Air Conditioning Design on the Psychrometric Chart: Step by Step

Every air conditioning design starts with two questions: what are the input conditions (outdoor air, indoor loads) and what are the required output conditions (temperature and humidity in the room). The psychrometric chart visualizes these conditions, lets you choose the right sequence of processes (cooling, mixing, heating, humidification) and calculate the capacities of the individual components. This article walks through the procedure in simplified form, on one example: an office for 100 people, summer operation without energy recovery.

Step 1: Establishing the design conditions

Outdoor air — summer design conditions

Design conditions are drawn from climate data, not from intuition. ASHRAE Climatic Design Data gives, for each location, values corresponding to 0.4%, 1% or 2% annual exceedance — look up your own site rather than borrowing a number from a nearby project. For this walkthrough we take a summer design day of 90°F (dry-bulb) at φ = 40% — on the chart that is $h = 34.9\ \text{Btu/lb}$, $W = 84.8\ \text{gr/lb}$, wet-bulb temperature about 71°F.

Indoor design conditions

The required conditions follow from the standards for thermal comfort. ASHRAE Standard 55 typically puts offices at 75–79°F / φ 40–60%. We choose 77°F / φ = 50% — enthalpy about $29.4\ \text{Btu/lb}$, humidity ratio $69.5\ \text{gr/lb}$.

Step 2: Calculating the indoor thermal and moisture load

• Sensible heat: people (100 × 222 Btu/h = 22,200 Btu/h) + lighting + IT equipment + solar gains. For the example, a total of 102,000–136,000 Btu/h (8.5–11.4 tons).
• Latent heat: evaporation of sweat (100 × 188 Btu/h = 18,800 Btu/h) + moisture from building materials. For the example, a total of 20,500–27,300 Btu/h.

The ratio of sensible to total load (SHR, sensible heat ratio) indicates how steeply the room-state line runs on the chart. For our office, $\text{SHR}=0.82$.

Step 3: Plotting the room state and the supply air

The indoor air state (77°F / 50% RH) is the starting point. From it we draw a load line in the direction set by the SHR ratio — it shows how the air state changes as it absorbs the thermal and moisture load. The supply air must lie on this line, usually at a temperature of 57–61°F. A lower supply temperature means a smaller flow rate but a higher risk of draft; a higher temperature, conversely, requires a larger flow rate.

Step 4: Mixing outdoor and recirculated air

The system supplies a portion of fresh outdoor air (the minimum per ASHRAE Standard 62.1) and recirculates the rest. Let us assume 30% outdoor and 70% recirculated air. The resulting mixed state lies on the line connecting the outdoor and indoor states, 30% of the way from the indoor point (that is, 70% from the outdoor point — closer to the larger mass fraction, the recirculation) — roughly 81°F / φ = 47%, $h = 31.1\ \text{Btu/lb}$.

Step 5: Cooling and dehumidification to the supply-air state

We cool the mixture to the required supply-air state (57–61°F). In doing so, the air condenses out the excess moisture. In a simplified view (the ideal case, without a bypass factor) the line first runs horizontally to the left (sensible cooling) to the dew point, then down and to the left along the saturation curve (dehumidification) — a real coil in fact heads toward the so-called apparatus dew point (ADP), and the supply air never fully reaches the saturation curve; the degree of deviation is expressed by the bypass factor.

$$Q_{\text{cool}} = 4.5 \cdot \dot{V} \cdot (h_{\text{mix}} - h_{\text{supply}})$$

Taking the supply air at 57°F / 95% RH ($h = 23.9\ \text{Btu/lb}$), the enthalpy difference is $31.1 - 23.9 = 7.2\ \text{Btu/lb}$. At a flow rate of 7,000 CFM that gives $Q_{\text{cool}} = 226{,}800\ \text{Btu/h}$, about 18.9 tons — part of which is the load from the fresh outdoor air, beyond the room’s own load from Step 2.

Step 6: Reheating and component selection

If the supply air is too cold or too humid after cooling (φ > 95%), we add a reheat coil — a horizontal line to the right on the chart (constant $W$, rising $t$). Based on the enthalpy differences and flow rates, we then select the capacity of the cooling coil, the heaters, the flow rate of the heat-transfer medium and the humidification capacity for winter operation. Every value has a direct visual equivalent on the psychrometric chart.

Winter operation: a different corner of the chart, the same logic

In winter the outdoor air is cold and dry and the room needs to be heated and humidified. Take a heating design day of 10°F / φ = 80% — again, pull the 99.6% value for your own site. The outdoor air has an extremely low humidity ratio ($W \approx 7.4\ \text{gr/lb}$), and its relative humidity after heating to 72°F drops to a mere 7%. Energy recovery with moisture transfer (an enthalpy wheel) can partly address this. Even so, humidification is practically indispensable for achieving ideal winter conditions in any building with mechanical ventilation.

Iterating the design by hand is tedious. In PsychroView you enter the outdoor and indoor air states, set the recirculation ratio, and immediately see the mixed state, the course of cooling and the resulting capacities — a change in one parameter is instantly reflected across the whole scheme.

Frequently asked questions

Why is the cooling capacity calculated from enthalpy, not temperature? A cooling coil removes both sensible and latent heat. The temperature difference captures only the sensible component; the heat of the condensing vapor is captured only by the enthalpy difference. Sizing on temperature alone leads to a permanently undersized coil.

Where on the chart is the mixed state of outdoor and recirculated air? On the segment between the two states, at the position set by the flow ratio — closer to the state with the larger mass fraction. With 30% outdoor air and 70% recirculation, the mixture is 30% of the way from the indoor point (70% from the outdoor point).

Where do I get the outdoor-air design conditions for my location? From ASHRAE Climatic Design Data, usually as the value with a 0.4% annual probability of exceedance for cooling and 99.6% for heating. Weather files (TMY3, EPW) serve the same purpose when you need the full hourly series.