Solving for Minimum Thickness of a Force Plate


Force plates are a popular way to measure the ground reaction forces generated by an athlete when running or jumping. It is important that the force plate is capable of withstanding these forces continuously by different athletes and be able to last a long time, as they tend to be expensive. A key factor in designing a force plate that meets these requirements is making sure that the plate itself has a thickness that is optimally measured. Some quantities that need to be taken into consideration when designing the geometry of a force plate are the maximum forces that could be acting on the plate and the material properties of the chosen material used in making the technology. Thickness is a crucial quantity in making sure that the force plate is resistant to fatigue.


The average force plate is composed of AISI stainless steel 304, which has a modulus of elasticity of 193 x 10^3 MPa and a Poisson’s ratio of 0.29 [3]. In order to accommodate force at maximum conditions, the force plate should be designed to withstand 5000 N. The geometry of the plate also needs to be taken into consideration. A standard size force plate manufactured by Bertec [1] is 16 in in width and 24 in in length. The last consideration that needs to be made is how much the force plate should be allowed to deform. In order to prevent fracture, the plate needs to be able to deform a small amount but not enough to alter force readings. For this calculation, we will assume that maximum deformation is 1 cm.


  1. Solve for maximum stress applied to plate: σ = F/A = 5000 N / (0.4064 m x 0.6096 m)

      σ = 20,182.3 Pa

2. Set up modulus of elasticity formula: E = σ/ε [2]

3. Insert into modulus equation: (1.93 x 10^11) = 20,182.3 / ε, ε1.05 x 10^-7

4. Plug into Poisson’s ratio equation: v = -ε(x)/ε(z), 0.29 = (1.05 x 10^-7) / (0.01/t)

From this, we find that t = 27,624.3 m which is an unreasonable value. This shows that there was an error in my calculation. Realistically, a force plate would have a thickness of roughly 2 in, such as the Bertec force plate.


[1] Bertec. (n.d.). Force Plates. Retrieved from

[2] Engineering ToolBox, (2005). Stress, Strain and Young’s Modulus. [online] Available at:

Use the Force (and/or Motion)

The Basics

Patent Title: Force and/or motion measurement system having inertial compensation and measurement thereof

Patent Number: US8315823

Patent Filing Date: June 30, 2011

Patent Issue Date: November 20, 2012 (17 months to issue)

Inventors: Necip Berme and Hasan Cenk Guler

Assignee: Bertec Corporation

U.S. Classification: Force or Torque Measurement (702/41)

Claims: 18

Some Background on Force Measurement Systems

Biomedically, force sensors are used to continuously measure a force that is being exerted by the person on the platform. They measure forces in three dimensions and plot them against time [1]. Force plates are becoming increasingly more popular with sports researchers and coaches who are looking to use more advanced technology to help improve the performances of their athletes. An example of an athlete who may benefit from using a force measurement sensor is a swimmer who is looking to improve their starts and turns [3]. Sprinters also may use these inventions to work on pushing off a starting block.

The Bertec force measurement system [2], specifically, aims to relate the force or motion measured with inertial compensation. The force plate can take the form of a balance plate or jump plate, as well as gait using a treadmill-like apparatus. An important distinction of this device compared to other force plates is that it also assesses the motion of the athlete. The invention utilizes a motion acquisition system to look at the movement of a person running or walking on the treadmill.

What are the Main Claims?

The Bertec force measurement system [2] is made up of a force measurement assembly which includes a surface for the subject to stand on and one or more force transducers. This invention also includes a motion base, an inertial compensation system, and a means of data manipulation. The motion measurement system described in this patent also claims the same components and functions. There is a method for determining the forces or moments that are applied to the system which includes rotating the assembly with the subject in multiple dimensions, acquiring force and moment quantities using the transducer, and mathematically correcting the values.Figure 1. Bertec force measurement system [2]Figure 2. Bertec force and motion measurement system with treadmill and motion capture system [2]

How it Works

A key component of the device is the inertial compensation system [2], which uses linear or rotational profiles to calibrate the device and determine the inertial parameters. The motion base uses applied motion profiles to displace force and is especially good for supporting a treadmill system, as it can hold a large weight that undergoes motion. Below are the equations used to describe the force-inertia relationship.

The top equation illustrates the inertial forces and the bottom equation represents the moments. The kinematics of the force measurement assembly (aG and w) can be measured using accelerometers and gyroscopes respectively.

Compared to Other Devices

The main difference between Bertec’s device and devices that came before it is its ability to switch out the means of acquiring data. The force and motion measurement system is able to be used with a motion capture system and treadmill or with a force plate which allows for versatility in training measurements. This makes it simpler for coaches to view the force and motion values associated with their athletes’ performances and makes improvements off of the reported values.


[1] Leno, P. (2019, October 30). How to use force plates in sports. Retrieved from

[2] Berme et al, Force and/or motion measurement system having inertial compensation and method thereof, US8315823, Bertec Corp, 2012

[3] Kistler. (2020). Biomechanics: faster, higher and stronger with performance analysis measuring technology. Retrieved from

The Sports Gene Chapter 2 Reflection: 10,000 Hours Rule

Make-up blog for 3/3/20

This week’s chapter of The Sports Gene focused on the “10,000 hours rule”, or the idea that a person can become an elite athlete by deliberately practicing their sport over thousands of hours. The main example that was looked at was the case of high jumper, Stefan Holm, who is one of the top high jumpers in the world despite the disadvantage of having a shorter height. He started training from a very young age and follows a very specific training plan which has led him to success in the sport. Comparatively, the book looked at another high jumper, Donald Thomas, who picked up the sport later in life and was not as trained in the technicalities of high jumping.

One of the distinguishing characteristics of the athletes that is interesting is the achilles tendon in each of them. When Holm’s achilles was studied, they found that it had become so stiff over time that it required quite a bit of force to bend it, making it act as a spring. This is a characteristic that was developed over time with training. Thomas, on the other hand had a very long achilles relative to his height which is something that cannot be developed over time. It is interesting to see how different characteristics of the achilles are beneficial for the same sport and that they are acquired in different ways.

I don’t believe that the 10,000 hour rule is relevant to all sports or to all people. In the case of Holm, it probably did apply to him due to him not being naturally built like most professional high jumpers. He was obviously very dedicated to the sport and putting in the deliberate practice is what helped him become successful. However, some people are naturally gifted athletes who can pick up a sport much more easily than the average person.

Epstein, D. (n.d.). Chapter 2. In The Sports Gene (pp. 18–37).

The Cold Facts on Icing

If you’re an athlete, there is a good chance that you have been told to ice your muscles after exercising. Icing is commonly thought to alleviate inflammation and soreness, as well as help to heal injuries caused by muscle overuse more quickly.1 There are different types of icing techniques popular in the world of athletics, ranging from a simple ice pack or frozen gel to cryotherapy and cold therapy chambers.2 Despite its wide use, there is some controversy regarding whether cold therapies are beneficial to the muscles or causing more harm than good.

Inflammation is an acute physiological response that is needed for tissues in the body to heal after exercising. Those opposing ice therapies claim that icing a sore muscle reduces its blood flow and slows the natural process of alleviating inflammation. While there is evidence that icing can help to reduce soreness in the short term after a workout, this reduction in the immune response can prevent the muscles from healing as quickly as they otherwise would.3 Many researchers have studied these countering views on the subject.


Figure 1. Cryotherapy machine [6]


One study aimed to see if topical cooling could improve recovery in eccentric contraction-induced muscle damage.4 They used a sample of 11 college male baseball players and put them into two groups; a control group and a group receiving topical cooling. The subjects used a barbell to complete 6 sets of 5 eccentric arm contractions. Those individuals in the cooling group received the ice 0, 3, 24,48, and 72 hours after the exercise for 15 minutes each. This was then repeated four weeks later. The researchers then analyzed the muscle hemodynamic changes, muscle damage markers, inflammatory cytokines, subject pain levels, and isometric muscle strength. The results showed that the subjects pain was similar between the two groups in the short term, but was greater in the later periods after the workout. The measured creatin kinase and myoglobin were significantly greater in the cooling group in the 48 and 72 hour periods than the control group. The cooling also resulted in higher hemoglobin concentration.4

Another study was conducted using 42 moderately active college aged males.5 The researchers had the subjects do 5 sets of 20 drop jumps, followed by lower body immersion in cold water. Three groups were used; one having a water temperature of 5 degrees Celsius, one with 15 degrees Celsius, and one control group. Measurements were taken on isometric knee extensor torque, countermovement jump, muscle soreness, and creatin kinase directly following exercise and 24, 48, 72, 96, and 168 hours after. The results for the countermovement jump showed that the warmer water group recovered more quickly than the colder water group. Creatin kinase remained elevated in all group except the warmer group, which returned to baseline at 72 hours. The subjects reported lower muscle soreness in the warmer water group as well.5

The research shows that icing sore muscles can be beneficial shortly after working out, but that people will possibly experience the same soreness later in time compared to people who don’t ice. It also makes it seem like using only slightly cold ice packs and water is more effective than using extreme cold. Athletes who ice should consider the amount of time they ice and the temperature they use when choosing cold therapies after a workout to avoid possible long term soreness and to improve with training.


Questions to Consider:

  • Do you think that using experienced athletes or people who only exercise occasionally was a more effective method of research?
  • Have your experiences with ice therapies been positive or negative?
  • What could a future study do differently to see the effects of icing on exercise?



  1. Cluett, J. (2019, September 25). How to Properly Ice an Injury. Retrieved from


  1. Gotter, A. (2017, February 2). Treating Pain with Heat and Cold. Retrieved from


  1. Aschwanden, C. (2019, February 5). Athletes love icing sore muscles, but that cold therapy might make things worse. Retrieved from


  1. Tseng, C.-Y. (2013). Topical Cooling (Icing) Delays Recovery From Eccentric Exercise–Induced Muscle Damage. Journal of Strength and Conditioning Research27(5), 1354–1361.


  1. Vieira, A. (2016). The Effect of Water Temperature during Cold-Water Immersion on Recovery from Exercise-Induced Muscle Damage. International Journal of Sports Medicine37(12), 937–943.


  1. (n.d.). 5 Cryotherapy Side Effects Therapists Should Watch For. Retrieved from