Flame Height Calculator

The Flame Height Calculator estimates flame height from heat release rate, fuel properties, and ambient conditions using established combustion correlations.

Flame Height Calculator Explained

Flame height is the average vertical distance from the burner or fuel surface to the tip of the luminous flame. Engineers use it to predict thermal exposure, clearances, and detector placement. It is a statistical measure over time because turbulent flames flicker and the tip moves.

The calculator uses peer-reviewed correlations based on heat release rate and characteristic diameter. For buoyancy-controlled fires, the Heskestad and Thomas relations are standard. For high-velocity jets, a momentum-driven relation is more appropriate.

Results depend on physical constants such as air density, specific heat, and gravity, plus consistent units. The tool defaults to standard air at 20 °C and sea-level pressure. You can override these if your site conditions differ.

How the Flame Height Method Works

The method models a turbulent diffusion flame as a buoyant plume fed by a heat source of size D and strength Q. Dimensionless analysis collapses a wide range of fires into simple power laws. The output is either a flame height in meters or a scaled height relative to the diameter.

• Compute or enter heat release rate Q from fuel data or tests.
• Provide a characteristic burner or pool diameter D. For noncircular burners, use an equivalent diameter.
• Form a dimensionless heat release parameter Q* using air properties and gravity.
• Select a correlation: buoyancy-dominated (Heskestad/Thomas) or jet-dominated for high exit momentum.
• Calculate mean flame height and, optionally, a range based on typical scatter in the data.

These steps are rooted in conservation laws and similarity scaling. They are not exact, but they match a large body of experiments within practical tolerances. Expect uncertainty bands of roughly ±15–30% depending on conditions.

Flame Height Formulas & Derivations

Below are the most-used formulas, with notes on units and derivation. Use SI units throughout unless stated otherwise. The coefficients assume Q in kilowatts and D in meters.

• Heskestad (buoyant diffusion flames, SI form): Lf = 0.235 · Q^(2/5) − 1.02 · D. Here Lf is flame height (m), Q is heat release rate (kW), and D is burner diameter (m). The 2/5 exponent follows from similarity of turbulent buoyant plumes.
• Heskestad (dimensionless form): Lf/D = 3.7 · Q*^(2/5) − 1.02, where Q* = Q / (ρ∞ · Cp · T∞ · √g · D^(5/2)). Use Q in watts, ρ∞ in kg/m³, Cp in J/(kg·K), T∞ in K, g in m/s². This form shows the role of ambient properties explicitly.
• Thomas correlation (historical variant, SI): Lf ≈ 0.23 · Q^(2/5) − 1.02 · D. Coefficients are very close to Heskestad’s and yield similar results in the valid range.
• Jet flame (momentum-dominated, indicative): Lf/D ≈ Cj · (Re · Sc)^1/2 · (1 + Kj/Fr)^−1/2, where Re is Reynolds number, Sc is Schmidt number, and Fr is Froude number based on exit velocity. This is useful when exit momentum is large and buoyancy is secondary. The calculator flags when a jet model may be preferable.
• Heat release from fuel data: Q = χ · ṁ · ΔHc, where ṁ is mass burning rate (kg/s), ΔHc is lower heat of combustion (kJ/kg), and χ is combustion efficiency (0–1). If you know area and heat flux, Q ≈ q″ · A, then D ≈ √(4A/π).

Derivation sketch: balance buoyancy power input with turbulent entrainment, use dimensional analysis with {Q, ρ∞, Cp, T∞, g, D}. The only dimensionless group governing height becomes Q*. Empirically, the flame tip scales as Q*^(2/5), with an offset in Lf/D for finite burner size. Coefficients arise from regression to controlled-fire datasets.

What You Need to Use the Flame Height Calculator

Have these inputs ready before you start. Using consistent units is essential for reliable results. If you lack some values, the calculator can fill in standard constants.

• Heat Release Rate Q (kW), or mass-loss rate ṁ (kg/s) and heat of combustion ΔHc (kJ/kg).
• Burner/Pool Diameter D (m), or equivalent diameter D = √(4A/π) for noncircular sources.
• Ambient temperature T∞ (K or °C), to set thermophysical properties.
• Air density ρ∞ (kg/m³) and specific heat Cp (J/(kg·K)); defaults: ρ∞ ≈ 1.204 kg/m³, Cp ≈ 1005 J/(kg·K) at 20 °C.
• Gravitational acceleration g (m/s²); default 9.81 m/s².

Typical ranges: D from 0.05 to 5 m, Q from 10 kW to tens of MW. If input combinations yield a negative Lf from the simple SI form, the calculator returns zero and advises switching to the dimensionless form. For very small laminar flames or very high-velocity jets, specialized models may be more accurate.

How to Use the Flame Height Calculator (Steps)

Here’s a concise overview before we dive into the key points:

1. Select the fire type: buoyant pool/burner or momentum-dominated jet.
2. Enter heat release Q in kW, or choose “Compute Q” and enter ṁ and ΔHc.
3. Enter diameter D in meters, or an area to convert to an equivalent D.
4. Confirm ambient constants (ρ∞, Cp, T∞, g) or keep the defaults.
5. Click Calculate to obtain Lf, Q*, and the method notes.
6. Review any validity warnings and the uncertainty range.

These points provide quick orientation—use them alongside the full explanations in this page.

Worked Examples

Small lab pool fire: Q = 50 kW, D = 0.30 m, ambient 20 °C. Using Heskestad (SI), Lf = 0.235 · 50^0.4 − 1.02 · 0.30. Since 50^0.4 ≈ 4.78, Lf ≈ 0.235 · 4.78 − 0.306 ≈ 0.82 m. Using the dimensionless form with ρ∞ = 1.204 kg/m³, Cp = 1005 J/(kg·K), T∞ = 293 K, g = 9.81 m/s² gives Q* ≈ 0.92 and Lf ≈ 0.77 m. What this means: Expect a visible flame about 0.8 m tall above the fuel surface.

Industrial burner flare: Q = 5000 kW, D = 1.00 m, standard ambient. Heskestad (SI) gives Lf = 0.235 · 5000^0.4 − 1.02 · 1.00. Since 5000^0.4 ≈ 30.1, Lf ≈ 0.235 · 30.1 − 1.02 ≈ 6.05 m. The dimensionless form yields Q* ≈ 1.38 and Lf ≈ 5.8 m. What this means: Plan for a 6 m flame and provide clearance to structures and detectors accordingly.

Assumptions, Caveats & Edge Cases

The correlations assume a turbulent diffusion flame in quiescent air. Real scenes often differ. Keep these points in mind when interpreting results.

• Wind and crossflow bend and lengthen flames; the vertical height may drop while centerline length increases.
• Enclosures, walls, and ceilings alter entrainment and can raise flames or cause intermittent impingement.
• Very small burners may be laminar, invalidating turbulent scaling; very large pool fires can tilt scaling via radiation feedback.
• High-velocity jets are momentum-dominated; use a jet correlation when Froude number is high.
• Flame height is a mean value; instantaneous tips can exceed the mean by 20–40% due to flicker.

When in doubt, run both the SI and dimensionless forms and compare. If results diverge greatly, reassess the inputs and the assumed fire regime. Field measurements or CFD may be warranted for critical designs.

Units & Conversions

Flame-height formulas are sensitive to units and constants. Mixing kW and W or m and ft will skew results. The table below lists common conversions used by the calculator and in reports.

Use these factors to convert inputs before calculation or to restate results for local standards. Keep internal calculations in SI to match the coefficients and derivations shown earlier.

Tips If Results Look Off

Strange outputs often come from unit mix-ups or a mismatch between fire type and correlation. Try these quick checks.

• Verify Q units: kW for the simple SI form; W for the dimensionless Q* denominator.
• Make sure D is in meters and represents the active burning area, not the vessel outer diameter.
• Confirm ambient constants and temperature; high altitude reduces ρ∞ and increases Q*.
• If Lf is negative from the SI form, switch to the dimensionless form or increase D accuracy.
• For high exit velocities, select the jet model instead of a buoyant correlation.

If the flame height seems too short, consider wind effects or radiation feedback in large pools. If it seems too tall, recheck that Q includes only combustion, not electrical or auxiliary heat sources.

FAQ about Flame Height Calculator

What is the difference between flame height and plume height?

Flame height ends at the visible luminous tip, while plume height continues above as hot gases rise and mix. The calculator focuses on the luminous flame.

Which method should I choose: SI Heskestad or the dimensionless form?

If you have standard ambient conditions and Q in kW, the SI form is fast and accurate. Use the dimensionless form when conditions depart from standard air or when validating against scaled experiments.

Can I use this for propane jet burners?

Yes, but select the jet correlation when exit momentum is high. If the jet slows and becomes buoyant, the Heskestad relation may better represent the visible flame height.

How accurate are these correlations?

Typical scatter is ±15–30% for well-characterized tests. Uncertainty increases with wind, partial confinement, very small burners, or very large pool fires with strong radiation feedback.

Glossary for Flame Height

Heat Release Rate (Q)

The rate at which chemical energy from combustion is converted to heat, usually expressed in kilowatts.

Burner Diameter (D)

The characteristic source size. For circular burners it is the physical diameter; for other shapes, use an equivalent diameter.

Dimensionless Heat Release (Q*)

A scaled measure of fire strength: Q* = Q / (ρ∞ · Cp · T∞ · √g · D^(5/2)). It collapses different fires onto common trends.

Buoyancy

The upward force on hot gases due to lower density relative to ambient air. Buoyancy drives entrainment and plume rise.

Specific Heat (Cp)

The amount of heat required to raise the temperature of a unit mass by one degree at constant pressure, for air about 1005 J/(kg·K) near room temperature.

Combustion Efficiency (χ)

The fraction of fuel chemical energy released as heat in the flame. Real fires rarely reach 100% due to incomplete combustion or heat losses.

Froude Number (Fr)

A ratio of inertial to gravitational forces. Large Fr indicates momentum-dominated jets; small Fr indicates buoyancy dominance.

Entrainment

The process by which ambient air is drawn into the flame and plume, controlling mixing, combustion, and flame shape.

References

Here’s a concise overview before we dive into the key points:

• G. Heskestad, “Fire plumes, flame height, and air entrainment”
• B. J. McCaffrey, “Purely Buoyant Diffusion Flames: Some Experimental Results” (NBSIR 79-1910)
• SFPE Handbook of Fire Protection Engineering: Fire Plumes, Flame Height, and Air Entrainment
• D. Drysdale, “An Introduction to Fire Dynamics,” 3rd ed., Wiley
• IFRF Combustion Handbook: Jet Flame Length Correlations

These points provide quick orientation—use them alongside the full explanations in this page.