Heat Load – Linear or not?
Hi all,
Back in November, I embarked on a research project to replace my home’s 1995-era heating and cooling system. I have learned so much already from this site and elsewhere and continue to learn.
I know it is popular on this site to go all-electric but I feel like I will get the best value from a hybrid system which will use the heat pump most often and costs less to install than an all-electric (for some reason I don’t understand).
I’ve been working on a heat load chart (attached) using the runtimes of my single-stage furnace as reported by my Nest and mean daily temperatures as reported by Environment Canada. I also included the modelled load which I got from my energy audit report. I also did a hvac sizing using this tool (https://hvac.betterbuiltnw.com/Common/Sites.aspx) and got ~32K.
Today I had a conversation with one of the local hvac companies and he said that heat load is not a straight line. It will curve up as the weather gets cooler, and thus proposes a 60,000 BTU/h furnace. (Note: My current furnace is a 92% efficient 50,000 BTU). This will be my first winter in this house.
My question is should I test my current system through winter, and keep charting to find out the truth about my home’s heat load OR can I make assumptions from the data I’ve gathered so far OR should I trust the hvac installers all of whom are proposing 60K furnaces?
Thanks!
Heat Load chart: (full res.) https://images.greenbuildingadvisor.com/app/uploads/2023/01/11145129/48563_1673466688_heat-load.png
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I'd be interested to see evidence that heat loss isn't basically linear. Here are 1500 days of gas usage plotted against HDD 65 and it sure seems linear. Maybe not if it gets especially cold? Surely a furnace contractor can show actual data to support this!
Regardless, you have a smaller existing furnace then the contractors are proposing, so if it held up during the coldest weather this year, the contractors are wrong.
"I know it is popular on this site to go all-electric but I feel like I will get the best value from a hybrid system which will use the heat pump most often and costs less to install than an all-electric (for some reason I don’t understand)."
Usually, the hybrid option uses a lower end heat pump, that's all.
"Usually, the hybrid option uses a lower end heat pump, that's all."
That's unfortunately what I'm learning, as I look at "dual-fuel" systems. Looks like 15-16SEER, 8.5 HSPF, and only two-stage vs variable-speed.
Not the end of the world - some single speed and two stage equipment is pretty efficient. Undersizing it slightly for heating can actually come pretty close to variable speed - the modulation on many ducted variable speed heat pumps isn’t all that great at warmer temps. Maybe 2:1?
@JasonK Which systems are you looking at?
I found a hybrid system from Carrier which is variable and 10 HSPF (https://ashp.neep.org/#!/product/53888/7/25000///0). But apparently the blower motor runs at a fixed speed with the variable heat pump, so I'm not sure if that's worth investing in.
I do wonder about the numbers though. Can the manufacturers fake their numbers?
I talked to one Trane dealer and mentioned to him that the XV19 doesn't do well at low temps. He told me that most manufacturers lie about their numbers, trying to tell me that Trane's numbers are 'true'. I have no way of knowing if this is accurate or not however I do know that I was not able to find Trane's performance data ANYWHERE on the internet. I just found the relatively poor performance numbers for the Trane on the NEEP website (https://ashp.neep.org/#!/product/28341/7/25000///0). Unfortunate because that unit is really quiet and I like that.
@tkzz maybe I'm just not used to the neep site, but I don't see that indicated as a dual-fuel system at all?
On Carrier's webpage, this is the best I see: https://www.carrier.com/residential/en/us/products/combined-heating-cooling/48vr. I don't see an "Infinity" dual fuel system.
Can you tell me what I'm missing?
Sure. If the "Furnace Model #" field on the left has a model number, then it is a hybrid system.
The "Indoor Model #" in the hybrid case refers to the coil in the plenum.
The system I mentioned is not an "Infinity" though.
Packaged systems like the one you linked to are an entirely different thing.
"Packaged systems like the one you linked to are an entirely different thing."
Apparently I have much yet to learn about HVAC systems. Thank you for the info!
There are some errors on the neep site in the Trane data by the way.
The COP should be in the 3ish range, but the Trane is not a cold climate model and falls off a fair bit as it gets colder. Ideally I would want something that can almost entirely replace the gas heating, but have the furnace there just in case.
What the contractor probably means is that one of the components of the equation dictating thermal loss through something (like insulation) involves the temperature differential between the two "sides" of that "something". That means if you maintain a constant temperature in your house, the colder it is, the more energy you lose. Windy days will also make you lose more. I'm not so sure the effect is severe enough that you'd really see in practice though. There is some advantage to having a little extra capacity for an unexpectedly cold day though. I would recommend you have an energy rater or engineer help you size things. Contractors are notorious for OVER sizing systems.
I think you can get pretty close using your "track it over the winter" method, but keep in mind that in many areas this winter has been mild, which would cause you to UNDER estimate the heating capacity you really need. In my area, for example, we have had a surprisingly mild winter (aside from a really cold week in late December), but last year we had near record low temperatures. If you size your system based on a single season's worth of data during a mild winter, you'll be undersized.
I'm not sure about your statement about all electric costing more than a heat pump? A heat pump IS all electric. Heat pumps are cheaper to operate because they "pump" heat -- in from outside, instead of making the heat outright like a burner or electric resistance element would do. Heat pumps "scavenge" residual heat from outside. That's where the efficiency comes from. In most cases, the heat pump will be cheapest to operate due to it using the lowest overall amount of energy to heat the space over time. In extremely cold weather, that might not be the case, but with a hybrid system you have a backup heat source so you'll have the best of both -- run the heat pump whenever it is able to run, and use the conventional system only on really cold days when it's needed.
Bill
Thanks Bill you have good point regarding the mild winter however temperature is temperature and if heat load is linear, I can use my chart to see what my load would be at whatever temperature I need to. In this case, 30,000 BTU/h at -22F (-30C). Toronto rarely hits -30 but it happens here and there. Therefore, to me, a 40,000 BTU/hr furnace would be good as opposed to the 60K one being proposed by the installer, but – back to my original question – I'm assuming heat load is linear.
My point about cost was not about electric vs heat pump operating costs, I meant to compare the installation, or capital cost of an electric heat pump system to a hybrid heat pump/gas furnace system. Operating costs are probably a wash at least where I am (Toronto, Canada) unless gas rates rise more which they might. I do like the idea of reducing my gas consumption as much as possible using a great heat pump unit, while still having the safety net of the furnace, particularly given that the installation cost of the hybrid is less.
This is a question I've wondered about. Basically all of building science assumes linearity -- it's the assumption behind R-values and U-factors. Air infiltration models assume that infiltration is linear with temperature difference. The degree-day as a unit implicitly assumes that heat loss is linear, that ten days at five degrees difference is the same thing as one day at fifty degrees.
I have to assume that if those models weren't useful they wouldn't have survived.
That said, no model beats direct measurement. What you are doing is going to give the best picture of your house's actual performance. The only question is how large of a sample do you need to feel comfortable with your results? It's still kind of early in the heating season. But it's pretty clear that a 60K system is going to be oversized.
With gas or oil-burning furnaces there wasn't much penalty for oversizing, often the next size up was just the same equipment with a different jet. In my climate the ductwork is sized for air conditioning anyway so oversizing the furnace doesn't mean increasing the size of the ductwork. But with heat pumps the cost goes up with the size so you do want to get it right.
Is the hybrid system heat pump and gas? One of the things about heat pumps is the output goes down as the outside temperature goes down. So one sized for your 90% temperature is going to be a lot smaller than one sized for your 99% temperature. I could see how that saves money.
Thanks, good info. Also aligns with my research so far. The installer must be misinformed (not surprising ha ha).
While my existing system works I'm going to continue sampling and aim for an early spring installation of the new system...
The hybrid systems I've been considering at are heat pump plus gas furnace yeah. I have been looking at specs on the neep website and have definitely noticed big differences in the falloff of heat output across different heat pump models. I've also noticed that energy use can go up quite a bit as temperature drops and output increases. There is a noticeable tradeoff between COP and max heat output which adds to the case for a hybrid system. There are also some units that just can't keep up regardless of energy use, such as the Trane XV19. Too bad because it seems like a sweet unit (quiet and compact).
I think the non-linear effects are effectively "swamped" by everything else, so the nonlinearities end up being so small that they don't really matter all that much. There are a lot of things that act together to "lose" energy in a house, since it's the walls where they're insulated, the thermal bridges in the walls, the windows, doors, all the little air leaks, etc. etc. etc. The final result ends up being pretty linear even if some of the individual components that make up that final result might not be.
You're right about gas furnaces too. Usually a number of different BTU ranges use the same size blower, so you can upsize the burner's BTU and not really change things a whole lot, since the combustion efficiency will still be whatever precent the rating of the furnace is -- all that happens is the cycle time gets shorter for the same conditions in the same house when you use a higher BTU rated furnace. There is no efficiency penalty, although there might be a comfort penalty if you oversize too far, since you need the blower to run long enough to stir the air sufficiently that temperatures throughout the house become relatively easy. I suppose you could compensate for a severely oversized furnace somewhat by setting a smart thermostat to run the blower more even if the burner isn't running, but that's probably not ideal. I doubt there would be any noticeable difference if you only upsized the furnace 10% or so though.
Bill
If you look at the actual physics of heat loss in a building, most of the terms are linear. There are a couple of non-linear terms such as the R value VS temp Bill mentioned and radiation loss but these are small overall.
Probably the only time you'll see inconsistent data for your runtime VS outdoor temp is when it gets warmer when solar heat gain which is variable can supply a good portion of the house heat.
Thanks for your feedback!
The solar gain is a fair point, but since I am measuring actual furnace usage, and on multiple days, the loss of heat from the reduced solar gain of the winter should be incorporated into my results by default. We have also passed the 'worst' days for solar gain according to this: https://marmottenergies.com/much-sun-heat-house/
Solar gain is going to cause you to underestimate heating load.
On a sunny day your heating usage is going to be much less as a sunless day with the same temperature. So by calculating heat usage against mean temperature, you're understating what the heat usage would have been without sunshine. But the design goal is going to be to size the system for the coldest time, which presumably is going to be in the middle of the night.
Interesting take ... I might be missing something, but I think this is accounted for since I am pairing up daily averages of furnace usage and temperature. Wouldn't the steepness of the line be the same if I looked at night time numbers only, assuming that it's a linear relationship?
Perhaps the important part is at what temperature should the max energy load be selected? Not the 'design temperature', because that wouldn't cover the coldest day. If the coldest day is -30C (-22F), pretty reliable for Toronto, then I'd be looking at a max load of 30,000 BTU/h. Easily covered by a 40,000 BTU/h furnace, and the 99% would be covered by a 2-ton heat pump.
Happy to be shown that this is wrong since I'm still learning.
You should use the design temperature. It will occasionally be colder than design temperature, and you be okay. The daily average of -22 is actually more conservative - design is an hourly measure.
For giggles, I pulled the degree day for YYZ for the last 3 years, there has been 11.9 degree days bellow -15C, zero -30C degree days.
It does feel like it gets cold here, but not that cold. Even when it happens it would be in the middle of the night, your heat not keeping up for an hour or two which will barely budge the temperature inside the house and will be back to normal by the morning.
No need to add in a fudge factor, stick to the 99% design temperature, the heat will work just fine.
Thanks guys... well it sounds like i'll be quite alright with the smaller 40K furnace that has a 25K lower stage and the 2 ton heat pump. I can play with the cutoff point to optimize for comfort or energy usage. The 60K furnace just sounded crazy and it's nice to hear that I don't need to go there!
By the way what is the design temp for YYZ based on your resource? I found 1 degree F but the hvac guy said it was -3?
SB1 calls for a -4F design temp, bit colder if you are further from the lake.
Thanks, -4 then, good to know!
That puts me squarely at 24,000 BTU/h.
Akos, what equations or terms are you referring to where there is non linearity?
Old houses aren't the best at stopping the wind from entering the building. That can lead to bigger heat losses even if the temperature stay the same. Maybe this is what he's thinking of.
In a modern house with a good air barrier, it doesn't matter as much so a linear relationship is a pretty good approximation.
Good point... my house is not modern but it has had updates done by a previous owner. I had an energy audit and the report said ACH4 (at 50 Pascals). What do you think?
Before reading this thread I thought that heat loss was linear with delta-T (difference between IDT and ODT). E.g., if you keep your house at 68, your heating load will be twice as high at ODT = 28 than it is at ODT = 48.
And I thought I had learned that on this site.
Is that the same as saying that heat load is linear with ODT?
It's linear with ODT, the y-intercept is non-zero. In fact, the y-intercept is IDT.
Thanks for clarifying. My ability to do math and visualize graphs isn't what it once was... hah.
My experience shows that heat loss is linear to outdoor temp. I have a well sorted out boiler setup with outdoor reset. The outdoor reset “curve” is actually a straight line for outdoor temp vs water temp and has worked well over a dozen winters. To me that is sufficient practical data confirming heat loss is a linear function.
Super. Thanks for your insight!
Heat loss is linear, but relative contribution of passive solar and waste internal heat gain (appliances, people) is not. In a super insulated house, you might not start using heat until it gets down to 10C or lower, at which point the curve will get steep pretty rapidly and then become linear.
If you're using a heat pump, energy usage will not be linear, since efficiency changes over temperature and load.
Q=UA∆T
Which equations would point to non-linearity?
Trevor makes two succinct and good points though. Stack effect would also increase.
That equation describes heat transfer due to conduction. Heat transfer is also possible due to convection and radiation.
Heat transfer due to radiation is described by the Stefan-Boltzmann law, which is proportional to the fourth power of temperature:
https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law
Convection is complicated because it is driven by the difference in density in a fluid at different temperatures and the change in density with temperature is not constant.
DC,
Without giving this too much thought, isn't the temperature variable in the radiation equation (Stefan-Boltzmann law) actually constant here? As we all know, radiation does care about delta T. Delta T will inform what is received in return, and of course solar radiation may dominate that. So I guess one could say as it gets really cold out, and if there is little solar gain, the received radiation degrades exponentially...?
Also, people above mentioned R value and some sort of non linear relationship and I still don't see where they were coming from there.
Convection, of course, is a bit of a chaotic factor when air sealing is poor.
Part of it is that R value is not constant with changing temperature -- R value varies a bit as the mean temperature through the insulating material changes. This variation is different for different insulating materials. Probably the best known example is polyiso's generally lower effective R value in very cold temperatures, but all materials are affected to varying degrees (no pun intended there).
I would say that *most* things involved here are linear, but not quite all. What you end up with is that the "most things" tend to dominate the overall system, and "swamp" (effectively obscure) any nonlinearities, so you end up with an overall system that tracks fairly linearly with temperature.
Bill
"isn't the temperature variable in the radiation equation (Stefan-Boltzmann law) actually constant here?"
As I think on it more, im wondering if that temp variable would actually be REDUCED when it's cold, since it would primarily be the temperature at the exterior we are concerned with for radiation (assuming radiation within the wall assembly is minimal). Not that it matters in a practical sense.