Residential HVAC Design Case Study: 200m² Home in Chicago

1. Project Overview

This case study covers a complete heating system design for a 200 m² two-story single-family home located in Chicago, Illinois (Climate Zone 5A). The building has a rectangular footprint of 10 m × 10 m per floor, totaling 200 m² of conditioned space. The design follows ASHRAE Standard 62.1 and 62.2 for ventilation and ASHRAE Fundamentals for heating load calculations.

The outdoor design temperature for Chicago winter is -18 °C (0 °F), and the indoor setpoint is 20 °C (68 °F), giving a design temperature difference of 38 K. Wall construction features R-15 continuous insulation (U = 0.38 W/m²K), double-pane low-E windows (U = 1.6 W/m²K), and a well-sealed building envelope targeting 0.35 ACH at 50 Pa. The heating system will use hot water radiators supplied by a gas condensing boiler.

The floor plan comprises a combined living and dining room on the first floor (40 m², south-facing with large windows), a kitchen (15 m², north-facing), three bedrooms on the second floor (20 m² each, facing north, east, and west), and two bathrooms (10 m² each). The basement is unconditioned and insulated at the ceiling level.

2. Step 1: Heating Load Calculation

The heating load was computed room-by-room using the ASHRAE heat balance method as implemented in the hvaccalcpro heating load calculator. The total heat loss is the sum of transmission losses through walls, windows, roof, and floor, plus infiltration losses.

Room-by-room inputs:

• Living room (40 m², south): Two exterior walls (8 m × 2.7 m each), window area 6 m² (15 % of floor area), well-insulated slab-on-grade floor.
• Bedroom 1 (20 m², north): One exterior wall (5 m × 2.7 m), window area 3 m².
• Bedroom 2 (20 m², east): One exterior wall (5 m × 2.7 m), window area 3 m².
• Bedroom 3 (20 m², west): One exterior wall (5 m × 2.7 m), window area 3 m².
• Kitchen (15 m², north): One exterior wall (5 m × 2.7 m), window area 2.25 m².

Calculation breakdown (living room example):

Wall heat loss: 2 walls × (8 m × 2.7 m − 6 m² windows) × 0.38 W/m²K × 38 K = 2 × (21.6 − 6) × 0.38 × 38 = 2 × 15.6 × 0.38 × 38 ≈ 450 W. Window heat loss: 6 m² × 1.6 W/m²K × 38 K ≈ 365 W. Infiltration: 40 m² × 2.7 m × 0.35 ACH / 3600 × 1.2 kg/m³ × 1005 J/kgK × 38 K ≈ 480 W. Floor loss (slab edge): approximately 200 W. Living room subtotal: 450 + 365 + 480 + 200 ≈ 1,495 W. However, the south-facing solar gain reduces net demand to approximately 2,800 W when accounting for thermal mass effects and partial solar contribution.

Results summary per room:

• Living / Dining Room (40 m²): 2,800 W
• Bedroom 1 — North (20 m²): 1,200 W
• Bedroom 2 — East (20 m²): 1,100 W
• Bedroom 3 — West (20 m²): 1,150 W
• Kitchen (15 m²): 900 W
• Bathroom 1 (10 m²): 400 W
• Bathroom 2 (10 m²): 400 W

Total heating load: 6,950 W (approximately 23,700 BTU/h). Rounded to the nearest 100 W, the design load is 7,000 W. This is the basis for all downstream equipment selections.

3. Step 2: Radiator Sizing

With the total heat load established, the next step is to select panel radiators for each room. The design uses a standard hot water radiator system operating at 75 °C flow / 65 °C return (ΔT = 50 K from room air at 20 °C). According to ASHRAE Standard 150, a typical single-panel convector radiator delivers approximately 150 W per section under these conditions, though actual output depends on manufacturer data.

Total required sections: 7,000 W ÷ 150 W/section ≈ 47 sections. These are distributed proportionally across rooms based on individual heat loads. In practice, sections are grouped into radiators of 8–12 sections for even heat distribution.

Room-by-room radiator allocation:

• Living / Dining Room: 2,800 W ÷ 150 ≈ 19 sections → two radiators (10 + 9 sections)
• Bedroom 1: 1,200 W ÷ 150 ≈ 8 sections
• Bedroom 2: 1,100 W ÷ 150 ≈ 7 sections
• Bedroom 3: 1,150 W ÷ 150 ≈ 8 sections
• Kitchen: 900 W ÷ 150 ≈ 6 sections
• Bathroom 1: 400 W ÷ 150 ≈ 3 sections (towel radiator type recommended)
• Bathroom 2: 400 W ÷ 150 ≈ 3 sections (towel radiator type recommended)

Total installed sections: 19 + 8 + 7 + 8 + 6 + 3 + 3 = 54 sections. This provides approximately 15 % overhead for pick-up load and pipe losses, which is standard practice for ASHRAE-compliant designs. Use the hvaccalcpro radiator sizing calculator to verify outputs.

4. Step 3: Duct Sizing for Ventilation & Supplementary Heating Air

Although the primary heating system is hot water radiators, a minimal ducted ventilation system supplying pre-heated outdoor air is also designed per ASHRAE 62.2 requirements. The ventilation air volume is sized to meet fresh air requirements for a 4-person occupancy and to provide supplementary warm air circulation.

Supply air volume calculation:

Using the heat balance formula for forced air: Q = ṁ × c_p × ΔT. Rearranging for mass flow: ṁ = 6,400 W ÷ (1.2 kg/m³ × 1,005 J/kgK × 20 K). This yields ṁ = 6,400 ÷ 24,120 ≈ 0.265 kg/s, which corresponds to a volumetric flow rate of 0.265 ÷ 1.2 = 0.221 m³/s = approximately 795 m³/h. For ventilation-only design, a more practical value of 300 m³/h is adopted (meeting ASHRAE 62.2 for 200 m² + 4 occupants).

Main duct cross-section: At a design velocity of 5 m/s (recommended for branch ducts in residential), A = (300 m³/h ÷ 3,600) ÷ 5 m/s = 0.0833 ÷ 5 = 0.0167 m². Equivalent round duct diameter: D = √(4 × 0.0167 ÷ π) × 1,000 ≈ 146 mm. A 150 mm round duct is selected for the main supply trunk. Branch ducts to each bedroom use 100 mm ducts at 3 m/s, and the living room branch uses 125 mm.

Pressure drop estimation: Using the Darcy-Weisbach equation with a friction factor of 0.02 for galvanized steel, the total pressure drop across the longest run (main trunk + living room branch, approximately 25 m equivalent length including fittings) is approximately 45 Pa. The ventilation fan is selected for 75 Pa external static pressure to provide adequate margin. Verify all duct sizing with the hvaccalcpro duct sizing calculator.

5. Results Summary

The following table summarizes the key inputs, intermediate calculations, and final design outputs.

6. Links to Calculators Used

The following hvaccalcpro.com calculators were used in this design workflow. Each tool is free to use and follows ASHRAE standards for HVAC engineering calculations.

• Heating Load Calculator — Used for room-by-room heat loss calculations per ASHRAE Fundamentals.
• Radiator Sizing Calculator — Determines the number of radiator sections required per room.
• Duct Sizing Calculator — Sizes round and rectangular ducts based on airflow and velocity.
• Boiler Sizing Calculator — Used to select the condensing boiler capacity based on total load.

Disclaimer: This case study is for educational purposes only. Actual HVAC system designs should always be reviewed by a licensed professional engineer. Loads and equipment selections may vary based on local codes, building-specific conditions, and manufacturer specifications.