Identify:
One of the major emphases in exercise and athletic training is proper breathing. Should I breath faster or slower? Deeply or shallowly? These are the questions that athletes and gym-goers face every day. And this emphasis on breathing is merited – proper breathing during exercise can better oxygenate the body, which in turn improves endurance, performance, and fat burn during exercise. The problem, though, is that many professional and non-professional exercisers alike do not know how to monitor their breathing during exercise. With the clear benefits of proper breathing during exercise and the lack of athlete experience in monitoring breathing, the need for a device to help monitor breathing during exercise is apparent. One possible device that could be used to monitor an exerciser’s breathing during activity is a strap that wraps around the user’s torso and contains a strain gauge. This strain gauge will measure pressure changes imposed on the strap by inflation/deflation of the torso during breathing, thereby determining the breathing patterns of athletes during activity.
However, designing this device is not a simple task. There are many components that would go into such a device: strap, strain gauge, monitors, and more. Each of these components requires calculations to determine the best type of component to use for the device. One example of this is the process that goes into deciding which strain gauge to use in the system. There are many strain gauges on the market today, but not all of these fit the needs of the system described above. Some strain gauges cannot withstand enough strain to be incorporated in this system. In order to decide which strain gauge is the most appropriate for this system, engineers must solve the problem of determining how much strain the strain gauge will be exposed to when used in the breathing strap and how sensitive their measurements should be.
Formulate:
Before doing any calculations, it is important to understand what a strain gauge is, how it works, and what exactly it measures. First of all, what is strain? Strain is a measure of the amount of deformation an object or material experiences due to an applied force. Strain gauges are designed along this principle of measuring deformation. They can measure either axial or bending strain, as depicted in Figure 1, depending on the type of strain gauge being used.
Figure 1. Common strain gauge configurations for measuring axial (left) and bending (right) strains.
Since the inflation of the lungs will mostly cause axial stretching of the strain gauge, we will look at strain gauges that measure axial strain. When strain gauges are stretched axially, they are displaced. The strain gauge responds to strains with a change in electrical resistance. So, as strain on a strain gauge changes, so does the resistance in the gauge.
One common calculation related to strain gauges is the calculation for gauge factor (GF), represented by the equation:
This relationship can be used in our case to help decide which strain gauge to use in the strap design based on gauge factor, changes in length, and base resistance values in different strain gauges. In the case of our strain gauge strap, we are trying to determine how much strain the strap will experience and what ΔR will give the ideal sensitivity for the strap system. Thinking about the strap system, we can determine the ΔR range that we want the strain gauge to experience based on how sensitive to strain changes we want the gauge to be. As stated before, the gauge responds to strain with a change in resistance. This ΔR will change more drastically as more strain is applied to the gauge. During exercise, the body experiences strain from breathing, small strains from turning of the torso during movement, and other small strains from outside forces like bumping the strain gauge during movement. Given that the strains we want to register and record (strains caused by inhalation) are relatively larger than strains from external sources (strains caused by small movements or bumps), we want our strain gauge to be less sensitive to very small ΔRs and more sensitive to slightly larger ΔRs. And, by using the equation for GF from above, we can calculate estimated ΔRs with different strain gauges to decide on a strain gauge that fits our needs.
In order to solve this, we need to measure or estimate values for all other variables in the GF equation besides change in resistance. These values include:
- Gauge factor: 2
- Assumption: Common metallic strain gauges have a GF = 2
- Length: 50 mm
- Assumption: This is a large gauge size since strains due to inhalation are likely to be large
- Change in length: 3 mm
- Estimated: Based on a measurement of one shallow inhalation, the change in circumference of the torso on inhalation is 3 mm, meaning that the strain gauge will also stretch this much.
- Resistance: 120, 240, 350 Ohms
- Variable: These three resistance values are standard for the size gauge we estimate using
Now that we have all the variables needed to solve for the change in resistance, we can begin solving the problem!
Solve:
Of these three ΔR values, the value with the 120 Ohm resistance is the smallest, meaning this gauge is the most sensitive to strain changes. Given that we want a resistance that is not extremely sensitive, one might argue that the 120 Ohm gauge may be eliminated from the options. However, none of the above solutions have ΔR values that are extremely sensitive, so it can be concluded that none of them will be hypersensitive to false strain readings. If anything, the gauges will not be sensitive enough to properly differentiate between shallow and deep breaths. Since the 120 Ohm gauge has the lowest ΔR, it is the most likely to accurately indicate subtle changes breathing patterns. The 240 and 350 Ohm gauges have higher resistance change values, meaning they might not be as sensitive to resistance changes caused by strain and may not be able to identify shallow breaths. Therefore, we can say that the gauge that best fits into our parameters is the 120 Ohm gauge.
This solution is somewhat sensible in that the assumptions are reasonable. All assumptions made for this problem represent legitimate conditions that could be experienced in a generic user population. However, while this is a reasonable solution, it is important to note that this is not an absolute solution. The assumptions made in this problem are not necessarily representative of all real-world conditions. For example, the ΔL of the strain gauge may change between users based on different lung capacities and body sizes. Additionally, the strain gauge length may be different; in this problem, one gauge size was chosen, but there are many different gauge types that could have been used. And using a different gauge type will change the problem calculations, changing the resultant strain gauge choice. This problem as a whole is limited in that it is difficult to say which Ohm resistance value is the best without actually trying different resistors in the system and performing physical testing. And, this problem only considers the use of strain gauges; flexi sensors and other pressure sensors may be a more viable alternative given the large resistance change values calculated for these strain gauges. But, with the basic assumptions made in this problem, the solution is a fair estimate of which strain gauge to start the design process with. With the most appropriate gauge decided, work can continue on with the design of the strap system in an effort to help athletes understanding and monitor their breathing patterns.
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