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Author Topic: Hive Temperature Calculations  (Read 4082 times)
BlueBee
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« on: March 28, 2011, 08:21:21 PM »

For those of you who like a little math, I thought I would provide some equations for estimating the temperature inside your hives.  Did I hear a collective sigh and a moan?  There goes BB again with his heated hives?  Not exactly.  The math applies to wood hives too.  

I agree with the crowd that bees don’t set out to warm up their entire hive, however depending upon the R value of the hive and air infiltrations, the bees heat CAN end up heating a hive rather substantially.

The hive temp equations are simplest if you calculate the hive temp based on a perfect R value and then adjust it later for air infiltration losses and solar gains.  The equations for heat transfer were discovered by Newton 300 years ago (http://en.wikipedia.org/wiki/Convective_heat_transfer).  Using modern building materials, the differential nature of Newton’s equation can be simplified to a simple energy relation equation we can all understand.

(Hive Surface Area/ R value) x (Temperature Inside – Temperature Outside) = BTUs of bee heat.

A full colony of bees can generate somewhere between 20 and 40 watts according to the literature I’ve seen and my casual observations.  1watt = 3.41 BTU/hour.  

A wood hive has a R-value of about 1.  A 2 deep hive has a surface area of about 14.5 sq feet.  Plugging these numbers in the heat loss equation we have:
(14.5/R1) x Delta T = 20watts x 3.41
Delta T = 4.7F.  Where Delta T is the temperature delta ABOVE the outside air temp.

A perfect wood hive with bees making 20 watts of heat would be at most 4.7F warmer than the outside air before accounting for air infiltration loses.  When you take those into account, then the math agrees very closely to what people believe; “ bees don’t heat the hive, they only heat the cluster”.

Now let’s run those same numbers with a foam hive having R10 insulation.
14.5/R10 * DeltaT = 20watts x 3.41
DeltaT = 47F.  

A perfectly insulated R10 foam hive will be up to 47F above the outside temperature if the bees are making 20watts of heat in the cluster.  In this case, the bees DO end up heating the hive along with the cluster.

This winter it got down to -6F here.  The math says a wood hive got down to -2F inside.  The math says a foam hive got down to 41F inside.  If you were a bee, which house would you prefer?  My bees are all alive; they seemed to prefer 41F over -2F.  
« Last Edit: March 28, 2011, 08:31:23 PM by BlueBee » Logged
MTWIBadger
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« Reply #1 on: March 28, 2011, 11:20:15 PM »

BlueBee,
What is your setup for heating your hive and insulating it?  In a weak trapout hive, I used two 7 watt lights under a SBB set on the ground covered with 2 inch foam insulation.  Only turned the light on when temps reached single digits or below and the hive is still alive.  May expand lighting to all four of my hives next year.
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BlueBee
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« Reply #2 on: March 28, 2011, 11:42:13 PM »

MTWIBadger, you’re one step ahead of me typing!  See my post “Bee Heater Construction” for some details of my setup.  My goal is to size the volume of my foam hives to the number of bees in the hive in such a fashion that the heat from the bee cluster will be sufficient to keep the hive temperature between 40 and 60F without electrical heat.   

In an insulated foam hive, the bees are not going to have to generate as much heat (equations above) to keep the queen warm, meaning they eat less honey which also means they have less waste products stored in their gut over winter.  I figure that is probably a good thing too.

This season my hive volumes were larger than ideal and hence I ended up adding electrical heat to keep the nucs in the desired temp range.  The nucs got between 10 and 20 watts because the hive volumes were bigger than I should have made them. 
 
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JRH
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« Reply #3 on: March 29, 2011, 09:43:59 AM »

(Hive Surface Area/ R value) x (Temperature Inside – Temperature Outside) = BTUs of bee heat.

A full colony of bees can generate somewhere between 20 and 40 watts according to the literature I’ve seen and my casual observations.  1watt = 3.41 BTU/hour.  

A wood hive has a R-value of about 1.  A 2 deep hive has a surface area of about 14.5 sq feet.  Plugging these numbers in the heat loss equation we have:
(14.5/R1) x Delta T = 20watts x 3.41
Delta T = 4.7F.  Where Delta T is the temperature delta ABOVE the outside air temp.

Now let’s run those same numbers with a foam hive having R10 insulation.
14.5/R10 * DeltaT = 20watts x 3.41
DeltaT = 47F.  

A perfectly insulated R10 foam hive will be up to 47F above the outside temperature if the bees are making 20watts of heat in the cluster.  In this case, the bees DO end up heating the hive along with the cluster.



These calculations all depend on WHERE in the hive you are measuring the heat and WHERE in the hive the cluster is located.  I am speaking from a full winter's experience with temperature probes suspended about an inch down through the hole in the inner cover in two hives.  (The hives are wooden and unheated.  There is a 1" thick piece of styrofoam insulation inside the outer cover.)  The probes show temperatures that ranged from 10 to 60 degrees higher than the outside ... hive temperatures as high as 60 degrees with outside temperatures a few degrees below zero on occaision.  This difference in temperatures, I think, would result in unrealistically high heat output calculations.

As cluster size decreases over the course of the winter, the hive temperatures have decreased as well.

On 50 degree days, hive temperatures at the probe have been as high as 88 degrees.

« Last Edit: March 29, 2011, 02:24:17 PM by JRH » Logged
BlueBee
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« Reply #4 on: March 29, 2011, 02:43:49 PM »

JRH, congrats on the instrumentation, I’m still working on computerizing mine. 

The math isn’t something I invented, that was done by Isaac Newton; the inventor of Calculus.  Unless the laws of physics work differently in Vermont, the trick will be interpreting how your data fits Newton’s equations. 

If you were reading 60F on 0F days, do you think the cluster may have been around your probe at that point?  The cluster does move up during the course of winter.  The bees in the cluster are activating their wing muscles to keep the cluster warm. 

You noted on a warm 50 degree day reading 88F.  I bet the bees like that!  That is an advantage of a wood hive on a sunny day.  There is so much heat hitting a hive on a sunny day that it can really add up.  Solar radiation is on the order of 100watts per square foot.  A 2 deep hive is likely to have about 2 sq feet incident to the incoming sunlight.  That’s 200watts of heat in.  About 10x what the bees can generate. 

Newton’s equations are really differential in nature and to get an exact calculation of heat flows you would need to integrate over the entire surface of the hive using Calculus.  In that case you would use the exact temp at each point on the inner surface of the hive for the math.  The simplified equation used here is an approximation of that integration result.  In this case I would guess the proper number to plug into the equation would be an average surface temp in your wood hive.  Probably the inside surface temp half way up the hive would be appropriate.

Keep us posted, it’s always great to have real data.

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JRH
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« Reply #5 on: March 30, 2011, 09:59:13 AM »

Unless the laws of physics work differently in Vermont, the trick will be interpreting how your data fits Newton’s equations.

I am not sure I questioned the equation.  I did say that where the cluster is relative to the temperature probe makes a big difference in the observations.

Using Newton's equation, I get 255 watts for a 60 degree differential between the temperature at the probe of my indoor-outdoor thermometer.  As I said previously, this sounds like a number that is higher than the likely output of a cluster of bees.

If someone has done a thorough and scientific study of the heat output of a cluster, I would be interested in reading it.

Regards,
Jeff Hills
Dorset, Vermont
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BlueBee
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« Reply #6 on: March 30, 2011, 01:29:25 PM »

I’ll say it again, Newton’s equation is differential in nature.  To compute the exact temperature inside a hive, you would have to use calculus and integrate over the entire surface area.  That would require more than 2 temperature probes.  The best you can do with incomplete data is make some approximate calculations.

The equation I posted is an approximation of integrating Newton’s law over the surface of a hive using calculus.  That means the temperatures you plug into the equation needs to be an average of the hive surface temperature; NOT the temperature above or inside the cluster.

An analogy to what you’re doing is measuring the temperature inside a house right above the furnace (or even inside the furnace) and claiming that is an average temperature for the entire house.   Not so.

Here’s a good article (often posted) to start learning about the temperature profile in a winter cluster.  
http://jeb.biologists.org/cgi/content/full/206/2/353

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JRH
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« Reply #7 on: March 31, 2011, 10:05:34 AM »

The equation I posted is an approximation of integrating Newton’s law over the surface of a hive using calculus.

The equation you posted and the general thrust of the post claimed to be a way to measure the heat output of the cluster in watts.

An analogy to what you’re doing is measuring the temperature inside a house right above the furnace (or even inside the furnace) and claiming that is an average temperature for the entire house.

That is not what I said.  I said that your equation would result in radically different results depending on the location of the probe relative to the location of the cluster.  Nothing more and nothing less.
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BlueBee
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« Reply #8 on: March 31, 2011, 10:37:15 AM »

Quote
The equation you posted and the general thrust of the post claimed to be a way to measure the heat output of the cluster in watts.

Actually the title of the post it is about computing the temperature inside a hive, not for computing the wattage of your bees.  Really the point I was trying to get across is that bees DO end up heating up their environment in a foam hive whereas they do not do so in a wood hive.  Basically confirming the standard Beeks mantra that “Bees don’t heat the hive, they only heat the cluster”.

Quote
I said that your equation would result in radically different results depending on the location of the probe relative to the location of the cluster.  Nothing more and nothing less.

Fair enough, I can’t argue with that.

Bee Energy output in watts:

If you want to know the heat output of your bees in watts, there is probably a better way to do than the argumentative direction this post has gone.  As you say, the location of your temp sensors throws off the equation here.  There is a simple good way for finding the wattage if that is what you really want to know.  I’ll make a new post later today detailing how you can do that.   
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JRH
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« Reply #9 on: March 31, 2011, 01:52:39 PM »

Really the point I was trying to get across is that bees DO end up heating up their environment in a foam hive whereas they do not do so in a wood hive.  Basically confirming the standard Beeks mantra that “Bees don’t heat the hive, they only heat the cluster”.

The conclusion of your post is that it's warmer in a foam hive than it is in a wood hive.  You say "they seemed to prefer 41F over -2F. " This implies that bees DO heat the hive.  The observation that a foam hive holds the heat better than a wooden one is fairly obvious.
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BlueBee
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« Reply #10 on: March 31, 2011, 03:00:42 PM »

Jeff, I think we’re probably agreeing with each other but our written words aren’t exactly conveying that sentiment. 

Quote
A perfectly insulated R10 foam hive will be up to 47F above the outside temperature if the bees are making 20watts of heat in the cluster.  In this case, the bees DO end up heating the hive along with the cluster.

What I think I said above was this:  The bees DO heat up an insulated hive, but do not appreciably heat up a wood hive.  Hence the beeks mantra holds for wood hives, but NOT for foam hives.

Quote
The observation that a foam hive holds the heat better than a wooden one is fairly obvious.

You would think everybody knows that!  However that was not evident in the forum this winter.  You must have missed out in the discussions this winter about insulation.  Many beeks don’t believe insulation warms up a hive.  They believe the old mantra “Bees only heat the cluster” applies in all cases.  At least that was my interpretations of their posts this winter. 
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BlueBee
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« Reply #11 on: April 01, 2011, 05:51:12 PM »

The point of this post is not to prove insulated hives are warmer than wooden hive.  I would hope that is fairly obvious to everybody by now.  A better use of the equation is for designing wintering systems for next year or spring buildup.   If you know how many watts your bees are generating (see my other post), you can design an enclosure of the proper volume and R-value to maintain your bees at about any temperature you want in your climate.  How much insulation you would need can be figured out from the equation I posted.  There is no need to make your bees suffer in hives that are 0F.

Take for example a 5 frame nuc.  People know from reading the forums that you want to pack them in a small hive (nuc) not a big one.  However how cold will that small colony get?  We know small colonies will freeze out due to a lack of heater bees.  What are you to do?

Well, using this math you can tune the thermal performance of the hive to the size of your colony to give them a better chance of thriving.  You can make an informed decision rather to use a wood hive, a 1” foam hive, a 2” foam hive, or even adding electric heat if you want.  The equation will predict the average temperature inside that hive.  (before accounting for air infiltration losses and solar gains).
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MarkF
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« Reply #12 on: June 01, 2011, 03:22:58 PM »

Does anyone know at what the bees would be the most comfortable. What temperature would the bees use the least food, raise the most brood move freely in the hive.
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Grieth
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« Reply #13 on: June 01, 2011, 03:45:07 PM »

Great discussion on heat.  It doesn't get so cold where I am, so MarkF's question is more important to me, coupled with the calcs for heat.  I would also like to know about cooling as it gets up to 40 centigrade here on the hottest summer days - would an insulated box (higher R value) potentially keep the excess heat in?  I have noticed in warmer climates that roof insulation slows heating, but also seems to slow cooling in the evenings. I am interested in your thoughts.
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derekm
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« Reply #14 on: August 04, 2011, 04:52:35 PM »

Does anyone know at what the bees would be the most comfortable. What temperature would the bees use the least food, raise the most brood move freely in the hive.
from the scientific literature it appears to be around 34C. So the trick is to insulate so the bees can heat the hive to 34C if they want to and keep down to 34C as well, we can keep the bees in their "office environment"
Using that temp, the edothermic heat output( bees heater full on) and ectothermic ( bees just chillin) output for volume of bees, the dimensions of the hive, the thermal conductivity of the hive material, you can work out the temperature range the bees can control with resorting to clustering or fanning.
I've done that and i 've manage to confirm the obvious Bee's do well in 37" diameter tree with 12" hole in the middle and only need to cluster when it gets below freezing and only need to fan when it way above 20C.I'm using this to see what temperature I need to open vents on a 2" thick polyurethane hive, and what cold its good for.
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rbinhood
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« Reply #15 on: August 04, 2011, 05:38:02 PM »

While you are at it why don't you try and redesign the work of mother nature....build a new bee.

For thousands of years the humble bee has managed to survive and some may even say thrive in a natural state, they adapt to the changes of the seasons no matter what is thrown at them.  Bees unlike humans do not need central heat and air or indoor plumbing in order to survive.  If you continue down this path you are on, the bees will soon be like the human race.....a bunch of fat, lazy, unhealthy couch potatoes. They will be waiting lined up on the landing board for you to hand feed them every ounce of nectar and pollen they need to survive, thus you are going to create another welfare state. 

Seriously....have you given any thought to how many problems you may be creating for the future of your bees?  What kind of new virus and pest, possably some we have never had to contend with that you may be helping to create by not letting nature take its course.

Don't get me wrong I think your discussion is very interesting, but you have to admit mother nature did a real good job when she designed the honey bee....what else on the face of this earth can take a cow pattie and turn it into the sweetest thing on earth HONEY!     ROFLMAO

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BlueBee
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« Reply #16 on: August 04, 2011, 06:44:40 PM »

Did mother nature design the bees to live in ¾” thick wood boxes?  Does a ¾” wood box emulate the thermal conditions in a tree cavity?  How many natural hives use foundation?  How many natural hives have 5.3mm fat cell bees?  How natural is it to ship millions of southern bees to the northern USA every spring?  What are the consequences of that?

The ‘don’t mess with mother nature’ genie came out of the bottle a LONG time ago! 

What I’ve been trying to do is better emulate the thermal conditions in the bee’s NATURAL home (tree cavities) giving our northern bees a better chance to survive.  I’m trying to head back towards nature, not away from it.

It might be bad for the economy, but I don’t enjoy buying new Southern bees every spring as much as some people do.
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rbinhood
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« Reply #17 on: August 04, 2011, 07:00:21 PM »

Are there not any cold hearty bees that will survive the northern winters.....not trying to be funny.....it is a serious question.  If so why not stick to that stock and stay away from those southern gal's.  I have purchased a few queens from northern breeders in the past and they did well here in the southeast but not as good as feral or mutts with no long linage with so called resistante traits toughted by many breeders.
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BlueBee
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« Reply #18 on: August 04, 2011, 07:12:08 PM »

We do have plenty of cold hearty bees here in Michigan, but they live in trees; not thin wood boxes.  We had 60% losses in cold wood boxes last winter.  It gets pretty cold here in the winter Smiley
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rbinhood
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« Reply #19 on: August 04, 2011, 07:25:01 PM »

 lau

You should just build them and igloo it would be warmer than an old thin wood box....lol
My girls would not know how to act if they could not pris around on Christmas day in their bikini and get some sun!
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