Science in Golden Cheetah
Wherever possible we choose to use published science.
Science that has been developed with the academic rigour demanded by the scientific method;
evidence based, peer-reviewed and original. This means we are able to provide the best
analysis available, but at the cost of a steep learning curve for new users.
So below, we try to introduce some of the most important concepts, why they are
important and how they might help you to improve.
Power and Duration - Critical Power and W’
How hard can you go, in watts, for half an hour is going to be very different to
how hard you can go for say, 20 seconds. Then thinking about how hard you can go
for a very long time will be different again. When it comes to reviewing and
tracking changes in your performance and planning future workouts you quickly
realise how useful it is to have a good understanding of your own limits.
In 1965 two scientists Monod and Scherrer presented a ‘Critical Power Model’
where the Critical Power of a muscle is defined as ‘the maximum rate of work that
it can keep up for a very long time without fatigue’. They also proposed an
‘energy store’ (later to be termed W’) that represented a finite amount of work
that could be done above that Critical Power.
In cycling parlance W’ would be referred to as the matchbook– the harder you go
the quicker it will be used up, but temper your efforts and you can ‘save a match’
for the last sprint. CP, on the other hand, is that intensity (or power output)
where you are uncomfortable but stable, akin to your TT pace. You know that if
you try to go any harder you are gonna blow up pretty quickly.
Monod and Scherrer also provided a mathematical formula to estimate the maximum power
you can go for any given duration using W’ and CP as parameters. This formula is
pretty reliable for durations between 2 minutes and an hour or so, but less reliable
for shorter and longer durations. So, over the last 50 years, variations of these
models have been developed to address this, and it still continues to be a topic of
great scientific interest.
We have implemented some of these models so you can get power estimates to predict
and review your training and racing. We have also implemented a wholly new model
called the ‘Extended CP model’ that is based upon bioenergetics.
Bioenergetics
We use complex sources of overlapping energy when we exercise.
These energy sources are anaerobic with a limited capacity and a high rate limit
(like W’) and aerobic with an unlimited capacity but a low rate limit (like CP).
Anaerobic Systems
In the first 10 seconds or so of high output work we draw upon energy stored within
the muscles that have immediate availability – so we can sprint all out for 10-30
seconds without drawing breath and at very high work rates. These chemicals are
phosphates called ATP (adenosine triphosphate) and PCr (phosphorcreatine).
Interestingly, after about 3 minutes of total rest these stores are largely replenished.
So for the next 50 seconds or so after those phosphates are depleted we primarily
get our energy from glycolysis and still without drawing breath. This is the
conversion of glucose into lactate. It takes us about 1 hr to recover and remove
all the lactate produced, but most of it is gone after about 10 minutes –
and we can speed up this clearance through light exercise – which is why a warm-down
is a good idea after intense exercise.
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Motor Units - Recruitment and Fatigue
Slow and Fast-twitch Muscles
Roughly 40% of your body weight is muscle; skeletal muscle that’s attached to
your bones via tendons and are controlled via conscious thought (“shut up legs,
pedal faster”), but also smooth muscle including arteries, the bladder, eye and
reproductive organs and of course cardiac muscle pumping blood 24x7 and again
without any conscious thought.
We’re going to focus on skeletal muscle. Our legs contain lots of different
muscle groups; the quadriceps, hamstrings, calves etc. These muscle groups work
together when we walk, run, kick and jump. Each muscle group in turn is comprised
of a large number of motor units (MU) that in turn contain a motor neuron and a
collection of muscle fibres. Our brain triggers a muscle group into action by
recruiting as many of its motor units as needed to meet the power we want. It does
this by firing the motor neurons that sends an electrical pulse to the muscle
fibres causing them to contract.
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Lactate - Shuttle, LT1, LT2 and Friends
Lactate
Lactate is a double edged sword; on the one hand it is the primary source of
30% of the glucose we generate within the body, but on the other hand it also
regulates metabolism — a safety mechanism within the body.
Lactate is produced when we burn glucose; aerobically and anaerobically. During
intense exercise it is mostly produced by the fast-twitch muscles that utilise
glycogen. However, it is not a waste product as was widely believed in the past;
it inhibits fat oxidation and also glucose utilisation within our muscle cells
— it even reduces muscle shortening and thus peak power. It is a 'brake'
to stop us going too hard, helping us to pace for the long run. But of course,
we might not want that to happen if we're winding it up for the finish straight!
Further, the mitochondria within our slow-twitch fibres and in fact most of
our bodily organs can utilise lactate to create glucose. So our body creates
it to regulate our metabolism, but will also use it for fuel, either when we
settle down a bit or by "shuttling" it in the bloodstream from the active leg
skeletal muscles to the smooth muscles in our heart and lungs.
Lactate also causes an increase in PGC-1a that results in increased mitochondria
biogenesis (we can also increase PGC-1a signalling and associated mitochondria
biogenesis by riding when fasted). This is an exciting area of development that
is beginning to suggest that lactate has significant beneficial effects rather
than being detrimental.
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Oxygen uptake - VO2max and "The Slow Component"
VO2max
It seems such a simple concept. VO2max is the maximum amount of oxygen
your body can use during intense exercise, measured in millilitres per
kg of weight per minute. Usually expressed as ml/kg/min. To determine
your VO2max you need some expensive lab equipment that measures gas
exchange; oxygen in and carbon dioxide out. This is typically measured
via a ramp test.
It is considered to be the best indicator of an athlete's cardiovascular
fitness and a good predictor of their aerobic performance. The more oxygen
you can use during intense exercise, the more 'fuel' you burn and the greater
energy you produce. In fact, in almost all endurance sports the VO2max
of world champions and elite athletes will be in the region of 70-90 ml/kg/min.
To put that into context, at the low end of the scale a sedantry, possibly
overweight and detrained athlete may have a VO2max as low as 30 ml/kg/min.
To relate this back to the lactate curve; LT1 typically occurs at about 50%
of VO2max in untrained athletes and can be as high as 80% of VO2max in trained
athletes, whilst LT2 typically occurs between 70% and 90% respectively.
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Cardiovascular System - Heart, Blood and Vessels
The Cardiovascular system is responsible for transporting oxygen, nutrients,
hormones and waste products around the body. For example, during exercise it
delivers the oxygen from the lungs and delivers fuel to the skeletal muscles
and also transports the CO2 back to the lungs and shuttle lactate away to be
re-used elsewhere.
It's a truck continually dropping off the food and and taking away the trash
and it is indisputably the single biggest determinant of endurance exercise
performance.
The Heart – Cardiac Output, Stroke Volume and Heartrate
The heart beats about 100,000 times a day pumping blood around the body;
typically shifting about 5-6 litres per minute at rest up to as much as 20-40
during intense exercise. It is pumped along two paths in a double-loop; the
pulmonary circuit to the lungs in order to release CO2 and acquire Oxygen and
the systemic circuit to deliver oxygen and fuel (and collect CO2 and lactate
etc) to the brain and body (e.g. skeletal muscle).
Total blood flow (cardiac output) is measured as the amount of blood pumped
out in one beat (stroke volume) multiplied by the number of beats per minute
(heartrate). To meet the demand as we exercise at increasing intensity both
heartrate and stroke volume will increase. At rest 5L might be 72bpm x 70ml
where at max we might pump 30L at 200bpm x 150ml. Elite and highly trained
athletes will have a stroke volume approaching 200ml and cardiac output at
210bpm of 40L litres.
There is no consensus on the relationship between increases in SV as you
increase exercise intensity; SV has been shown to plateau (or even peak)
at roughly 50% of vo2max, but that it has also been shown to increase all
the way up to maximal effort. Studies are beginning to suggest that this
pattern may be related to blood volume and training history; the higher
your blood volume and fitness then the more likely you are to see a
progressive increase all the way to vo2max.
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W’ Expenditure and Reconstitution - W’bal
Matches and Pacing – W’bal
Unless we’re riding the pursuit or a very flat time trial, when we train
and race we tend to ride sustained efforts interspersed with recovery. These
intermittent bouts might occur when we climb a hill, or sprint out of a corner
or bridge a gap. In fact almost all training and racing away from the turbo
tends to be variable because of this.
Now, we know from the Critical Power model that when we work above CP we
start eating into our limited W’ stores. If we keep going hard enough for
long enough we will blow when it’s all gone. But, we also know that it will
also be replenished over time too.
When we work below CP the energy stores within the muscles are restocked.
The further below CP we are the faster we will recover, and for the first
30 seconds of recovery we get the most bang for buck as blood-flow into
the muscles is still high from the previous bout
Dr Skiba et al provided a formula for tracking the levels of W’, called W’bal
that we can plot alongside power. It is particularly useful for assessing
workouts for likely failure before attempting them and also for reviewing and
comparing intervals within a single workout, even when they are of differing
durations.
It is likely that in the near future you will see W’bal appear on bike computer
headunits to show you the capacity remaining as you race.
Analysing Power Data
Average, xPower and NP
When you first start using a power meter you notice that power tends to move
around a lot more than, say, your heart-rate.
When you stop pedalling power drops to zero immediately, but HR may take 30
seconds or so to recover. In truth, although the power meter says zero watts
when you stop, the body’s physiological response continues for roughly 30
seconds, as HR drops, breathing recovers and more complex energy system
processes continue.
This means that if we want to use power output as a measure of training
stress we will also need to translate those simplistic power readings into
something that reflects the associated physiological processes and their
half-lives.
This is what Dr Andrew Coggan’s Normalised Power and Dr Phil Skiba’s
xPower are doing; they ‘smooth out’ the power data to reflect the
underlying physiological processes. Whilst the underlying assumptions
and maths differ slightly they both yield a power output that will reflect
the stress of the variable power values more accurately than just taking
a simple average — they represent a constant power output that
places the same stress as the variable data that was recorded.
Skiba/Literature | Coggan/TrainingPeaks |
Variability Index | Variability Index |
Relative Intensity | Intensity Factor |
xPower | Normalised Power |
BikeScore | Training Stress Score |
Critical Power | Functional Threshold Power |
W’ | Functional Reserve Capacity |
W’bal | dFRC |
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Training Management
Training – Stress and Strain, Form and Fitness
The reason we train hard and rest easy is to place stress on the body during training
sessions to signal adaptions that occur when we rest. But finding the right balance
between work and rest, training and recovery can be quite difficult. We need a model
that can quantify this relationship and help us get the best bang for buck from our
training but also ensure we don’t overdo it and get sick.
When we place stress on our bodies we cause it to strain; for example when untrained
an athlete might find riding for 1 hour at 200w very hard. The strain on their body may
be very high – they will be so destroyed at the end that they need a day or two of rest
before considering doing any training. But after 6 months of regular training the same
stress (1 hour at 200w) will apply much less strain on the athletes body and be something
they could perform daily.
Thinking in cycling terms, when we have good ‘form’ we are able to perform at high workloads
without too much strain, but as we lose ‘form’ we struggle to perform at the levels we used
to find much easier. As we get fitter we need to apply more and more stress to elicit the
same strain. If we push it too far and apply too much stress with insufficient rest we risk
becoming ‘overtrained’; our bodies become so fatigued they need an extended period of rest
to completely recover before we can start training again.
To make life simpler metrics like BikeScore and TSS take into account the athlete’s current
capability via CP and FTP, so they are stress
scores relative to the athlete’s current
capability; where Work (in Joules) is an absolute measure of stress. Also, we all respond
differently to training; high-responders will see a more dramatic increase in performance
from the same training load that a low-responder does. It is important to remember this when
assessing outcomes and planning future training and it would be useful for models to take
this individualisation into account.
More ...
Aerodynamics - Virtual Elevation
CdA
The aerodynamics of a cyclist and their bike has a huge bearing on the maximum
speed they can get at any given wattage.
When cycling without a draft, typically during an individual time-trial or
bike leg of a triathlon, roughly two-thirds (or more) of effort is spent pushing
air out of the way. The more streamlined and slippery we can become in the wind
the faster we go for the same watts. The drag coefficient for a cyclist is called their
Cd
; if A is the rider's frontal area then the drag coefficient times
their frontal area is their
CdA
sometimes called their "drag area".
The lower the CdA the more slippery they are. It can range from 0.5 (square meters)
when sat up on the hoods, 0.3 when low on the drops and all the way down to 0.2
with aerobars, helmet and a TT bike. Amazingly, Graeme Obree reduced his CdA to
0.17 for his hour record but his posture was pretty extreme!
Professional athletes spend thousands of dollars, and several days, testing
different positions and equipment in a wind-tunnel in an attempt to quantify and
improve their CdA. The smallest changes in positioning can result in massive
improvements; in a TT position on aerobars it is possible to see a 10% reduction
in CdA just from "shrugging". But other changes, like getting very low, might
make you more slippery but at a cost that your ability to lay down power is
compromised — we need to find the tipping points and make tradeoffs with
testing, and the testing can become endless.
Crr, Rho and Friends
Aside from CdA there are a number of other factors that will affect how fast
you go for any given power output.
Given we spend so much effort pushing air out of the way it should come as
no surprise that the density of the air (
Rho
) can make a massive
difference to how fast we go for any given power output. Air gets thinner as
you go to altitude, its why hour records might be attempted there (lets ignore
the fact there is also less air to breath). Aside from altitude, air density is
also affected by humidity, temperature and air pressure; we can calculate the
air density if we have all three of these.
Pushing air out of the way isn't the only thing you pedal against, the tyres
on the road have a coefficient of rolling resistance or
Crr
; even
skinny road tyres might have a range from 0.0025 up to 0.005. Luckily there are
lots of folks testing them so you don't have to. But changing tyres really can make
you faster (or slower).
Remaining factors include;
weight
if you're riding on the flat
or downhill then extra weight can be advantageous as momentum and gravity
help you go faster; but as the road tilts upwards its gonna need more
power to overcome. Typically, on a 2% slope an 80kg bike and rider will
need 233w to maintain 25 km/h, every 1kg of weight extra costs another
2w to go the same speed. Similarly for 17km/h on 5% and 10km/h on 10%
every kilo will take 2-3w of power to lift to the top.
And of course, wind is the most obvious problem. Riding with a 20 km/h headwind
or sidewind is no fun; but riding with a 20km/h tailwind is great! So
windspeed
and just as importantly wind direction (
yaw
)
can have the biggest impact on how fast we can go for any given power. Lastly
we have
acceleration
; every time you speed up you use power to do
that, unless you're rolling downhill.
Virtual Elevation - aka The Chung Method
Ultimately we all want to get faster on the bike. Assuming you have done
all you can to shed unwanted pounds there really isn't much you can do
to change the wind, air density the course profile or gravity.
That leaves our tyres (Crr), bike and posture (CdA) to work on. To avoid
spending lots of money on time in a wind-tunnel there is a practical approach
called 'Virtual Elevation' (VE) devised by Dr Robert Chung that can be done
outside using a power meter and speed sensor.
In the past, in order to test position and equipment and calculate our CdA
we needed to know accurate values for; weight, speed, windspeed and yaw, power
Crr, Rho, incline, gravity and acceleration. So a field test would typically be
performed on a still day on a flat road; removing the need for the windspeed,
yaw, incline and gravity terms. Then looking at speed for each run it would be
possible to check if a position was faster or slower. But riding without wind
and hills was almost impossible to do outside of a velodrome. And even then
velodromes have problems because (believe it or not) riding around the track you
(and others there at the same time) will create your own tailwind!
How Virtual Elevation works
The single most important thing we do is to run multiple loops on the same course
with a power meter; every run will have the same overall elevation change (none),
same distance and experience the same environmental conditions whilst the power
output and speed will vary.
Because wind can change direction or bluster it is still a good idea to perform
these tests in a sheltered environment on as windless a day as possible. We need
to eliminate it from our calculations.
The effects of slopes, gravity, air density will be the same for each run; we have
not eliminated their effect by riding a loop but we have made them identical for each
run. We can also assume that as a rider we weigh the same in each run. But we need
to make sure we don't brake, lose air from our tires or change position, because
none of these things are going to be taken into account.
If we do this then the power we used for each lap was used to overcome;
- rolling resistance in the tyre (Crr)
- elevation changes (slope changes)
- accelerations (speed changes)
- air resistance (CdA)
This can then be converted to a relatively simple formula to calculate power used
based upon Crr, Cda, speed and accelerations, gravity and slope, acceleration,
weight etc.
The clever bit is what Dr Chung does with this formula; it is solved for slope instead
of watts. So we end up with a formula that combines all of those opposing forces into
a virtual slope we had to ride up and down to get around our loop. Hence the name
'Virtual Elevation'.
We can then make some educated guesses about what Crr and CdA were and plot the associated
virtual profile. Now since each lap is performed in a single position and
the physical elevation change at the start and end of a loop is zero we need to adjust
Crr and CdA until the start and end of a lap in the VE plot are the same.
Estimating using Virtual Elevation
The example shown to the right (courtesy of Dr Chung) shows a field test
of 7 laps where the rider had his hands in one position for the first several laps
then changed hand position part way through the test.
When the estimate for CdA and Crr are correct the VE plot for a lap will show the
start and finish point at the same elevation (i.e. they will be level). We can see
that the top left plot is clearly wrong as each lap finishes higher than it started;
the CdA estimate is too low. The top right shows the CdA has gone up but still
each lap finishes slightly higher than it started. Its only in the bottom two plots
that we can see a level start and end for any given lap; those are the laps that were
performed with the associated CdA and Crr.
In fact, the exact point at which the rider switched his hands from one position
to the other is easily spotted – two-and-a-half laps from the end. The change in
hand position was actually quite small: the first 4 laps were with the hands on
the bar tops, the last two-and-a-half laps were with the hands on the brake hoods.
The wind conditions were not quite calm (though the wind was neither strong nor
blustery) so this example shows that small differences in aerodynamics can be
spotted even under non-ideal conditions. Of course, the better the conditions,
the fewer the laps and the more precisely and reliably you can pin down the
differences.
This is what Aerolab in GoldenCheetah does; it plots this virtual elevation from a ride
as you adjust estimates for Crr and CdA until you can see a good fit for the elevation
profile. If you have sufficient laps and variations in positions you will be able to
determine which lap yielded the best results – and thus identified a good position and
its associated CdA.
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