Designing a Portable VO2max test


Although there currently exists equipment to measure cardiovascular fitness and aerobic endurance, it is not readily available to athletes or personal trainers due to its large size and bulkiness, see figure 1.  For example, if endurance athletes want to know their VO2max, they must go to a lab and pay for a test.  This is both expensive and inconvenient. As such, a need exists for a more portable VO2max test that is user-friendly and available for purchase on the retail market. Designing a portable piece of equipment to measure aerobic endurance utilizing this technology would benefit many people in their fitness training.  One of the most important design criteria when designing a VO2max test is the dimensions of the tube that carries the inhaled and exhaled air, particularly, the diameter and length, as can be seen in figure 1. This is because the dimensions of the tube are directly related to type of air flow (laminar vs. turbulent), and it is crucial that the air flow remains laminar when entering the syringe for analysis1. If this equipment was redesigned to be more compact and portable, the dimensions of the tube would also have to be adjusted.  Therefore, if one were to redesign a modern metabolic cart on a smaller scale, it would be necessary to calculate the new length and diameter of the tube, which could be accomplished using Reynolds number. Solving for this value would thereby enable proper design of a portable, compact and user-friendly VO2max test, beneficial for personal trainers, athletes, and health professionals.

Figure 1. VO2max measurement through a modern metabolic cart during a graded exercise test on a treadmill.


VO2max is simply a numerical measurement of your body’s ability to consume and utilize oxygen during intense exercise. It is generally considered to be the best indicator of cardiovascular fitness and aerobic endurance. During a VO2max test, one is hooked up to a breathing mask while exercising on a treadmill at an intensity that increases every few minutes until exhaustion. While exercising, the volume and gas concentrations of inspired and expired air is measured. Generally, a higher VO2max indicates better aerobic fitness because it means that your body can take in a large amount of oxygen and successfully deliver it to your muscles, allowing you to run faster for a longer period of time.  Thus, after a subject takes a VO2max test, he leaves the lab with a good idea of his current fitness level. Athletes are particularly interested in knowing their VO2max because it is a scientific way of judging their progress and provides accurate results that reflect their aerobic fitness. But another demographic group who could benefit from this new device would be cardiac patients, as well as ICU patients. Critical illness can significantly affect metabolism, so an accurate measurement of aerobic fitness can help determine the energy requirements of ICU patients. A precise calculation of energy expenditure may prevent overfeeding or underfeeding. Therefore, portable VO2max tests would also benefit hospital personnel and allow them to easily transport the device, making it more convenient and readily accessible to all patients.

In the photo above, you can see that there is a tube attached to a mouthpiece worn by the man performing a VO2max test. This tube is typically very long; most tubes used with today’s metabolic carts are approximately 2 meters long or more2. A newly designed and more compact VO2max test would most likely be equipped with a much shorter tube. Therefore, other adjustments in dimensions, such as diameter and length, would need to be made to ensure laminar slow. Laminar flow of air into the metabolic cart is important because it allows for the most accurate analysis of the air being exhaled3. In order to measure VO2max, three parameters must be measured by the VO2max cart: 1) the expired ventilation rate (breathing rate * amount of air expelled), 2) % CO2 expired, and 3) % O2 expired. Therefore, laminar flow of expired air into the metabolic cart is especially important for measuring these parameters.

The nature of a Newtonian fluid flow in a pipe depends on the pipe diameter, the density, the viscosity of the flowing fluid, the length of the tube, and the velocity of the flow. Since the air we expel is a Newtonian fluid, we can use an equation involving these variables to determine whether the flow through a tube is laminar or turbulent. Flow in pipes is considered to be laminar if the Reynolds number is less than 2300, and turbulent if the Reynolds number is greater than 4000. Therefore, we can use the dimensionless Reynolds number, a ratio of dynamic forces of mass flow to the shear stress due to viscosity, to solve what the dimensions of a tube for a metabolic cart should be in order that laminar flow is ensured.

Reynolds number: Re = pvd/u


        p = density of fluid [kg/m3]    v = velocity [m/sec]


        d = diameter [m]       u = dynamic viscosity [Pa*sec]

First, it is necessary to solve for the diameter of the tube, which will be the unknown in the equation Re = pdv/u.  Once the diameter is solved for, the hydrodynamic entrance length will be solved for. The length of the hydrodynamic entry region along the pipe is called the hydrodynamic entry length. It is a function of Reynolds number of the flow. In the case of laminar flow, this length is given by: Lh,laminar = (.05)*(Re)*(d). The length of the tube must at least be as long as the hydrodynamic entry flow, in order to have fully developed flow. Typically, metabolic carts are very large, with very long tubes, but if this system could be reduced, to a very small box where all of the gas analysis would take place, the user would prefer to be closer to the box and connected to it via a shorter tube.  Therefore, for a design such as this, choosing a tube with the shortest length possible but at least as long as the hydrodynamic entry length would be best.  It is already known that the density of exhaled air is 1.2 kg/m3, the velocity of the air we breathe is 2m/s, and the dynamic viscosity of exhaled air is 1.983*10-5 Pa*s 4. Therefore, knowing these three variables, 1) viscosity 2) velocity, and 3) density, setting the Reynolds number to be less than 2300 and plugging these values in will allow us to solve for what the diameter of the air flowing through the tube in these conditions would be.  After the diameter is solved for, the length can be solved for by keeping the same values for density and viscosity, and using the hydrodynamic length equation, Lh,laminar = .05*Re*d.  This length would be the minimum length possible that still ensures laminar flow through a tube.


Re = pvd/u and Re must be less than 2300 for laminar flow, so:

[(1.2 kg/m3)*(2 m/s)*(d)] / (1.983*10-5) < 2300.

Solve for d:

d < .02 m

We now know that the diameter must be less than 2 cm, to ensure laminar flow. If we choose 1cm to be the diameter of the tube being designed, it is then possible to use the hydrodynamic length equation to solve for what the minimum length of the tube should be.

Solve for Hydrodynamic Length:

Lh,laminar = .05*Re*d

Lh,laminar = (.05)*(2300)*(.01m)

Lh,laminar =1.15m

From these calculations, the optimal dimensions of a VO2max testing device tube which ensures laminar flow would be a diameter of 1cm and a length of 1.15m. However, these values are approximate and were obtained by making many assumptions, and basing values off of already existing studies. In order to be more precise, velocity could be measured in a separate experiment at varying exercise level intensities, because 2 m/s may not be appropriate for all users of this device. Additionally, there are assumptions made from using the Reynolds equation, including assuming a constant viscosity, and negligible inertial and body forces.
References and Recommended Further Reading

[1] Respiratory analyzer for exercise use

[2] A metabolic cart for measurement of oxygen uptake during human exercise using inspiratory flow rate.

[3] Galdi, Giovanni, Ed., Heywood, John, Ed., and Rannacher, Rolf, Ed. Fundamental Directions in Mathematical Fluid Mechanics. Birkhauser Verlag, Basel, 2000.

[4] Measurement of Lung Tissue Viscous Resistance Using Gases of Equal Kinematic Viscosity

[5] Metabolic cart for Critically ill patients

How It Works: Heart Rate Monitors

Recommended Further Reading 

Wearable Photoplethysmographic Sensors—Past and Present

Optical Heart Rate Monitoring: What You Need to Know

Heart Rate Monitors – How do they work?

Best heart rate monitors and HRM watches

Five Challenges of Optical Heart Rate Monitoring

Wearable Device Technology for Accurately Monitoring Heart Rate from the Wrist

ECG vs PPG for heart rate monitoring which is best?


The heart’s electrical system


Heart rate monitor for swimmers

Heart Rate Monitor
Patent 12459494 Filed on July 2, 2009
Issued on January 21, 2010
Inventors: John Mix and Roar Viala
US Classification: 600/508
20 claims

This invention is an electronic athletic training device which measures heart rate for the purpose of aiding swimmers while training.  The main components of the device include a light sensor that measures changes in light due to blood flow in the skin, a micro-processor that calculates heart rate based on changes in the light detected by the infrared sensor, and a component to convert the output to audio signals representative of heart rate. To use this device, a user would position the infrared sensor near the temple using a clip that is attached to the strap of the user’s goggles. Additionally, the user would wear an earpiece which receives the audio signals. This device also has the ability to be powered by an internal lithium-ion rechargeable battery, be operated with a power button, and store the history of the user’s heart rate during workouts.

I think this invention could be useful for Olympic swimmers as well as ordinary people who are interested in heart-rate-training and enjoy swimming.  For those interested in using this device for heart-rate training under moderate-intensity exercise this could be a very useful device. I think this is interesting because if I were to design a swimming workout based on my target heart-rate I would want to use this device. For swimmers, monitoring and maintaining target heart-rate for aerobic activity can be challenging using a typical wrist watch heart rate monitor, because it requires them to look at their wrist while swimming. I can understand how frequently glancing at a wrist heart rate monitor to get your heart-rate can be an annoyance for a swimmer. Therefore, this invention is novel because it removes that task altogether by providing the user with an audio rather than visual representation of heart rate.

The technology of this device consists of infrared sensors that sit against the skin, and a microprocessor that is coupled to the sensors which calculates the number of beats/minute and generates output signals to an earpiece. The engineering behind this device is based on the principle of measuring the change in light through the user’s skin due to blood flow. Once that information is obtained, it is possible to calculate the heart rate by measuring the background noise with a separate infrared sensor and then subtracting it from the light measured via the infrared sensor at the skin’s surface.  The micro-processor then generates a correction factor for calculating the heart rate based on background noise.  Audio signals are generated through a transducer attached to the ear or temple wherein the transducer communicates the heart rate to the user’s ear where sounds are transferred. Aside from the actual device, the user also has the option of processing workout data from the heart monitor to generate a graphical representation of his/her heart rate on a computer.

Figure 1. device showing infrared sensor and earpiece components of heart rate monitor

This patent search was conducted on Espacenet. The source of this patent can be found here.





Have you ever found yourself at the gym on an elliptical or treadmill wondering if there was better and faster way to do cardio for fat loss? A new style of training known as high intensity interval training (HIIT) might just be your solution. Many fitness bloggers who advocate HIIT say that it is better than moderate intensity steady state (MISS) cardio because it burns more calories in a shorter amount of time as well as increases your metabolism and burns calories even after you are done working out due to something called the EPOC effect. On the other hand, there are some people who say that moderate intensity steady state cardio is better than HIIT cardio because MISS primarily uses lipids as a fuel source, and therefore burns more fat. But is one really better than the other?

In 1996, Dr. Izumi Tabata performed a study on the effects of moderate intensity training and HIIT, in order to better understand which method was more effective for preparing olympic athletes for events. For his experiment, he studied two groups. The first group exercised at 70% of their VO2max  five times a week on a treadmill. He compared this protocol with the Tabata protocol and found that the Tabata group was exercising at an intensity of 170% VO2max.  In the end, the two groups both had increases in aerobic capacity, but when anaerobic fitness was analyzed, the Tabata protocol group increased by 28% while the other group remained the same.  This means that high-intensity interval training actually improves both anaerobic (muscle building) and aerobic (fat burning) body systems, while moderate intensity exercise only improves the aerobic system. Additionally, the Tabata group lost more weight on average and gained more muscle than the MISS group. The results obtained from this study ultimately helped legitimize a movement away from chronic cardio and toward high-intensity workouts.


HIIT is a type of training in which intensity and heart rate is varied throughout a workout, as opposed to MISS which is exercising on a treadmill, elliptical, etc. and maintaining your heart rate around 125 bpm for 30 to 60 minutes. During the high intensity intervals, your heart rate should be around at least 160 beats per minute, and during the low intensity intervals around 100 bpm. A typical HIIT workout might look something like this:

Exercise 1: Push-ups

Exercise 2: Jump Squats

Exercise 3: Burpees

Exercise 4: V-ups

Start with push-ups. Perform them for 20 seconds at a high-intensity. Rest for 10 seconds, and then go back to doing push-ups for 20 seconds. Once you complete eight sets of push-ups, rest for one minute. Next, move on to jump squats and repeat the sequence of 20 seconds on, 10 seconds off. Once you finish eight sets of jump squats, rest for one minute, and then do burpees. After burpees, finish the workout with V-ups.

EPOC: Excess Post-Exercise Oxygen Consumption

Since you burn roughly the same amount of calories during a HIIT and MISS workout, The big debate over HIIT vs MISS cardio for fat loss comes down to how many calories you burn after a workout. Most of the misinformation circulating around HIIT vs MISS cardio is centered around EPOC. This term simply refers to the process of restoring your body to a normal resting state after exercising. During this time, your body uses energy and burns calories while recovering and building muscle. The big debate is whether the EPOC after doing a HIIT workout has significant effects on weight loss or not. One fitness blogger said that “new age Tabata style workouts burn 50-70 calories during a workout and 300-400 post workout over the next 24 hours.” The truth is, you are more likely to burn around 300 calories during a HIIT workout and about 40 after. The claim made above would require an EPOC of over 100%, and since EPOC generally doesn’t surpass 30%, this claim was clearly not based on scientific evidence, and can be very misleading to uniformed readers. One study  reported an EPOC of 25% after a very intense and strenuous high intensity workout and 10% after a moderate intensity workout, but even though high intensity workouts have a higher EPOC than moderate intensity workouts, the amount of additional calories burned due to the EPOC effect is not very significant. It is important to keep in mind that although these numbers may appear to be convincing, the difference in calories burned, is only about 30 calories, which is much easier to achieve simply by dieting.

Even though the EPOC theory turned out to be false after all, one study  did show that HIIT training increases muscle mass and therefore increases the capacity to burn fat, so in the long run, HIIT could actually be booting your metabolism.  HIIT also has a lot of other health benefits to offer. For example, one study found that HIIT training greatly improved cardiovascular endurance and that subjects who went through two weeks of HIIT training experienced a drop in their resting heart rate, indicating better cardiovascular health. Some people forget that their heart is a muscle. If you keep it beating at a constant rate, then it doesn’t have to work harder, and therefore it isn’t getting any stronger. This can be a problem for people who regularly stick to the elliptical or treadmill and never reach at least 80% of their max heart rate.

Overall, there is not a big difference in the number of calories burned between HIIT and steady-state cardio, but HIIT may have some additional anaerobic and cardiovascular health benefits. Deciding whether to do HIIT versus MISS can also depend on a variety of other factors. For example, your diet. If you are on a low carb diet, or are carb cycling, you may want to do a MISS workout on low carb days rather than a HIIT workout because HIIT requires a lot of carbohydrate (glucose and glycogen), whereas MISS primarily uses lipids for energy. Also, if you are doing weightlifting in addition to cardio, MISS might be a better option because HIIT offers some of the same benefits as weightlifting. Another thing to consider is that HIIT is very strenuous, and it may be challenging to jump right into an advanced HIIT workout especially if you are just beginning an exercise program. That being said, if you are the type of person who prefers weightlifting and doesn’t need to incorporate as many body weight exercises into your workout regime to build muscle, then by all means, stick to weightlifting and steady state cardio. However, if you like doing HIIT workouts either because they take less time to do or because they don’t require any fancy gym equipment, that’s also fine. Whatever your personal fitness goals and workout preferences are, the most important thing is always to listen to your body and do what’s best for you.


Questions and comments:

Which do you personally prefer, HIIT or MISS?

If you previously did HIIT because you believed you were burning hundreds of calories post-workout, do you think you will still continue doing HIIT now that you know the after burn effect isn’t true?

Comment below if you’d like to share any thoughts about HIIT or if you have any questions.

Thanks for reading:)


Recommended Further Reading

Metabolic adaptations to short-term high intensity training: a little pain for a lot of gain,

Effect of Exercise Intensity, Duration and Mode on Post-Exercise Oxygen Consumption

Effects of moderate-intensity endurance and high-intensity intermittent training on anaerobic capacity and VO2max

8 Benefits of High-Intensity Interval Training (HIIT)

High-intensity interval training for health and fitness: can less be more?

Two weeks of high-intensity aerobic interval training increases the capacity for fat oxidation during exercise in women