An engineer is calculating the cooling load for each room to be served by a new rooftop unit. Solar and transmission heat gains through the windows, walls, and roof and internal heat gains from lights, people (sensible), and equipment add up to the room sensible heat gain (BTUHS). Latent heat gains from people and any process moisture gain (e.g., from a fountain or, in a laboratory, a water bath) add up to the room latent heat gain (BTUHl). With that information, how does the engineer determine the supply-air quantity (in cubic feet per minute) for each room and select a rooftop unit to meet the loads?

Converting BTUHS to supply-air flow seems simple:

BTUHS = 1.1 × cfm × (Troom - Tsupply air) (1)

where:

1.1 = 60 min per hour × 0.24 Btu per pound mass per degree Fahrenheit (specific heat of air) × 0.0764 lb per cubic foot (density of moist air at typical supply-air conditions)

But is it? What should the supply-air temperature be? If the design is based on 56°F supply air, but the selected unit delivers air at 59°F, a room will be about 15-percent short of cooling capacity.

If this were an applied chilled-water unit, the engineer could select a cooling coil to match the load. But the unit is direct expansion, so the engineer has to work with the cooling coils and capacities manufacturers have pre-selected. What size rooftop unit will meet the load and deliver the desired supply-air temperature? Besides meeting the space cooling load (sensible plus latent), the unit must cool outside air and overcome fan heat.

Most rooftop-unit manufacturers provide tables or computer programs to help engineers select units. The user needs to know the ambient temperature (dry bulb), desired supply-air flow, and cooling-coil entering-air conditions (dry bulb/wet bulb). How does an engineer determine cooling-coil entering-air conditions and supply-air flow? Changing the flow of supply air changes the temperature of supply air a unit can deliver, while changing the temperature of supply air changes the flow of supply air required to meet a space's sensible-cooling load (Equation 1).

A manufacturer's selection program reports gross cooling capacity for stated conditions. How does gross cooling capacity relate to space cooling capacity?

The spreadsheet evaluates three units — 75-ton draw-through (Column C), 90-ton draw-through (Column D), and 90-ton blow-through (Column E) — for one project. Columns C, D, and E show how capacity and configuration affect ability to meet the calculated load. Column E also shows how relaxing the design indoor humidity (55 percent instead of 50 percent) affects performance.

Columns F and G of the spreadsheet compare a 75-ton blow-through unit and a 60-ton draw-through unit for another project.

Figures 1 and 2 show the psychrometric process for a 75-ton draw-through unit (“DT-75” in Column C of the spreadsheet) and a 75-ton blow-through unit (“BT-75” in Column F of the spreadsheet), respectively. Column B of the spreadsheet lists the state points in figures 1 and 2.

### Lines 11 to 13 (outdoor-air conditions)

The spreadsheet calculates specific humidity (pounds of water per pound of dry air) for design dry-bulb temperature and mean coincident wet-bulb temperature. These values are an important part of documenting design criteria for a project. They are used in subsequent calculations.

In selecting a rooftop unit, some engineers check loads at both peak cooling (dry-bulb) temperature and peak dehumidification (wet-bulb) temperature. Peak dehumidification load usually occurs at a lower outdoor temperature than peak cooling load. The temperature of the air entering the condenser will be lower, so the rooftop-unit cooling capacity (determined from manufacturer data) might increase enough to meet the higher dehumidification load. The spreadsheet makes comparing performance at peak cooling temperature with performance at peak dehumidification temperature easy by calculating the two cases in adjacent columns.

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### Lines 15 and 16 (supply- and outdoor-air flow)

Supply-air flow is calculated from Equation 1 using an assumed supply-air temperature. A temperature of around 58°F usually is a good place to start for package rooftop equipment. Smaller equipment applied at loads close to rated capacity might have a slightly higher supply-air temperature. Units with capacities greater than the load might deliver lower supply-air temperature. The spreadsheet helps with the trial-and-error process of balancing supply-air flow and supply-air temperature -- each change in flow changes unit capacity and resulting supply-air temperature, which, in turn, changes the flow required to meet the space sensible load.

Outdoor-air flow is the outdoor-air quantity (usually the minimum) a unit will introduce at peak load conditions. It might be determined from ANSI/ASHRAE Standard 62.1, Ventilation for Acceptable Indoor Air Quality; a table in the building code; or the amount necessary to make up exhausts and pressurize the building.

### Lines 18 to 21 (indoor-air conditions)

Enter the design indoor dry-bulb temperature and humidity. Look up the corresponding wet-bulb temperature and specific humidity on a psychrometric chart, or use a calculation tool.

### Lines 23 to 25 (return-air plenum)

If a design utilizes a return-air plenum, return air at room temperature passes through the plenum on its way to the rooftop unit. As it passes through the plenum, return air picks up heat from recessed lights, the plenum walls, and the roof (if on a top floor).

Return-air-plenum-temperature rise is a trial-and-error, iterative heat-balance calculation. Heat into a plenum comes from the plenum walls, roof, and recessed lights (about 35 percent of the power input to recessed fluorescent lights). Heat leaving the plenum is heat picked up in the return-air stream plus heat retransmitted through the ceiling. Heat in has to equal heat out. The iteration process is as follows:

• Step 1: Calculate room airflow with no heat transmission from the plenum into the occupied space.

• Step 2: Calculate plenum-temperature rise using the airflow from Step 1, with BTUHS equal to the plenum heat gain, with no retransmission through the ceiling.

BTUHS = 1.1 x cfm x ΔT

• Step 3: Recalculate room airflow, including heat transmission from the plenum (Q = U x A x ΔT), using the ceiling U-value and the plenum-temperature rise from Step 2 as delta-T. (Ceiling U-value consists of a still-air film [heat flow down] on the room side, the ceiling tile, and a still-air film on the plenum side. Air velocity in the plenum is low enough to use the value for still air. Ceiling U-value usually is around 0.33 hr-sq ft-°F per British thermal unit.)

• Step 4: Calculate a new plenum-temperature rise (repeat Step 2) with the new airflow to get a new plenum delta-T.

• Step 5: Recalculate room heat gain and airflow with the delta-T between the two calculated previously. Repeat until the result converges.

Determining return-air-plenum temperature is part of calculating cooling load. Typical values are about 2°F for interior office spaces and 4°F to 5°F for a top floor, which experiences heat gain through the roof.

In the case of ducted return, there is no return-air-plenum-temperature rise. The spreadsheet does not explicitly recognize return-duct-temperature rise. Return-duct-temperature rise usually is rather low, unless the duct passes through unconditioned space. Return-duct-temperature rise could be entered in place of return-air-plenum-temperature rise.

Page 3 of 3

### Lines 27 to 35 (return fan)

A return fan, if present in a unit, adds heat to the air passing through it.1 Enter the static pressure and fan efficiency from the fan selection so the spreadsheet can calculate fan heat gain. The return-fan-brake-horsepower calculation includes allowances of 5 percent for belt and drive losses and 90 percent for motor efficiency (assuming the motor is in the air stream). Users can alter those values (or any of the formulas in the spreadsheet) to suit their application.

### Lines 37 and 38 (mixed-air conditions)

The spreadsheet calculates mixed-air conditions. Mixed air is the combination of minimum outside air and return air (after it has passed through a return-air plenum and return fan, if present).

### Lines 40 to 45 (blow-through supply fan)

A blow-through supply fan, if present in a unit, adds heat to the air passing through it. Enter the static pressure and fan efficiency from the fan selection so the spreadsheet can calculate fan heat gain. The supply-fan-brake-horsepower calculation includes allowances of 5 percent for belt and drive losses and 90 percent for motor efficiency (assuming the motor is in the air stream).

Blow-through-supply-fan heat raises the temperature of air entering a cooling coil. Higher entering-air temperatures increase cooling-coil capacity (basically because of a larger difference between entering-air temperature and mean refrigerant temperature in the coil). That capacity increase is part of why a blow-through unit delivers more space-cooling capacity than the same unit in a draw-through configuration. On the other hand, a blow-through unit tends to be physically larger than the same unit in a draw-through configuration. The reason is the space required at the fan outlet for fan discharge air to spread out and cover the cooling coil evenly.

### Lines 47 to 51 (cooling-coil entering-air conditions)

The spreadsheet calculates the dry-bulb and wet-bulb temperatures of the air entering a cooling coil. These are the entering-air conditions to use with the manufacturer's data or selection program. These temperatures will change with changes in outdoor-air conditions, outdoor-air quantity, supply-air quantity, and design indoor conditions and are affected by whether the unit has a return fan or a blow-through supply fan.

### Lines 53 to 60 (cooling-coil performance)

Unit total and sensible capacities come from the manufacturer's performance data or selection program. The spreadsheet calculates the resulting cooling-coil leaving-air conditions.

### Lines 62 to 67 (draw-through supply fan)

A draw-through supply fan, if present in a unit, adds heat to the air passing through it, raising the supply-air temperature, sometimes by several degrees. Enter the static pressure and fan efficiency from the fan selection so the spreadsheet can calculate fan heat gain. The supply-fan-brake-horsepower calculation includes allowances of 5 percent for belt and drive losses and 90 percent for motor efficiency (assuming the motor is in the air stream).

The increase in supply-air temperature is a disadvantage of the draw-through supply fan -- fan heat raises the temperature of the air supplied to the diffuser, increasing the airflow required to meet the space sensible-cooling load. For a system, such as a laboratory's, that has high minimum airflows and uses a lot of reheat, draw-through-supply-fan-temperature rise can be an advantage ¡ª the fan energy, which is necessary to move the air, offsets reheat energy that otherwise would be required. Some engineers like draw-through fans because they lower the relative humidity of the air going down a duct, reducing the risk of condensation in the duct. (The air leaving the cooling coil is nearly saturated. Adding a few degrees of fan heat raises the dry-bulb temperature without changing the moisture content, so relative humidity decreases.)

### Lines 69 to 74 (duct-rise allowance)

The spreadsheet has an option to allow for duct rise. If a duct passes through unconditioned space, the heat gain into the duct is part of the rooftop-unit cooling load (psychrometrically, it is a space load) and must be recognized.

If an uninsulated supply duct passes through a return-air plenum, supply air will pick up plenum heat. Removing heat from the plenum will reduce heat transmission to an occupied space through the ceiling. For that reason, allowing for duct rise in a return-air plenum without recognizing a corresponding reduction in heat gain from the plenum to an occupied space will result in a small amount of double counting. Some engineers ignore that double counting because it functions as a small safety factor.

### Lines 76 and 77 (available net capacity)

The spreadsheet calculates the net cooling capacity available to a space (after deductions for fan heat and other losses). These are the capacities to compare to the calculated space cooling loads.

The difference between unit capacity and available net or space capacity is significant. In the examples on the spreadsheet (which are from real jobs), space sensible-cooling capacity (the BTUHS in 1.1 x cfm x ÄT) is only about half of the nominal unit tons.

### Lines 79 to 82 (capacity-to-load comparison)

These lines show whether a selected unit meets calculated loads. Excess capacity (safety factor) shows up as a positive percentage; shortfalls show up as negative percentages.

Engineers need to use judgment when evaluating these results. A shortfall of a few percent might be OK, especially if remedying it means jumping to a much larger unit size. An oversized unit will short-cycle, reducing effective dehumidification capacity.

If a unit is low on sensible cooling, but has excess latent capacity, increasing the airflow can shift some latent capacity to the sensible side. As airflow increases, entering-air temperature decreases (slightly), while unit sensible-cooling capacity increases.

### Lines 91 to 106 (load summary)

These lines summarize the components that make up the load.

### Conclusion

The spreadsheet is a tool to help engineers select rooftop units and perform a heat balance on the air stream in a rooftop-unit system. As with any computer program or application, the spreadsheet is subject to data-entry errors and mistakes introduced by moving cell data or modifying formulas. The spreadsheet is not password-protected, and the formulas are not locked. Users are responsible for how they use the spreadsheet.

### Reference

1. Williams, G.J. (1989, January). Fan heat: Its source and significance. Heating/Piping/Air Conditioning, pp. 101-103, 108-112.

Did you find this article useful? Send comments and suggestions to Executive Editor Scott Arnold at scott.arnold@penton.com.

A longtime member of HPAC Engineering's Editorial Advisory Board, Kenneth M. Elovitz is an engineer and the in-house counsel for Energy Economics Inc. His knowledge of and experience with HVAC, electrical, and life-safety systems allow him to understand system function and performance, including interactions among disciplines.