# Delta T of insulated roofs for purposes of cooling load calculations

| Posted in Energy Efficiency and Durability on

It puzzles me when observing local contractors apply ocSPF to the underside of roof sheathing in my northern CZ-4, Mixed Humid, HDD=4442, CDD=1476 location (Louisville area). We have about the same number of days of Cooling as we do Heating.
When applying insulation to the ceiling above a Vented attic, though IRC/IECC recommends R-49, the local code only calls for R-38 and that’s what most (all I’ve observed) contractors do. On the occasion that an Unvented attic is called for, those same contractors apply 5.5″ between the roof rafters and call it a day.
The following questions pertain to COOLING Load:
It seems to me that the first thing that happens when one moves the insulation to the roofline is that one encounters a delta T that is about 3 times that at the ceiling level (and three times the Cooling Load at peak design temp.)
A.. Vented attic: Ceiling delta T = about 100 deg at the upper surface of the insulation in a well vented attic with 75 deg inside temperature (100-75=25).
B.. Unvented attic: Roofline delta T = about 150 deg at the roof sheathing with 75 deg inside temp. (150-75=75).
Do I have reasonable assumptions for the outside temperatures upon which the delta Ts are figured ?
The next thing that occurs is that, due to the pitch, the roof area increases by some factor, say, a factor of 1.2 for an 8:12 pitch.
Finally that 5.5″ of ocSPF at the roofline would be about R-20.6 in the cavity but the assembly, assuming a framing factor of 0.2 for the roof, would be about R-16.5.
Is that a reasonable framing factor assumption for the roof framing ?

In all, it seems that these contractors are moving from a legitimate R-38 at the ceiling assembly (a couple inches of SPF plus about 8+” of cellulose with very little reduction due to the framing factor) and using an R-16.5 roof assembly over a 20% larger surface area with 3 times the delta T. That would be roughly a 38/16.5 x 1.2 x 3 = 8.3- fold increase in that portion of the Cooling Load.

What, if any are the errors in my assumptions and reasoning ?
What might be the rationale used by those contractors ?

Even if the local folks maintained the same R-value in moving from the ceiling assembly to the roof assembly there would still be at least a 3-fold increase in delta T and hence Cooling Load due to the change in delta T alone. I can see that in more northern CZs where the insulation level for heating is already higher and the CDDs are relatively few, this can largely be ignored. But here in the mid-west and further on south I think this is an even more pertinent question. (I have only observed a dozen or so construction/insulation contractors in this area and certainly not all).

I’d appreciate insights on this.

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### Replies

1. GBA Editor
| | #1

Ted,
Q. "What, if any are the errors in my assumptions and reasoning?"

A. Before addressing possible errors, let's address confusions. First, you discuss this case: "When applying insulation to the ceiling above a vented attic..." But no one does that. If the attic is vented, the insulation goes on the attic floor. Maybe you meant to write "unvented attic" instead of "vented attic"?

Here's a possible error: you wrote, "Vented attic: Ceiling delta T = about 100 deg at the upper surface of the insulation in a well vented attic with 75 deg inside temperature (100-75=25)." I'm not sure what you mean by this equation. Do you think that the delta T is 100 degrees or 25 degrees? If the delta T is 100, you seem to be assuming an attic temperature of 175 degrees, which is too high. If the delta T is 25, you seem to be assuming an attic temperature of 100 degrees, which is too low.

When it comes to the increased surface area of a house with an unvented attic compared to a house with a vented attic, you are right -- but energy modeling software (or Manual J software) takes that into account if the person using the software enters the data correctly.

2. GBA Editor
| | #2

Ted,
The bottom line is that a person using Manual J software (the software used for calculating heating and cooling loads) doesn't have to worry about the factors you list, if (and this is an important "if") you enter the data correctly. The software works. The big problem is bad data entry by contractors who are deliberately trying to add fudge factors.

You are, of course, correct that R-20 or R-16 insulation installed along the roofline performs significantly worse than R-38 installed on the attic floor. (Fortunately, this is intuitively obvious, so there is no need to perform calculations to understand this fact.)

Heat will flow through an R-19 assembly at twice the rate that it will flow through an R-38 assembly. If you double the R-value, you cut the heat flow rate in half.

GBA has always urged those who want to install insulation along the roofline that it's important not to skimp on R-value. For more information on this issue, see It’s OK to Skimp On Insulation, Icynene Says.

3. | | #3

150F at the roof deck is a gross overestimate of the average daytime shingle temperature, and overestimates even the peak temperature of even a black EPDM roof if it has a pitch of 4:12 or higher. (Flat roofs can get much much hotter than that for the peak temps though.)

100F attic temperature is a gross UNDER estimate of the peak temperature of a vented attic (especially if you're presuming roof deck temperatures north of 140F.)

Roof decks cool by both radiation and convection on the exterior far more than they can by convection cooing under the roof deck in the attic. The cooling effect on the roof deck & attic of attic ventilation is measurable, but quite modest, a much lower affect than roof color or pitch.

Take this as a pretty good bedtime story on the topic:

4. | | #4

Martin,
When I reread my initial questions, I see that they were poorly phrased in several spots. I apologize for the trouble.
That sentence should have read "When applying insulation to the ceiling BELOW a Vented Attic" or perhaps a better way to say it would have been "When applying insulation to the attic floor of a Vented Attic.

In any case Dana got my drift.

My understanding now is:
That temperature of the top surface of the insulation on the attic floor of a Vented attic is much higher than than the 100º (yielding a ∆T of 25º) that I had thought; and that the temperature of the roof sheathing above the insulation of an Unvented attic is much less than the 150º (yielding a ∆T of 75º) that I had assumed. So the ∆Ts are much higher than the 25º I had been using; and in the second case, much lower than the 75º that I assumed.

Though I will have a Manual J done by a professional when the time comes, I have been trying to do my own Heat Loss/Gain Calculations during the meantime and have thus far, using my previous assumptions, come within 10% of the HERS rater. I had suspected that my assumptions were incorrect and I am hoping to refine my inputs.

I'm trying to calculate Peak Cooling Load Conditions. Would anyone care to hazard a guess as to what these temperatures would be for Cooling Conditions at peak design temp of 93º, in the mixed-humid northern CZ-4 ?
Instead of 100º I should use _____. And, instead of 150º I should use _____.

Thanks to you both. I'm off to do my bedtime reading as assigned by Dana. "I'll be baak"

5. GBA Editor
| | #5

Ted,

There are many towns and cities named Louisville. If you are referring to Louisville, Kentucky, then the outdoor design temperature that you should use for your cooling load calculation is 93°F. Here is a link to the source of that information:
https://www2.iccsafe.org/states/Virginia/Plumbing/PDFs/Appendix%20D_Degree%20Day%20and%20Design%20Temperatures.pdf

6. Expert Member
| | #6

Once you're at R30 or so in the attic, whether at the roof deck or the attic floor, the peak roof or attic temperature has a fairly limited effect on the peak cooling load, which becomes dominated by window gains. There's also a thermal lag, a time delay between the roof temp peaking and the ceiling temp peaking, an artifact of the thermal mass of the materials.

So using a steady-state model of delta-T & R will lead to load number much higher than reality, even if it were possible to know the peak temperature of the roofing with any accuracy without knowing the emmissivity and solar reflectance of the roofing, and the radiant temperature of the sky. Manual-J and other methods take short-cuts with simpler models, and rely more on outdoor ambient temperature and average humidity inputs. Peak roof temps are high, but relatively brief in duration compared to slower moving factors such as outdoor air temperatures. And in an insulate assembly the difference on peak load between a peak roof temp of 125F and 175F is remarkably small compared to the spikes in load that come with direct solar gain through west facing windows.

If you want to model this yourself to play around with different options to see how things affect load peaks and total energy use, download a copy of DOE-2 or better yet, BeOpt (which has DOE-2 underpinning it), and simulate the house:

7. | | #7

Martin,
I have used that 93º and the 10º recommended in that publication for all of my peak load calculations. I was trying to get a handle on the impact of solar insolation on the unshaded roof as it impacts the peak load calculations. The reference that Dana gave me, though I have not yet completed it, indicates that the temp of the junction between the roof sheathing and the foam reaches 175º in Central Florida. That gives a ∆T for that assembly of 100º for a period of time. In my location I'm sure it's not that high, but I don't know what it might be.
Dana,
I have have used a self developed spread sheet that begins with the temperature curve over a 24 hour peak design day in summer and calculated the heat gain for each hour of the day using specific individual R-values for each window and door; accounted for each layer of the wall assembly; lighting; appliances; people; hot water generation; projected infiltration (fog pressure testing will ensure); latent heat; and the Los Alamos formula for a Slab-On-Grade.
I have used the SHGC, overhang depth, height, and orientation of each individual window and door to calculate the Solar Heat Gain for each hour of a peak design day.
To the first group of hourly calculations I have applied Conduction Time Series calculations for a light-moderate mass home to the gains for each and every hour of the day.
To the hourly Solar Heat Gain Calculations I have applied Radiant Time Series calculations for each of the hours of the day during which Solar Heat Gain Occurs.
I have combined these two sets of figures (CTS & RTS) to give me the projected Heat Gain for each individual hour of the day.
I have reasonably good confidence in everything with the exception of a few points: The Los Alamos formula for heat gain through the ground for a Slab-on-Grade is pretty rough but I think it's about the best information that I am able to obtain. Then there are those ∆Ts. I had a suspicion that my values were inaccurate but I had not encountered any information that really put a number to actual temperatures experienced across an insulated roof assembly or the temperature experienced at the top of the insulation on an attic floor in a Ventilated attic. I have learned a lot , though I'm only half way through the reading assignment you gave me. It appears that any information that I get will be pertinent to Florida in particular or the 'southern tier' as opposed to the Louisville, KY area. But, I'll keep reading.
It was my ignorance about these values and the ∆Ts they create that made me wonder about by observations of contractors applying foam to the underside of roof sheathing in my original question
Once I've finished plowing through the first article I'll move on to what I can glean from the last two references, DOE-2 and BeOpt2.
I do understand your point about the relatively minimal impact of a short period of high solar insolation, once subjected to Conduction Time Series, on the final heat gain calculations, and peak cooling load.
If your interested, the graph of my peak design day 24 hour cooling loads, based on my prior ∆T assumptions, is attached. The peak cooling load of 8,023 Btu occurs at around 5 PM.
Thanks Again!

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