Check my math please

[bigtiller]

If 68 degrees needs 1000 gallons of propane to achieve,,,, how many gallons of propane is needed to reach 70 degrees?

I came up with 1029 but it's been a long time since algebra class.

We have decided to raise the temperature in the house this year. It's only been one day since the big cold front moved down from our friends up north and we are already tired of winter!

 

[LD1]

correct as far as algebra is concerned, but there is more to it than that.

the warmer your house is, the quicker it will loose heat to the outside. (greater temp spread transfers heat quicker).

The amount of propane needed isnt going to be linear. As well as different winters. This winter may be colder, it may be warmer.

 

[uglyboywith11fingers]

you may be a bit low... general rule of thumb is 2% to 2.5% increase in energy consumption per degree F increase.
and as LD1 says, many other factors come into play... like insulation level, wind exposure, average outside temp in winter.

Pete

 

[zzvyb6]

Thermal problems are exponentials (nonlinear), so

All things being the same as last year, then since

1000 = e^(q*Temp) gives q = 6.90775528 . This is the thermal efficiency constant of your house at about 68 degrees.

so: e ^ q * New_Temp) ~ 1226 gallons. Its a little more complicated than that because of considerations for absolute zero, etc, but...

You might consider a lower night time setback temperature to help out, but it will use fuel to get back to 70.

Setting it to 72 degrees would take 1501 gallons.

 

[mjarrels]

This thread makes my head hurt!

mark

 

[bigtiller]

I used 1000 gallons as a base line because for the past 15 years it has used an average of 936 gallons, so I just rounded up a little. Plus, I heat the garage with part of that 936 and that part is infinitely variable.

So I guess I should raise my estimate to 1200 and hope I am high.

zzvyb6
I knew there were some math majors out there and you told me exactly what I wanted to know. If I would have tried a little harder in school ....... next time!

 

[CobyRupert]

We have decided to raise the temperature in the house this year. It's only been one day since the big cold front moved down from our friends up north and we are already tired of winter!

"We" decided ehh? Ok, sure, if that's the story you're sticking to. :laughing: (p.s. Your wife isn't going to be swayed to turn it back down to 68 no matter how much fancy math or thermodynamic equations you impress her with. )

 

[zzvyb6]

Just think: If you set the temp back to 66 degrees, you would only use 816 gallons.

The q factor is actually 0.10158463645 based on the usage at 68 degrees. so e^(q*temp) gives you the gallons.

In Michigan right now, propane is about $2.00 per gallon. The State is strongly suggesting to top off NOW because after January 1st, the price usually leaps as homeowners realize they are almost out. Funny how that works, eh ?

My dogs let it be known CLEARLY that it was 70+ or else your gonna need a Rug Doctor. I bit the bullet, pulled the trigger, sucked it up, etc. to run an 800' natural gas line. Paid for itself in one year (furnace and hot water were fuel oil). As I get older, 72 deg. seems more comfortable....

 

[dave1949]

The relative humidity makes a big difference in how a given temperature feels on your skin. That is something to consider if your house tends toward dry in the winter.

I have also noticed our large south windows, which are big radiant heat losers after dark, can make it feel cool when sitting near them. The only reasonable cure I know for that is thermal drapes.

 

[bigtiller]

I have to admit, this 70 degrees feels pretty nice, I think 68 is a thing of the past. We have a whole house humidifier on the return side of the furnace but I haven't turned it on yet, the sump pump is still running 3 or 4 times an hour so when it slows down some more I will turn on the humidifier.

If I knew what e^(q*temp) means, I might be tempted to play with the calculator.

 

[zzvyb6]

'e' is the basis for natural logarithms.

Natural logarithm - Wikipedia, the free encyclopedia

so the thermal constant times the temperature desired is the power that 'e' is raised to.

The solution to many so called first order differential equations involves 'e' or its converse, the 'ln' function.

It's usefulness is in the multiplication of numbers by adding their logarithms. If you ever used a slide rule back in the day, that's how a slide rule works. You add the 'lengths' of a numbers on the rule to multiply them. When something cools down or heats up or if you let the air out of a tank or fill it, the pressure or temperature at any instant in time is governed by this math property.
In most cases, the value of a new vehicle vs. time or mileage is also well defined by the curve shape that this function has: the fastest drop occurs at the beginning and finally settles down to a worth that's just above the junk yard value. For some vehicles the 'time' constant is swift. For others, it's pretty slow. There's actually a brand factored into this time constant for some products.

 

[newbury]

"We" decided ehh? Ok, sure, if that's the story you're sticking to. :laughing: (p.s. Your wife isn't going to be swayed to turn it back down to 68 no matter how much fancy math or thermodynamic equations you impress her with. )

GAD!! 68?

We keep the house at 63 now and wear flannel shirts if we get chilly. Right now it's 63 and I'm comfortable in a T-shirt because I was just "exercising" unloading a trailer an hour ago.

Which brings up an old guy's story.

Back in '85 SWMBO, her 7 yr old son and I had just moved into a house in Alexandria, Va after getting married on Feb 29th, 1984. She and her son hailed from Mississippi and it was their first full year in Virginia. The house was poorly insulated and no storm windows. Energy was cheap, but so was I.

I'd set the temp back to about the mid 50's or lower for the night and up to 65 for when people were up and about.

One cold winter morn I was sitting in the library browsing the bulletin boards on my Commodore 64 and heard the son coming down the stairs making a breathing out sound (woosh) every few steps. He came into the library, looked at me with wide eyes in amazement and said "I've NEVER seen my breath inside before!!"

Now after 7.5 anniversaries she's comfortable with cool temps and warm clothes. And the now 37 year old son is comfortable running his house in Memphis cool in the winter. Based on comparing heating bills with local friends with similar sized houses SWMBO and I have probably saved about $400 a year in heating bills.

The adapting to cool temps with clothing seems right and natural to me. Now letting the house heat up and preserving some modesty in the summer is different. I can only take off so much I drew the line at 80 degrees for the summer, and that crept down to 78 recently.

 

[MossRoad]

60's - YIKES! We keep our house at 72 minimum with the furnace thermostat, but it rarely comes on because the wood burner keeps it at 74-76 most of the time. Its nice sitting around in light weight pajamas in the middle of winter in a warm, dry house.

 

[CurlyDave]

So far, I have not seen any correct answers.

The original question has left out an important piece of data--the average outside temperature over the time period to be considered. Most HVAC men would call the energy required to maintain the difference between the average outside temperature and the inside temperature for a day one degree-day. If you just take the temperature in Fahrenheit and use that in the equation, you are assuming that the average outside temperature for the entire heating season is 0 degrees F, which I don't think would be true in Iowa.

If the average outside temperature is greater than 0 degrees F, the propane required will be greater than that calculated in the early posts.

* * * * * *

In zzvyb6's post we are getting into the equations for radiative heat transfer, which is typically very small compared to the usual convective heat transfer from a house to the environment. The usual practice is to express temperature in degrees Kelvin, which is (degrees Celsius + 273). This component of heat loss from a house is small enough so that most engineers ignore it for typical temperatures. It starts to become significant somewhere around 300 degrees F, and at high enough temperatures is the dominant heat transfer mechanism.

But, your house is never going to in a environment where radiative heat transfer will be significant compared to convective.

 

[CurlyDave]

So far, I have not seen any correct answers.

The original question has left out an important piece of data--the average outside temperature over the time period to be considered. Most HVAC men would call the energy required to maintain the difference between the average outside temperature and the inside temperature for a day one degree-day. If you just take the temperature in Fahrenheit and use that in the equation, you are assuming that the average outside temperature for the entire heating season is 0 degrees F, which I don't think would be true in Iowa.

If the average outside temperature is greater than 0 degrees F, the propane required will be greater than that calculated in the early posts.

* * * * * *

In zzvyb6's post we are getting into the equations for radiative heat transfer, which is typically very small compared to the usual convective heat transfer from a house to the environment. The usual practice is to express temperature in degrees Kelvin, which is (degrees Celsius + 273). This component of heat loss from a house is small enough so that most engineers ignore it for typical temperatures. It starts to become significant somewhere around 300 degrees F, and at high enough temperatures is the dominant heat transfer mechanism.

But, your house is never going to in a environment where radiative heat transfer will be significant compared to convective.

 

[buckeyefarmer]

There is no "I" in team, but there is a "Me" if you want to jumble it up a bit...

Actually there is an I in TEAM.... Just look at the A hole.

 

[quicksandfarmer]

Curly Dave has it.

People in the heating business use degree-days. You can read about them here:
Degree day - Wikipedia, the free encyclopedia

You can get the degree-day history for your area here:

NCDC: U.S. Climate Normals -

You also need to know how many days are in your heating season.

The annual degree-days for your area gives a baseline of how much heating is required to maintain an inside temperature of 65F. For each degree higher, add one degree-day for each day in your heating season.

For the math nerds in the crowd, the underlying assumption is that the amount of heating required is directly proportional to the difference between the inside temperature and outside temperature. That assumption seems unreasonable on its face, but it is the basis of the Manual J calculation that is used to design just about every residential HVAC system.

 

[dave1949]

<snip>

For the math nerds in the crowd, the underlying assumption is that the amount of heating required is directly proportional to the difference between the inside temperature and outside temperature. That assumption seems unreasonable on its face, but it is the basis of the Manual J calculation that is used to design just about every residential HVAC system.

Since the OP has a baseline for how much propane is used for 68*, he could run the calculations for that and see how well it matches his actual consumption. Any difference might be useful as a % correction factor to apply to other temperature targets?

 

[txdon]

Math is like love – a simple idea but it can get complicated
so
when it gets empty fill it.

 

[dave1949]

Math is like love – a simple idea but it can get complicated
so
when it gets empty fill it.

No No No. It's better to insist that according to the TBN Braintrust, that tank can't be empty. :laughing: