Howto: 3D Climate measurements on mattress samples
There are numerous different materials available that can be used make mattresses. Moreover, most of them available are in different densities of with certain additives. In addition, a mattress is nowadays usually made up of several layers, and it is clear that a chosen composition or even a particular layer can strongly influence the climate behavior of the whole.
Comparing the heat accumulation and ventilation properties of the different materials and their combinations can help to choose the right mattress construction for your needs. This can be achieved by building 3D stacks of materials with sensors inside, and by applying a heat and moisture source on top.
1. Build a 3D stack
Depending on the type of research question, the 3D stack can simulate a complete mattress construction (including ticking and filling materials), or can be build from a single material. The first option can reveal for instance if a particular layer blocks or enhances the transmission of your heat and moisture. The second type of setup will provide more in depth information on the heat and moisture management of that material.
To capture the temperature and humidity inside the 3D stack, several sensor arrays are positioned within the stack at predetermined positions. In some cases this will require to slice the foam block in different layers.
2. Apply heat and moisture
There are 2 ways to apply heat and moisture to your setup. The first method is by using real test subjects, and the second is the use of standardized heat and moisture sources. A real human body will provide a more realistic situation, but will introduce a variability that needs to be accounted for. There can be a big difference in microclimate among test subjects. But also certain circumstances like food or stress can change the microclimate and thus influence the results from the same person. A standardized heat and moisture source will provide reproducible results, and it therefore recommended for material comparisons.
A second point of attention is the loading (and unloading) time. Depending on the thickness of the different layers, it can take a considerable amount of time for the heat and moisture to reach down to the lower layers of your setup. In some cases it will never even reach the lower layers. To have a clear view on the material behavior, it is important to apply the heat and moisture until a steady state occurs. The same reasoning goes for the time to recover to the initial state.
3. Analyse your data
3.A. Transient behaviour
From the time history of temperature and humidity in the layers underneath the heat and moisture source, the thermal isolation and the moisture permeability properties of the sample material are derived (heating/sorption phase), as well as the recuperation of the material to its original state (cooling/desorption phase).
The evolution of temperature and humidity as a reaction on the placement and removal of the heat and moisture source is modeled as a step response. After a time delay (Δt1 for the placement and Δt0 for the removal of the damper), the temperature and humidity curve reveal an exponential course and are modeled accordingly.
In this graph y0 (environment temperature and humidity) and y1 (temperature and humidity directly underneath the damper) represent the boundary conditions, while y1′, y1” and y1”’ are the conditions in the region of interest at the first, second and third layer.
This approach provides 4 parameters which describe the transient behavior: a time constant and a time delay, both for loading and for unloading. Physically, the time constant represents the time it takes the system’s step response to reach 63.2% of its final value. After 3 times the time constant, the value approaches 95% of its final value. The time delay represents the time needed before a measurable change in micro-climatic conditions occurs
3.B. Steady state
At the end of the loading phase, the sample micro climate is assumed to be in equilibrium (steady state), and the corresponding depth profiles are analyzed.
Similar to the time constant of the previous paragraph, a distance constant (δ1) can be calculated which represents the distance at which the temperature or humidity is decayed to 63.2% of its final value, while the temperature or humidity is near 95% of its final value at a depth of 3 times
the distance constant. Below this depth there is no measurable influence of the applied heat or moisture.
Additionally, the total amount of moisture can be estimated from the spatial distribution of the sensor values.
The spreading of the temperature and humidity in a plane also contains valuable information. The spreading is quantified by fitting a gaussian curve through the data points. The resulting value for sigma will be a measure for the width of the fitted gaussian curve and thus for the spreading of the parameter under investigation (at a distance of 3 times sigma, no measurable influence of the applied heat or moisture can be noted)
