Acute/short-term effects of stretching


Stretching is a critical component of many regimens seen in clinical and fitness settings. Whether you’re a person who prefers to stretch before/after your routine, many people will attest to the physiological benefits of stretching. Proponents of stretching believe that it improves performance during exercise and prevents injuries and soreness. Some would go so far as to say that an individual may not be stretching enough when they repeatedly experience pain or injury after their workouts with no signs of improvement. Despite these enduring beliefs, the science behind the benefits of stretching is questionable. For the purposes of this blog post, we will focus on the acute, short-term effects of stretching on performance during exercise.

Three forms of stretching  used in exercise and rehabilitation settings include dynamic stretching, ballistic stretching, and static stretching. Dynamic stretching is a type of stretching which involve fluid-exaggerated movements. Ballistic stretching utilizes fast countermovements. Static stretching involves extending target muscles to a limit point, and maintaining that position for an interval between 10 and 30 seconds. In order to minimize injuries, static stretching is encouraged for non-athletes.

Numerous scientific studies have shown that have shown that static stretching results in an improved joint range of motion  (ROM) and greater flexibility in the muscles targeted by this technique. Conversely, research has also shown that stretching before exercises can result in a lower force output generated in the muscles that are targeted. Compliance is the lengthening of muscle fibers in response to an applied force. According to an article cited by the the National Institute of Health (Anderson, 2005), increased compliance (which occurs a result of stretching) has been linked to a decreased ability to absorb force at rest, whereas decreased compliance results in a muscle being able to withstand higher tension. This is significant because, when sarcomeres are stretched to the point that the actin and myosin filaments do not overlap, the force absorbed is transmitted to the muscle fiber cytoskeleton; resulting in fiber damage (regardless of a muscle’s joint ROM). Thus, compliance may result in decreased performance depending on the type of exercise performed. Another issue that arises related to the use of stretching before exercise is the type of stretching utilized. Science has shown that muscle fibers can experience tension when stretched as little as 20% of their total length1. Thus, it is difficult to establish a universal standard describing correct stretching techniques. In addition, improved joint ROM can be attributable to extraneous factors (such as increased pain tolerance); making the strength of its relationship to stretching highly questionable.

There are a plethora of studies conducted that attempt to quantify the effect of stretching on performance. One study, conducted by researchers at Sahmyook University in 20182 examined the effects of stretching on muscle strength, endurance, and endurance in a non-athletic sample of 13 active collegiate male students. These subjects were separated into three groups: those who did not perform any warm ups before exercise  (NWU), those who performed aerobic warm ups in the form of power walking for ten minutes (AWU) before exercise, and those who performed aerobic warm ups with static stretching for ten minutes (ASU). All three groups performed isokinetic muscle testing. The stretching used in the study consisted of straddling, seated calf stretching, and standing quadriceps stretching for the lower body. Two repetitions of each stretching motion were performed for 20 sec each and the entire stretching program took 5 min to perform. All subjects rested for 1 min after warming up and then underwent isokinetic muscle testing of the knee joints. The sequence of performance of each warm-up exercise was individually randomized. In the successive weeks, each group was tested according to the type of warm-up performed. The testing was conducted for 3 weeks, and all groups were allowed a week to rest in between tests.

In order to quantify the results in each group, a knee extension/flexion isokinetic  dynamometer was used. Participants were asked to extend and flex the knee by exerting their maximum strength as fast as possible while keeping their trunk up against the backrest during the test and to hold onto the handles. The subjects performed the maximal test of four repetitions. Each maximal test was conducted with an angular speed of 60°/sec to measure isokinetic muscle strength and an angular speed of 180°/sec to measure isokinetic muscle power. In addition, the muscle endurance test was conducted with an angular speed of 240°/sec. The exercise was conducted twice prior to testing to familiarize the subjects with the test, thereby achieving optimal results. The subjects were verbally encouraged and allowed to view their torque graphs during testing as a form of visual feedback to increase motivation.  To analyze muscle strength, power and endurance, measurements of the left and right knee joints were divided into each independent variable before data processing was performed. In addition, psychological evaluations in the form of questionnaires were administered to subjects before and after workouts for individuals in all three groups. These assessments utilized a 5-point Likert scale (1, very bad; 2, bad; 3, average; 4, good; 5, very good). The Kruskal–Wallis rank test were used to examine the differences of variables among groups and the Wilcoxon test was used to investigate psychological conditions before and after warm-ups within times in each group. A Mann–Whitney post hoc test was implemented to detect any significant differences in the Kruskal–Wallis test. The significance of all data was established at p ≤0.05. The results from the table have been included in figures attached to this post. The data is shown in the bottom of this point via a hyperlink. 

Based on the results of this experiment, the researchers concluded that there was no significant effect of the type of warm-up activity on performance in any of the tests performed in this study. Shown in Table 2, at 60°/sec (which is an angular speed for rating muscle strength), the NWU showed higher rates for both the extensor and flexor. However, the researchers determined that the difference was not statistically significant Shown in Table 3, at 180°/sec (an angular speed associated with rating muscle power), AWU and ASW groups attained higher rates for the flexor and extensor, respectively, although the difference was not statistically significant. The total work at 240°/sec (which reflects muscle endurance) was higher in ASW for both the flexor and extensor than NWU and AWU, though not statistically significantly. These results are shown in Table 4. In a similar manner to the trends seen when evaluating athletic performance, the individuals in the ASW group marked higher scores on their psychological assessments than the AWU and NWU groups. The results are shown in Table 5. However, the researchers determined that the result were not statistically significant.

Overall, while there appears to be some merit to the psychological benefits of stretching before exercising, its effect on athletic performance remains inconclusive. However, if you find that stretching helps improve your outlook/state-of-mind during the course of your workout, I would highly encourage you to continue your routine.


Questions to Consider

  1. Based on the experiment, do you believe that stretching before a workout provides any benefits/advantages towards performance?
  2. Does this post affect your views towards stretching?
  3. Would you encourage someone seeking to exercise more frequently to stretch before/after their exercises?



  1. Andersen JC. Stretching before and after exercise: effect on muscle soreness and injury risk. J Athl Train. 2005;40(3):218–220.
  2. Park HK, Jung MK, Park E, et al. The effect of warm-ups with stretching on the isokinetic moments of collegiate men. J Exerc Rehabil. 2018;14(1):78–82. Published 2018 Feb 26. doi:10.12965/jer.1835210.605


Whole Body Air Displacement Plethysmographic- Problem


In order for whole body air displacement plethysmographic machines such as the BodPod to function optimally (so that viable data can be collected), it is crucial that laminar flow is maintained throughout the machine’s ventilation system at all times. Imagine that you are an engineer (imagine that!)  tasked with manufacturing the tube components for the Bod Pod.

If the flow rates in the inlet and outlet tubes are equal, the volumetric  flow rate of air in the tubing system will be 0.25 cubic meters/second , and the BodPod functions in laminar/laminar-like conditions, what are the ideal dimensions for the diameters of the inlet and outlet tubes in the Bod Pod?



  • Flow rates are equal in the inlet and outlet tubes
  • The tubes are cylindrical  
  • Laminar flow is maintained at all times
  • Pressure changes are negligible
  • Air circulating inside the BodPod has similar thermodynamic/kinematic properties ambient air at room temperature
  • Temperature conditions of the device are identical to those at room-temperature

A link has been included to a power point presentation that contains diagrams that will aid readers in solving this problem:



Figure 1: Schematic of Adult-Sized Bod Pod and circuitry components that will be used as a reference for this problem.





According to the 4th page of the patent filed by the manufacturer, Life Instruments Inc., it is okay to assume laminar conditions inside the tubing ventilation due to the fact that flow rate inside the inlet and outlet tubes are always set to values of low magnitudes. Literature in courses such as Signals and Systems show that low flow rates result in low generation of acoustic noise by  air circulation systems.


I was unsuccessful in locating some sort of testing standard that establishes set values for the volumetric flow rates of air in laminar conditions. There appears to be any information pertaining to any testing protocols the manufacturer used for design verification purposes in the original 510(k) form filed with the FDA. To establish an appropriate flow rate value for this test question, I searched for similar problems online. In short, the values for the volumetric flow rate of air (Q) ranged from 0.1 to 0.8 cubic meters/second in my searches. I decided to use a value of 0.25 cubic meters/second in this problem. By assuming that the values for Q are equal for both tubes, it is possible to design both tubes with an equal diameter. Thus, along with other reasons that will be outlined later in this section, all the solver is required to do to calculate the correct value in this problem is to use one equation.

Normally, pressure fluctuations trigger changes in tubings and pipes create flow gradients in closed ventilation systems. Because of this, mathematical expressions such a Boyle’s Law and Bernoulli’s equations are used to solve changes in volume and volumetric flow when pressure fluctuations occur. According to page 4 of the patent filed for the Bod Pod, the authors state that the use of pressure transducers which are coupled to the inlet and outlet tubes helps monitor any pressure changes that occurs in the tubing; automatically adjusting the pressure settings in the tubes to more optimal levels through negative feedback. This is done in order to maintain a constant flow rate (and thus, laminar flow throughout the circulation system). Later on in section 4 of the patent,  the manufacturers also state that constant air flow can be maintained with the addition of rotary pumps to the circulation system (which are not actively displayed in any of the figures included).

The manufacturer’s statements in the patent confirm the presence of temperature-sensing circuitry in the inlet and outlet tubes that control the internal temperature of the environment inside the tubing and the pod itself. Thus, any temperature fluctuations that could create flow gradients in the device’s tubing are negligible since they are always corrected in  rapid fashion. This also eliminates the need for Fourier’s law to solve the value of Q in this problem.

Assuming that the tubing is cylindrical eliminates the need to solve for any hydrodynamic radius  values(which are used in equations associated with fluid flow in which tubes/pipes are any shape that is non-cylindrical).


By assuming that the air inside the device’s circulation system behaves in a similar fashion to ambient air, and that the conditions inside the circulation system are similar to those at room-temperature and that the device is used in STP conditions, it is possible to estimate the value of the kinematic viscosity of air (which is needed to solve the value for the diameter of the tubing using the Reynolds number equation along with the value of the flow rate given in the problem description and the upper-limit value of the Reynolds number associated with laminar flow).




In order to solve for the value of the tube diameter, the solver must utilize the following equation:

Re = QD/v ,

Re = reynolds number

Q = volumetric flow rate of air

D = pipe bore or tube diameter

v = kinematic viscosity

Reynolds number flow rate equation-16umdck  <— Click the link to view a more detailed image of the equation


NOTE: Pipe bore is equivalent to the diameter of the tube, and this equation is applicable to both pipe and duct installations.

First, the value of Q is already provided in the description. So the reader is already provided one unknown.

Second, the reader is told in the problem description and background section to assume laminar conditions in the circulation system. The Reynolds number value used in this problem is 2300, which is the established upper limit for laminar flow. All values at or below this number is considered laminar flow.

Third, since the reader is told to assume that the air circulating through the inlet and outlet tubes are similar in kinematic/thermodynamic behavior to ambient air at room temperature, the reader can assume that air inside the circulation system has the same kinematic viscosity as ambient air at room temperature. This value is 1.494 x 10-5 meters ^2/ second.

At this point, the only unknown that the reader is left with is the value of D, or the tube diameter. After plugging all the known values into the above-aforementioned equation and solving for the value of D algebraically, the reader should arrive at a diameter value of approximately  0.13708 meters.




[1] Dempster Phillip, Michael Homer, and Mark Lowe (2004). United States Patent 20040193074A1. Retrieved from


[2] Engineers Edge. “Kinematic Viscosity Table Chart of Liquids” (2019). Machinery’s Handbook, 29th edition.  Retrieved from


[3] Foster, Trevon. “Laboratory Flow Meters: Flow Measurements In the Lab” (2015). Titan Enterprises, Ltd. Retrieved from

Air Displacement Plethysmography: How It Works Patent Post

Body Fat is an important health statistic. Whether you are a person who dreams of obtaining “rock-hard” abs on the beach, a person aiming to shed a couple of pounds for the new year, a doctor assessing a patient’s risk of cardiac arrest, or just a general fitness enthusiast, body fat is the rave of today’s exercise culture. Although there is a negative connotation associated with body fat, it is an essential nutrient. Fats are needed to boost energy levels and numerous metabolic processes. Generally, a healthy individual is considered to have a body fat value in the range of 18-25%. However, excessive fat levels have shown a positive correlation with mortality.

Historically, body mass index (BMI) has been used more often by doctors to evaluate a person’s overall fitness. But a health study in the American Journal of Clinical Nutrition determined that an individual’s body fat is more effective in assessing his/her risk of developing chronic disease than BMI due to the failure of the latter in differentiating between fat-free mass (bone, water, lean tissue) and the weight of fat mass in the body. An individual may be on the lower end of the obesity spectrum in terms of total weight, but still possess an enormous risk of cardiovascular diseases due to having too much body fat.

Based on these facts, one could argue that healthcare professionals should deviate from the practice of collecting patient’s BMIs and focus their attention solely on calculating patients’ body fat percentage. However, measuring an individual’s  body fat is an arduous process due to the amount of time need to procure data and make calculations, which require a good understanding of topics such as calculus. and conversation of mass (nasty math/physics). For that reason, BMI  is more commonly used despite the lower confidence in this data. Thus, there is a high demand for technology that can assess an individual’s body fat percentage in an accurate and timely manner.

Air Displacement Plethysmography is an emerging technology that utilizes air perturbations that occur when a subject enters a confined space in order to determine their body fat levels. Please click here to view figures collected from a US patent filed for the BodPod: an air plethysmographic apparatus manufactured by Life Measurements Instruments, a medical device company based in Concord, California.

The Bod Pod consists of an air circulation system (represented by item 60 on figure 2) linked to a plethysmographic measurement chamber (pointed out by item  50 on figure 2). The air circulation system (embodied in greater detail by  Fig 3 of the patent), comprised of one or more pumps, acts as both a source of circulation and filtration within the chamber by using ambient air (air that is derived from a temperature-enclosed environment). Clean air is pumped into the chamber via an inlet tube (represented by item  86) while contaminated air is moved out of the chamber through an outlet tube (represented by item 88), where it is later filtered and recycled. The result is a clean and controlled air environment that is maintained throughout the duration of the BodPod’s operation. Inside of the Bod Pod are plethysmographic measurement components(represented by item 56 and 58 on Figure 2) that record perturbations in the volume of air inside the chamber before and after a subject enters in order to calculate the subject’s body volume by subtraction. For those who aren’t familiar, a plethysmograph is an instrument that measures displacements in a fluid within an enclosed environment (in this case, the BodPod chamber). In order to gather accurate data, it is imperative that the volume of air in the chamber is recorded before a subject enters the chamber. Once all data has been collected, it is wirelessly  transmitted to a computer for further analysis using software provided by Life Instruments. Once the subject’s body volume has been determined, it is immediately inserted into Siri’s Equation to calculate the subject’s body fat percentage.



Dempster Phillip, Michael Homer, and Mark Lowe (2004). United States Patent 20040193074 A1. Retrieved from