# Do “R” Values Add proportionally

For winter camping it is recommended to use a sleeping pad with an R value greater than 5.

Can you alternatively use two closed cell 2.5R pads one on top of each other?

If using an inflatable pad with an R value of 5 and a closed cell with an R value of 2.5 will you effectively have a 7.5R value set up?

-
See also this question: outdoors.stackexchange.com/questions/4999/… – Wills Apr 17 '14 at 10:25

Yes, the R-value will add of your different layers. If you wear layer A with R=5 and layer B with R=2.5, the overall insulation value will be R=7.5.

To explain this a bit, we think of two layers or flat walls which interact only due to thermal conduction. This is just a model and in reality other effects will come in play. The Fourier Law for thermal conduction (relative to the surface) of one layer states:

``````heatFluxDensity = thermalConductivity / thickness * temperatureDifference

[W/m²]          = [W/(mK)]            / [m]       * [K]
``````

The R-value is stated as a material property as

``````R = thickness / thermalConductivity
``````

with the unit [m²K/W] which leads from Fourier law to

``````R = temperatureDifference / heatFluxDensity
``````

Adding several layers, we can use the electrical analogy and are able to add the resistances of each layer to an overall resistance.

Knowing your material properties (which might be difficult in the clothing industry), assuming a temperature gradient or a heat flux, you can then evaluate the other using this equation:

``````heatFluxDensity = (innerTemp - outerTemp) / (R1 + R2 + ... + Rn)
``````

Wiki

Insulation

Relating to outdoors

Mathematical model

-

In calculating the R-value of a multi-layered installation, the R-values of the individual layers are added.

I would imagine a slight diminishing return as the r-value is a laboratory measurement in ideal condition which is not quite the same as on the field (variable temperatures, moisture, air movement, etc.).

-
I don't think in reality the R-value (resistance) through layering would implicitly be lower than the sum of the layers. The caught air between the layers are decreasing the thermal conduction and therefore increasing the resistance of your system. Air movement (convection) is just relevant at the outer shell where you may have high wind speed and this outer influence isn't changed through layering a lot. Still moisture is an issue. – Wills Apr 18 '14 at 18:19
You might be right. If you have a material where the air is enclosed, stacking two of those items could allow for more airflow and possibly be less efficient? Either way, I think a field trial with the actual gear is better when possible. – ppl Apr 19 '14 at 3:05