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# How do I calculate how long a furnace has 2 work 2 compensate a given temp drop?

#1
12-27-14, 08:02 AM
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Join Date: Sep 2013
Posts: 159
How do I calculate how long a furnace has 2 work 2 compensate a given temp drop?

I am trying to understand the dynamics of heating a home after the furnace size was calculated.
Say you have a 60000BTU furnace to heat a 2000 sqft home.
At the beginning of the heating season you brought the in house temperature near the point set on the thermostat and since then the temperature has been fluctuating around that value as the house lost heat and that was compensated by the furnace

At this point I have two questions:
-how do you set how much the temperature can drop before the thermostat calls for heat?
-How can I calculate equivalent temperature rise of let's say 1000BTU/h delivered in an 1000 cubic feet volume?

The point with my last question is this: if it is possible to configure the temperature drop before the thermostat calls for heat I would like to know how long the furnace will have to work to bring the temperature back to the set point

#2
12-27-14, 08:33 AM
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I'm trying to follow your logic here. You have a thermostat that does all that for you. Are you going to start calculating when to run the furnace to recover ?

Most thermostats will turn the heat on when the temperature has dropped somewhere between a quarter of a degree up to a degree. You can purchase a thermostat where the amount of differential is changeable. In my opinion it's better to allow a wider temperature swing so that the furnace runs longer..... rather than setting the differential real tight and have the furnace run every few minutes.

I'm not sure you could calculate how long it would take the furnace to recover. That depends on several values including outside air temperature. Here again... they offer an outside temperature probe that connects to the thermostat and can calculate recovery using outside air temperature.

#3
12-27-14, 08:44 AM
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Join Date: Dec 2014
Posts: 123
Unscientific but true

Last question first: you'll have to factor in whether it's a windy day or not. Wind has a big influence on the rate of heat loss/recovery per given outside temp. Furnace has to fight ongoing chill factor while recovering to a set temp indoors.

#4
12-27-14, 08:44 AM
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To your first question. It's controlled by the thermostat. Some allow you to adjust how far the temp drops below the set point before turning on the furnace while others use a fixed amount like one degree f.

Your second question is a bit on the complex side and I don't know why you'd need or want to know but I suppose it's a good math problem if you're snowed in and looking for something to do. First you need to determine the mass of the air you are heating. This will vary with the air pressure, humidity and temperature. I don't know what you'll do with the value once you've calculated it but I suppose you could then figure the heat loss of your home. Still, I don't see how it would help or be required in the operation of your thermostat.

#5
12-27-14, 08:55 AM
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Join Date: Sep 2013
Posts: 159
I'm trying to follow your logic here. You have a thermostat that does all that for you. Are you going to start calculating when to run the furnace to recover ?

Most thermostats will turn the heat on when the temperature has dropped somewhere between a quarter of a degree up to a degree. You can purchase a thermostat where the amount of differential is changeable. In my opinion it's better to allow a wider temperature swing so that the furnace runs longer..... rather than setting the differential real tight and have the furnace run every few minutes.

I'm not sure you could calculate how long it would take the furnace to recover. That depends on several values including outside air temperature. Here again... they offer an outside temperature probe that connects to the thermostat and can calculate recovery using outside air temperature.

Two are the reasons why I am looking for a configurable temperature drop on the thermostat
-as you also said having a furnace that starts and stops every 10 minutes (let's say old house with no insulation on the main floor, just brick veneer, air gap, sheating and drywall) is not economical and it will reduce the efficiency of your furnace
-knowing or being able to set the temperature drop will allow me to calculate the BTU required to rise the temp... actually using a precise indoor thermometer might work :-) for this purpose but I have to watch the furnace/thermostat for a couple of cycles

#6
12-27-14, 08:59 AM
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Join Date: Sep 2013
Posts: 159
Last question first: you'll have to factor in whether it's a windy day or not. Wind has a big influence on the rate of heat loss/recovery per given outside temp. Furnace has to fight ongoing chill factor while recovering to a set temp indoors.
There must be a correspondence between BTU and temp rise
The other factors that contribute to heat lose will just influence how much longer the furnace will run compared with ideal conditions (no heat loss)

#7
12-27-14, 09:05 AM
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Join Date: Sep 2013
Posts: 159
To your first question. It's controlled by the thermostat. Some allow you to adjust how far the temp drops below the set point before turning on the furnace while others use a fixed amount like one degree f.

Your second question is a bit on the complex side and I don't know why you'd need or want to know but I suppose it's a good math problem if you're snowed in and looking for something to do. First you need to determine the mass of the air you are heating. This will vary with the air pressure, humidity and temperature. I don't know what you'll do with the value once you've calculated it but I suppose you could then figure the heat loss of your home. Still, I don't see how it would help or be required in the operation of your thermostat.
I am trying to figure out if my ducts are adequate for what I am getting and what would be the CFM to be set on the blower to properly heat the house. I have weak air flow in the basement (see my other thread)

when they size the ducts they use an air change value and I do not know what that for heating. All the tables that I have seen around show the values for ventilation (that is to refresh the air not to heat is or cool it)

#8
12-27-14, 12:16 PM
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Join Date: Sep 2013
Posts: 159
I think that all the above can be reduced to this:
Sensible Heat
The sensible heat in a heating or cooling process of air (heating or cooling capacity) can be expressed as

hs = 1.08 q dt (1)

where

hs = sensible heat (Btu/hr)
q = air volume flow (cfm, cubic feet per minute)
dt = temperature difference (oF)

Example - Heating Air
An air flow of one cfm is heated from 32 to 52oF. Using (1) the sensible heat added to the air can be expressed as:

hs = 1.08 (1 cfm) ((52 oF) - (32 oF)) = 21.6 (Btu/hr)

I am still puzzled by the conversion from minutes to hours but that is probably due to 1.08 coeficient

A graphical representation of the above equation is depicted here:

I am kind of surprised that I have to find all these by myself.
On the same site there are equations for calculating air velocity in relation with cfm and duct size...

With all the above one should be able to properly size the ducts for each room

#9
12-27-14, 09:42 PM
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Join Date: Mar 2004
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Posts: 1,794
a) Modern intelligent thermostats work to maintain a certain number of cycles per hour and the temp swing varies a little as the load changes. Honeywells work this way - not sure of others.

b) It's impossible to accurately establish the amount of time it would take to heat up due because the specific heat and mass of the building materials and furniture is impossible to estimate. When the house is heating up you also have heat loss which varies with the outdoor temperature and wind.

With all the above one should be able to properly size the ducts for each room
It's really not that complex, but the ducts have to be sized for the cfm of the furnace. The branch lines to each room get sized to deliver proportional airflow relative to load.