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  1. #1
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    Confused Formula: number of minutes to increase or decrease temperature 1 degree fahrenheit

    Hello, I need help deriving a formula!
    As the title says, the goal of the equation is to give me the number of minutes it will take to increase (or decrease) a home's temperature 1 degree fahrenheit.
    This formula is for a program I am trying to write for a home automation system that is linked with a smart thermostat.
    I'm aware that there is a lot of unique "constants" involved in this formula, and all of these constants can be ignored by using a common average. The constants (such as insulation R rating and HTM) can be ignored because there will be an offset number to account for all of these constants that will be adjusted by trial and error.

    Outside temperature and inside temperature are probably the only 2 factors that need to be included in this equation. These 2 temperatures will be automatically provided.

    Example of what I am looking for, Say it is 35f outside and 69f inside, how many minutes will it take (assuming normal conditions like insulation and proper furnace size) to get the temperature to 70f
    Any help is greatly appreciated.

  2. #2
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    Quote Originally Posted by Larance View Post
    I'm aware that there is a lot of unique "constants" involved in this formula, and all of these constants can be ignored by using a common average. The constants (such as insulation R rating and HTM) can be ignored because there will be an offset number to account for all of these constants that will be adjusted by trial and error.
    Hmmm, so you conveniently whitewash the actual difficulty of this issue by first ignoring the real-world variables with a "common average", whatever that is, then claim that trial-and-error will allow you to account for all these constants with a single offset...wow...

    So, you will somehow find a magic number to make up for all the differences in wall thickness, wall insulation values, fenestration and related weatherproofing, exterior wall construction, attic insulation, attic insulation location (at the ceiling vs. at the roof), roof material, attic ventilation, number of floors in the dwelling, outdoor air enthalpy...(I'm sure there's more...) - there's a reason that data modeling software for building envelopes is complicated and expensive. There are no "normal conditions"...

    Some fellows have been able to simplify the question (for instance, here), but notice that even this simple explanation includes the phrase "To find the total amount of heat flow through your home, you just do this calculation for all the surfaces of the building envelope, the boundary between conditioned and unconditioned space"...there is no shortcut.

    Since you're using a "smart thermostat", ostensibly for setback purposes through some means or another, you'll want to see the related article here. Again, the author states, "Yes, it's true you have to consider the equipment because if recovering from a thermostat setback means that your heat pump kicks the electric resistance heat on, your bill may be higher. Right-sized heating and cooling equipment and equipment that can adjust its capacity to meet the loads also impact the effectiveness of setbacks. So does a lot of thermal mass in homes (though most furniture doesn't have a lot of thermal mass)."...so, again, there are no normal conditions. You cannot brush aside all the variables with terms like "normal", "proper", "common average", and "offset to account for all of these constants".

  3. #3
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    I feel like I should explain how the program will work.
    1st of all here is what I mean by constants. I understand there is many factors to take into consideration, these factors cannot be calculated by the user.
    For example let's say the unique numbers in the formula for a particular home are 2*2+136*pi*sqrt(500)........this all combined together equals ONE number. Rather than the user finding all of the individual numbers, all they need to do is use trial and error to get as close as possible to that ONE number.
    So here is how the program will work; the program will gather inside temp, outside temp, and the distance the homeowner is away from the home. When setting up the program the user will enter in a number, this number represents the average amount of minutes it takes for them to travel one mile towards their home. Note this is the number that they will be offsetting rather than calculating all important variables.
    So let's say the program calculates that it will take 5 minutes to increase the home temperature 1 degree fahrenheit.
    And let's say that the user said it takes them 5 minutes to travel a mile closer to their home.
    So here is what the program will do, when the user is 1 mile away, the thermostat will lower 1 degree, 5 miles away, lower it 5 degrees (winter operation/heat)
    So the theory is, the farther you are away from home, the more you save, and by the time you get home your house will be at the proper temp.
    I hope you can see now that by adjusting the minutes per mile you can overcome heat-loss and other crucial factors. My only goal is to get as close as possible to the number most people will be using, that way when users first use the program they don't come home to a house that is 60f.
    The reason for doing it this way is so the program is user friendly (so everyone can use it).
    Also this program is going to be targeting those with old inefficient furnaces.

  4. #4
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    Trial and error bro. I'm sure some mathalete pointy hat engineer nerd could come in here and calculate it, but absolutely nothing can replace real world experience.

    A lot of us guys have poured countless hours of our lives into control systems and I myself to this day look at sequences I wrote 15 years ago that have been working fine and think to myself "wtf was I thinking when I did this".

  5. #5
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    I'm all ears for any suggestions. Just keep in mind anyone must be able to set this up.
    Also remember, if it's crazy, but works, it's not crazy!

  6. #6
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    Seems similar to Honeywell Lyric's Geofencing. Never used them though. Guess you could calculate run time per degree and droop times over a period of time as in typical optimal start stop programs, then use the distance and average time of of travel as an offset. Still wont be perfect unless weather and traffic conditions are the same from day to day.

  7. #7
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    Sounds like you need an equivalent of a specific heat value for the home. However I'm not really sure you could hope to compute such a parameter from a few simple inputs. Doing a proper load calculation is a more complex process. If you then add to that the fact the the actual equipment may never have actually been based on the load calc as well as possibly the ducts being incorrectly sized and installed leading to a different level of performance to what you would expect I'm not sure you can distill all this into a simple equation.

    Many thermostats use some form of learning algorithm to do what you are trying to do. Start off with a best guess and then based on a actual performance refine the start times over several days.

  8. #8
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    I haven't looked at Honeywell lyrics geofence, but I know Nest with Automatic has a similar function. To overcome traffic the user will put in the normal time to travel one mile. This way they never come home to a cold home, they just won't save as much when in traffic, which isn't a big deal.
    I have came up with a formula to calculate average BTU/hrs of heat loss. All that is needed for the formula is inside temp, outside temp, and home square footage. I guess heat loss is the only variable that will be constantly changing. So I need to take a look at the definition of a BTU in order to convert a lb of water to a square foot of air at STP. That will get me the time it takes to drop the home temp 1 degree, then I will have subtract that from the furnace BTU/hr to get the time it takes to increase the home temp one degree. (After converting furnace BTU to sq ft of air at STP) does this look like a plausible way of doing it?

  9. #9
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    When it gets cold enough outside, there can be a point in time when there will be no increase in indoor temp no matter how long the heater runs.

  10. #10
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    Won't that be when the heatloss is greater than heat gain? The formula I'm asking for will represent this, the number of minutes required will to increase the temp one degree will be approaching infinity as the heat loss approaches the heat gain of the furnace.

  11. #11
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    Or heat loss equals heat gain.

    But back to your original question . . . Post #2 highlights the difficulties of your quest. The rate of heat loss will increase as the difference between the two temps increase, so there is no one factor that will apply to all applications.

    The number of minutes to increase the temp 1*F will change as the temps change.


    Quote Originally Posted by Larance View Post
    Won't that be when the heatloss is greater than heat gain? The formula I'm asking for will represent this, the number of minutes required will to increase the temp one degree will be approaching infinity as the heat loss approaches the heat gain of the furnace.

  12. #12
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    What information is missing? I will be able to have the program calculate the temperature difference

  13. #13
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    Quote Originally Posted by BBeerme View Post
    Or heat loss equals heat gain.

    But back to your original question . . . Post #2 highlights the difficulties of your quest. The rate of heat loss will increase as the difference between the two temps increase, so there is no one factor that will apply to all applications.

    The number of minutes to increase the temp 1*F will change as the temps change.
    In principle this sort of thing can be addressed by a higher order equation - either a higher order polynomial, exponent or even logarithmic relationship if necessary. The real issue I think are factors that cannot be represented by real world installation issues - for example the real heat output of a furnace which may be different to its value when new, airfow issues plus accurately modelling the heat loss for every structure based on a simple equation.

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