Help me bust this comical Manual J calculation
Calling all energy nerds. Double check my math. I have a manual J calc in my hands with some weird results. I could go over every little error (some obviously intentional), but you have seen these kinds of things before. What I want to talk specifically is heat loss through the wall. His report does not show the design temps, so I am trying to work backwards through the calculations to figure it out. That’s where I need your help to double check my thinking.
The inputs:
Wall construction – 2×6 frame construction (assuming 16″oc), R-34 closed cell 2lb spray foam, R-2 Board insulation, brick finish. (this is not the actual insulation values. I told him the whole wall values were R36, but I guess the software didn’t have the exact option he was looking for so he made this up himself (actual wall construction is 2×6 studs, blown cellulose, 3″ polyiso exterior, brick).
Area – 1559 (close enough)
Sensible Loss = 5725 BTUs
So, forget the fact that the wall construction is way off (R24 vs R38), let’s focus on how he’s able to get that many BTU loss.
According to EngineeringToolbox.com, I see the formula to calculate heat loss through a material as…Heat Loss = (U-Value) x (wall area) x (temperature difference)
So if I want to solve for “Temperature difference”, the formula needs to be…
Temperature Difference = (U-Value x Wall Area) / Heat Loss
In this case, we know that he says the heat loss is 5725 BTUs. If my figuring is correct, his wall construction up there adds up to a whole wall value of R24, which makes the U value .0416.
So, if my basic math skills are right…
(.0416 x 1559) / 5725 = 89.45 degrees!
Am I thinking about this right?
For the record, the actual details are…
R38 wall, which has a U-Value of .0263
Area – 1613
Correct design temperature difference = 70F-13F = 57 degrees
That results in a 2400 BTU heat loss through the walls.
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Replies
It may not be as bad as I thought.
Another way to get to the number is to look at the infiltration load, thanks to Dana Dorsett's work on another post. He is calculating a infiltration CFMs of 173 in the winter which equals a heat loss of 13,265 BTU.
In the other post, Dana tells me to (quoting him here but putting in the new numbers)...
"... multiply CFM by 60 minutes/hr, which gives me 10,380 cubic feet per hour. For that to add up to 13,265 BTU/hr means there is 13,265/10,380 = 1.277 BTU per cubic foot of ventilation flow, which implies in indoor to outdoor temperature difference of about 1.277 / 0.018= ~71F temperature difference..."
Read more: https://www.greenbuildingadvisor.com/community/forum/general-questions/98349/common-heating-loads-be-much-higher-cooling-zone-4a#ixzz4IBOBBlZV
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So maybe it isn't quite as terrible as a difference of 89 degrees, but 70 degrees for our outdoor design temps assumes that we are keeping our indoor thermostat on 80F in the winter.
Clay,
A couple of points. First, the units. The usual unit used to report a heat loss calculation is Btu/h, not Btu.
You are calculating a heat loss rate -- per hour.
You are correct about the heat loss formula. The heat loss formula for determining transmission losses through floors, roofs, and walls is Q = A • U • ΔT. In other words, the rate of heat flow through a building assembly (in Btu/h) is equal to the area of the assembly (in ft²) times the U-factor (in Btu/ft² • hr • F°) of the assembly times the ΔT (in F°).
Your math is correct.
0.0263 * 1613 ft² * 57 F° = 24,180 Btu/h
You haven't attached a document, so we can't really figure out what went wrong with the calculation you're referring to. If a consultant or a contractor performed the calculation, then your questions should be directed to the consultant or contractor.
For more information, see How to Perform a Heat-Loss Calculation — Part 2.
Thanks Martin. You've got a decimal in the wrong place for my U factor, but thanks.
The deal is that I'm trying to reverse that formula to figure out what this contractor is using as his temp difference. But in my first post I think I am overestimating his whole wall R value. All I have on the report is the description, not the actual RValue or U factor, so I took the description and tried to calculate the R value. In my 2nd post, I work at if from a different direction and get a different temp difference, so I think I have it figured out now. He's using I must be overestimating this guys whole wall R value. Based on the description, I was figuring an R24 whole wall, but crunching the numbers based on 70F delta T it must be R18.
Clay,
Oops! Thanks for catching my decimal place error. I have corrected it.
A 2x6 studwall 16" o.c. runs about a 25% framing fraction, and with R34 (5.25" of R6.5/inch) ccSPF + R2 of continuous foam over the sheathing will come in at about R20 whole wall (all-in, air-films included), or U0.050.
If you did 24" o.c. stud spacing the framing fraction will be about 20%, raising it up to ~R22 whole wall or U0.046.
With 5.5" of half-pound ocSPF instead of the ccSPF it would be about R18.5 (U-0.054) whole wall for 16" o.c. spacing, R20 (U0.050) if 24" o.c..
With 5.5" of cellulose cavity fill and 3" of polyiso that would run about R34.5-ish (U0.029) if 16" o.c. or R36-ish (U0.028) if 24" o.c..
That's a pretty significant difference from the R34 cavity fill + R2 continuous option.
If you can share your ZIP code/postal code we can better estimate what the outside design temp is, and the proper delta-T you should be using. For code compliance you should be using an interior temp of 68F, not 70F (but you can set the temps anywhere you like- it'll usually keep up even if you set it to a sweaty 85F), and use the 99th percentile temperature bin, not the 99.6th or some other temp for the outdoor design temp unless local codes demand otherwise.
Thanks Dana. I knew I could count on you! You've looked up the design temps for me in the past...
"According to ACCA datasets the 99% and 1% outside design temps for Lexington are +10F and 89F respectively:
http://articles.extension.org/sites/default/files/7.%20Outdoor_Design_Co...
According to AHRAE it's +12.7F and 89.3%
https://www.captiveaire.com/catalogcontent/fans/sup_mpu/doc/winter_summe...
"
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OK, when it's +10F outdoors and +68F indoors it'll be a 58F delta, if I can still do that math in my head... ;-)
So figure on U0.030-ish for the walls (... x 58F = 1.74 BTU/hour per square foot of wall ) and it'll be close enough for heat load calculation purposes, without getting into the minutae of how much the polyiso really needs to be derated for temperature. It's performance most of the season would be slightly better than that, and when it's really cold slightly worse, but the magnitude of the difference is somewhat "in the measurement noise" of the other error factors (such as the real vs. estimated air leakage, etc.)
Thanks again Dana. So updating this other guy's Manual J calcs to solve for his temperature difference, he has...
(.050 walls) x 1559 / 5725 = 73 degree Delta T. That's a pretty harsh winter day for central Kentucky (or a balmy 83F indoor temp!).
...or the absolute coldest day of the past 50 years in Lexington?
The all-time record low temp for Lexington was a none-too-balmy -21F (yup, 21 below!) back on 23 January 1963:
http://www.kyclimate.org/factsheets/recorlowtemp.html
So, if you sized it EXACTLY for a 73F delta-T and it hits -21F again you'd still need some sweaters, with an indoor temp of 52F.
With an interior design temp of 68F and a 73F delta you'd be at -5F outside, which probably does drop below that at least once every decade or so. The last time was in 2004, but a decade before that it bumped on -20F again:
http://weather-warehouse.com/WeatherHistory/PastWeatherData_LexingtonBluegrassArpt_Lexington_KY_January.html
You'll note that it hit well into negative double digits a few times in the 1980s too, but it's silly to design to temps that may not occur more than a couple of times over the lifecycle of the heating system- auxilliary heating (or sweaters & blankets) make more sense.