Windows

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Purpose

To assess the R value, solar gain (SHGC) and visual transmission (VT) of windows with and without multiple storm windows to determine at what point where solar gain exceeds losses, for particular orientations. Storm windows can be easily made from mylar and cork.

A spreadsheet goes with this file. To get a copy of the spreadsheet (.xls format) Click Here

If you don't have an application that can read a .xls file, you can get one from SUN Microsystems for free. Click Here

Window Energy Loss

Windows lose energy to ambient air by conduction, convection, radiation and air leakage.

For every window there is an air film upon it, both inside and outside. Adjacent to that thin air film is air. Indoor warm air comes in contact with the air film which is likely to be cooler if it is cold out. The warm air imparts its energy to the air film and warms it up. The air is now cooler so it falls. In front of every window you can envision almost a waterfall of cool air constantly falling to the floor in front of the window or glass door. As soon as that cool air falls warm air from the room rushes in to take its place. This convective loop is recognized as a cold draft. Energy is lost from a warmer inside to a cooler outside by conduction and convection. The air film on a window has an R value. If the air is still the R value is 0.68. If its windy or in wind conditions, the R value is 0.17 Btu-hr/SF-Degree F.

Air leakage is one of the leading causes of energy loss in non energy efficient buildings and the air leakage from windows can be a significant contributor to this problem. A NFRC rating includes the air leakage from a window. The value is given as air leakage in cubic feet per minute (CFM) per square foot of window. The air leaks out of a window at just about every single joint, to some extent. Smaller windows and windows with divided lights are more likely to have higher leakage just due to the fact that they have more joints per unit area than larger ones.

If you stand in front of a cold window, you may feel the window taking the heat away from your skin. This is due to the fact that your body is radiating heat energy and that energy is moving from a warmer location to a cooler one. In this case, the window

Solar Insolation Data

There are 2 major sources for this data, both necessary

The first source is ASHRAE data. The ASHRAE manuals have tables of solar insolation by latitude. These values are computed. The information is given for all horizontal orientations, meaning north, south, east, west, nne, sse, ssw and so forth. It provides data for every sunlight hour of the day, for the 21st day of every month of the year. The information is in Chapter 27, Fenestrations. The 1997 ASHRAE fundamentals handbook is online at ftp://ef12517-2.tu-sofia.bg/Books/Engineers%20Handbooks/ASHRAE_Handbooks_1997-2000/IP/1997/F29p.pdf . Scroll down to page 29 and from there find the page that corresponds to your own latitude. To see an example of this page, Click Here

If you don't know your latitude, try looking up your city or town in Wikipedia. You will find the information you are looking for on the right

A window means a vertical face or a piece of double strength glass (DSA) covering a hole in the facade of a building which is vertically oriented, or, in a plane oriented at 90 deg to the plane formed by grade. ASHRAE data does not take into account various atmospheric conditions that can reduce the solar intensity given in the table by 50% or more. The 'A' in DSA is a quality designator.

The second source of data you need is called Redbook data. Online you can get "The Solar Radiation Data Manual for Flat-Plate and Concentrating Collectors" from http://rredc.nrel.gov/solar/old_data/nsrdb/redbook/ Redbook data is actual measured data. The data is for a range of vertical tilts but only facing south. Its given for flat plate collectors. There is also data for Average Climatic Conditions. The margin of error is in the vicinity of 10%. The Redbook data is given by state and then city. Use the 30 year average option.

Adjusting the Data

In this example, we start with the Redbook Data for Detroit, Mi. This is what the Redbook data looks like. Click Here

Detroit happens to be at the center of the Earth's surface if you look upon it from exactly the right angle.

We will be using the solar radiation for flat plate collectors facing south at a fixed tilt. We want the tilt of 90 degrees because that is the same as a window on the side of a building.

Obtain the ASHRAE data. The following page is from the 1985 Fundamentals Handbook, Chapter 27, Fenestrations, page 27.24, table 24, which is the Solar Intensity and Solar Heat Gain Factors for 40 Deg North Latitude. Click Here

ASHRAE data is the SHGF for each month and for each orientation. The numbers reflect the amount of incident solar radiation after it has passed through a sheet of DSA glass. They also assume a clearness factor of 1 and ground reflectance of 0.2.

DSA glass has a thickness of approximately 1/8" where Single Strength glass has a thickness of approximately 3/32". Detroit is at about 42 deg N latitude.

The first thing we note about the data is the units. We must adjust the numbers so they are all in the same units. The Redbook data gives solar insolation in terms of kWh/m^2/day. The ASHRAE data gives solar heat gain factors in terms of Btu per hour per SF of glazing.

If we consult the table in Redbook, the average insolation for Januaary is 2.6 kWh per square meter per day. We want to start by converting this to Btu's. 1 kWh is 3413 Btu. Multiplying, we obtain 8873.8 Btu per square meter per day. One square meter is 10.76 square feet, so we divide by 10.76 to obtain the Btu's per SF. The result is 824.70 Btu per sf per Day.

In general terms, to convert kWh per square meter to Btu's per square foot, mulitply by 3413 and divide by 10.76 to obtain 317.19 as a conversion factor. You can multiply Redbook numbers by 317.19 to convert them to Btu's per sf.

The ASHRAE data is given for the 21st of the month for each month. In this case we are going to look at Jan 21. We see for a south facing window the half day total is 813 Btu-hr/SF.

IF you attempt to reverse the ASHRAE data to obtain direct solar insolation you would take the SHGF for the defined glass and the VT and divide the given SHGF by those numbers. The SHGF for a piece of glass or a window takes into account the heat transfered through the plate of glass which involves more than just direct solar insolation. There is heat generated by objects in the environment and scattering of radiation by various atmospheric conditions as well as terrestrial conditions.

Atmospheric conditions such as a lot of pollution, dust, humidity or cloud cover can greatly reduce the amount of solar insolation you recieve. ASHRAE data is computed knowing what the solar insolation is before it even strikes the atmosphere. According to the ASHRAE data if there were no obstructions to that incoming solar radiation the full days total should be around 1626 Btu per sf of glazing. The Redbook data is an average for the particular month and the margin of error is around 9%. On perfectly clear, pollution free days, the solar insolation will be higher than the average and vice versa on bad days.

This tool from sustainable by design, http://susdesign.com/windowheatgain/index.php, lets you calculate how much solar heat gain you get from windows for a variety of parameters. He has data for a few cities. He has Madison Wi. which would be the closest city to Detroit. If you select that city you get a list of clearness factors for every month of the year. If you take the ASHRAE data and apply his clearness factors, you start to come closer to Redbook data for each particular month. The lower peninsula of Mi. experiences very cloudy days from October to January from lake effect and Madison Wi. is on the other side of the lake so it does not get this effect. The actual insolation values for Detroit are even lower. The ASHRAE SHGF data is given for a clearness value of 1.0 and a ground reflectance of 0.2. If we had the clearness factors for Detroit, then we would not need to try to normalize the data to Redbook.

The solar heat gain takes into account the instantaneous heat balance for a sunlit glazing material. Some of the incoming solar radiation is reflected, some is absorbed and converted into heat energy and some is transmitted. The amount transmitted or reflected depends on the angle of the sun and the angle and orientation of the window. The window glass will heat up. Some of this radiation energy is moving outward away from the window to the ambient air by convection and radiation heat transfer. Some of it is moving to the interior space by the same mechanisms. The SHGF is the ratio of the solar heat gains to the incident solar radiation.

We would like to know what the SHGF would be for all window orientations for any given month. In the month of January the ASHRAE full day total is 1626 Btu's per SF of fenestration, for a south facing window. The Redbook data is 824.70 Btu's per sf of fenestration area per day, as a measure of insolation, not SHGF. To normalize the ASHRAE data to Redbook data we divide the ASHRAE data into the Redbook data. 824.7 / 1626 yields 0.50. If you took the Redbook data and computed the result after pushing the radiation through a piece of DSA glass, or applying the SHGF for it to the data, then you would have a number that you can compare to the ASHRAE data. In general terms, the Redbook values are ~50% of the ASHRAE value, for January. The conversion factor is different for each month. This value for every month is found in the spreadsheet under "Conversion Factor". Using Redbook data in the fashion above is an attempt to adjust the ASHRAE data to clearness factors that we don't have. This is complex. ASHRE gives the VT and Glazing SHGC at specific indidence angles. The sun may be almost normal to a vertical glazing facing south in December could be closer to the 70 degrees in June.

We can now use that percentage to figure out more realistically what the actual insolation is upon windows of all orientations. We go across the Half Day Totals in the ASHRAE manual, take the value given, multiply it by 2 for a full day, then, in the case of January, divide it by 2 to get something closer to what Redbook would have had if we had that data. The only orientations we are interested in at this time is N, S, E and W as in our model house we don't have facades facing in any other directions. We determine the conversion factor from south facing windows because we have that data in both ASHRAE and Redbook. We then take the ASHRAE half day totals, multiply by 2 and apply the conversion factor to windows of other horizontal orientations such as N and E. Note that east and west are the same. If your building design is not oriented exactly N to Solar South or East to west, then you do have windows facing in the other orientations.

If you refer to the page on sunlight you will find that 43% of the incoming solar radiation is in the visible portion of the electromagnetic spectrum and 49% is in the short wave or near Infrared. In the spreadsheet we multiply the total adjusted insolation for an average day of that particular month by 0.43 to obtain the gain in the visible portion of the spectrum and by 0.49 to obtain the gain in the infrared portion of the spectrum.

This exercise must be repeated for every month.

Generic Plate Glass Windows

For a generic window, obtain data from:

http://www.coloradoenergy.org/procorner/stuff/default.htm The Colorado Energy .org website. Choose professionals corner from the list on the left. Or you can obtain similar data from http://buildingsdatabook.eren.doe.gov/TableView.aspx?table=5.2.8

We think of R value as the resistance to the movement of heat through some sort of a solid or even a gas. The rate of movement depends on the thickness of the solid or gas in question. The units of R value are Square Feet-degrees F-hour/ Btu. It is a measure of the energy transferred per Square Foot of a surface, per hour, given a temperature difference between the 2 sides of the surface in degrees F. The heat or energy is measured in Btu or British Thermal Units. A Btu is roughly the amount of energy produced in burning a single wooden match. The R value given for most materials is determined under very specific test conditions. The R value is only valid under the same conditions. An example is that if insulation is tested with the warm side at 72 deg. F and the cold side at 40 deg. F, then the R value will not be the same when the cold side is at -10 deg F.

A single pane of glass has an R value of 0.91. Double insulating glass has various R values which depend on the air space between the 2 panes of glass. For a 3/16" air space the R value is 1.61. For 0.25" its 1.69, for 0.5" its 2.04 and for 0.75" its 2.38. The numbers for triple insulating glass are as follows: 0.25" air spaces has an R value of 2.56 and 0.5" spaces has an R value of 3.23

Notice that 2 panes of glass with a 3/16" air space has a lower R value than the 2 panes of glass would contribute. This is due to the fact that the inside surface of one pane cools the other resulting in radiant heat loss. If the gap is too large then convective currents can arise inbetween the 2 panes of glass and transfer heat from the warmer side to the cooler side. Ideally, the air space is between 5/8" and 0.75".

R values may be given for the center of glass only and not near the frame. The frame of a window can act as a thermal bridge making the whole window R value different from the center of glass R value. For more information http://en.wikipedia.org/wiki/Insulated_glazing under Thermal Performance.

An air film is a stagnant layer of air on a heat transfer surface. From the Colorado Energy resource, a typical air film has an R value of 0.17 and an air space of 0.5" to 4" has an R value of 1

The solar heat gain coefficient (SHGC) is the fraction of solar radiation admitted through a window both by direct transmission and by energy absorbed and then released inward. Shading coefficients (SC) may no longer be in use for window labelling but can be very important. Shading coefficients measure how much solar energy is transmitted through the window.

The SHGC can be converted into the SC by removing the effects of framing and dividers. To accomplish this divide the SHGC by the quantity (0.87 * FDF (framing and divider factor)). This value of 08.7 comes from the ASHRAE handbook of fundamentals. It is the value for the center of glass shading coefficient. The formula is SC (of just the glass) = SHGC / (0.87 * FDF)

The Framing/Divider factors read as follows:

Source http://www.energy.ca.gov/efficiency/blueprint/pdf/archived_bprint_pdf/bprint57.pdf

According to the ASHRAE fundamentals handbook, Fenestration, page 29.25, the Center glaszing VT of 1/8" thickness clear glass is 0.9 and the center glazing SC is 1.0. The SHGC range from 0.86 to 0.67 with a range of incidence angles from 0 degrees to 70 degrees.

Table 11 gives the Total windows SHGC at normal incidence. If we consider a fixed frame window, the SHGC is 0.75. The total window VT at normal incidence for a fixed frame window is 0.78. The total window VT takes into account the frame, which is usually opaque. The total window SHGC takes into account the heating contribution of the frame.

We want to model the energy lost and gained through standard plate glass windows before adding any storm windows. At the top of the spread sheet we start by putting in the fixed values or constants for single pane glass windows, insulating glass, which is a double paned window with no treatments and then add storm windows. For each entity, we indicate the R value, the VT and SHGC. We will use the values we obtained from Colorado Energy above.

Selecting Specific Windows

You want to select the windows you are going to use and refer to the manufacturers performance specifications specifically for those windows. Put that data into the spreadsheet. For Window selection. Visit http://www.efficientwindows.org/ or http://www.nfrc.org/

Mylar Storm Windows

Mylar Optical Properties http://usa.dupontteijinfilms.com/informationcenter/downloads/Optical_Properties.pdf

Mylar has optical properties very similar to ordinary window glass with respect to transmittance at various wavelengths.

Mylar Physical and Thermal Properties http://usa.dupontteijinfilms.com/informationcenter/downloads/Physical_&_Thermal_Properties.pdf

The thermal coefficient of linear expansion of Mylar® is 1.7 ´ 10–5 in/in/°C (9.5 ´ 10–6 in/in/°F).

The Thermal Conductivity of Mylar is 3.7 E10-4 cal-cm/cm^2-sec-deg C, Density is 1.390 g/cm^3 and specific heat is 0.28 cal/g/deg C.

Convert Thermal Conductivity to Imperial Units. 3.7 E10-4 cal-cm/cm^2-sec-deg C

1 square centimeter = 0.00107639104 square feet

1 hour is 3600 seconds

Deg C to Deg F : (9/5)*Deg C + 32

1 calorie = 0.00396566683 btu

The denominator: 0.00107 sf/cm^2 * 1 hour/3600 sec * 1 deg F / ([9/5* 1 deg C] + 32)

= 2.9899 E-7 * 1 / 33.8 = 8.875739E-9

The numerator is 3.7E10-4 cal-cm * 0.00396566 btu/cal * 0.393 inches/cm = 0.0933 btu-inches

The quotient is: 0.00000057664 / 8.875E-9 = 64.97 per 0.393 inches of thickness

1 mil is 0.001 inches. Therefore, mylar has an R value of approximately 0.163 per mil of thickness. To achieve something near glass you need about 6 mil mylar. The R value is not in the mylar rather in the air film and the air space between the window glass and the first sheet of mylar and between mylar sheets.

For the purpose of this model we will treat mylar just like a 1/8" piece of window glass. The difference between a single pane of glass and double pane window is an R value of 1.17. That accounts for the material and the air space. For every layer of glass or mylar that we add to the storm window, we will use a VT of 0.9 and a SHGC of 0.87 for that layer.

Note that in the optical properties the specific mylar used is Mylar 92D. It is also indicated that the thickness is 23 micrometers, this is equal to 0.9 mils. The 92 is a thickness designator.

To make mylar storm windows you can use cork as the frames. You can tape or glue the mylar film to the frame. Multiple layers of cork can build up a thickness of 1/2" air space. You may want to add some sort of a knob or a string so you can pull it out. When complete just shove the mylar storm window into the existing window frame.

Storm Windows and Vt and SHGC

Whether you are using glass or mylar it is important to realize that every layer will reduce both the visibility through the window and the SHGC. The amount of reduction is given with the manufacturers performance specifications.

Start with the VT of a double pane window at 0.81. When you add the first storm window, that blocks the light in the visible spectrum by 10%, allowing 90% to pass through. The VT of the whole window after adding the first storm window is (0,81 * 0.9) 0.729. When you add the second storm window the VT is (0.729 * 0.9) 0.6561.

The SHGC of a double paned clear glass window is 0.75. The SHGC after adding the first storm window is (0.75 * 0.87) 0.6525 and after adding a second storm window the SHGC is (0.6525 * 0.87) 0.567.

Modelling Energy Loss or Gain of Windows

The energy lost or gained with various types of glazing options and assemblies is in the spreadsheet.

We look at the effects of adding additional layers of glazing to determine how many layers of glazing it takes before the window gains more than it losses, for all orientations. We are interested in knowing the thermodynamics for a 24 hour period. Solar gain occurs during the number of daylight hours given for that month, divided equally before and after solar noon.

Solar noon is usually not the same as noon on the clock.

The spreadsheet gives gains and losses per square foot (SF) of glazing. To find the total gain or loss multiply by the square footage of the fenestration.

We also look at the Redbook data to see how many heating and cooling degree days there are each month. Using that information we can determine which months are heating dominated, cooling dominated and transition. We determine that June, July and August are cooling dominated months, May and September are transition months and all other months are heating dominated months.

The basic heat transfer formula is Q = Delta-T/R * A

where, Q = heat lost or gained

Delta T is the difference between the thermostat setpoint and ambient conditions

R is the R value of the window assembly

A is the area of the window. In all cases we use 1 SF so you must multiply the result by the actual square footage of your fenestration.

Q lost or gained per hour uses the above formula to compute the energy loss or gain through the window given the difference between the ambient air temperature and the thermostat set point. The R value is particular to the type of glazing and the number of layers modelled

The ambient temperature swings much like the shape of a sine curve between the average daily low and the average daily high. Conduction energy transfer is computed at both of these ambient temperatures and each one is assigned a 12 hour interval for the total energy loss.

The Q net per day - the total solar gain per day for that month minus the loss per day

Only conduction heat loss has been considered. It is also important to take into account convective heat loss. The SHGC takes into account the heating and heat transfer associated with radiation energy losses. The leaks around the window contribute to the total air exchanges per hour of the entire interior and are taken into account with the load calculations for the interior space.

The thermostat set point is different for heating dominated months and cooling dominated months. For transition months, both temperatures are modelled separately.

Bug Screens

Don't forget these. They lower the transmission of insolant solar energy by 24%. If you have these you must multiply your total gain by 0.76 for each square foot glazing that has this obstruction.

Window Sizing, Overhangs And Window Treatments

Algorithm: Determine solar gain need from energy load analysis, size the fenestration to meet that need to the extent desired for the month desired, size an overhang to prevent overheating as you progress from the worst case scenario to a cooling dominated month, determine number of storm windows required for that particular window, given its orientation and solar gain, determine window treatments on a room per room basis, if necessary, based on the energy load for that particular room, at different months of the year.

The Detroit, Mi. area is a heating dominated climate. The entire house as well as each room individually will be modelled for its energy loss and gain. When we know how much solar heat we need to meet our needs during the worst time of the year, which is December, the first thing we are going to do is adjust the size of the aperature (window size) to something reasonable to meet that need.

It is quite likely that an aperature that is designed to meet most of the need in December is going to cause overheating in February. We want to design overhangs to block the appropriate amount of direct sunlight every month so that our energy input meets our needs. This may mean designing an overhang that allows full direct sunlight in December, about 50% by March 21 and no direct sunlight by June 21.

Since this house design has a sunspace on the south side, the sunspace is acting as an overhang for the south side of the house. The depth of the sunspace will be designed to allow direct sunlight in December to pass right through the sunspace and into the living space. The sunspace itself will also require and overhang to help prevent overheating. Both of these parameters will be accounted for in the sizing of the sunspace and overhangs.

We will determine on a room by room and window orientation basis which windows get storm windows and how many, based on the energy load analysis for that room.

We may find that there are certain rooms that have windows that will always lose more than they gain and adding multiple layers of storm windows could be both expensive an unwieldly. We may choose to get some foil faced mylar, the same material available for attic radiant barriers and make operable foil shades for some of those windows. These shades can be let up when someone is using a room and wants natural lighting but otherwise kept down, especially in the winter, to avoid heat loss

As we incorporate each change, we recompute the total energy lost or gained for around the clock, for the 21st day of each month, for an entire year. There are a multitude of solutions to this problem. The solution chosen will depend on the goals. If the goal is to meet the heating need at the worst time of the year, which is Dec. 21st, with 100% solar, at a design temperature of -10 deg F, this will require a very large aperature and means to avoid overheating the rest of the year.

The final analysis spreadsheet will design aperatures, overhangs, storm windows if necessary and operable insolation, if necessary for a range of goals. These goals will be based on average temperature and wind conditions as well as design conditions

If you want to get a quick idea on a room by room basis of what size window you need or how an existing window is performing, you can apply the Conductive Heat Load Equation to the room in question. Q = Delta(T)/R * A.

Compute the area of all exterior walls, ceilings abutting attic spaces and floors abutting unconditioned basements. If a wall is next to conditioned space then delta(T) will be zero. Put the appropriate R value into the equation for the barrier in between ambient and conditioned air. Compute each barrier separately and sum the results together. The result of your computation will be the total heat lost or gained for the space. If the space is wide open to another space, you can draw an imaginary dividing line and treat it as an interior wall. When you are done with the computation, add in your Q for windows and doors, take the result and divide it by the floor space. That will give you your heat lost or gained per SF of floor area. Doors are computed just like windows and walls. Get the R value of the door and its area and plug those values into the equation. This simple computation does not take into account energy losses by infiltration which can be significant depending on how leaky the structure or object is

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