Earth Tube Cooling Length Calculator

Earth tubes (ground-coupled air heat exchangers) temper incoming ventilation air by running it through a buried pipe. Because soil temperature a few meters below grade changes slowly compared with outdoor air, the ground can act as a seasonal heat sink (summer cooling) or heat source (winter preheating). This calculator estimates the tube length needed to cool air from an inlet temperature to a desired outlet temperature using a simplified exponential heat-transfer model.

What this calculator is doing (conceptually)

As air flows through a long pipe, it exchanges heat with the surroundings. The temperature difference between the air and the ground is largest near the inlet and shrinks along the pipe. That produces diminishing returns: every extra meter helps less than the previous meter as the outlet temperature approaches the ground temperature. In an idealized steady-state model, the air temperature approaches (but never goes below) the ground temperature.

Governing relationship

With a constant overall heat transfer coefficient and constant properties, the outlet temperature can be modeled as an exponential approach to the ground temperature:

Solving for required length L (when the target outlet temperature is above the ground temperature) gives:

Length formula

L = (ṁ · cp) / (h · π · D) · [ -ln( (Tout − Tg) / (Tin − Tg) ) ]

Variable definitions

• Tin: inlet air temperature (°C)
• Tg: ground (soil) temperature at burial depth (°C)
• Tout: target outlet air temperature (°C)
• D: pipe inside diameter (m)
• L: pipe length (m)
• h: overall heat transfer coefficient (W/m²·K), treated as a constant here
• ṁ: mass flow rate of air (kg/s)
• cp: specific heat of air (J/kg·K)

How mass flow is obtained from your input

The calculator converts volumetric flow rate to mass flow rate using an assumed air density:

ṁ = ρ · Q, where Q = (flow in m³/h) / 3600 and ρ ≈ 1.2 kg/m³.

Interpreting the result

• Longer length pushes the outlet temperature closer to the ground temperature, but the improvement per meter decreases.
• Higher airflow increases required length because more heat must be removed per second (higher ṁ).
• Larger diameter increases surface area per meter (π·D) and tends to reduce required length in this model (all else equal). Real systems may differ because diameter also affects velocity and convection.
• Targets near Tg require disproportionately long tubes. If you want air within a degree or two of the ground temperature, expect the length to grow rapidly.

Worked example

Given: Tin = 32°C, Tg = 15°C, Tout = 22°C, D = 0.15 m, flow = 150 m³/h.

1. Convert flow to m³/s: Q = 150 / 3600 = 0.0417 m³/s
2. Mass flow: ṁ = ρ·Q = 1.2·0.0417 ≈ 0.050 kg/s
3. Compute the log term:
   • (Tout − Tg) / (Tin − Tg) = (22−15)/(32−15) = 7/17 ≈ 0.4118
   • -ln(0.4118) ≈ 0.887
4. Using the calculator’s default overall heat transfer coefficient h = 10 W/m²·K and cp ≈ 1005 J/kg·K:
   • (ṁ·cp)/(h·π·D) = (0.050·1005)/(10·π·0.15) ≈ 10.7
   • L = 10.7 · 0.887 ≈ 9.5 m

This indicates that, under the model assumptions, roughly 10 meters of 150 mm tube could cool 32°C air down to about 22°C when the ground is 15°C at the tube depth.

Typical ground temperatures (rough guide)

Ground temperature depends strongly on depth, moisture, shading, and seasonal history. The values below are only broad, order-of-magnitude guides for “a few meters depth” in different climates.

Assumptions & limitations (important)

• Constant overall heat transfer coefficient: The model uses a fixed h = 10 W/m²·K to lump internal convection, pipe conduction, and soil conduction together. In reality, h varies with air velocity, pipe roughness, pipe material/thickness, soil type, and soil moisture.
• Constant ground temperature: The soil is treated as an infinite reservoir at a constant Tg. Real soil temperature changes with depth, season, rainfall, and prolonged operation (thermal saturation around the pipe).
• Steady-state, 1-D model: Startup transients, daily cycling, bends/manifolds, and entrance effects are ignored.
• Air properties fixed: Air density and cp are assumed constant (reasonable for quick screening, but not exact across wide temperature/humidity ranges).
• Condensation and latent heat not modeled: If humid air is cooled below its dew point inside the tube, condensation can occur, affecting heat transfer, pressure drop, drainage requirements, and hygiene/maintenance considerations.
• No pressure-drop / fan power check: Required fan energy and acceptable pressure losses are not evaluated here, yet they often constrain practical tube diameter and length.
• Target constraints: Cooling below the ground temperature is not physically achievable with this passive model. If Tout ≤ Tg, the logarithm term becomes invalid (or implies infinite length).

Use this calculator for early-stage sizing and comparisons (e.g., “How does required length change if airflow doubles?”). For design-ready decisions, use site-specific soil data and a model that accounts for moisture, seasonal variation, condensation, and pressure drop—or consult a qualified HVAC professional.