Is the heat loss calculation linear --at all?

john123

Suppose you have an expert-type heat loss done and it comes in at 80,000 BTU's per hour with an indoor temp set at 70*F and an outdoor design temp of 30*F. Can you say that it's 2,000 BTU's per hour per degree F? ((80,000/(70-30))

OR if the heat loss was done on a "base" indoor temp of 68*F to account for the presence of inhabitants etc., can you say that it's 80,000/(68-30)=2,105 BTU's per hour per degree F?

So that if you were going to replace the boiler and want to cover a lower range of outdoor temperatures-- say 10*F, can you use the old heat loss and recalculate (extrapolate) at 80,000 plus 20x 2,000 for a total 120,00 BTU's per hour?---or more simply 60x 2000=120,000 BTU's per hour? And use this new heat loss calculation to specify your new boiler.

Hot_water_fan

I think it is linear enough to do that. That’s how the manufacturers teach it too. But besides that, I’d size the boiler for the actual design temp to start, add a bit (maybe 20-40%) to cover for setbacks and such. Then roll. It won’t really matter - the sizes of boilers are pretty lumpy. 

ChrisJ

I've found infiltration is not linear.

In my case, the temperature is fairly linear from around 20F-50F.
Below 20, infiltration starts ramping up and I forget exactly how unilinear it is, but it's a pretty big increase as it goes below 0F.

Jamie Hall

Not to worry. The basic assumptions in the equations used for heat loss are that it is linear. Are those assumptions correct? Well... no. But they are close enough for normal ranges of outdoor temperatures that you can use them.

As @ChrisJ notes, though infiltration losses are NOT linear, and do increase significantly as the temperature difference increases. Again, within a normal range -- OK. But if you live in a windy area, or it gets much below zero part of the time, I'd be adding a fudge factor (oh excuse me: "a qualified engineering adjustment". That sound better?)

STEVEusaPA

There's enough fluff in a proper Manual J that I would never oversize. Emphasis on proper.
I'd say tight, sealed up houses are more linear, leakers, much less so.

john123

Thanks for your input. This is theoretical question---in practice the answer may be different for all the reasons a "fudge factor" is often used??? The problem is that, with a program, you enter all the data and then the program does all the calculations for you. From first principles, I understood you added up all the heat loss (areas x U value) and then just multiplied that by the delta temp difference between the set point and the outdoor design temp----to get the BTU's per hour. That would make it linear based on each degree of difference, I am guessing the science says the heat loss is the same whether it is based on the difference between 70* F and 69* F or based on the difference between 11* F and 10* F. But do you think or know whether the program has a non-linear factor for example for air infiltration depending on the outside design temperature. It seems that it should not based on the science but if anyone knows or can lead me to a source, it would be helpful.

Jamie Hall

Actually, based on the science, the infiltration factor is non-linear, since infiltration is driven by pressure difference -- and is very closely proportional to the square of the difference.

The problem, of course, is that the pressure difference driving infiltration is not solely determined by the temperature difference. Not only is the pressure difference from temperature altered by the geometry of the structure,. it's also driven -- usually even more than by temperature -- by wind speed and direction in relation to the geometry of the structure.

@STEVEusaPA is quite correct in saying that usually there is enough fluff in the really good programs to handle the infiltration (and other errors) to produce a conservative value -- for most conditions.

hot_rod

I would guess from a temperature only perspective it would be linear. That is how outdoor reset curves work

But wind, infiltration, and solar  gain would play a part along with building use

john123

Does temperature difference actually create pressure and actual air movement? Is that why you perhaps sometimes really feel the cold in uninsulated houses in very cold conditions. Perhaps like you feel the air is very slightly moving from your body towards the cold walls? I thought it was all radiant but maybe there is very slight air movement too?

In heat loss calculation programs, I thought each wall/door/window was subject to an average wind speed and average direction. Perhaps those averages would change with the change to a lower design day temp. Are these programs that sophisticated?

Once again, the question is whether you can use the result of a heat loss with one design day temperature to accurately interpolate or extrapolate for a different design day temperature. I suppose you could plot a curve but if it is linear, then you can do it yourself.

EdTheHeaterMan

@Jamie Hall Love the QEA Factor. I will no longer use the fluff, or fudge, or even Kentucky Windage... ever again. I love Technical terms like that!


I just looked at an old hand written load calc form from the Hydronics institute (I=B=R Form 1540 WH) to see how they account for infiltration. That form uses the volume of the conditioned space for the multiplier and a factor to represent the type of construction and then the ∆T based on the published outdoor design temperature.


So as far as the GAMA folks are concerned (I=B=R is now part of GAMA and therefore part of AHRI) the infiltration is linear. But that form may be obsolete by today's standards (see screen shot of page 3 in the attachment)

Does anyone do loads by hand with a pencil and paper anymore?

hot_rod

In your home its call drafts where the air movement across your skin causes the room to feel cooler. Outside we call it the wind chill factor. Dan referred ut to cold 70 when walking down a supermarket frozen food aisle 

The air temperature is 70 but the food cases pull heat from your bare skin causing that cold sensation

A heat loss calculation us an exact point in time. Assuming all the measured or known variables at one point in time gives you a number

I don’t know that you could ever accurately measure all the variables the go onto a load calc

To answer your question you could run the calculations with various temperature only changes and see what that looks like
If you are using a software it should  be easy to make that change and graph the result

Hot_water_fan

From my limited experience, outdoor temperature is the variable that matters. I’ve tried measuring wind and solar gain and it doesn’t move the needle, probably because it’s a harder to measure. If someone has more advanced measurements for these, or others, please show me! 

hot_rod

If you have a leaky house and identify that leakage number with a blower door test, you would have some actual data to crunch into the load calc

Dave Carpentier

And dont forget about non-condensing appliances that dont have sealed air intakes.
The colder it gets outside, the more the unit runs and sucks cold air into the building either thru a dedicated combustion air intake, or thru envelope cracks and holes via old-school intake.
Not an issue with sealed intake condensing heaters though.

ChrisJ

hot_rod said:

If you have a leaky house and identify that leakage number with a blower door test, you would have some actual data to crunch into the load calc

Except a blower door test doesn't tell you how the actual chimney effect behaves in the structure vs outdoor temperature. It just tells you how leaky it is.

I haven't bothered with my house because I don't need a test to tell me it's drafty, I know it's drafty.


Similar, I stopped using a pool thermometer. I don't need a thermometer to tell me if I think the water is cold or warm. I stick my hand in.

hot_rod

ChrisJ said:

hot_rod said:

If you have a leaky house and identify that leakage number with a blower door test, you would have some actual data to crunch into the load calc

Except a blower door test doesn't tell you how the actual chimney effect behaves in the structure vs outdoor temperature. It just tells you how leaky it is.

I haven't bothered with my house because I don't need a test to tell me it's drafty, I know it's drafty.


Similar, I stopped using a pool thermometer. I don't need a thermometer to tell me if I think the water is cold or warm. I stick my hand in.

The more accurate the data you enter into the calculation, the more accurate the answer. ACCA shows infiltration categories from Tight to Loose. With Loose resulting in 6X more heat loss. A blower door test would at least tighten up this assumption.

I can measure a piece I am turning on my lathe with a tape measure or micrometer. Depends on how accurate of a number I want

Room by room loose is also important, as a garage would probably have more leakage then an insulated below grade basement room.

To the OP, Chapter 2 in Modern Hydronic Heating and Cooling goes through all the components and variables of a heat load calc. Plenty of math to help answer the "how come" questions.

exqheat

Precision is available from indoor reset, to tame the usually oversized system. Nature tells the surveyor, fudge for error.

john123

thanks for all the comments

So I did a simple heat loss myself by measuring all the surface areas, finding their U values, adjusting the U values up or down as I thought necessary to reflect the "condition" of the surfaces, and then multiplying by those U values, and then multiplying the sum by the difference in temperature between the thermostat and the record outdoor low temperature.

So I didn't use the "base" temperature; there was no adjustment for wind or direction or face (I just took the overall average), no adjustment for the openness of the adjoining properties etc..

But the formula was linear! I believe.

Then I had the heat loss done by an expert, complete with the blower door test and very accurate measurements, broken down by direction etc., using one of these very complicated computer programs. I am guessing he put all the numbers into the computer and pushed the green button. The design day temperature he used, was a modestly cold number but nowhere near the record. I recalculated it based on the record outdoor low temperature but used a linear relationship to the delta T.

I believe my original calculation was linear with respect to the delta T and could/can be adjusted quickly to different outdoor design day temperatures. The question is are these sophisticated Heat Loss programs, or the sophisticated heat loss calculations behind them--- linear or almost linear with respect to the delta T. If you want to take the sophisticated computer calculated heat loss number, and adjust it to a different outdoor temperature, how close will you be?

So could you say to a customer (Me), "your heat loss at the outdoor temperature of xx*F is yyy k Btu's per hour; this boiler has an output of zzz k Btu's per hour at that outdoor temperature and you'll be comfortable. If you want to be comfortable at the "record outdoor low (of this city---) aa* F, the heat loss will be BBB k BTU's per hour and you will need to have a higher capacity boiler.....and the price will be ...???

You can do this easily on the fly if the formula is linear.

exqheat

Most contractors do not do the calculations. They replace what is there, after asking, "How was the heat before?" Most are oversized before as they did not know how to size. Best practice is to tame that boiler hour to hour with an indoor boiler temperature reset. No matter the size the boiler will be operating at less than design temps 90% of the time. So let's tame what ever you install. Simply make sure it will cover you at design temps.

The Steam Whisperer

As someone state earlier, Air leakage is very much non-linear, especially at extreme temperatures. From my old ASHRAE in my Mechanical Engineering Text, if you are have a medium tightness home, the air leakage rate at 50F outdoor is 0.6 Air changes per hour. The same structure will have an air leakage rate of 1.2 Air changes per hour at -10F with the same 15 MPH wind.

Also, up to date outdoor reset curves at not linear, likely in part due to the fact that the type of heat emitter effects how much the system responds as water temperatures rise. IIRC, all of Tekmar'ss reset curves accelerate in extreme temperatures, not matter what type of emitter.

On a practical note, I typically calculate heat loads from historic monthly fuel usage and temperature data and calculated estimates of the efficiency of the current equipment when operating at the loads shown be the historic fuel usage. This usually gives me a heating plant capacity for a building at around 60% of peak design load. When extrapolating out to the design load, and add 15% to make up for the accelerated air leakage, when calculated for older buildings that use steam or hot water systems. For buildings with typical forced air systems, this may not work, as DOE testing has shown that these buildings leak significantly more due to the presence of the ductwork system ( about 12% increase) and the air leakage rate doubles from a non ducted building when the fan is running.

Hot_water_fan

The design day temperature he used, was a modestly cold number but nowhere near the record. I recalculated it based on the record outdoor low temperature but used a linear relationship to the delta T.

A bit surprising perhaps, but you should not use the absolute coldest temperature. You use the design temp.

GGross

@john123

With software calculated manual J, you can just change the design outdoor temperature, and generate a new load based on whatever outdoor conditions you specify. I have done this many times to show contractors the load required for a project at different outdoor temperatures, as well as to better determine supply water temperatures required at different outdoor temps to better set a heating curve. The process to change the temp takes less than a minute in my experience.

The Steam Whisperer

Hot_water_fan said:

The design day temperature he used, was a modestly cold number but nowhere near the record. I recalculated it based on the record outdoor low temperature but used a linear relationship to the delta T.

A bit surprising perhaps, but you should not use the absolute coldest temperature. You use the design temp.

If you are sizing conventional fired systems, using the design temperature is what to do. This usually will cover 98% of the heating season. However, if using heat a heat pump, its much more complicated. The problem is that as you drop below design temperature, the heating capacity of the heat pump is steadily dropping I.E. ....Here in Chicago, the design temperature is about 0F, However, we have hit -25F as records. A fired system that is designed right on will be able to keep a building warm at 70F when it is 0F outside with let's say 100,000 btu/hr, so for the most part it will be able to maintain the building at 45F if it is -20F outdoors ( more or less, depending on ground contact tempering for example), also needing 100,000 btu/hr. However, with a heat pump, when you're below design temperature (0F) the heat pump capacity is now lower, so you can no longer producing 100,000 btu/hr so you can no longer maintain a 70F differential between the outdoors and indoors. The interior temperature will now drop lower than the 70F differential. This issue seems to currently be ignored in design calculations. As an example, we have a client that had a Heat Pump system installed to heat a large space. They could heat to 70F when it was 0F outdoor. However, when we had some extreme extreme outdoor temperatures ( -10 to -12F) a year or two ago, and they could not get the building above 40F. I have not been able to find what the COP is for a heat pump at 0F versus -25F, but I bet it is quite significant in a percentage or reduced heating capacity.

Hot_water_fan

If you are sizing conventional fired systems, using the design temperature is what to do. This usually will cover 98% of the heating season. However, if using heat a heat pump, its much more complicated. The problem is that as you drop below design temperature, the heating capacity of the heat pump is steadily dropping I.E. ....Here in Chicago, the design temperature is about 0F, However, we have hit -25F as records. A fired system that is designed right on will be able to keep a building warm at 70F when it is 0F outside with let's say 100,000 btu/hr, so for the most part it will be able to maintain the building at 45F if it is -20F outdoors ( more or less, depending on ground contact tempering for example), also needing 100,000 btu/hr. However, with a heat pump, when you're below design temperature (0F) the heat pump capacity is now lower, so you can no longer producing 100,000 btu/hr so you can no longer maintain a 70F differential between the outdoors and indoors. The interior temperature will now drop lower than the 70F differential. This issue seems to currently be ignored in design calculations. As an example, we have a client that had a Heat Pump system installed to heat a large space. They could heat to 70F when it was 0F outdoor. However, when we had some extreme extreme outdoor temperatures ( -10 to -12F) a year or two ago, and they could not get the building above 40F. I have not been able to find what the COP is for a heat pump at 0F versus -25F, but I bet it is quite significant in a percentage or reduced heating capacity.

Right. You should size the heat pump to the heat loss (based on output, just like a condensing boiler that also can lose capacity at low outdoor temps). Or incorporate a backup source to cover the shortfall. No big deal.

The Steam Whisperer

Hot_water_fan said:

If you are sizing conventional fired systems, using the design temperature is what to do. This usually will cover 98% of the heating season. However, if using heat a heat pump, its much more complicated. The problem is that as you drop below design temperature, the heating capacity of the heat pump is steadily dropping I.E. ....Here in Chicago, the design temperature is about 0F, However, we have hit -25F as records. A fired system that is designed right on will be able to keep a building warm at 70F when it is 0F outside with let's say 100,000 btu/hr, so for the most part it will be able to maintain the building at 45F if it is -20F outdoors ( more or less, depending on ground contact tempering for example), also needing 100,000 btu/hr. However, with a heat pump, when you're below design temperature (0F) the heat pump capacity is now lower, so you can no longer producing 100,000 btu/hr so you can no longer maintain a 70F differential between the outdoors and indoors. The interior temperature will now drop lower than the 70F differential. This issue seems to currently be ignored in design calculations. As an example, we have a client that had a Heat Pump system installed to heat a large space. They could heat to 70F when it was 0F outdoor. However, when we had some extreme extreme outdoor temperatures ( -10 to -12F) a year or two ago, and they could not get the building above 40F. I have not been able to find what the COP is for a heat pump at 0F versus -25F, but I bet it is quite significant in a percentage or reduced heating capacity.

Right. You should size the heat pump to the heat loss (based on output, just like a condensing boiler that also can lose capacity at low outdoor temps). Or incorporate a backup source to cover the shortfall. No big deal.

While it may not appear to be a big deal, however, it appears that this is not being done so it likely there are going to be freeze ups in buildings or the building will be uninhabitable for many people that cannot live in 40F temperatures for extended periods. So it can be a very big deal.

ethicalpaul

But wait didn't you say that even a fired system will only hold around 45 degrees during these bitter cold days? 45 is ok but 40 is panic-inducing? With both kinds of systems, without proper design and/or backup there are problems, why is only the heat pump one scary?

A fired system that is designed right on will be able to keep a building warm at 70F when it is 0F outside with let's say 100,000 btu/hr, so for the most part it will be able to maintain the building at 45F if it is -20F outdoors

Hot_water_fan

While it may not appear to be a big deal, however, it appears that this is not being done so it likely there are going to be freeze ups in buildings or the building will be uninhabitable for many people that cannot live in 40F temperatures for extended periods. So it can be a very big deal.

I’m not pro-freezing anyone! Contractors need to do their jobs. 

ChrisJ

What's the design temperature in Chicago IL?

Since it looks like extremes are -20F on a rare occasion for a short time, I'm assuming design temp is around 0F?

Jamie Hall

Whether you are worried about freezing your clients or not -- remember that in most jurisdictions you can't get a Certificate of Occupancy unless you can show that the heating system can hold temperature -- usually around 70 on the design day. For a DIY job, no big deal -- until you try to sell the place or remortgage it. For a pro., this can be a big deal...

exqheat

So designing for design temp makes the case that your boiler will be oversized the rest of the time.
All the more case for indoor boiler temp reset.

STEVEusaPA

exqheat said:

So designing for design temp makes the case that your boiler will be oversized the rest of the time.
All the more case for indoor boiler temp reset.

…or modcons
…and/or buffer tanks

ChrisJ

Jamie Hall said:

Whether you are worried about freezing your clients or not -- remember that in most jurisdictions you can't get a Certificate of Occupancy unless you can show that the heating system can hold temperature -- usually around 70 on the design day. For a DIY job, no big deal -- until you try to sell the place or remortgage it. For a pro., this can be a big deal...

The good news (I guess?) is mine can hold temp down to about -40F sustained even with the small 10% pickup factor.  Our design day temp is +6 here but the record low is -19.

hot_rod

The 97.5% design dry bulb temperature, the temperature that the outside air is at or above 97.5% of the year.

EdTheHeaterMan

So could you say to a customer (Me), "your heat loss at the outdoor temperature of xx*F is yyy k Btu's per hour; this boiler has an output of zzz k Btu's per hour at that outdoor temperature and you'll be comfortable. If you want to be comfortable at the "record outdoor low (of this city---) aa* F, the heat loss will be BBB k BTU's per hour and you will need to have a higher capacity boiler.....and the price will be ...???

You can do this easily on the fly if the formula is linear.

This query sounds la-la-like Ya-Ya-You are having a Pa-pa-problem with the ca-ca-cold weather. Ma-ma-maybe you should put on an over ca-ca-coat if you are Sha-sha-shivering that much!

The Steam Whisperer

Chicago design temp is about -1 F on the north side and +2 F on the south side., record lows are -20 to -25F, which used to occur around every 10 years or so.... now not so often, it seems. -10 used to be just about every winter, now not so often. What I am trying to point out is that with systems that maintain their output capacity with very little dependence on outdoor temperature are usually good to go even for record lows. They will still protect most buildings from in record lows. For older buildings, that safe temperature is typically around 45F (based on studies of religious structures by the Interfaith Coalition on
Energy). Dropping below 45F, freezing up pipes, freezing temperatures in plaster that cause the layers to separate and the finishes to fail, are getting really close.
So with conventional systems, this hasn't been a problem, especially with the massive oversizing, with still continues today by most engineers, in my experience. However, if the system output is dependent on on the outdoor temperature like heat pumps, this would require a load calc and design requirement to maintain the building at probably 45F or higher at record design. I don't think this is being required anywhere.

ethicalpaul said:

But wait didn't you say that even a fired system will only hold around 45 degrees during these bitter cold days? 45 is ok but 40 is panic-inducing? With both kinds of systems, without proper design and/or backup there are problems, why is only the heat pump one scary?

A fired system that is designed right on will be able to keep a building warm at 70F when it is 0F outside with let's say 100,000 btu/hr, so for the most part it will be able to maintain the building at 45F if it is -20F outdoors

The 40 degrees interior temp is panic inducing because of the above and that instance occurred in a high mass building ( which tends to act as a thermal flywheel and creates ground contract tempering) and at maximum lows of about -10F.
Very few structures appear to have back up heating.... especially buildings under 100,000 sq ft. I am not aware on any requirements for back up heating in buildings utilizing heat pumps or for that matter condensing boilers. I think if this is examined we will probably find the potentially most sensible solution to heating needs.... a both/and approach which uses the most efficient and least polluting source for typical day (60% load for 90% of the heating season) peak loads and a back up source like fossil fueled to handle the last 10 %. Using this 60% load design target can really change how efficiently even conventional heating plants work. It allows the use of very simple non condensing equipment to be used and still provide a very large percentage of the efficiency advantage of mod cons.
For baseload design and checking for record design seems to be the best longer term combination.

exqheat

Why not use an indoor reset technology.
Removing the old system, (back-up) is a waste of energy and adding risk if you lose power to the electrics.

Jamie Hall

On backup heat. There is a small, but finite, probability that any building without any backup will lose electrical power from time to time. That's just reality. Now that being so, if that occurs when it is below freezing outside and likely to stay so for the duration of the backup -- and there is a finite probability that that will be several days -- you have two choices: on site reliable backup power and heat, or the ability to drain all the water out of the building. No, you may never need it. If you do, you'll be a much happier camper.

I recently acquired oversight of a salvage and recovery job on a lovely country house which lost power in the winter and was not properly taken care of (by another party). We're looking at several hundred thousand dollars in repair and salvage costs... and it is unlikely that insurance will cover it.

The Steam Whisperer

exqheat said:

Why not use an indoor reset technology.
Removing the old system, (back-up) is a waste of energy and adding risk if you lose power to the electrics.

I strongly agree...especially when it is steam or hot water. The electrical needs of many residential and light commercial steam boilers is about 20 watts or less. You have to add additional power for pumps in HW and some Steam systems ( steam systems with pumps only need about 1/80th or less power than a similiar hot water system). A tiny generator, probably even a solar powered battery system would keep the steam running. For forced air you'd need a generator set.

There is basically silence on these issues in the "expert" reports that have been written about going all electric heat pumps.

ChrisJ

The Steam Whisperer said:

exqheat said:

Why not use an indoor reset technology.
Removing the old system, (back-up) is a waste of energy and adding risk if you lose power to the electrics.

I strongly agree...especially when it is steam or hot water. The electrical needs of many residential and light commercial steam boilers is about 20 watts or less. You have to add additional power for pumps in HW and some Steam systems ( steam systems with pumps only need about 1/80th or less power than a similiar hot water system). A tiny generator, probably even a solar powered battery system would keep the steam running. For forced air you'd need a generator set.

There is basically silence on these issues in the "expert" reports that have been written about going all electric heat pumps.

With a mv steamer you don't need anything external....
What was the reason they stopped making them?

The Steam Whisperer

ChrisJ said:

The Steam Whisperer said:

exqheat said:

Why not use an indoor reset technology.
Removing the old system, (back-up) is a waste of energy and adding risk if you lose power to the electrics.

I strongly agree...especially when it is steam or hot water. The electrical needs of many residential and light commercial steam boilers is about 20 watts or less. You have to add additional power for pumps in HW and some Steam systems ( steam systems with pumps only need about 1/80th or less power than a similiar hot water system). A tiny generator, probably even a solar powered battery system would keep the steam running. For forced air you'd need a generator set.

There is basically silence on these issues in the "expert" reports that have been written about going all electric heat pumps.

With a mv steamer you don't need anything external....
What was the reason they stopped making them?

I think it was the upgraded safety requirements of having dual gas valves. It probably would take having two MV pilots, so the cost was higher than previously.