# Extrapolating input values from a heat/loss gain report

I’m trying to confirm that the heat loss/gain calcs for my house used the correct values for wall, window, ceiling and slab insulation. The report doesn’t show those input values, but instead shows numbers for BTUH/ft^2. If I just divide that number by the design deltaT, will that give me the implied imperial u-value?

They also used the wrong ACH50 value (1.5, vs design of <0.6, and actual turned out to be 0.22). Is there anything approaching a linear relationship between ACH50 and expected heat loss due to infiltration? Like if I just multiply their number by 0.22/1.5, is that going to be way off? There’s also an “adjustments” line item that is negative. Maybe the software wouldn’t allow an input below 1.5ACH, and they added this adjustment to compensate?

This report was done a couple of years ago, subcontracted through my builder who is no longer reachable, so getting them to answer questions about it might be difficult.

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## Replies

There are crude conversions for ACH/50 to ACH/natural, but they are very crude indeed. The ACH50 number only determines the size, not the locations of the leaks, and location matters. See:

https://www.greenbuildingadvisor.com/article/blower-door-basics

Any conversion you try to make based on ACH/50 has 50-100% error bars on it to the first standard deviation.

If you can scan and post the load calculation summary there may be some hints to glean.

Those same crude conversions will be in effect in any modeled heat loss prediction based on ACH50. I'm just wondering if the formula used is linear, or is there something it that changes the relative importance of the ACH50 as the value changes. I.e., will 1ACH result in half the predicted heat loss of 2ACH, and double the heat loss of 0.5ACH?

I've attached the report.

Yes- half the ACHnatural would be half the heat loss.

For what it's worth, superinsulated homes I have monitored will have a Btu/sf/hdd right at about the ACH50. Let's define superinsulation as hdd divided by 120 for ceilings and 180 for walls and ACH50 of 1.5 or less. Dana is technically correct on the ACH calculation. In my experience, there seems to something else at play when we get to super airtight housing, more efficiency than the just the straight ACH calculation component would indicate. Cosmic forces perhaps.

When I ran some Passive House numbers a while back vs superinsulation this enforced my theory on ACH50 aligning with Btu/sf/hdd for heat load. Passive House did not have twice the insulation but was at least twice as airtight as my monitored homes and used about half the energy for heating.

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What's the consensus then on BEopt calculations for changes in airtightness? Is the feeling that BEopt (or other accepted calculation) is accurate, or erring on the side of caution with regard to the energy impact of airtightness?

Lance; If memory serves me correct and once in a while it does not, Max Sherman at LBL wrote about "infiltration heat recovery". The theory was heat lost through the building envelope due to infiltration was not just a straight loss but some of the heat was retained within the building composition, hence the heat recovery. This is way above my pay grade but it says calculating infiltration heat loss is complicated. As The Who sang those many years ago, "I Can't Explain".

Doug and Lance,

Learn more here: "A Mathematical Model for Infiltration Heat Recovery" by C. R. Buchanan and M. H. Sherman.

So there's a non-linear relationship between infiltration rate and energy loss; decreasing returns with increased airtightness. Still, I think shooting for maximum airtightness is worthwhile especially from an envelope durability point of view.

Thanks Martin!

As I read it, there are more than expected increasing returns with increased airtightness. Ie low flow rates show increased heat recovery.

Trevor; In looking at your report there is a breakout for infiltration as a percentage of heating load (19.6%). This is at an assumed 1.5 ACH50 by the energy modeler. You are an uber tight .22 ACH50, you should be able to adjust the % of heating load for infiltration accordingly. I also see 5.2% for ventilation, does this square with your projected ventilation requirement and the efficiency of the HRV?

My previous post would not apply to ACH50 of less than .6. The correlation between ACH50 and Btu/sf/hdd for heating is just an observation I have made over the years in energy monitoring for new, existing and improved residential buildings.

I have a suspicion that the correlation you've seen between BTU/year and ACH50 is a coincidence more than anything. That's a pretty narrow range of ACH50 you're looking at (0.6-1.5), and your sample size is probably not overly large.

I just experienced a similar correlation of numbers. I was trying to compare the modeled values in the report above to the ones in my PHPP, which are all metric. I accidentally used the per year values in kWh, instead of the demand number in kW. It took a while for me to notice my mistake, because by some weird coincidence, the kWh/year numbers came out to almost exactly the BTU/h numbers in the other report.

I see the correlation on older homes with much higher ACH50 relative to Btu/sf/hdd, homes in the 5 and 6 ACH50 range. With an improvement in airtightness and thermal performance on these homes the 2 numbers seem to track each other.

In drafty homes, infiltration heat loss is a high percentage of total heat loss, this we know. Copious insulation would not likely make a drafty home energy efficient. It is why Passive House has such stringent levels for airtightness and R-values, they must both be in place for very high performance.

Trevor,

To answer your original question. If you divide the 1.1 Btuh by 72 degrees and take the inverse of that, you get R65 walls. It that what you have? Wow that's high! If you don't have those, maybe the report assumes a heat loss per square foot of floor area.

I have some problems with the report, the primary one is that the unit "Btuh" is really "Btu/h". Grr.

Aside from my gripe, are the areas listed on page 1 your actual floor areas? If so, and you don't have R65 walls, then perhaps the report uses 1.054 Btu/h per square foot of floor area to calculate the heat loss through the walls: 1.05 rounds up to 1.1 on the third page of the report and 1.054 times the total square footage of 2769 ft^2 = 2919 Btu/h through the walls at design temperature. At any rate, unless you really do have R65 walls, that's my best guess as to what's going on here.

It's really about R57, using the PHPP method. I don't know what method they used, but it's close enough that I assume they just have a different way of calculating it. We also don't keep the house at 72F, so that somewhat cancels out the R-value over-estimation. They over-estimated the windows too, using centre of glass u-value instead of whole assembly u-value.

The btuh for btu/h substitution is an almost ubiquitous mistake.

I don't remember the square footage for most of the rooms. Based on the conservatory, it looks to me like they used the square footage including the thickness of the exterior walls.

The thing I don't agree with is their entry for "hydronic". I'm guessing that's meant to be heat lost through the bottom of the slab when the in floor heat is operating. But given the total heat going into that is about 15,000BTU/h, they're saying 14% of that is lost? Seems pretty high.

Btuh: mistake or common nomenclature for HVAC contractors? Either way, it irks some of us engineering types that a generated report that can't be changed doesn't use proper units.

It's the common contractor shorthand, much in the same way that they conflate BTUs with BTU/hr depending on the context. Most of them understand the difference, but (surprisingly) some don't quite get that a BTU is a fixed amount of energy that is not time dependent vs. a energy rate.

The number of people who conflate kilowatts and kilowatt-hours are similar. It gets even more confusing when these folks are conflating them in the context of battery storage, where a 5 kwh battery can deliver 8 kw of power.

If you want a really indepth understanding of the AIM2 infiltration model used in the F280 calculations used here in Canada, read this attached pdf.