neoglucogenesis cycle. However when power demand becomes too high the recycling becomes deficient and the stored glycogen ultimately depletes. The total amount of work or energy that can be drawn from this glycogen reserve in one sustained effort is called anaerobic capacity W'
W' is a surprisingly small amount of energy. For most professional cyclist W' is between 15 and 25 kJ and in a 1 hour time trial almost 95 % of work is drawn from the aerobic process and only 5 % from the anaerobic reserve
There is also a third source of work, the Alactic Anaerobic cycle that uses a stored amount of Phospho Creatine PCr. The corresponding total energy storage is even much smaller than W' and it will be used only at very high demand of power, such a in a sprint, a short burst or at the exhaustion of W'. This alactic energy storage will be exhausted or depleted in a few seconds of extreme exercise.
The power-duration data will naturally split into 4 categories of energy management zones.
1. The Easy exercise or EE zone , when exhaustion never occurs, the power demand is so low that no energy is drawn from the anaerobic capacity W'. All power is aerobic although with a varying contribution of fat- and sugar burning.
This intensity zone may be called Aerobic zone, Easy zone, Restore or Recovery zone
The aerobic load is the total amount of aerobic energy referred to a 1 hour ride at power level RT
Aerobic Load = Total Aerobic energy / (3600 x RT)
2. The Hard or Slow Death exercise or HE zone, when anaerobic capacity W' is depleted slowly and the sustainable time Tlim is between approximately 15 minutes and more than 1 hour. The threshold between easy and hard exercise is extremely important because it identifies the threshold between non-exhaustible and exhaustible exercise. Let us call it threshold for recovery RT. There are strong arguments to identifying RT as being approximately equal to the Maximal Lactate Steady State MLSS
This intensity zone may be called the Slow Death zone SD
The Slow Death Load is the total amount of anaerobic energy spent in the SD zone referred to the anaerobic capacity W’
SDL = Anaerobic energy spent in SD zone / W’
3. The Severe exercise or SE zone, when anaerobic capacity W' is depleted fast and sustainable time is between 2 minutes and approximately 15 minutes.
In this (and only this) zone we can apply the classical Critical Power model i.e.
Plim = CP + W'/Tlim
This zone where the anaerobic reserve is quickly depleted may also be called Fast Death or Burn zone.
The Fast death Load is the total amount of anaerobic energy spent in the FD zone referred to W’
FDL = Anaerobic Energy in FD zone /W’
The threshold between the hard and the severe exercise zone is called SCP or Super Critical Power. SCP actually is the lowest power that elucidates the power at maximal oxygen uptake and that will result in ventilatory exhaustion. Therefore at total power SCP the aerobic contribution is equal to CP or MAP.
4. The Short Burst or Explosive exercise zone, when power demand is so high that it can be sustained between a few seconds and 1 minute. For these very short times the totality of W’ can not be used because the necessary force and muscle contraction speed would be inhuman. A W’ of 20 kJ to be spent in a burst of 10 seconds would mean an average power of 2000 W during the full 10 seconds. The very best sprinters produce at most 1500 W during 1 or 2 seconds
Next figure shows the 4 power zones, Easy (green), Hard (Orange), Severe (Red) and Short Burst (Black).
A historical confusion
Tlim sits in the denominator of both hyperbolic relationships. If we insert Tlim = infinite then Plim becomes equal to CP or RT. So which one is the correct power that you can sustain indefinitely long ? Originally CP was defined to be indefinitely sustainable. This means that CP was the extrapolation of data in the slow death zone. However around 1992 fatigue testing in cycling were introduced at power levels in the fast death intensity zone. The resulting asymptotical value was no longer indefinitely sustainable but people still called it CP ! Today we still call it CP but now we know that this CP is equal to the maximal aerobic power MAP and that RT is the real level that you can ride on for the whole day without exhaustion. In real life when exercising at the level CP (MAP) sustainable time is rather short say between 15 and 30 minutes.
The main metabolic zones are further subdivided into physiologically significant training zones TZ according to a scheme established by Frank Vandewiele after years of practice as a trainer and coach of cyclists, runners and kayakers. These zones are defined as follows
Recovery zone : From 0 to 60% of RT
FATMax zone : from 60%RT to 75% RT
CARBMax zone : from 75%RT to RT
Hard, or Slow Death zone : From RT to SCP
VO2max zone : From SCP to P5
High Anaerobic or Fast Death zone : From P5 to P2
Explosive zone : All above P2