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### Heat Gain Calculations

#### Introduction

Heat gain sources include:

• Solar Gain of direct sunlight through windows
• Solar Gain of sunlight directly on building surfaces and conducted through walls/ceilings into the space
• Warm outdoor air infiltrating the space and brought in via power ventilation
• Lighting and Equipment running in the space producing waste heat

The largest source of heat gain depends on the type of building, mainly how much and what type of glass it has and how the glass may or may not be shaded, and the type of roof.

### Basic Formulas

The formula used to calculate heat gain from thermal conduction (outside ambient temperature during the cooling season) is the same basic formula as the Heat Loss Formula, [(Square Foot Area) x (U-Value) x (Temperature Difference)]. If the space is mechanically cooled, every BTU of heat that gets in above the set-point, must be removed to maintain the desired temperature.

The amount of humidity in the indoor air is influenced both by the outside weather conditions and what is going on inside the conditioned space. Just as it takes 970 BTUs to vaporize a pound of water, it takes 970 BTUs of cooling energy to condense a pound of water vapor. (In reality, the condensed water gives up 970 BTUs into the colder air conditioning medium.) If humidity will be removed by condensation on a conventional air conditioner coil, then the formula is: (Cooling BTUS Required) = (970 BTUs) x (pounds of water removed). Humidity can also be removed via ventilation air, desiccant dehumidification systems and energy recovery systems. These systems do not use vapor condensation in order to remove humidity.

Sun light transmitted directly through windows (glazing) represents a huge potential cooling load. This load is calculated according to a ‘solar gain factor’ per square foot of glazing. The solar gain factor is a complicated series of factors multiplied together starting with the transmittance factor of the glass, and ending with all possible shading devices/methods and adjusted for local weather (cloud cover).

All of the electricity used by lighting and equipment inside the house eventually ends-up as BTUs of heat. These BTUs off-set heating requirements during the heating season, but are a source of cooling load the rest of the year. Every kWh contains 3,413 BTUs of heating energy.

Therefore, the formulas needed to calculate Heat Gain include:

• Building Surfaces: (Square Foot Area) x (U-Factor) x (Temperature Difference) = BTUs per Hour
• Glass Areas: (Solar Gain Factor) x (Square Foot of Window Area per direction/face of building)
• Lighting and Equipment Load: (kWh Total Load) x (3,413 BTUs/kWh) = BTUs per Hour
• People Load: (Number of People) x (200 to 400 BTUs/Person per Hour) = BTUs per Hour
• Ventilation Load: (CFM) x (60 Minutes/Hour) x (Number of People) x (0.018) x (Temperature Difference) = BTUs per hour
• CFM = as required by code per person per hour of occupancy
• 0.018 = specific heat of air factor (BTUs per Cubic Foot per degree F)
• Temp Difference = outside to inside SENSIBLE.

All of these loads added-up per hour, forms the basis for the Heat Gain Calculation.

### Rules of Thumb

Solar Gain through building envelope is estimated the same way that it is for heat loss. There is a difference for surfaces that are exposed to direct sunlight and the surface characteristics that affect absorption versus reflection of the sunlight. However, these differences are very difficult to accurately calculate and in the end, don’t make a lot of difference for most facilities when weighed against other more significant factors. For facilities in hot climates, radiant barriers (reflective coatings and foils) are being used to successfully reduce building heat gain. However, it is my opinion that these barriers reduce their value if they are improperly installed – in direct contact with other materials where the reflective value is minimized, or they are promoted for use in colder temperature applications. This is because radiant barriers are very effective at reflecting IR energy; but once the IR is converted to heat, the primary method of heat transfer is via conduction, where radiant barriers have very little value. Therefore, use caution when considering the ‘effective R-value’ claimed by some product merchants. Another thing to consider regarding temperature difference are spaces adjacent to areas hotter than the outdoor ambient, such as ceilings under very hot attics or offices located in or next to much hotter production areas.

Solar Gain through windows can be accurately calculated IN THEORY for peak-day design conditions. The formula starts with the BTUs per Square Foot per direction of glass for the location of the facility (North Latitude). This factor is generally called the ‘Solar Isolation Factor’ available from ASHRAE and a few other source. Several solar power web sites offer factors based on the gross power producing potential of a given site. These may or may not be good sources for BTU data, as their kW ratings are for electric production, not thermal gain. The factor is the ‘gross’ BTU gain that is influenced by MANY variables, including seasonal shading, fixed building shading, interior shading, transmission co-efficient of the glass, and hourly weather conditions. High-end calculation programs take all of these factors into consideration on an hourly basis. Others may use a monthly factor. West-facing glass is often the most critical factor for heat gain, because the sun’s high over-head angle during the summer months means that less sunlight comes through south-facing glass.

Lighting and Equipment does work that ends up as waste heat. A 40 watt fluorescent tube produces a lot more light than a 40 watt incandescent bulb and is therefore more efficient, but they both produce 40 watts worth of BTUs (40 x 3.413 = 136.52 BTUs per hour) All of the electricity used by small equipment operating within the conditioned space ends up as BTUs of heat. It is generally easy to estimate the heat gain from lighting because of the occupancy schedule. The difficult part of estimating the heat gain from equipment is estimating the load factor(s). Equipment is not always running at its name plate rating. Therefore, unless a piece of equipment is truly in continuous operation, the name plate rating should be factored to get a more realistic estimate of heat gain. For certain types of existing smaller facilities, such as an office, it may be easier to look at the electric bills for months that contain no electric heating and no or minimal cooling and consider that number of kWh to be the lighting and equipment load.

People Load means the sensible BTUs from body heat. There is also a latent load from breathing and a ventilation requirement for fresh air because people are breathing. However, these loads are generally account for as ventilation loads, and not necessarily called ‘heat gain.’ Typical BTU load per person is 200 – 1,000 BTUs per hour with 400 being typical worker and 1,000 for sports activities.

Ventilation Air is required by most local building codes for NON-RESIDENTIAL facilities. Some codes may allow ‘intelligent control’ which allows a CO2 monitor to be installed and the volume of ventilation air adjusted according to CO2 levels. More common, ventilation air is controlled by an ‘Occupied/Un-Occupied’ setting on the controls based on an assumed number of occupants. ASHRAE Standard 62-1989 suggests ranges from 15 to 60 CFM, but typical requirements for non-smoking, non-industrial spaces are 15 – 25 CFM per person.

For more information about solar gain through windows from an on-line source, see www.efficientwindows.org

Source: Text Bob Fegan 12/2008; Table on BTU per person heat gain from www.engineeringtoolbox.com 9/2005; diagram of window heat gain from www.efficientwindows.org 9/2005;

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