### Image Credits:

1. by o5com from flickr.com, used under a Creative Commons license

1.
Feb 15, 2012 6:57 AM ET

Discussion is Good
by John Brooks

Julius Sumner Miller is Not-So-Silly

JSM: "What happens is that the less dense air is pushed up by the colder air"

Allison, why do YOU think Julius Sumner Miller would say such a thing?

2.
Feb 15, 2012 8:41 AM ET

Edited Feb 15, 2012 8:42 AM ET.

Response to John Brooks
by Allison A. Bailes III, PhD

I'd say that's pretty much correct, John. On one level, the physics is pretty simple. If something accelerates upward and rises against the force of gravity, there's a force pushing it upward. What I have a problem with is someone saying that warm air (or heat) doesn't rise when it clearly does.

3.
Feb 15, 2012 10:51 AM ET

I agree with Martin (and Allison)
by Michael Blasnik

I really see it as two sides of the same coin. The only shortcoming in saying that hot air rises is perhaps omitting the fact that cold air falls (if that isn't obvious from the first statement). I think these two statements provide a pretty good explanation.

An analogy I might use is two people of the same weight on a see-saw each holding a 10 pound bar bell. Then one of them drops their bar bell and so they go up and the other person goes down. Now what caused them to go up? Well, technically it's because the other side of the see saw is now heavier and so gravity pulled that side down which pushed up the lighter side. But it's also true to say that their side of the see saw got lighter from dropping the bar bell so they caused the see saw to go up. To extend the analogy, dropping the bar bell is heating up the air in the house and the fulcrum of the see saw is the neutral pressure plane.

4.
Feb 15, 2012 11:22 AM ET

an interesting subject
by John Brooks

I especially liked some of your answers for Lucas Durand in this GBA blog:

I think you have an exceptional understanding of Air movement and 3d networks

and Kudos to Lucas Durand for asking some very interesting questions

5.
Feb 15, 2012 11:28 AM ET

Edited Feb 15, 2012 11:29 AM ET.

Love that analagoy!
by Allison A. Bailes III, PhD

I love that analogy, Michael, and will use it in the future when explaining this. Thanks!

Your analogy just reminded me a little of another bit of physics. Some people who've had an introductory physics course love to go out and correct anyone who uses the term 'centrifugal force.' (Yes, I was one of those people many years ago.)

"No, no, no," they say, "there's no such thing. You mean centripetal force. Centrifugal force is nothing more than inertia."

Those who go further and take an intermediate mechanics class find out that physicists do actually use centrifugal force in calculations. Sure, it's referred to as a fictitious force, but it has some utility in solving problems.

6.
Feb 15, 2012 11:44 AM ET

Another Michael Blasnik Insight
by John Brooks

I recently clipped this snipit from another forum...
I found it to be very helpful

7.
Feb 15, 2012 4:02 PM ET

Along those lines
by K Willets

Suction doesn't exist.

Wikipedia has a fairly easy-to-read page on the stack effect.

8.
Feb 15, 2012 4:15 PM ET

Edited Feb 15, 2012 4:36 PM ET.

Concerning Suction
by John Brooks

Kendall... Julius Sumner Miller makes the same point in this video
JSM: "and I must advise you... to put the word Suction... out of your vocabulary...It is UNACCEPTABLE!"

But of course he is being a word policeman
not that there's anything wrong with that

9.
Feb 15, 2012 5:52 PM ET

Word Police
by Allison A. Bailes III, PhD

Kendall & John, suction is like centrifugal force. It misleads if you don't understand that the force is really coming from the other direction. As long as you understand the nature of the forces, though... Oh, wait. I'm not going down that path with yet another concept. Not here anyway. ;~)

10.
Feb 15, 2012 6:05 PM ET

That force is called buoyancy.
by Joe Schmo

and density, temperature, and pressure all play a role in creating buoyant flows. almost all of the discussion above is just a simplification of these phenomena. hot air rises (relative to cooler air), heat naturally tends to flow from hot to cold, etc. A practical discussion of this topic is probably warranted since some of these flows are unlikely or easily disrupted in building construction especially if paths are obstructed, pressure and elevation differentials are small, or exterior or ambient conditions are too similar. Bottom line, it can be quite difficult to get the theoretical flows you expect in a house.

11.
Feb 15, 2012 6:07 PM ET

Clarification
by Joe Schmo

Consider entrainment instead of suction for terminology.

12.
Feb 15, 2012 6:34 PM ET

Edited Feb 15, 2012 6:35 PM ET.

I too am a fan of word
by aj builder, Upstate NY Zone 6a

I too am a fan of the word buoyancy in regard to fluid dynamics.

13.
Feb 15, 2012 7:18 PM ET

Focusing on the plight of the Hartfords in Maine...
by Dana Dorsett

There's never a subsidy for changing fuels, but rare is the market in the lower 48 of the US where in addition to nailing down all the low-hanging fruit of air sealing & spot insulation, putting in a decent mini-split heat pump isn't going to be cost-effective relative to heating with oil, and relegating the oil-burner as backup, or to meet the design-condition peak loads. At 15-17cent/kwh electricity and a climate cold enough that the mid-winter average COP of the mini-split is only 2 (in most places it would be higher) heating with a mini-split would be well into double-digit dollar savings over \$3.50 oil, and at \$4 oil it's approaching a 40% discount.

The mean January temp in Dixville ME where they live is roughly +19F, a temperature at which better mini-splits have a COP of about 2.5, so their seasonal average out of the thing would likely be 2.5 or slightly better, even if it's only pulling 1.5 when it's 0F outside (a temp at which point kicking on the oil burner wouldn't be so dramatically more expensive, and may even be necessary.) During the shoulder seasons in ME when the average outdoor temps are 40+ a mini-split would have a COP of more than 3.5. A 1.5-2 ton mini-split is ~\$4- \$5K installed, and could probably provide more than 80% of the annual heating for them. If it's displacing even 500 gallons of \$3.90 oil use a year, replacing it with a in increased power bill at roughly half the cost, it doesn't take a net-present-value analysis to figure out if it's cost-effective. Sub 5-year paybacks are typical (it could be sub-3 years if oil prices continue to climb.)

And if oil falls to \$2 again they could adjust their mini-split use accordingly.

14.
Feb 16, 2012 8:48 AM ET

Here to Learn
by John Brooks

Here is a John Straube quote from BSC BSD-014
"The air within a building during the wintertime acts like
a bubble of hot air in a sea of cold air."
Allison, If I take a drinking glass...turn it upside down and carefully push it underwater...
Is it fair to say that the interface at the bottom of the glass between the water and air is a neutral pressure plane?

15.
Feb 16, 2012 9:47 AM ET

Response to John Brooks
by Allison A. Bailes III, PhD

Indeed, John, it must be. If there were any unbalanced pressure there, things would still be moving. If the system is in equilibrium, the forces and pressures are balanced. In that paper by Straube, which I believe is pretty much the same as what he wrote in his textbook, Building Science for Building Enclosures, he discusses houses, where the interface is air-to-air, and the same thing happens.

When the house is perfectly sealed at the top and open at the bottom (the inverted cup), the neutral pressure plane is at the bottom. When it's perfectly sealed at the bottom and open at the top, the neutral pressure plane is at the top. In both cases, there's no flow because the pressures are balanced at the only leakage pathway. Put a hole in the side or sealed end, and then the air starts flowing.

16.
Feb 16, 2012 11:26 AM ET

Edited Feb 16, 2012 12:01 PM ET.

by Garth Hood

"Heat rises, heat rises, heat rises! Oh and by the way heat also travels in every other direction as well!"

I believe a statement like this can be very misleading.

I was taught that heat, in general, moves from hot to cold (and technically not the other way as heat has energy and cold does not). Temperatures are always trying to equalize and we can reduce heat loss but not eliminate it.

It is not a particularly complicated process but it can be confusing when one person is saying that heat rises and another is saying that it doesn't. I'm in the "heat travels in every direction but hot air rises" camp. You can add to that, if you want, that hot air steals heat from the building as the air escapes through holes in the building envelope. We can also get into a further discussion of heat movement by radiation, conduction and convection. All of which all refer to heat but only the latter has anything rising.

The important thing is the clear promotion of basic building science principles so an average person can, for example, understand the importance of air sealing and insulating under a slab. And why in a well sealed house insulation needs to be added to the structure in a balanced way - and not R60 in the attic but nothing under the slab because "heat rises" - which is old school teaching.

Just my two cents worth...

17.
Feb 16, 2012 11:32 AM ET

Analogy
by John Brooks

If I push the upright bottle underwater....
Is this a good analogy for an imaginary house (heated in winter) with only one open door at the bottom?

see attached photo

18.
Feb 16, 2012 11:34 AM ET

Response to Garth Hood
by Allison A. Bailes III, PhD

"The important thing is the clear promotion of basic building science principles..." That's exactly what I'm after, too! When people say that heat does NOT rise, they're wrong. As you say, heat travels in all directions, and upward is one of them.

Now, on another issue you raised, I'd say insulating under a slab is not important unless you're in climate zone 5 or higher or have radiant heat embedded in the slab. Most of the heat loss happens at the perimeter, and that's where the insulation needs to be.

19.
Feb 16, 2012 11:38 AM ET

Edited Feb 16, 2012 11:38 AM ET.

Response to John Brook

John,
Any analogy comparing a plastic soda bottle to a house is likely to be misleading, because a plastic soda bottle is airtight. Houses aren't airtight, which is why we measure airtightness with a blower door -- to determine a home's air leakage rate.

I suppose you can use a soda bottle for your future analogies, as long as you first take a red-hot paper clip and poke one thousand holes in the side of the soda bottle.

20.
Feb 16, 2012 11:46 AM ET

I agree with Martin...
by Allison A. Bailes III, PhD

John, you have to be careful with analogies because it's easy to take them too far and then you have to add all kinds of qualifying statements. Even with the red-hot paper clip, the analogy still doesn't hold up because in your example, the fluids are air and water, nor have you added a heater to your little plastic water bottle.

21.
Feb 16, 2012 11:56 AM ET

Followup to Allison A. Bailes
by Garth Hood

I live in a cold climate so I won't disagree with your comment regarding sub-slab insulation as pertains to heat loss. I do have concerns that an un-insulated slab might still have issues with condensation in humid conditions.

In any case I am a believer in performance modelling and testing. Sophisticated heat loss/gain software can accurately show where insulation is and isn't needed within the building envelope.

22.
Feb 16, 2012 12:03 PM ET

Edited Feb 16, 2012 12:04 PM ET.

Response to Garth Hood
by Allison A. Bailes III, PhD

Hear, hear! We do a lot of energy modeling here, and I couldn't agree more.

On the topic of condensation on slabs in warmer climates, mostly I see that in carports. If it's happening inside a house, it's usually a basement, and the best way to deal with that is by adjusting the dew point of the air downward.

23.
Feb 16, 2012 1:41 PM ET

Edited Feb 16, 2012 1:44 PM ET.

Variation of Bud Poll's Illustration (in French)
by John Brooks

Allison.. I am just trying to learn here.
this is my attempt at a hybrid drawing of Straube's Cylinder and Bud Poll's "Worksheet"
I am trying to learn by doing(and making mistakes)...... so please correct my math, units and concept if I am on the wrong track

24.
Feb 16, 2012 6:24 PM ET

Delta pressure illustration
by Bud Poll

Hi John,
Your math is correct and you are trying to show the potential pressure difference between two columns of air 10 meters high with one near 0° C and the other near room temperature, 21°C, your numbers are of course in Kelvin. What the equation gives you is the potential pressure difference. It is your drawing that will place that difference at the top of the warm air column as the bottom is open and thus zero pressure difference.

The 0, 5, 10 on the outside are not explained and there should probably be only one 10 pa indication on the inside at the top and it should be negative. My decision to include the barometric pressures I felt was necessary to complete the explanation illustrating how the negative 10 pa pressure comes about and to provide a reference for the stacking effect of the different columns of air. If you want to reference your drawing to Straube's, then show a positive 10 pa on the outside.

Bud

25.
Feb 16, 2012 6:48 PM ET

Edited Feb 16, 2012 6:54 PM ET.

Response to John Brooks
by Allison A. Bailes III, PhD

John, you're definitely on the right track, but as Bud pointed out, you seem to have put the pressures on your diagram incorrectly. If you reference to outside pressure, calling that 0, the air at the bottom of your cylinder would be 0 Pa. As you rise inside the tube the pressure relative to outside rises and becomes positive. At the top, it would be the 9.93 Pa you calculated and would be positive (not negative), so the air inside the cylinder would be pushing harder on the walls and ceiling than the air outside. Put a hole there, and the air leaks out at the top. That results in the air below it moving up and cold outside air coming in at the open bottom.

Of course, this is very simplistic model and real houses have a lot more complexity, but it illustrates how the stack effect works. I like Straube's extension of the cylinder illustration with another one open at the top, then one open at top and bottom, and then the open top & bottom cylinder being heated around the middle.

26.
Feb 16, 2012 7:14 PM ET

I think I see the confusion
by John Brooks

My 0,5,10 numbers on the outside of the cylinder are meant to indicate the barometric pressure OUTSIDE....
I think I should have spaced the labels further from the cylinder

The numbers Inside the tube are meant to indicate the absolute INSIDE barometric pressure.

does that make more sense?

If and when I get this Illustration right I was planning to "open" both ends and to work on other variations.

27.
Feb 16, 2012 7:20 PM ET

Edited Feb 16, 2012 7:22 PM ET.

Response to John Brooks
by Allison A. Bailes III, PhD

Since barometric pressure changes about 3.4 Pa per foot of height (increasing downward), your numbers outside should be 0 at the top and about 110 Pa at the bottom, John.

Also, if you use that formula from Straube's book, you're not getting absolute (barometric) pressure inside. It gives you the Δp between inside and out.

28.
Feb 16, 2012 7:32 PM ET

I don't mind making mistakes
by John Brooks

I will chew on the feedback ....

29.
Feb 16, 2012 7:36 PM ET

Edited Feb 16, 2012 7:38 PM ET.

Aeronautical engineering...
by aj builder, Upstate NY Zone 6a

Aeronautical engineering... many moons ago... still have my fluid dynamics text books... somewhere.

Wow... much more fun to fly and build homes and planes now verses those courses! Back to addition and subtraction these days... Diffy Q and all... have at if Brooks.

We harness all the hot air generated at this site and we could build a "hot air stack elevator" to the moon. Send me first. But first an IPA awaits my attention.

30.
Feb 16, 2012 8:03 PM ET

Correction
by Bud Poll

Allison,
You are correct. I'm not used to Straube's diagrams and it looks like his arrows don't agree, but the answer is obvious and I should not have been confused.
Thanks,
Bud

31.
Feb 17, 2012 10:11 AM ET

from the peanut gallery
by 5C8rvfuWev

this has been one of the best recent discussions on GBA for the likes of me. Being able to follow along on the math has made it so I feel like I'm getting more than a rote grasp of what's going on for the first time. Much appreciated.

32.
Feb 18, 2012 6:20 AM ET

Edited Feb 18, 2012 10:10 AM ET.

Adapting Bud Poll's Illustration... 2nd Attempt
by John Brooks

Ok, I think I see where I went wrong.
I think I was much "closer" last Sunday when I posted an in-progress illustration at Home Energy Pros
http://homeenergypros.lbl.gov/forum/topics/the-science-of-hot-air-rising...

In my attempt to create a "French" version of Bud Poll's worksheet....
I got confused...and...
I lost sight of what was going on "outside" ...
(and the OUTSIDE is a major influence here)

Let me try this again in "English"

33.
Feb 18, 2012 11:02 AM ET

Edited Feb 18, 2012 11:03 AM ET.

...
by Lucas Durand - 7A

John,
Your illustration reminds me a little of a hot water tank - but with a hole in the bottom.
Or rather, a large solar storage tank.

34.
Feb 18, 2012 6:49 PM ET

Picture Is Getting Clearer
by Bud Poll

Great illustration John and thanks for catching my errors.

It amazes me how much of a role barometric pressure plays in our residential energy setting and yet it is a pressure we cannot see with our manometers and one that is rarely mentioned in our training, at least not in this simple manner.

Bud

35.
Feb 18, 2012 8:22 PM ET

"Connected" to the Atmosphere
by John Brooks

Bud,
As far as I know you are the only one who included the "weight" of the atmosphere(ocean of air) in your illustrations...and labeled the "stacks" side by side

I think I had my first Atmosphere "Aha" while watching Julius Sumner Miller Videos.

I also had an "Aha" when I read a recent comment by Colin Genge (Retrotec founder)
Colin: "Atmospheric pressure adjusts inside and out almost instantaneously even for a tight house. It would be in the order of a few seconds at most."

36.
Feb 18, 2012 8:48 PM ET

NPP Response
by Bud Poll

Good catch John, that rapid response is part of what I was missing in the transition to leakage above and below with a neutral pressure plane (NPP) somewhere in the middle. One of the details that becomes evident with this approach is that the stack effect pressures are there independent of the leakage. A tight house has the same stack effect pressures working on it as a leaky one, assuming the same height. But the location of that NPP in a tight house could swing rapidly with inside activities, windows, doors, and exhaust appliances. And when it moves, the pressures adjust accordingly.

Interesting
Bud

37.
Feb 18, 2012 9:15 PM ET

Barometric pressure, Pascal's Principle...
by Allison A. Bailes III, PhD

Bud, why do you think barometric pressure plays a role in residential energy use? It's the same inside and out. The pressure differences induced by wind, the stack effect, and mechanical systems are what matter.

John, that very fast transmission of pressure in fluids is called Pascal's Principle. It's why we can turn on a Blower Door and get the reading almost immediately. It's why hydraulic jacks work. And it happens at the speed of sound because it's transmitted exactly the same way.

38.
Feb 18, 2012 9:35 PM ET

Physics 101
by John Brooks

Allison, I never went beyond Physics 101 in school

I apologize for getting too geeky sometimes...but this stuff fascinates me

I don't want to go to the Fight Club ... I want to talk about Building Physics

39.
Feb 18, 2012 9:48 PM ET

Barometric pressures
by Bud Poll

Hi Allison, You said " Bud, why do you think barometric pressure plays a role in residential energy use? It's the same inside and out."
But it's not. That is what the diagram John and I have been working on is trying to illustrate. The barometric pressure on the inside includes the height of the warm air on the inside and that is sufficiently lighter, that when added to the final few feet of atmosphere we see the pressure difference we can stack effect. Straube's equation even calculates this difference between the inside and outside barometric pressures based upon those last few feet.

A column of atmosphere commonly ends at sea level with a pressure of 14.7psi or 101325 pa. When we break down the 101325 by feet we get approximately 3.5 pa per foot of elevation (near sea level). In the diagram I used 3.75pa on the outside and about 7% less on the inside because the air is warmer. That results in about 0.25pa less pressure per ft on the inside.

Flue draft, attic venting, stack effect, and that elusive neutral pressure plane can easily be explained by stacking up the related columns of air.

Bud

40.
Feb 18, 2012 9:50 PM ET

Edited Feb 18, 2012 10:07 PM ET.

Easy for you
by John Brooks

Allison, maybe this stuff is easy for you to visualize ....
Just like some people can visualize in 3D and others really have to work at it
I have a hard time visualizing stack and convection and nuetral pressure planes...yada,yada

I think it would be a good thing to design houses in hot & mixed climates that "work" (provide good comfort)with just a couple of mini-split air conditioners

I think we can all learn something from the Old Guys ...Including Julius Sumner Miller
and the guys that designed stuff like this

41.
Feb 18, 2012 10:19 PM ET

Gravity doesn't matter
by Allison A. Bailes III, PhD

Bud, let's take a step back and clarify our terms. Barometric pressure is the absolute pressure we read with a barometer. With no wind, stack effect, or mechanical systems inducing pressure differences, the barometric pressure will increase as you go down from the top of a house to the bottom. It changes about 3.4 Pascals per foot of height.

A house that is 20' tall will have a barometric pressure at the top that is about 68 Pa lower than the pressure at the bottom. That's more pressure difference than we apply to a home during a Blower Door test (typically 50 Pa in a single point test). Yet why, if the Second Law of Thermodynamics says that air moves from high pressure to low pressure, will the air in the bottom of the house not push its way upward?

Because of gravity, that's why. That fundamental force of nature completely cancels out the effect of that pressure difference that it created in the first place.

So again I say the only thing you need to worry about are the relative pressures created by wind, stack effect, and mechanical systems. You're making this more complicated than it really is.

42.
Feb 18, 2012 10:29 PM ET

Barometric pressures
by Bud Poll

Allison, I do tend to make things more complicated, but it is the process of straightening them out that helps me understand them better. :)
You said "So again I say the only thing you need to worry about are the relative pressures created by wind, stack effect, and mechanical systems." Leave out the wind and mechanicals for the moment and explain where the pressures come from in stack effect?

Bud

43.
Feb 18, 2012 11:35 PM ET

Edited Feb 18, 2012 11:43 PM ET.

Free copies of "Fluid
by aj builder, Upstate NY Zone 6a

Free copies of "Fluid Dynamics For Dummies" for all.....

You guys are killing me, but keep going.... Interesting.

Temperature change, density change, weight change, gravity, free movement....

A lifesaver ... Due to buoyancy....
http://abs-airbag.de/us/

44.
Feb 18, 2012 11:36 PM ET

It's temperature...
by Allison A. Bailes III, PhD

Bud, the relative pressures in the stack effect result from temperature differences.

45.
Feb 18, 2012 11:58 PM ET

interesting
by John Klingel

I find this interesting. "In summer, it moves downward as it follows the cool, dense air." This seems to cloud the issue if the intent is to educate The Confused. HEAT moves down w/ cooler air? OK, I understand that there is no such thing as "cold", but only less heat/energy relative to something else. Technically, everything has heat until it hits the magic -452 F or whatever it is. But it seems to confuse the issue to say that heat is going down with cooler air. Maybe "less-hot air" is moving down?

46.
Feb 19, 2012 1:04 AM ET

Progress
by Bud Poll

Allison "Bud, the relative pressures in the stack effect result from temperature differences."

Correct, and those temperature differences create a weight difference between the column of outside air and the column that passes down through the house. At the height of the thermal envelope both columns would weigh the same, looking up. But, from there down each foot of outside air would add 3.4pa, using your number. On the inside, with a 35° F temp difference (bottom of John's diagram 275°K outside and 294°K inside) we see air that weighs app. 7% less per volume. Thus 3.15pa per foot. In your 20' tall example, those last 20' would add 68pa on the outside and 63pa on the inside, giving us a delta p of 5 Pascals. If we plug 20' (6.1 m) and those two temperatures into Straube's equations we get 5.1pa.

Paul Morin gave me the American version of that equation,
Pa. = 0.0067 x H x T
H = distance from the neutral pressure plane in feet
T = the Fahrenheit inside and outside temperature difference
Here we get Pa = 4.7pa, close enough.

All we are doing is illustrating the way air stacks up at different temperatures to provide us with the pressure differences we see and call stack effect.

Bud

47.
Feb 19, 2012 9:08 AM ET

Response to John Klingel
by Allison A. Bailes III, PhD

John, if you read my original article on the stack effect (http://ow.ly/99ONq), you'll find an explanation and a diagram of the stack effect working in reverse in summer. Let's go back to John Straube's quote about the house containing a bubble of warm air in a sea of cold air in winter. Because of the house air being less dense, it can rise.

In summer, the house is a bubble of more dense air surrounded by less dense air. Holes at the bottom and top of the house will allow the cool, dense air to fall out of the bottom, which then brings the warm, less dense air in at the top.

Now, houses are complex objects, attics get very hot, and it's certainly possible to get warm air to rise up and out in summer, too. It all depends on the relative densities and pressures.

48.
Feb 19, 2012 9:20 AM ET

Response to Bud Poll
by Allison A. Bailes III, PhD

Bud, mixing the barometric pressures into your example only confuses what's going on. As I mentioned above, higher pressures at the bottom of a stack due to the weight of all the air above it don't cause the air to move up into the lower pressure area because gravity balances it out. Yes, of course, gravity is involved because of the different densities of cooler and warmer air, but you're better off just dealing with the relative pressures created by those differences and eliminating the absolute pressures from your explanation.

49.
Feb 19, 2012 9:54 AM ET

Back where we started

Allison,
I'm with you. We're back where we started. As home performance contractors have been saying for years, "A negative pressure of 50 pascals with respect to the outdoors" -- we're comparing the indoor pressure with the outdoor pressure.

There is no benefit from confusing our explanations with barometric pressures.

50.
Feb 19, 2012 10:54 AM ET

original blog statement
by John Klingel

Allison: Agreed. Sure. "...will allow the cool, dense air to fall out of the bottom, which then brings the warm, less dense air in at the top." I'm not disagreeing w/ the statement in the preceding sentence or the physics. I'm only concerned about the potential confusion that might be generated by this statement in the original blog: "...In summer, it (heat) moves downward..." The cool air is going down, not the heat (as we generally think of it, ie, relative warmth).