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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. 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.
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.
Given that work in joules can be calculated by multiplying power by time it is very tempting to use this to measure the stress of a ride. But as we get stronger and more efficient those joules become easier to produce, and thus the training stress accrued in the workout should reflect that. To account for this we need some kind of score that takes into account how hard the ride is based upon our current capability.
They reflect the stress by taking into account the relative intensity of the workout. This intensity factor is computed as a ratio of the xPower to our current CP. This intensity is then multiplied by the ride duration to get an overall stress score; the higher the stress score the bigger impact it will have had and likely the more recovery we will need the day after.
But there is still a problem, we know that work at high intensities for short durations elicits a different strain to work at low intensities for longer durations and there comes a point where more pain will give little gain. To counter this Dr Skiba introduced Ae and An TISS that are weighted differently for low and high intensity work and allow us to track these training stresses separately. 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. 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 w 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 w will apply much less strain on the athletes body and be something they could perform daily.
As we get fitter we need to apply more and more stress to elicit the same strain. 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.
These represent the training impulse of the impulse-response model. We can look at the gain factor to identify if the athlete is a low or high responder, or likely somewhere in between. This gain factor helps to link the training impulse to the predicted response. These load and gain factors are then used as an input into two functions that quantify the response; fitness or PTE, positive training effect that accumulates over the longer term 50 days and fatigue or NTE, negative training effect that accumulates over the shorter term 15 days.
Importantly, these functions will also reflect de-training too — if your training load eases or stalls your fitness and fatigue will reduce; and changes in your performance will either increase slightly if it is a short-term taper, or drop if it is a longer term training break. Lastly, Banister recommended resetting and checking the gain and time constants every days; by fitting recent performance outcomes with the recent training load.
More recent studies have confirmed that these constants will change over time, but will also differ according to training intensity and training modality. It is a variant of the Banister IR model and is described in a comprehensive article on the TrainingPeaks website. The PMC is claimed to address a number of shortcomings of the Banister IR model that; 1 it is not tied to physiology 2 it assumes there is no upper limit to performance 3 fitting model parameters every days requires valid data to model against 4 it is over parameterised 5 these parameters can vary by individual, intensity and sport.
It is debatable whether these perceived shortcomings have any material impact on the utility of the IR model or if they are addressed by the PMC. But it is clear that the PMC has been embraced by the cycling community and has been instrumental in providing a means for the layman and many professional coaches to adopt an IR approach to managing their training.
It is often described as the most important tool for the cyclist lucky enough to own a power meter. Rapid increases in short-term load ATL often called the 'ramp rate' tend to indicate that training load is increasing too fast to sustain, but this is also indicated by the third metric Training Stress Balance TSB which is computed as the difference between the long and short term loads.
A TSB lower than to indicates a risk of injury or illness through overtraining or insufficient rest assuming you have more than 42 days of data. 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. Amazingly, Graeme Obree reduced his CdA to 0. 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.
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. And of course, wind is the most obvious problem. 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. 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!
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'. 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. 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.
To all those volunteers who selflessly give their time and without whom amateur sport would not exist. Download Version 3. Mac OS X Older versions and resources You can download older releases of Golden Cheetah. There is a User guide and a FAQ. The full Golden Cheetah source code is freely available from Github. Development Releases.
Critical Power Chart. Ride Plot. Ride Summary. Critical Power Delta Compare. Model Estimates. Peak Power. Tutorials What's New in GoldenCheetah 3. It's my cycling life on a website - wherever I go. Analysis and data at your fingertips. If you are self coached Cycling Analytics is an incredibly valuable resource. Its simple to use for the novice but the richness of the data and the statistical analysis it suitable for all classes of rider who like to analyse their performance.
All of the data you need to follow any training program at the best price online. Cycling Analytics is a powerful and flexible analysis tool for both coaches and athletes. As a keen cyclist it allows me to track my performance, and drill down into specifics if I need to. As a coach it allows me to organise and plan for my athletes, enabling them to reach their potential as cyclists.
Here's a ride. Go there and click around and see what else this can do. Upload a ride without making an account and what this does with a single ride. Here is what you need: A bike This one's important. A power meter Or a heart rate monitor. A bike computer Most devices are supported. An account Create one now. Here is what you get: A clean interface to all your riding. The basic details of all your rides on a calendar.
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