Why maximum body mass for measurements isn’t just one number when talking pressure mapping systems

We often receive the following question from our customers

What is the maximum body mass I can apply when I run measurements with the Moticon sensor insoles?

In sports such as basketball or athletics, you find rather tall athletes with a lot of muscularity resulting in high body weight. Once these athletes engage in dynamic movements such as sprints or jumps, the resulting ground reaction forces that have to be measured for biomechanical purposes easily add up to an equivalent of two to three times body weight.

So it is of great importance to look at these edge cases of your investigation when it comes to the applicability of a measurement system. While the article’s headline calls for a simple number in terms of maximum measurable body mass, reality in fact requires some additional explanation. So let’s look into this topic in a little bit more detail.

The quick anwer

For those who are not eager to dig deepter into physics, we’ve put together a table that gives you an estimate of the maximum measurable body mass for each Moticon sensor insole size. So you just have to pick your size and the corresponding movement type to get to the maximum body mass that can be measured with Moticon sensor insoles.

For the above stated estimates, first, maximum vertical ground reaction forces were determined in typical dynamic sports movements such as fast sprinting and jumping. The maximum force readings were related to the athletes‘ body mass to find the multiples of body mass that occur in these activites. Finally, the maximum measurable body masses resulted from a backwards calculation, using the maximum measurement range of Moticon’s sensor insole pressure readings and the typical multiples of body mass previously determined.

Remember that the estimates given it this section are ballpoint figures. The absolute maximum rates depend on a variety of influencing factors which are described in the following sections.

Pressure matters for answering the maximum measurable body mass

All commercially available in-shoe measurement systems on the market, as of the date of this article, use varying numbers of pressure pressure sensing technology to determine the vertical ground reaction force vGRF between the foot and the ground. In fact, the vGRF is not measured directly but derived from the pressure readings and the loaded surface area. The pressure readings, on the other hand and unfortunately, are subject to a whole variety of influencing factors that are difficult to control. This is also the reason why it is so challenging to accomplish accurate force readings from in-shoe measurement systems, compared to force plates.

The why and how of the aforementioned topic is explained in separate articles, covering how ground reaction forces can be determined from pressure distribution and the pros and cons of in-shoe measurement systems compared to force plates. For now, we shall be satisfied with becoming clear that we need to know the maximum measurable pressure range in order to come up with an answer to the question about the maximum measurable body weight.

One body weight can result in different pressure readings

In the following imaginary example, one and the same male individual is in a single legged stance position. He only varies the way of standing by shifting forward to get from a flat standing position (case 1) to a tip toe standing position (case 2). You can draw from your own experience when we state that there is a much higher pressure underneath the foot when standing on the toe tips, although the body weight does not change compared flat standing. The mathematical explanation for it follows below.

The individual’s body mass m is 73 kg which results in a body weight Fg equalling 716 N and acting perpendicular to the ground’s surface. The body weight generates a vertical ground reaction counter force vGRF of the same magnitude. The vGRF is the value to be measured by the Moticon sensor insoles. As there are no dynamic effects involved in this static case, the vGRF is equal to the body weight Fg.

Furthermore, we assume that the pressure distribution across the loaded sensor insole area is completely homogenous for both single legged stance positions. This means that at any discrete location on the loaded surface, you can find the same amount of pressure. This is not exactly a realistic case as the human foot’s bone and tissue structure, in reality, cause areas of higher an such with lower counter pressure when standing on the ground. But the example serves as a showcase, which will eventually help to answer the article’s main question. The loaded areas equal 100 % and 25 % of the total sensor insole area for the flat standing (case 1) and the tip toe position (case 2), respectively.

With these numbers, we can easily calculate the mean pressure distribution for case 1 and case 2.

F_g = vGRF = m * g = 73 kg * 9.81 m/s²
F_g ≈ 716.1 N

The subjects Moticon sensor insole size is S6 and its total area A is 188.2 cm². For the two cases, the effective area calculate as

A_case1 = 100 % * A = 100 % * 188.2 cm²
A_case1 = 188.2 cm²

A_case2 = 25 % * A = 25 % * 188.2 cm²
A_case2 ≈ 47.1 cm²

With the general equation for pressure

P = F / A

P: pressure
F: perpendicular force
A: surface area

the mean pressure values for case 1 and case 2 result as follows

P_{mean, case1} = F_g / A_case1 = 716.1 N / 188.2 cm²
P_{mean, case1} ≈ 3.8 N/cm²

P_{mean, case2} = F_g / A_case1 = 716.1 N / 47.1 cm²
P_{mean, case2} ≈ 15.2 N/cm²

We see that the effective pressure increases for a smaller loaded surface area. In addition, the effective pressure dramatically increases when we measure dynamic movements as opposed to this static example, such as sprinting or jumping. We will look at a realistic example further down this article. However, there are a few lessons you can take away from this simple example.

How the maximum measurable body mass is determined

We continue with the above example for the tip toe standing case and the given assumptions in order to show the way how the maximum measurable body mass can be calculated. Therefore, we need to know the maximum measurable pressure range of Moticon sensor insoles which is specified as

P_max = 50 N/cm²

The sensor insole size remains the same. As body weight equals ground reaction force in this case, we can directly calculate the body weight as follows

F_gmax = P_max * A_case2 = 50 N/cm² * 47.1 cm²
F_gmax = 2.355 N

and the maximum measurable body mass results as

m_max = F_gmax / g = 2.355 N / 9.81 m/s²
m_max ≈ 240 kg

It is important to comprehend that this maximum measurable body mass is only valid for this particular measurement case. Make sure you make some estimates according to the introductory table for your own measurement case or make your own calculation following below practical rules.

A real example for how force and pressure relates to each other

In this example, we finally look at a real measurement case of a short sprint sequence that can be seen in the video below. The example shall serve to verify the assumptions we have made for the introductory selection table.