Papi Calculator

Precision Approach Path Indicator Calculator

PAPI Indication Calculator

Enter the desired glide slope, PAPI settings, and aircraft position to calculate the PAPI light angles and the visual indication the pilot would see.

Results:

Pilot angle is calculated as arctan(Eye Height / Distance). PAPI angles are set relative to the desired glide slope based on separations.

Visual representation of PAPI light angles and pilot’s approach angle.

What is a PAPI Calculator?

A PAPI (Precision Approach Path Indicator) calculator is a tool used to determine the settings of PAPI lights or to understand the visual indication a pilot will see based on their approach angle relative to the runway. PAPI is a visual guidance system that helps pilots acquire and maintain the correct vertical profile (glide slope) during the final approach to landing. A PAPI calculator helps in setting up these lights or simulating their appearance.

Pilots, airport designers, and aviation technicians use a PAPI calculator to ensure the PAPI system is correctly calibrated for the desired glide slope of a runway. It involves calculating the precise angles at which each of the four light units in a standard PAPI bar should be set.

Common misconceptions include thinking PAPI directly controls the aircraft (it’s purely visual) or that all runways have the same PAPI settings (they vary with the desired glide slope).

PAPI Calculator Formula and Mathematical Explanation

A standard PAPI system consists of four light units placed in a line or bar, usually on the left side of the runway. Each unit projects a beam of light, split horizontally – white in the upper part and red in the lower part.

The angles are set relative to the desired glide slope (G), typically with separations (S_inner, S_outer) in minutes of arc (60 minutes = 1 degree).

• Angle of Light 1 (closest to runway, lowest angle): G – (S_outer + S_inner/2) / 60 degrees
• Angle of Light 2: G – (S_inner/2) / 60 degrees
• Angle of Light 3: G + (S_inner/2) / 60 degrees
• Angle of Light 4 (furthest from runway, highest angle): G + (S_inner/2 + S_outer) / 60 degrees

For example, with G=3°, S_inner=20′, S_outer=20′:

• Angle 1: 3 – 30/60 = 2.5°
• Angle 2: 3 – 10/60 = 2.833°
• Angle 3: 3 + 10/60 = 3.167°
• Angle 4: 3 + 30/60 = 3.5°

The pilot’s approach angle relative to the PAPI is calculated using trigonometry: Pilot Angle = arctan(Pilot Eye Height / Distance to PAPI). The indication seen depends on which angles the pilot’s angle falls between.

Variables in PAPI Calculations

Variable	Meaning	Unit	Typical Range
G	Desired Glide Slope	Degrees	2.5 – 3.5
S_inner	Inner Light Separation	Minutes of arc	10 – 30
S_outer	Outer-Inner Light Separation	Minutes of arc	10 – 30
Eye Height	Pilot Eye Height above PAPI	Feet or Meters	10 – 150
Distance	Distance from PAPI	Feet or Meters	500 – 50000
Pilot Angle	Calculated Pilot Approach Angle	Degrees	1 – 5

Practical Examples (Real-World Use Cases)

Example 1: On Glide Path

A pilot is approaching a runway with a 3-degree glide slope PAPI (set as above). The aircraft is 1 nautical mile (6076 feet) from the PAPI, and the pilot’s eye height is 318 feet above the PAPI datum.
Pilot Angle = arctan(318 / 6076) * 180/PI ≈ 3.00 degrees.
Since 2.833° < 3.00° < 3.167°, the pilot sees 2 White and 2 Red lights – "On Glide Path".

Example 2: Slightly High

The same aircraft is now at 6076 feet but with an eye height of 340 feet.
Pilot Angle = arctan(340 / 6076) * 180/PI ≈ 3.20 degrees.
Since 3.167° < 3.20° < 3.5°, the pilot sees 3 White and 1 Red light – "Slightly High". The PAPI calculator confirms this.

How to Use This PAPI Calculator

1. Enter the desired glide slope for the runway.
2. Input the angular separations for the inner and outer PAPI lights (20′ and 20′ are common).
3. Enter the pilot’s eye height above the plane of the PAPI lights.
4. Enter the horizontal distance from the aircraft to the PAPI installation.
5. Select the units (feet or meters) used for height and distance.
6. Click “Calculate”.
7. The results will show the four PAPI light setting angles, the pilot’s current approach angle, and the visual PAPI indication (e.g., “On Glide Path”), along with a visual representation of the lights. The chart also visualizes these angles.

The PAPI calculator provides immediate feedback on the visual cue the pilot receives.

Key Factors That Affect PAPI Calculator Results

• Desired Glide Slope: The fundamental angle the PAPI is set to guide aircraft along.
• PAPI Light Separation: The angular differences between the light units determine the sensitivity of the PAPI system and the width of the “on glide path” corridor.
• Aircraft Eye Height: Different aircraft have different pilot eye heights above the wheels when on approach, affecting the perceived angle.
• Distance to PAPI: The pilot’s approach angle changes with distance for a given height.
• PAPI Installation Position: The distance of the PAPI bar from the runway threshold affects the Eye Height Over Threshold (EHOT) when on glide path. Our PAPI calculator assumes a reference datum at the PAPI.
• Atmospheric Conditions: While not directly in the calculation, shimmer or refraction can slightly affect the visual appearance at long distances, though the PAPI calculator deals with the geometric angles.

Frequently Asked Questions (FAQ)

Q1: What does PAPI stand for?
A1: PAPI stands for Precision Approach Path Indicator.

Q2: How many lights are in a standard PAPI system?
A2: A standard PAPI system has four light units arranged in a horizontal bar.

Q3: What does “2 Red, 2 White” mean on a PAPI?
A3: It means the aircraft is on the correct glide slope.

Q4: What if I see 4 red lights?
A4: Four red lights indicate the aircraft is significantly below the correct glide slope – “Very Low”.

Q5: What if I see 4 white lights?
A5: Four white lights indicate the aircraft is significantly above the correct glide slope – “Very High”.

Q6: Why use a PAPI calculator?
A6: A PAPI calculator helps in understanding the relationship between the PAPI settings, aircraft position, and the visual indication, useful for setup, training, and simulation.

Q7: Can PAPI be used in all weather conditions?
A7: PAPI is a visual aid, so its effectiveness is reduced in low visibility conditions (fog, heavy rain, snow). It requires the pilot to see the lights.

Q8: Is the PAPI glide slope the same for all aircraft?
A8: Yes, the PAPI system is set for a specific glide slope for the runway, intended for use by all aircraft approaching that runway. However, larger aircraft might aim for a slightly higher position within the “on glide path” zone.