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Dew point calculation

Dew point calculation

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Radiant gone wild - more "mythunderstandings" about basement floor heating, comfort and radiant cooling
Copyright 2010 Robert Bean, R.E.T., P.L.(Eng.) All world rights reserved

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Despite the 100+ years of formal research and over 10,000 years of recorded history, radiant heating and cooling is still for some strange reason treated as a popular science experiment.  To address several discussions stemming from people not knowing if they could just heat the basement and let ‘heat rise’ to misunderstanding about radiant cooling, to the definition of comfort - I’ve penned a few words of wisdom to address these and other issues.

Comfortable buildings or bodies that are comfortable?

Once again, we have to get over the fact that we don’t condition buildings we condition people which means we have to understand comfort is a state of mind interpreted not by what the ‘room temperatures’ is, but what the 166,000 +/- thermal sensors in the skin are picking up and communicating to and interpreted by our brain (see work by Egan, Johnson, Farrell et al)

What does this mean?

It means comfort exist both as a physical and psychological reality measured not by a building or by its thermostats but by the occupant, in other words, Table 1: Ranges of comfortpeople do not feel the heat loss of the building they feel the heat loss from their bodies...and this is the most important part – people don’t work on 1’s and 0’s …people work on grey or what we call fuzzy logic (see Table 1).  

What does this mean?

It means you can’t dictate someone to ‘be comfortable’ based on digits like 72 deg F dry bulb temperature (see work by Rohles et al).  There are ranges of comfort based on environmental and physical factors and there are ‘fuzzy’ thresholds of discomfort (see PMV work by Fanger et al).  

Here’s a few simple examples;  a numerical based room heat thermostat satisfied at 68 deg F (contacts open), creates perception of discomfort in some people, yet place the same person in a car with color coded controls in the presence of similar thermal conditions they are likely to express comfort.

Just from relocating from the house to the car there is a perceived change that exists psychologically due to cultural no numbers on the thermostat - just coloursconditioning (numbers on house thermostats, colors in cars). That same effect can be demonstrated with furniture, color and light (Rohles, Gagge et al). In one study that Fanger did, subjects preferred lower ambient temperature in red light than in blue light. Comfort can also happen with a slightly different twist in offices when people think they have control over their environment with a window, fan and or thermostat -  when they have control they tend to perceive higher levels of comfort - this has been demonstrated in research and in the field…just ask the controls contractors who have installed ‘faux’ thermostats or have recalibrated thermostats to serve the clients psychological needs instead of the client’s physical needs.  You can even have the phenomenon where someone has paid for something like floor heating in the basement only and will then claim the main floor is heated with radiant heating even though it is several degrees cooler than their physical desire for greater floor comfort.  Their psychological denial over what they paid and thought they were getting allows them to exist with their physical discomfort due in part to what they don’t have….all weird and wonderful stuff in the world of thermal comfort.

So first thing, as a psychological phenomenon, designers must appreciate they are dealing with as many subjective perceptions as there are to be occupants in the space; and each of these occupants consciously and unconsciously interprets thermal sensations from localized parts of their body which then leads to both general and specific interpretations known as perceptions about the environment expressed as discomfort.

So now that you have an extremely abridge discussion on weird comfort stuff let’s answer in general terms one of the 22 myths we feature at the site...can you heat the entire home with just the basement floor?

Assuming the occupants fall under the bell curve defined by a combination of environmental and physical factors satisfying something like 80% to 90% of the population and assuming the only thing separating the occupants feet from the floor is socks and assuming in the first instance that they have installed a hard conductive low VOC flooring for indoor air quality and assuming they are in contact with the floor for anything other than a temporary period of time (for giggles say more than 10 to 15 min); extrapolating from research, suggest (all other factors being equal) that if the floor temperature is within 79 deg. F. to 83 deg. F less than 10 to 15% of the population will complain (Olesen et al)  about the temperature of the floor (give or take 5%)…again there is no 1’s(ones) or 0’s (zero’s) in comfort …only grey, fuzzy and frequently distorted perceptions. For a second example, if they use a textile based floor such as your grandmas old groovy shag carpet or your new-age cousin who jumped into the recent trend to grandmas’ carpet choices on steroids - monster shag, the perceived localized foot comfort is based on a range between 70 deg. F. to 82 deg. F. We’ll get back to groovy carpet choices in a minute.

So lets’ use 79 deg. F. as our floor surface temp for comfort with socks and the space temperature is controlled to 72 deg. F. operative temperature (Top).

Simplified Top is the average of the dry bulb (Tdb) and mean radiant (Tmrt),

 = ((Tdb + Tmrt)/2)

(for those in the know – know that I know its a bit more detailed than that but it’s close enough for this conversation).

At 79 deg. F. and a heat transfer coefficient of a nominal 2 Btuh/sf/deg. F., the floor under maximum load could deliver a combined radiant and convection output equivalent to:

= (79 deg. F. - 72 deg. F.) * 2 Btuh/sf/deg. F.

= 14 Btu/hr/sf ,

or for 1800 sf of floor area a load of 25,200 Btu/hr.

[The heat transfer coefficient of a nominal 2 Btuh/sf/deg F is approximately 50% radiant and 50% convective. The split is influenced by the MRT, room geometry and any external influences such as fans.]

So here’s the thing, in a 6,500+ heating degree day year climate zone, 14 Btu/hr/sf exceeds the required output for any home built to high performance standards such as Passivehaus or R2000. But let’s have a bit of fun and go with 79 deg F and 14 Btu/hr/sf for giggles and take a trip into the basement.

Lets TRY a hypothetical load in the basement based on 40% of the main floor load (if you don’t like 40% use your own ratio  – it’s my party and I can TRY 40% if I want too…), 40% of 25,200 = 10,080 Btu/hr or roughly 8 Btu/hr/sf if you take out the unheated areas (assume 1300 heated basement floor, i.e. 500 sf unheated).

The required basement floor surface temperature becomes ,

= 72 deg F + ((8 Btu/hr/sf)/(2 Btuh/sf/deg F))

= 76 deg F,

which in this hypothetical case would be 3 deg F cooler than the required main floor temperature of 79 deg F. ergo you won't be heating the main floor to 79 deg F if the basement only needs to run at 76 deg F.

Let's for a moment, set aside choices of flooring in the basement and agree at this point it would be a bad choice to rely on the basement for comfort conditioning of the main floor. One would have to run both a CFD and an FEA model to see the convective , radiative and conductive transfer to establish the actual required basement floor temp to deliver the main floor surface temp (ergo resulting in the operative temp) but without taking several days to model this I can say with reasonable accuracy to heat the main floor to 79 deg F the basement floor would have to be just a tad on the hot side…even if we forgo the main floor temp of 79 deg F and just work with 72 deg F operative temp the basement floor would have to produce a combined load of 35,280 Btu/hr or roughly 27 Btu/hr/sf. 

The 27 Btu/hr/sf equates to app. 86 deg F surface temp which exceeds slightly the comfort level for socks on tile or grandmas groovy shag carpet. But hey, If you just cranked the surface up to say 95 deg F you could forgo the carpet or tile, sprinkle kitty litter on the floor, pretend you’re at the beach with your fancy umbrella drink and depending on which way you swing, watch the half naked volleyball girls and boys on Sports Net.

But I digress…let’s go back to the question…IF hypothetically the high performance home had a main floor design flux requirement of say 6 Btu/hr/sf at maximum load (10,800 Btu/hr) the required floor temperature becomes,

= 72 deg F +((6 Btu/hr/sf)/(2 Btuh/sf/deg F))

= 75 deg F.  

75 deg F. meets ASHRAE Standard 55, however if one had bare feet on tile at 75 deg F it may for some to feel neutral to slightly cool but it would be ok for  for carpets, linoleums and wood  - but put this into perspective - 75 deg F is going to be warmer than the floor in a forced air heated space.

So one solution if  you want a warmer floor, is to reduce the heated floor area (i.e. from 1800 sf down to 900 sf) which boost the flux load (from 6 Btu/hr/sf up to 12 Btu/hr/sf) and thus the surface temp (75 deg f up to 78 deg F.) to improve localized foot comfort perceptions without overheating the occupants at maximum load.

Anyhooo…at maximum load of 6 Btu/hr/sf and tiled floors, using say 8” tube spacing the average fluid temperature is appx. 77 deg F (using ASHRAE Fig. 9 Nomograph).

If you designed the system for a 10 deg F differential the supply temperature would be,

= 77 deg F + (10 deg F / 2) = 82 deg F.

Sans an academic physiology debate, that is roughly 16 deg F cooler than your blood temperature.  Which is a very weird construct for some since the floor whilst in it’s heating mode is actually cooling your body so you can remain comfortable….bizarre eh? I can say that cause I’m Canadian eh?

Now here’s where radiant shines from an energy perspective. What radiant has over other systems is its innate ability to enable boilers, heat pumps, and geo or  solar thermal system to achieve close to their maximum engineered performance. Most of the radiant claims on efficiency are caribou candies but you can’t argue the COP’s and combustion efficiencies achieved with low return temperatures in heating and high return temperatures in cooling.  Rather than spoil the fun, why don’t those who know…check out the COP of a heat pump or combustion efficiency of a boiler when the return temperature at maximum load is,

= 77 deg F – (10 deg F delta t/2)

= 72 deg F,

…yes for those who raised their eye brows – the return fluid temperature is equivalent to the designed space temperature…watch what that does to efficiencies.

So let's go back again and look at the basement assuming the same split of 40% the basement load becomes roughly 4300 Btu/hr or 3 Btuh/sf.  If we add back in the upstairs load of 10,800 Btu/hr we’re up to 15,120 Btu/hr for a basement flux of,

= (10,800 Btu/hr + 4,300 Btu/hr) / 1300 sf

= 12 Btu/hr/sf,

this results in a floor surface temperature of,

= 72 deg F + ((12 Btu/hr/sf)/(2 Btuh/sf/deg F))

= 78 deg F.

78 deg F is within comfort conditions (see Table 2) and with some convective help would stabilize the basement space while conditioning the entire home without Table 2: Floor surface temperatures based on enclosure performance and available floor area.heating in the second floor. The convective help could be small fans or architectural features to create natural drafts…sloped roofs to a cooler wall with transfer grills to and from the basement etc…

Again the above is a general overview based on hypothetical cases…for the snipers in the readership…change the numbers to your own delight and accuracy; and understand that I understand my picture changes as your numbers change.

If we agree on that then let’s continue.

Some other considerations:

Thermal lag and heat rising

Radiant energy is not slow nor does heat from a radiant panel 'rise'...radiant energy travels at the speed of light from hot to cold. The thermal lag associated with startup is not the same as the instant surface response based on emissivities and differential temperatures.

Lag at start up is dependent on the differentials between the various temperatures of the outdoors, in-space, slab/panel and back temperatures (earth and in-space), enclosure performance; the fin efficiency of the slab including the tube, spacing, depth, specific heats, conductivity and, resistances in, on and under the floor, and the controls employed to ‘wake up’ the system.  Again as a reminder, in a high performance home the fluid temperatures are not hot – they are tepid at best and with modern low mass conductive flooring options and basic analogue weather compensating controls there is similar controllability one would find with other heating systems.

Put it into perspective…we’re talking about heating the floor under maximum load to 75 deg F +/- …that’s only three or four degrees above space temperatures. For lower loads (say 95% of the year we hardly need any heat delivered to the floor) – that’s why you don’t need sophisticated expensive systems - one heat source, once circulator, one analogue weather compensator and one thermostatic non electric radiator valve with remote actuator and spring loaded bypass valve across the radiant manifold and you have a simple elegant system. 

Affordability

Affordability is relevant; expensive to one is affordable to another…I learned a long time ago not to be the financial advisor by saving money on IEQ systems for people who’ll then spend what they saved on outdoor furniture and boutique coffees.

Solar loads

With regards to solar loads: in the presence of shortwave energy (solar), the heated floor at 75 or 76 deg  becomes an absorber not an emitter and can be used to distribute or shed excess heat gains. If people are concerned with overheating due to solar gains then keep the shortwave energy off and out of the building.

Radiant split and latent vs. sensible loads

The radiant component in a floor heating system is long wave energy and represents approximately 50% of the heat transfer from the floor which is very similar to the ratio of sensible heat lost from the body at low level activities (watching TV, reading etc.)  and wearing light clothing.  This long wave energy from the floor is not absorbed by the body as most think but rather heats up the cooler room surfaces which reduces the radiant losses from the body…ergo it’s not the heat you are gaining but the heat you are not losing that contributes to your comfort (recall you already produce excess heat to the tune of 400 Btu/hr again sans any academic debate on activity, clothing, gender, physical attributes).

In a high performance home the interior surfaces are warmer in winter and sans discussion on internal gains, cooler in summer…i.e. in winter you wouldn’t need any heat from a mechanical system if heat produced by the body augmented by heat from fridges, freezers, lights  was sufficient to maintain comfort, but unlike winter, you ‘ll need to get rid of the sensible heat in the summer….but unlike the summer latent loads (with moisture); heat created from the sun, lights, motors, compressors and some of our body heat is sensible (no moisture) which radiant cooling is perfectly suited.

Radiant cooling

In radiant cooling, the floor is lowered to a temperature based on a lower heat transfer coefficient since the convective component is essentially reduced to zero and the heat absorption is almost all radiant. The cooling coefficient for a floor is a nominal 1.2 Btu/hr/sf/deg F. +/- 0.1.

For a hypothetical cooling load of say 10 Btu/hr/sf the required surface temperature becomes,

= 78 deg F – ((10 Btu/hr/sf)/(1.2 Btu/hr/sf/deg F))

= 70 deg F.  

(66 deg F floor surface temperature is considered the lower end for people wearing normal footwear).

Going back with our tiled floors and 8” o.c. spacing the average fluid temperature for cooling is approximately 68 deg F., for a 8 deg F differential, the return temperature to the heat pump would be,

= 68 deg F + (8 deg F / 2)

= 72 deg F,

….now again...go back and look at the cooling plant efficiency with 72 deg F return temperatures.

Regarding latent loads: they have to be considered - maintaining a lean air mixture is required to prevent condensation on any cooled surface, regardless of the HVAC system, i.e.: the ventilation air has to be introduced to the space dry enough to absorb the latent loads from people, infiltration, grooming, cooking, cleaning etc.  A 70 deg F surface temperature for comfort cooling and dew point limitation corresponds to app. 75% RH at 78 deg F space temperatures.  Evaluations like this are done using the psychrometric chart, a sample shown below (l) with a finite element analysis for a floor cooling system shown on the right.

 

75% RH doesn’t serve any building or health science needs whereas 50% does. At 50% RH and a space temperature of 78 deg F the dew point is app. 58 deg F. leaving a huge safety margin….normally 2 to 3 deg F is adequate (as shown above in the left hand side image). So determine your space dew point at 78 deg F and reduce the absolute moisture in the incoming air (based on  moisture produced/deleivered by the occupants, infiltration etc.) and deliver that lean air mixture to the space through the ventilation system or provide in space dehumidifiers. If you live in a dry climate like I do, dehumidification is not typically our problem but humidification is...so again your mileage may vary depending on the geography, occupants and building performance.

If you haven’t yet checked the performances of 72 deg F return temps through heat pumps and boilers I would encourage you to do so for your own entertainment….I can tell you this...every engineer at the manufacturing plant will kiss your feet when you can make his/her stuff do what it was designed to do…

Sustainability, energy and exergy efficiency

One of the messages in this is direct coupled earth systems (without compression or combustion) become attractive at 72 deg F fluid temperatures…even if the earth system could supply enough cooling and heating for 75% of the year, the balance could be made up with solar for a truly sustainable exergy and energy efficient system. If solar isn’t an option at least the non renewable is limited, the efficiency is close to perfection with entropy losses minimal.

 

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