IN
DEGREE PROJECT ENGINEERING PHYSICS, SECOND CYCLE, 30 CREDITS
STOCKHOLM SWEDEN 2019,
Analysis of current methods when using ergometer cycles for training and testing of fitness
GÖRAN FRANSSON
KTH ROYAL INSTITUTE OF TECHNOLOGY
1
Table of Contents
1. INTRODUCTION ... 3
1.1 O
BJECTIVES OF THIS REPORT...3
1.2 L
IMITATIONS...3
2. BACKGROUND ... 4
2.1 M
EASUREMENT OF FITNESS,
STAMINA OR CONDITION...4
2.1.1 VO
2max ...4
2.1.2 Establish VO
2max ...4
2.1.3 Heart rate versus workload ...4
2.1.4 Relationship workload to heart rate is unidirectional ...4
2.1.5 Summary ...4
2.2 D
EFINITION OF WORK...5
2.2.1 Power of work ...5
2.2.2 Predictability ...5
2.2.3 Pedaling technique ...5
2.2.4 Cadences’ relation to work ...5
2.2.5 Inertia of the flywheel ...5
3 MEASUREMENT ... 7
3.1 M
EASUREMENT SETUP...7
3.1.1 Mathematical model...7
3.2 M
EASURING A TEST SUBJECT...9
3.2.1 First 30 seconds ...9
3.2.2 Next 30 seconds ... 10
4 CONCLUSIONS ... 12
4.1 M
EASURING WORK... 12
4.2 B
IOLOGICAL WORK VERSUS WORK ACCORDING TO PHYSICS... 12
4.3 F
UTURE ENHANCEMENTS... 12
APPENDIX: POTENTIAL USE OF RESULTS ... 13
A.1 P
ROFILING THE HEART... 13
A.1.1 Max heart rate (MHR) ... 13
A.1.2 80% of MHR ... 13
A.1.3 60% of MHR ... 13
A.1.4 90% of MHR ... 13
A.1.5 Resting heart rate ... 13
A.1.6 Threshold terminology ... 14
A.1.7 Work load response (WLR) ... 14
A.1.8 Heart rate variability ... 14
A.1.9 Recoverability ... 14
A.1.10 Heart drift ... 15
A.2 T
ESTS TO PROFILE THE HEART... 15
A.2.1 Sub max test with constant resistance ... 15
A.2.2 Sub max test with constant cadence ... 16
A.2.3 Establishing the 80% threshold ... 16
A.2.4 Establishing the WLR ... 16
A.2.5 Relating the profile to gym and consumer product ... 16
A.3 U
SING THE PROFILE TO ADJUST TRAINING AND TESTING... 16
A.3.1 Comparing test subjects ... 16
A.3.2 Measurement of fitness ... 16
A.3.3 Improving work load response (WLR) ... 17
A.3.4 Heart drift ... 17
A.3.5 What is the heart rate a product of? ... 17
REFERENCES... 18
3
1. Introduction
Over 60 years have passed since Per-Olof Åstrand published his “Experimental studies of physical working capacity in relation to sex and age.”[1] that today still is the basis of much research and training. His theories and simple methods have proven useful for many years, but the advancement of methods and analysis of results have not been at the same pace as the development of technology of the equipment that could be used. Especially the development of computer science opens many possibilities to measure the work performed on an ergometer.
1.1 Objectives of this report
The author of this report has during since 1990 at different times been involved with Dr Paul Balsom with choices of technology to measure physiological data during training. One project was part of Dr Balsom’s doctoral thesis in 1995 [2], where the author of this report, through his business TenFour Sweden AB, supplied technology and software.
This report will summarize the evolvement of methods and techniques used for testing and training. In research, advanced and expensive test equipment is most often used. It would be optimal to use less advanced equipment for training, but still be able to get indications as to what the tests would show if using more advanced equipment. It is important from a motivational point of view, to give accurate feedback to an athlete and coach, even if the test equipment is not the most advanced.
Secondly this project will analyze the approximations made today in testing methods, and Dr Balsom’s doctoral thesis explain what is important to consider when interpreting the results from tests. Different test equipment will provide different values, and it is important to compare apples with apples. It is also important to find what results are important for what is being tested.
As a conclusion this report will offer some suggestions for methods and technologies that could be used.
Most biometric data are compared from time to time with the same individual. There are some attempts to compare an individual to another individual, and the report will analyze if the proposed methods could be used for that, and if so, how.
1.2 Limitations
This report will not attempt to define the term fitness but will define what biometric data can be used to describe properties that have some relevance to what is typically considered fitness.
2. Background
In sports and athletics, there has always been an interest in being able to improve the capabilities of doing as much work as possible, for as long time as possible and sometimes with the additional requirements as speed and precision. Today, measuring a person’s performance is also important in looking at public health.
Because of our new lifestyle, sitting down doing very little physical exercise, we also need to go to the gym, or do other physical exercise.
2.1 Measurement of fitness, stamina or condition
Per-Olov Åstrand and Irma Rhyming [1,3] were two of the pioneers in this field. One of the more
fundamental assumptions is that oxygen is a good method of establishing the energy consumed while doing exercise.
2.1.1 VO
2max
If a person has a high level of oxygen consumptions, it can be concluded that he can perform a lot of work.
It has also been a belief that by doing different type of physical exercise, one can increase the maximum amount of oxygen being consumed, increasing the VO2max. To make VO2max more comparable between people, one often divides VO2max with the person’s body weight.
2.1.2 Establish VO
2max
To test true VO2max, one needs expensive equipment and the test must be performed in a way that the test subject reaches total exhaustion. P-O Åstrand developed together with his future wife Irma Ryhming in 1954 [3] a sub maximum test that estimated the VO2max, without expensive equipment. Tests based on their research is often called “Åstrandtest” and is simple, but it has some approximations that limit the accuracy.
2.1.3 Heart rate versus workload
One of the more fundamental principles established by Åstrands is that the heart rate measured in beats per second, is linear to the work being performed in a region where the body is primarily doing aerobic work, meaning that the muscles have enough oxygen, and do not produce lactic acid.
The simplified test only measured one value of heart rate, at a certain load. One is instructed to select a load that is appropriate for the person. When we in 2006 made some tests on a ergometer, we realized that more data points would be able to tell if the tests were done at an appropriate level. If three data points would form a straight line, one could conclude the tests were done in the appropriate intensity. By gradually increasing the intensity, one can also find at what heart rate the linearity is broken, and thereby establish the threshold when the lactic acid starts to form, because of an anaerobic process.
In 2012, Elin Bak Ekblom suggested an improvement of the simplified test [4,5], to include two data points, and thereby establish the slope of the linear relationship. This is in line with the enhancements of the tests that we had considered in 2006, but still does not take away some of the uncertainties that multiple points of data would mitigate.
2.1.4 Relationship workload to heart rate is unidirectional
Another complication with looking at the heart rate is that it is basically impossible to estimate the work, even if the heart profile is known, and the heart rate curve is known. Yet many try to estimate the work accomplished by looking at a heart rate curve. It is however possible to estimate a heart rate curve, if the person’s heart profile is known, and the profile of work is known.
2.1.5 Summary
Because the heart rate is only linear in a fairly small interval, about 20 bpm, it is better to use testing methods that vary in power, so that the heart rate becomes the same, from one time to another. By measuring the power to produce the same heart rate, one has a much bigger interval of linearity. If measured power is 110% compared to a previous test, one can conclude that the fitness has increased by 10%.
5
2.2 Definition of work
The biggest challenge with performing simplified tests is to understand what one really is measuring, and how accurate it is being measured. Often it is attempted to estimate the work performed by measuring one thing, but assuming the other factors are irrelevant. What might be worst is that what is considered work according to world of physics, might be different from how a human experience it. If you for example hold a weight in the air in a fixed position, you perform no work according to physics, but after some time your heart rate goes up, and you get tired.
This uncertainty has made most tests restricted to try to keep everything that is not measured constant.
Already in 1991 we found how important it was to reduce the variability in the tests. During the years we have also looked at what has been considered measured, but when looked at it more closely, might not have been measured in the right way.
2.2.1 Power of work
A person tested on an ergometer is often measured by some know force applied in some form, multiplied with the cadence, and a factor specific to the ergometer to make the measurement in Watt. An elite bicyclist can for example “put” 500 W into a bicycle for a longer period, while a “normal” person might be able to
“put” only 150 W into a bike for a longer period. If we take the example with 150 W, it means that the 9 kJ in one minute, or 270 kJ in 30 minutes. On bikes in a gym, this number is often translated to kcal, and the number on the display would say that the exercise was at 70 kcal, which is not a lot. More than likely, if the bike shows how much exercise has consumed in energy, it would be probably showing around 300 kcal. It is a common belief that the effectiveness in terms of energy being put into the bike is about 20-25%. One can speculate as to what the other energy is used for, and some tests the author has done indicate that just lowering the saddle will create a different heart rate for the same work load measured in the bike.
2.2.2 Predictability
Another troubling thought is how the efficiency varies with the work load. In other words, are we really measuring energy consumed in relationship to heart rate? Some research has established that there is a difference between calculated energy “produced” in a rowing machine, than a test bike. The author believes that a lot of this could be explained by the changes of efficiency, and that the total energy consumed if these cases could predict a heart rate. On the other hand, it is probably not possible to estimate the energy consumed based on the heart rate curve alone.
2.2.3 Pedaling technique
Looking at the results of the tests was helpful in understanding the true work performed by the person. The person was instructed to use different cadence in a certain pattern. Measuring the actual cadence compared to instructed cadence showed some differences. More importantly, the variation of force in the chain was considerable. For an elite cyclist, it is not a surprise that the more evenly one can use “pedal force”, the more effective the bike moves forward. That is why professional bikers use clips to fasten the shoes in the pedals, to not just push down, but also forward, backwards and upwards.
2.2.4 Cadences relation to work
From the tests, one can suspect that the higher the cadence, the smaller the difference is between bikers.
This would indicate that 80 cadences might not be exactly 33% more work than 60 cadences. On the other hand, if the work load in the bike would be 0, for example disconnecting the chain from the bike, a person at 80 cadences would get tired more quickly than a person at 60 cadences. In order to establish the true factor, one would need to find other ways, more expensive, to measure energy consumed, but it is to simplify the picture too much to say that cadence, no matter what technique used, is always linear to total work load. This has in later years been confirmed in research [6]
2.2.5 Inertia of the flywheel
The test made in 2006 also showed, when starting to look at energy required to change the cadence, that the inertia of the flywheel of the bike must be considered. In some of the tests, short intervals of 5 seconds were being used where flywheel resistance was kept constant, but cadence was increased from 60 to 80.
The first model assumed that the work load during those 5 seconds were 33% higher. During the first second, the force used to increase the speed was much higher, making the total work load much higher for
those five seconds. During the next 25 seconds, when the cadence was supposed to go back to 60, the person got some extra rest, while the wheel slowed down. In other words, the work load profile during those 5 seconds is very different than a “square curve” of 33% higher workload.
The tests made in 2006 did not test the effects of the flywheel in detail, but it is clear that the complexity becomes higher, if shorter sprints are included. The manufacturer Monark has an ergometer that does take the inertia of the flywheel into account.
7
3 Measurement
As a physicist it is easy to lose hope that anything can be accomplished in a world with so many
uncertainties. By understanding the scope of these uncertainties, it is however possible to relate this to what doctors and coaches are really looking for. This project will explain how physics can be used to understand how best to perform repeatable results.
As mentioned in the introduction, the report is not trying to define fitness. However, it is interesting if certain properties of the heart could be measured, and later be used to predict a heart rate curve. For a trainer, physician or even the individual, it is desirable to train between different thresholds. A heart patient will have some desired curves, a person fighting obesity will have another, and an elite ice hockey player a third. Because of the Work Load Response (WLR) property, it is very hard for a person while training to adjust the work load to achieve a specific response.
This paper is focused on what happens in probably one of the most controlled environments, an ergometer.
It is basically the same equipment used by P-O Åstrand. Even if the ergometer is highly controlled, there are still some environmental factors that should be considered.
3.1 Measurement setup
In 2006 the author performed experiments to more accurately measure the actual work put into the ergometer. It was believed that commercial ergometers from manufacturers such as Monark measure work accurately, but it would be nice to also use a consumer product, affordable for wider testing. Most high- quality ergometers today still use a weight basket, that can be loaded with certain weights, that creates a certain resistance on the flywheel. There is also equipment available today to measure the force produced in the pedal shaft, with tension meters. A simpler approach used by the author was to measure the tension in the chain driving the flywheel. By displacing the chain a small amount with a wheel, and measuring the force pushing the wheel to make the chain straight again is a linear function to the tension in the chain. In this way the work and effect could be measured.
R=Leverage distance to force meter (S) a= differential from straight chain L= Distance from center to pedal
S=Force meter d= distance from tangent of pedal
cogwheel to measurement point
l= Radius pedal cogwheel r= Leverage distance to center of
measurement wheel
3.1.1 Mathematical model
Force meter (S) measures ”weight” in the span 0-5 kg and generate by an amplifier a linear voltage between 0 till 5V. Weight of the leverage rod generates an output of 750 mV at rest.
F (force in chain) can be calculated from f (force pushing down the measurement wheel):
F=(f/2a)*sqrt(a^2+d^2) ˛ (a<<d) ˛ F=fd/2a fv (force measured in force meter) is: fv=fr/R Fv (force pressing on pedal): Fv=Fl/L
Mv (Weight on pedal in) and mv (weight measured in tensiometer): Fv=Mvg, fv= mvg This combined: F=mvgRd/r2a
And: MvL/l=mvRd/r2a ˛ mv= MvLr2a/Rdl ˛ mv= (2Lr/Rdl)Mva
with l=0.11m, L=0.177m, d=0.187m, R=0.71m and r=0.36m ˛ mv= 8.73Mva
If pedal weight (Mv) of 100 kg is to be measured (mv) as no more than 5kg the displacement (a) should be no more than 5.7 mm
If k = mv/a ˛ k=8.73Mv At Mv=2.8kg
k is 24.4kg/m or 24.4 mV/mm in the weight measurement device where 0-5kg is calibrated to 0-5V To verify the linearity, Mv was kept constant and a was varied
Displacement (a) of chain in mm on X-axis
Y-axis is mV (820-1020), which represents an mv of 0,82-1,02 kg. The load on the pedal Mv is 2,8kg. The theoretical k = 24,4mV/mm (yellow). Least mean square gives k = 22mV/mm (pink).
9
3.2 Measuring a test subject
Date: 2006-10-02 Performed by Göran Fransson Test subject: Göran Fransson Sigtuna, Sweden
The author, which is far from an elite athlete, put himself through a test, measuring the force with a sample rate of 1kHz. Number on x-axis represents sample count. First observation is that the force on the pedals varies during a revolution with two tops per revolution. In bicycling, the number of revolutions per minute is usually referred to as cadence.
The test bike is of type “spinning”, which means that the flywheel is heavy, with a large inertia.
3.2.1 First 30 seconds
The curve indicates that the cadence increases for the first 10 seconds and the force is fairly constant during the first 20 seconds, and the cadence is also constant between 10 and 20 seconds (60 rpm). At 20 seconds the force is temporarily increased hitting 3 V, which represents a weight of 45 kg on the pedal. After this effort the cadence is kept steady with the same average force applied, but because cadence is higher (90 rpm) work performed is approximately 50% higher.
3.2.2 Next 30 seconds
During the next 30 seconds, the cadence is kept at 90 rpm. Between second 32 and 35 an attempt to apply force more evenly is made, as professional cyclists do. Same work is performed, but with much lower top force and bottom force. At 43 seconds the force breaking the flywheel is increased and more work need to be performed to keep cadence constant. At 53 seconds the braking force is reduced again on request of the test subject, in order to be able to maintain cadence.
Zooming in on 30-34 seconds shows the difference in force applied. The firxt second, there is a force between 0 and 200% (0.75V is calibrated 0N applied). During more even distribution, it is 50%-150% of average force.
11
In preparation for the test, an electronic filter was designed to filter out “noise” from the uneven structure of the chain. Because of the sampling frequency of 1kHz, it shows that it is by looking at the unfiltered value, it is also possible to with high precision to measure the cadences with only measuring the “noise”
from the chain. Measurement of changes in speed of pedal movement could be used for calibration.
The averages of 0.1 second clearly shows the variation of force applied, while the 1 second average shows no difference between the period of “normal” biking and “professional” biking.
4 Conclusions
The measurements made by a very simple device shows the magnitude of the issues to take into consideration. In order for a ergometer to be similar to a real bicycle, the flywheel needs to have considerable inertia. This means that work from a theoretical calculation could be considerably different that work experience by the test subject.
4.1 Measuring work
In many test situations, the subject is asked to cycle at a certain cadence under a certain resistance or load.
It is assumed that the subject stays close to the cadence predicted. It is also assumed that the force that is the resistance to the flywheel is constant no matter what cadence is maintained. During the tests performed, it was possible with one device, a tensiometer of the chain, to measure both cadence, and force applied with a resolution of 1kHz
4.2 Biological work versus work according to physics
Physics defines the term work as force multiplied by distance. This can be calculated by measuring the force and cadences as in this example.
The heart rate is also shown to have a linear reaction to oxygen consumed in a certain interval, which in terms also has a relationship to energy consumed by the muscles. It is however only within certain parameters that one can say that the heart rate is linear to the work performed in an ergometer.
The equipment used in the tests above show that the force applied to the flywheel is the same for cadence 60 as cadence 90. This is often used in tests to calculate the work performed to be the same. It is also probably true in many cases, but the variation in speed of the flywheel is not calculated.
It is believed that the variation of speed in the flywheel, will change the biological work. Therefore a professional cyclist try to apply as even of a force as possible. Another way to try this is to first use cadence 60, and then double the resistance and lower cadence to 30. If it was not a difference in work load, there would be no reason to have gears on a road bike.
4.3 Future enhancements
The measurement device used is believed to measure two very important aspects of work performed, force and distance. It also showed a big variance in force applied, and the energy needed to change the speed of the flywheel is not neglectable.
By measuring the change in the angular velocity of the flywheel, it is believed that even more accurate results of performed work would be possible. Traditionally, speed of bikes and cadences is measured by lap time of the wheel. With current technology, especially accelerometers, it is believed that the motion pattern can be analyzed for change in speed (acceleration) which could be used for measurement of force applied.
Measuring the acceleration of the flywheel could be used as the sole measurement, assuming the breaking force of the flywheel is known. The breaking force of the flywheel could be measured by measuring the retardation of the flywheel with no force applied. This would also include all other frictions such as chain and ball bearings.
This could in theory also be used on a road bicycle, to measure resistance on the road, where the body weight is representing most of the inertia. These advanced methods are however outside the scope of this report.
13
Appendix: Potential use of results
The objective of this report was to analyze what aspects of work an ergometer tests, and how that relates to expected heart rate which is often used to calculate fitness. Many new aspects of heart rate response was discovered during the 25-30 years work has been done with Dr Paul Balsom. Research done in this field has also started to see some of these. Further research in the cross section between the physics discussed in theis report and current research in physiology. This appendix tries to summarize some of those aspects.
A.1 Profiling the heart
For the purpose of describing a person’s heart, the term “profile” will be used, that includes properties of the person’s heart. Some properties seem to be genetically based while others are environmental. Some of the environmental properties seemed to be possible to change with the help of exercise, and some are possible to change with medication. For the purpose of treating different heart diseases, research has been made to try to describe the heart with a mathematical function. It is commonly believed it is a differential equation with 15 to 20 dependencies. This report will not go into that level of detail but will highlight some that the author believes could be relevant for the scope of this paper.
A.1.1 Max heart rate (MHR)
One of the most known properties is what is termed max heart rate. It varies from person to person. It is uncommon to have a max heart rate of 220 bpm, and it is uncommon to have it lower than 160 bpm. There is no research known to the author that indicates that the heart rate indicates level of fitness, and there is no research known to the author that would indicate that the max heart rate can be increased. There are a number of “age formulas” that try to estimate the max heart rate. The most commonly used formula is 220 minus the age. That would indicate that the max heart rate would drop 1 bpm per year. The author has an estimated max heart rate of between 195 and 200 bpm. This paper shows that there are better values than max heart rate to use as properties in the heart profile. During the 25 years of being involved in research, the author has continuously checked his profile, and there is not a decrease of 25 bpm during these 25 years. It does not prove that that there is no change of max heart rate, but it gives clear guidance to not use the age formula.
A.1.2 80% of MHR
The reason max heart rate has a lot of focus is that it is believed that at approximately 80% of heart rate, there is a change in how energy is produced in the muscles. Above 80% there is a buildup of lactic acid, and the process is often referred to as anaerobic. During a constant work load, that has the heart working above 80%, the heart rate will not stay constant. After doing work in that range, the heart reacts different during the exercise, indicating a “back log” of oxygen levels. Since the heart is a muscle, that also needs oxygen, anything over 80% is a negative spiral.
A.1.3 60% of MHR
There is a similar change of processes around 60%, where it is believed that under 60% the body has time to use fat as “fuel”. Between 60% and 80% the fuel is mainly carbohydrates, which burns “faster”. For the purpose of this paper, it is not interesting to know the exact chemical process, but it is common belief that the relationship between work load and heart rate is most linear in the span of 60% and 80%.
A.1.4 90% of MHR
A third level that is often mentioned is approximately 90% of MHR. A normal person can only perform work above 90% for maybe 30 seconds. Above 90% there is so much buildup of lactic acid, and other processes, that makes the person “hit the wall”. It is believed that certain training can extend the period of work. An example of this is an elite 400 m runner.
A.1.5 Resting heart rate
Lastly there is a level of heart rate that often is mentioned as possible properties in a profile, the resting heart rate, that is normally between 50 and 70 bpm. The resting heart rate is by most not considered to be of interest in terms of physical fitness. It seems to vary more based on psychological factors, and health. Stress and other emotional distress can often be detected. Some research shows that the variability of the resting heart rate during a period of a few minutes at rest could indicate a fitness level, but not the level itself.
A.1.6 Threshold terminology
To complicate things even more, as written above, it is only approximately at 60%, 80% and 90% that these changes happen. They are often referred to as thresholds. Since they are only approximately a fraction of max heart rate, which is also an approximation, the author believes that it is better to use methods to establish the bpm that represents the threshold. For the sake of not introducing new terminology, the report refers to the thresholds as 60% threshold and so on, but there are some suggestions on how to establish them, without first having to establish the max heart rate.
A.1.7 Work load response (WLR)
Other properties that seems to be personal in the heart profile is the response to work load changes. Since the heart rate is among many things controlled by the oxygen level in the blood, increased work load will not be detected immediately. If the workload is increased while on an ergometer from cadence 60 to 80, it is commonly believed that the workload increases by 33%. Different individuals will react more or less quickly to this change. Most people seem to have adjusted within 60 seconds, and it is likely that this property could change based on level of fitness. In this report, this property will be referred to as number of seconds, and we will term it “work load response” (WLR).
A.1.8 Heart rate variability
Another property that can possibly be related to the WLR is the heart rate variability. It is a fairly new property that is being looked at, and it measures the time between beats, and it is believed that high variability might be a measure of good fitness. Therefore it can be related to WLR, but it is outside the scope of this paper.
A.1.9 Recoverability
A property of the heart that is often talked about, but seldom quantified in numbers, is the recoverability. A common way to measure it is to measure the time it takes for a person’s heart rate to reach some level that is considered a recovered state. The 60% threshold could for example be used. What this report highlights is that the recoverability also depends on the entire exercise’s load profile.
15
A.1.10 Heart drift
One property of the heart’s behavior that sometimes is used for the unexplainable is what is called “heart drift”. It is easy to observe that if a person performs two sessions of 10 minutes each right after each other, the second session will have a higher heart rate. The tests show that there might be some correlation between recovery and fitness, and it shows that heart drift could be predicted in many cases. More research has been done after the tests that are in this report [7-10]
This diagram shows 3 tests performed by Dr Paul Balsom at three different times, with a few weeks in between. A fourth test was done by author (green), and the predicted heart rate is followed fairly well
A.2 Tests to profile the heart
The “Åstrandtest” suggests measurement of the workload at a heart rate between 130 bpm and 160 bpm.
Unfortunately, many subjects will be above their 80% threshold at 160 bpm. A large majority will be in the linear zone of aerobic process. This test does not require an ergometer, but an ergometer will give more data, that will be useful for further analysis. If an ergometer is not used, it is important to keep the same resistance for the remainder of the test.
A.2.1 Sub max test with constant resistance
The first test that is useful to perform is to start the exercise at a load that represents 120 bpm of heart rate, at cadence of 60 rev/min. After 90 seconds of the test, record the heart rate. After additional 30 seconds, measure the heart rate again, and increase cadence to 65 rev/min. Repeat the procedure and increase cadence with 5 rev/min, until the 90 second heart rate is more than 3 bpm lower than the heart rate measured 30 seconds later, or if the subject is starting to feel lactic acid or other strong fatigue. One can also hear on the persons breathing that they are going over the 80% threshold. This test is supposed to be a sub maximum test, the person should not be very tired at the end of this test.
A.2.2 Sub max test with constant cadence
As an alternative to increasing cadence if there is an ergometer with defined weights, adjust the weights until the heart rate is around 120 bpm at cadence of 60 rev/min. Increase weight with approximately 10% of weight that gives a heart rate of approximately 120 bpm, instead of increasing cadence.
A.2.3 Establishing the 80% threshold
The highest stable heart rate could for this first test’s purpose be considered the 80% threshold. If the heart rate is being recorded every second with the help of a heart rate monitor, one can probably detect a
“threshold” in the graph between the last stable heart rate, and the next measuring point. The heart often avoids going over this threshold for 5 to 10 seconds extra. Once it is through the threshold, it increases the heart rate, without an increase in load.
By plotting the curve of cadence or weight, or even better the power expressed in Watt, to heart rate, there should be a linear relationship. If some of the last point of testing falls below the line, more than likely, the person went through the 80% threshold before the first point below the line.
A.2.4 Establishing the WLR
Another useful property to take from this simple test, if heart rate is measured once per second is to measure the slope of the curve as the heart increases its bpm, directly after increased load. This slope is representing the WLR specified above. This is more investigated in later tests.
A.2.5 Relating the profile to gym and consumer product
With the help of this test, a maximum heart rate can me assumed to be 125% of the value established as the 80% threshold. As mentioned earlier in this report, some of these numbers are only estimations, but for the purpose to what they are used, it is a good idea to consider this to be the maximum heart rate. If this number is used in any device or training equipment, the feedback on performed work in different zones for example will be calculated properly.
A.3 Using the profile to adjust training and testing
By knowing the 80% threshold, and the maximum heart rate estimated above, exercise and testing can be performed with much higher accuracy. Exercises and tests should be designed to also include a warmup period to adjust the session to the same level of heart rate at 70% of maximum. If the load or pace that produce this heart rate is lower one day, it is probably because the subject is not at the same level of performance.
There could be many different reasons for this, and it is outside the scope of this report to go into details of all possible reasons, but some reasons could be an infection, not recovered from earlier exercise, not enough sleep, or low on energy or water as resource. It is important to use the heart to adapt the level of training already in the warmup.
A.3.1 Comparing test subjects
By always starting an exercise program at the same level and adjusting the program on the feedback as to at what percent of the designed warmup load is producing the desired heart rate, the predictability of the entire exercise is very good. In 2015 and 2016, some tests were performed to test this theory. A training program was designed by Dr Paul Balsom that has a warmup period, followed by test periods. The results of this shows that, as long as the load profile of the exercise is kept constant, the heart rate response is predictable, not just for one person, but also between persons.
A.3.2 Measurement of fitness
One of the most interesting takeaways from this is that if one measures a person’s work load at for example 70% of max, one can predict the work load at other levels of heart rate. The work load at 70% of maximum heart rate could therefore be used as a measurement in how a person’s capacity changes, as long as other aspects of the tests are kept constant. This report suggests that by measuring the percentage difference between two, in time separated, capacity could be a measurement of “fitness”. The same person on the same equipment is probably performing that much better, without any improvement in technique.
17
A.3.3 Improving work load response (WLR)
Another value that could be used to indicate fitness is the ability to respond to changes in workload. By changing the workload in a controlled fashion, one can measure whether the response time to changed work load goes down. By having quicker response to increased work load, it is likely that the person also
recovers faster. With certain exercises, probably “interval training”, one can improve a person’s WLR.
A.3.4 Heart drift
In doing exercise with heart rate above 80% threshold, it is likely that it creates what is sometimes referred to as heart drift. It is also related to how well a person recovers, but it seems like once a person has been above the 80% threshold, he/she will never get rid of the heart drift. It could be related to the ability to withstand lactic acid. By adjusting the work load in the beginning of the exercise to the same heart rate every time, the heart drift could possibly used as a measurement of resistance towards lactic acid, which is important in sports where lactic acid is impossible to avoid.
A.3.5 What is the heart rate a product of?
The most important lesson learned while doing experiments with ergometers and heart rate for this report is that the heart rate at any moment, is dependent not on the work load for that moment, but a result of the entire exercise, including what level of heart rate as the exercise begins. This also shows the importance with warm up, and cool down, and even to keep the heart rate at a certain level even during “rest” in the middle of an activity. If you during the rest period sit down or lie down, the heart rate goes down, which slows down the recovery.
References
1. Åstrand, P.-O (1952) Experimental Studies of Physical Working Capacity in Relation to Sex and Age. Copenhagen: Munksgaard
2. Balsom, Paul D & Karolinska institutet. Dept. of Physiology and Pharmacology (1995). High intensity intermittent exercise: performance and metabolic responses with very high intensity short duration work periods. Karolinska Institute, Stockholm ISBN: 91-628-1490-7
3. Åstrand PO, Ryhming I (1954) A nomogram for calculation of aerobic capacity (physical fitness) from pulse rate during sub-maximal work. J Appl Physiol 7(2):218–221
4. Ekblom-Bak E, Bjorkman F, Hellenius ML, Ekblom B (2012) A new submaximal cycle ergometer test for prediction of VO2max. Scand J Med Sci Sports 24(2):319–326.
doi: 10.1111/sms.12014
5. Björkman, F., Ekblom-Bak, E., Ekblom, Ö. et al. (2016) Validity of the revised Ekblom Bak cycle ergometer test in adults. Eur J Appl Physiol (2016) 116: 1627. doi: 10.1007/s00421- 016-3412-0
6. Mazzoleni M, Battaglini C, Martin K, Coffman E, Ekaidat J, Wood W, Mann B (2018). A dynamical systems approach for the submaximal prediction of maximum heart rate and maximal oxygen uptake. Sports Engineering. 21. 31-41. doi: 10.1007/s12283-017-0242-1.
7. Stirling JR, Zakynthinaki MS (2009) Last word on point: counterpoint: the kinetics of oxygen uptake during muscular exercise do/do not manifest time-delayed phases. J Appl Physiol 107(5):1676 doi: 10.1152/japplphysiol.00896.2009
8. Stirling JR, Zakynthinaki MS, Billat V (2008) Modeling and analysis of the effect of training on _VO2 kinetics and anaerobic capacity. Bull Math Biol 70(5):1348–1370. doi:10.1007/s11538008- 9302-9
9. Stirling JR, Zakynthinaki MS, Refoyo I, Sampedro J (2008) A model of heart rate kinetics in response to exercise. J Nonlinear Math Phys 15(3S):426–436. doi:10.2991/jnmp.2008.15.s3.41 10. Stirling JR, Zakynthinaki MS, Saltin B (2005) A model of oxygen uptake kinetics in response to
exercise: including a means of calculating oxygen demand/deficit/debt. Bull Math Biol 67(5):989–
1015. doi:10.1016/j.bulm.2004.12.005
TRITA -SCI-GRU 2019:381
www.kth.se
