# Solving for Minimum Thickness of a Force Plate

Identify

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.

Formulate

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 . 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  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.

Solve

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 

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.

References