Learning Exercise
Thermodynamic Sizing of Cold-Climate Heat PThermodynamic Sizing of Cold-Climate Heat Pumps: Balance Point Analysis and Inverter COP Deratingsumps: Balance Point Analysis and Inverter COP Deratings
An interactive computational laboratory exercise for engineering and building science students. Learners investigate the non-linear relationship between building envelope heat loss and cold-climate inverter heat pump capacity degradation across sub-freezing ambient temperatures. Students compute thermal balance points and size supplemental electric resistance elements using the HVACLogic simulation engine.
- Material:
- HVACLogic: Deterministic Building Science & Thermodynamic Simulation Suite
- Date last modified:
- September 10, 2026
- Created by:
- Miad Saadidi
- License:
-
HVACLogic is an open-access, deterministic engineering simulation suite developed for mechanical engineering educators,... see more
Exercise
ENGINEERING STUDENT LABORATORY EXERCISE: COLD-CLIMATE HEAT PUMP SIZING
Tool Link: https://hvaclogic.org/calculators/heat-pump-size
1. DESIGN SCENARIO
Building Location: Chicago, IL (Climate Zone 5)
Conditioned Floor Area: 2,400 sq ft
ASHRAE 99% Winter Design Outdoor Temperature: -2 deg F
Indoor Heating Setpoint: 70 deg F
Total Building Heat Loss at Design: 48,000 BTU/hr
2. STUDENT EXERCISES
Exercise A: Envelope Heat Loss Coefficient (UA)
1. Calculate the design temperature difference: Delta T = 70 - (-2) = 72 deg F.
2. Calculate building UA: UA = 48,000 / 72 = 666.67 BTU/(hr-deg F).
3. Express building heat loss as a function of outdoor temperature T:
Q_loss(T) = 666.67 * (70 - T).
Exercise B: Heat Pump Inverter Capacity Modeling
Open https://hvaclogic.org/calculators/heat-pump-size.
Select a 3.0-Ton (36,000 BTU/hr nominal at 47 deg F) cold-climate variable-capacity inverter heat pump.
Record maximum heating capacity and COP from the simulator:
- At 47 deg F (AHRI rating): Capacity = _____ BTU/hr, COP = _____
- At 17 deg F (Low-ambient rating): Capacity = _____ BTU/hr, COP = _____
- At -2 deg F (Winter Design condition): Capacity = _____ BTU/hr, COP = _____
- At -15 deg F (Extreme operating limit): Capacity = _____ BTU/hr, COP = _____
Exercise C: Thermal Balance Point
1. Plot Building Heat Loss vs. Heat Pump Capacity from -15 deg F to 60 deg F.
2. Determine the Thermal Balance Point where Q_loss equals Q_hp.
3. State whether the heat pump operates continuously below this point.
Exercise D: Auxiliary Resistance Heater Sizing
At the winter design temperature (-2 deg F):
1. Compute heating deficit: Deficit = Q_loss(-2 deg F) - Q_hp(-2 deg F).
2. Convert thermal deficit to electric power: Auxiliary kW = Deficit / 3,412.14.
3. Adding a 10% safety margin, specify the required commercial electric strip heater size (kW).
Exercise E: Engineering Critical Thinking
1. Explain why oversizing heat pump cooling capacity to meet winter heating loads causes summer indoor humidity control problems.
2. How does inverter modulation reduce part-load cycling losses compared to single-stage equipment?
3. DELIVERABLES
Submit hand calculations for Exercises A, C, and D, the completed data table from Exercise B, and concise answers to Exercise E.
Disciplines
Technical Notes
The exercise utilizes the open-access HVACLogic Heat Pump Sizing module (https://hvaclogic.org/calculators/heat-pump-size). All computations run entirely client-side using validated equations from ASHRAE Fundamentals and AHRI Standard 210/240. Works on desktop, laptop, and tablet browsers.
Requirements
Prerequisite knowledge of basic thermodynamics (heat transfer rates, sensible heat equations) and a modern web browser with JavaScript enabled. No local software installation or programming experience required.
Topics
Heat Pumps, Applied Thermodynamics
Building Science, COP Degradation
Balance Point Analysis, ACCA Manual S
Inverter Compressors, Decarbonization
HVAC Engineering
Type of Task
Learning Objectives
1. Quantify the non-linear degradation of heat pump capacity and COP under declining outdoor temperatures.
2. Determine building thermal balance points analytically and graphically.
3. Calculate supplemental auxiliary electric resistance heating requirements (kW) to satisfy ASHRAE 99% winter design conditions.
4. Evaluate trade-offs between equipment oversizing, capital expenditure, and summertime indoor humidity control.
Assessment
Evaluation is based on:
1. Mathematical accuracy in calculating the building UA coefficient and heat loss rate (25%).
2. Correct graphical or numerical determination of the thermal balance point (25%).
3. Rigorous sizing calculation of auxiliary electric backup heating in kW (25%).
4. Depth and engineering rigor in answering the thermodynamic sizing trade-off questions (25%).