Footlambert (fL): Aviation Photometric Glossary

Introduction

The footlambert (fL) is a non-SI unit of luminance, historically and practically significant in aviation for measuring and specifying the brightness of cockpit displays, simulators, and airfield lighting. While global aviation is moving toward SI units (notably the candela per square meter, or nit), footlamberts remain common in U.S. regulatory documents, legacy aircraft, and mixed-standard environments. Understanding the footlambert’s scientific definition, correct application, and conversion is essential for compliance, safety, and operational effectiveness.

Scientific Definition

A footlambert is defined as the luminance of a surface emitting or reflecting one candela per square foot, divided by π:

[ 1~\mathrm{fL} = \frac{1}{\pi}~\mathrm{cd/ft^2} ]

This definition is rooted in the physics of diffuse (Lambertian) surfaces, which emit or reflect light uniformly in all directions. The 1/π factor ensures that the measured luminance corresponds to the perceived brightness from any viewing angle, a critical parameter for aviation displays and lighting.

Key relationships:

• 1 fL = 0.3183 cd/ft² (since 1/π ≈ 0.3183)
• 1 fL = 3.426 cd/m² (nits)
• 1 fL = 0.001076 lamberts (L)
• 1 fL = 0.0003426 stilb (sb)

These conversions are standardized in NIST, ICAO, and CIE documentation, and are essential for converting legacy requirements to modern SI units.

Industry and Alternative Definitions

In aviation and the broader audiovisual industry, the footlambert is sometimes informally (and incorrectly) calculated as “projector lumens divided by screen area (in square feet),” yielding lumens per square foot (illuminance, not luminance). While quick, this shortcut ignores reflectance and the 1/π factor, which are vital for measuring what a pilot or user actually sees.

Table: Scientific vs. Practical Definitions

For regulatory and safety-critical aviation use, always use the scientific definition and proper measurement technique.

Photometric Quantities in Aviation

• Luminous Flux (Φ): Total visible light output, measured in lumens (lm).
• Luminous Intensity (I): Light output per solid angle, measured in candelas (cd).
• Illuminance (E): Light incident on a surface, measured in lux (lm/m²) or foot-candle (lm/ft²).
• Luminance (L): Light leaving a surface per unit area per direction, measured in cd/m² (nit) or fL.

Footlambert–SI Conversion

[ 1~\mathrm{fL} = 3.426~\mathrm{cd/m}^2 ] [ 1~\mathrm{fL} = 0.3183~\mathrm{cd/ft}^2 ]

Example:
A cockpit display requirement of 30 fL translates to:

[ 30~\mathrm{fL} \times 3.426 = 102.78~\mathrm{cd/m}^2 ]

The 1/π Factor and Lambertian Surfaces

The 1/π in the footlambert definition comes from the physics of perfectly diffuse reflectors (Lambertian surfaces):

[ L = E \times \rho / \pi ]

• L: Luminance (fL or cd/m²)
• E: Illuminance (fc or lux)
• ρ: Reflectance (0 ≤ ρ ≤ 1)

For surfaces that are not perfectly diffuse (e.g., glass, glossy displays), direct luminance measurement is required, as calculations from illuminance may not be accurate.

Aviation Applications

Cockpit Displays and Instrumentation

The footlambert is still used to specify the minimum and maximum brightness of cockpit displays and warning indicators, particularly in U.S. and legacy standards. Ensuring displays are readable in all lighting conditions is crucial for flight safety.

Flight Simulators and Training Devices

Simulator manufacturers and operators often encounter fL requirements in device qualification standards. Accurate measurement of screen luminance (not just projector output or screen area) is essential for realistic training and regulatory compliance.

Airport Lighting and Signage

While SI units are now standard globally, many FAA and U.S. airport specifications still reference footlamberts for illuminated signs and lights. Conversion to cd/m² is routine for international operations and procurement.

Typical Aviation Luminance Requirements

*Values may vary by authority and context.

Measurement Best Practices

• Direct Luminance Measurement: Use a calibrated luminance meter at the pilot’s eye point for displays, simulators, and signage.
• Calculation from Illuminance: Only valid for diffuse surfaces of known reflectance; otherwise, direct measurement is required.
• Clarify Units: Always state whether a measurement or requirement is in fL, cd/m², or another unit, and use standard conversion factors.

Avoiding Common Errors

• Do not confuse luminance (fL) with illuminance (lm/ft² or foot-candle).
• Always use the scientific definition for compliance and safety.
• Refer to the latest regulatory documents for accepted units and procedures.

Key Standards and References

• ICAO Annex 14: Aerodromes
• FAA AC 150/5345-44
• RTCA DO-160 / EUROCAE ED-14
• SAE ARP4256
• MIL-STD-3009

Summary Table

Best Practices

• Always use the correct unit and conversion: 1 fL = 3.426 cd/m².
• Prefer direct luminance measurement for compliance and calibration.
• Know your surface properties—Lambertian or not—to choose the right calculation method.
• Stay updated: Check current ICAO, FAA, and manufacturer standards.
• For simulators, ensure “footlambert” is not misapplied for illuminance.

Conclusion

The footlambert (fL), equal to 1/π candela per square foot, remains a vital unit in aviation for luminance specification and compliance, especially in U.S. contexts. Aviation professionals must understand its scientific meaning, avoid shortcut calculations, and use proper measurement techniques to ensure safe, effective, and regulatory-compliant lighting and display systems.

For further technical detail, consult ICAO Annex 14, FAA AC 150/5345-44, and RTCA DO-160 documentation.