# R Value Green Roof Calculation Energy Modeling

Answer:

Hi John, thanks for your question regarding calculating the R-value for a green roof.

For those who aren’t familiar with what an R-value is, it is the amount of thermal resistance an object has. A higher R-value for an object means that the object has more resistance to heat transfer, or it will take more time for heat energy to transfer through that object.

Thermal resistance for objects that comprise a roof (plate-like) is defined as the length of the energy path (L) divided by the object’s conductivity constant k times the surface area of the object A. The equation for this would be L / k*A.

The U-value (conductance) is simply the inverse of the R-value.

Materials like insulation naturally have high R-values, as they are used to reduce heat transfer, while materials like metal are natural conductors of heat energy and have low R-values.

In order to calculate the R-value of a green roof, one would have to determine what the composite R-value is for all of the materials that comprise that roof. For this article I am only speaking about conductive heat transfer (convective and radiation heat transfer are beyond the scope of this short answer).

Let’s assume linear conductive heat transfer for simplicities sake. In order to determine the composite R-value of the green roof system, you need to find the R-values of each individual component, including (but not limited to) the roof deck, insulation, waterproofing layer, drainage layer, soil/plant medium and vegetation. In this case, the thermal resistances (R-values) of each component can be added together to determine a total R-value for the composite green roof such that R1 + R2 + … + Rx = Rtotal. As I stated before, the U-value would simply be the inverse of the R-value.

Now of course, actual green roofs are much more complex than this and the heat transfer won’t be exactly linear or only conductive in nature. But this type of calculation would give you a rough estimate.

The soil or planting media and vegetation may be more difficult to obtain an exact R-value for because of its varying moisture content. It’s not simply a static object like a roof deck or insulation. Its properties are constantly changing because it’s a living thing. Also, the drainage layer may have varying R-values for both wet and dry conditions.

It’s important to remember that the R-value will not be uniform across the entire roof. An article in the February 2006 edition of the ASHRAE Journal on green roofs explained that the R-value of the roof varied across it from R-17 in the middle to R-38 at each end.

But this article also mentioned a significant fact. Green roofs not only have higher overall R-values than conventional roofs, they also lower the outside surface temperature, which is just as important when modeling energy savings. A conventional roof can have an outside surface temperature of

130 degrees F during the summer while a green roof may reduce that temperature to 90 degrees F.

Using Fourier’s Law for conductive heat transfer, you can see that total heat transfer Q = U * (T2 – T1) where T2 is the outside temperature and T1 is the inside temperature and U is the conductance (inverse of thermal resistance). So you can conclude from this algebraic equation that there are two ways to lower the total heat transfer Q, either through increasing the thermal resistance (R-value) or lowering the temperature difference between T2 and T1. A green roof should do both of these, which is why they are such a good choice as an energy efficient roof in just about any region.

An energy modeling software such as DOE-2 should be able to calculate the R-value much more precisely. I recommend that you find a registered professional mechanical engineer with experience in energy modeling for green roofs. This problem is much more complex than any solution that can be provided here or anywhere online and will require the services of a professional engineer.

I hope this helps. Good luck!

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Answer:

Hi John, thanks for your question regarding calculating the R-value for a green roof.

For those who aren’t familiar with what an R-value is, it is the amount of thermal resistance an object has. A higher R-value for an object means that the object has more resistance to heat transfer, or it will take more time for heat energy to transfer through that object.

Thermal resistance for objects that comprise a roof (plate-like) is defined as the length of the energy path (L) divided by the object’s conductivity constant k times the surface area of the object A. The equation for this would be L / k*A.

The U-value (conductance) is simply the inverse of the R-value.

Materials like insulation naturally have high R-values, as they are used to reduce heat transfer, while materials like metal are natural conductors of heat energy and have low R-values.

In order to calculate the R-value of a green roof, one would have to determine what the composite R-value is for all of the materials that comprise that roof. For this article I am only speaking about conductive heat transfer (convective and radiation heat transfer are beyond the scope of this short answer).

Let’s assume linear conductive heat transfer for simplicities sake. In order to determine the composite R-value of the green roof system, you need to find the R-values of each individual component, including (but not limited to) the roof deck, insulation, waterproofing layer, drainage layer, soil/plant medium and vegetation. In this case, the thermal resistances (R-values) of each component can be added together to determine a total R-value for the composite green roof such that R1 + R2 + … + Rx = Rtotal. As I stated before, the U-value would simply be the inverse of the R-value.

Now of course, actual green roofs are much more complex than this and the heat transfer won’t be exactly linear or only conductive in nature. But this type of calculation would give you a rough estimate.

The soil or planting media and vegetation may be more difficult to obtain an exact R-value for because of its varying moisture content. It’s not simply a static object like a roof deck or insulation. Its properties are constantly changing because it’s a living thing. Also, the drainage layer may have varying R-values for both wet and dry conditions.

It’s important to remember that the R-value will not be uniform across the entire roof. An article in the February 2006 edition of the ASHRAE Journal on green roofs explained that the R-value of the roof varied across it from R-17 in the middle to R-38 at each end.

But this article also mentioned a significant fact. Green roofs not only have higher overall R-values than conventional roofs, they also lower the outside surface temperature, which is just as important when modeling energy savings. A conventional roof can have an outside surface temperature of

130 degrees F during the summer while a green roof may reduce that temperature to 90 degrees F.

Using Fourier’s Law for conductive heat transfer, you can see that total heat transfer Q = U * (T2 – T1) where T2 is the outside temperature and T1 is the inside temperature and U is the conductance (inverse of thermal resistance). So you can conclude from this algebraic equation that there are two ways to lower the total heat transfer Q, either through increasing the thermal resistance (R-value) or lowering the temperature difference between T2 and T1. A green roof should do both of these, which is why they are such a good choice as an energy efficient roof in just about any region.

An energy modeling software such as DOE-2 should be able to calculate the R-value much more precisely. I recommend that you find a registered professional mechanical engineer with experience in energy modeling for green roofs. This problem is much more complex than any solution that can be provided here or anywhere online and will require the services of a professional engineer.

I hope this helps. Good luck!

**Related Advice:**