Papi Calculator

PAPI Indications Calculator

This PAPI calculator helps pilots understand the visual indications of the Precision Approach Path Indicator lights based on their height and distance from the PAPI units and the runway threshold.

Height Boundaries at Different Distances

Distance from PAPI (ft)	Below 4 Reds (ft)	1W 3R Range (ft)	2W 2R Range (ft)	3W 1R Range (ft)	Above 4 Whites (ft)

Heights (above PAPI datum) at which different PAPI indications are seen at various distances.

PAPI Height Boundaries vs. Distance

Visual representation of the height boundaries for PAPI indications at different distances from the PAPI units. H1 (top), H2, H3, H4 (bottom) are plotted.

What is a PAPI (Precision Approach Path Indicator)?

A PAPI, or Precision Approach Path Indicator, is a visual aid system installed beside airport runways to provide pilots with glide slope guidance during the final approach to landing. It typically consists of four light units arranged in a line perpendicular to the runway edge. These units project beams of light, split horizontally into red and white sectors, allowing pilots to determine if they are on the correct glide path, too high, or too low.

The PAPI calculator helps pilots and aviation students understand the geometry of the PAPI system and predict the visual indications at different distances and heights. It’s crucial for maintaining a safe and stable approach. While experienced pilots use the visual cues directly, a PAPI calculator can be used for training and understanding approach profiles.

Who Should Use It?

Student pilots, flight instructors, and experienced pilots can use a PAPI calculator to understand the relationship between their altitude, distance, and the PAPI lights. It’s also useful for airport designers and technicians involved in PAPI installation and calibration.

Common Misconceptions

A common misconception is that the PAPI provides the exact same glide path for all aircraft. While the angles are fixed, the pilot’s eye height relative to the aircraft’s wheels varies, meaning the wheel crossing height over the threshold can differ slightly. Another is confusing PAPI with VASI (Visual Approach Slope Indicator), which is an older system with a different light configuration and often a greater range but less precision close in.

PAPI Calculator Formula and Mathematical Explanation

The PAPI system is based on simple trigonometry. The core idea is to establish a desired glide path angle (GPA) that the aircraft should follow.

1. Nominal Glide Path Angle (GPA): This is determined by the desired Eye Height over Threshold (EHT) and the Distance from Threshold to PAPI (DTP):
   
   GPA (radians) = atan(EHT / DTP)

GPA (degrees) = GPA (radians) * (180 / π)
2. PAPI Beam Angles: A standard 4-unit PAPI has its beams set at angles relative to the GPA, using the angular separation (S). The angles for the four units (from farthest to nearest to the runway edge) are typically:
   
   Angle 1 = GPA + 1.5 * (S/60) (degrees, S is in minutes)
   
   Angle 2 = GPA + 0.5 * (S/60)

Angle 3 = GPA - 0.5 * (S/60)

Angle 4 = GPA - 1.5 * (S/60)
3. Heights at Distance (DFP): At a given Distance from PAPI (DFP), the heights above the PAPI datum corresponding to the lower edge of the white sector (or upper edge of red) for each unit are:
   
   H1 = DFP * tan(Angle 1 * π/180)

H2 = DFP * tan(Angle 2 * π/180)

H3 = DFP * tan(Angle 3 * π/180)

H4 = DFP * tan(Angle 4 * π/180)

The pilot will see:

• 4 Whites: Above H1 (Slightly high or more)
• 3 Whites, 1 Red: Between H1 and H2 (Slightly high)
• 2 Whites, 2 Reds: Between H2 and H3 (On Glide Path)
• 1 White, 3 Reds: Between H3 and H4 (Slightly low)
• 4 Reds: Below H4 (Low or more)

Variables Table

Variable	Meaning	Unit	Typical Range
EHT	Eye Height over Threshold	feet	30 – 75
DTP	Distance from Threshold to PAPI	feet	500 – 1500
S	Angular Separation between beams	minutes of arc	20 – 30
DFP	Distance from PAPI	feet	500 – 30000
GPA	Nominal Glide Path Angle	degrees	2.5 – 4.0
H1-H4	Heights corresponding to beam boundaries	feet	Varies with DFP

Practical Examples (Real-World Use Cases)

Example 1: Standard ILS Glide Path

Assume a runway where the PAPI is set to co-locate with a 3-degree ILS glide slope, EHT is 55 feet, DTP is 1050 feet, and separation is 20 minutes. A pilot is 1 nautical mile (6076 feet) from the PAPI.

• EHT = 55 ft
• DTP = 1050 ft
• S = 20 min
• DFP = 6076 ft

The PAPI calculator would first determine the GPA (approx. 2.99 degrees). Then it would calculate H1, H2, H3, and H4 at 6076 ft. The on-glide path window (H3 to H2) would be around 302 ft to 337 ft above the PAPI datum (which is close to runway elevation at that point). If the pilot’s eyes are at 320 ft above the PAPI datum at that distance, they see 2 whites and 2 reds.

Example 2: Steeper Approach

Consider an airport with obstacles requiring a steeper 3.5-degree glide path. EHT might be 60 ft, DTP 980 ft, S 20 min. At 4000 ft from PAPI:

• EHT = 60 ft
• DTP = 980 ft
• S = 20 min
• DFP = 4000 ft

The GPA is around 3.5 degrees. The PAPI calculator would show the on-glide path window (H3-H2) at 4000 ft to be between roughly 232 ft and 255 ft above the PAPI datum.

How to Use This PAPI Calculator

1. Enter EHT: Input the desired Eye Height over Threshold in feet. This is often based on the aircraft type and runway setup.
2. Enter DTP: Input the distance from the runway threshold to the PAPI light units in feet.
3. Enter Separation (S): Input the angular separation between the centers of adjacent beams in minutes of arc (e.g., 20 or 30).
4. Enter DFP: Input your current or desired horizontal distance from the PAPI units in feet.
5. Calculate: Click “Calculate” or observe the results updating automatically.
6. Read Results: The primary result shows the on-glide path height range at your specified distance (DFP). Intermediate results show the heights (H1-H4) defining the boundaries for 4W, 3W1R, 2W2R, 1W3R, and 4R indications, and the calculated GPA. The table and chart show these boundaries at various distances.

Use the PAPI calculator to visualize the glide path. If you are at distance DFP and your altitude (eye height above PAPI datum) is between H3 and H2, you should see 2 whites and 2 reds.

Key Factors That Affect PAPI Calculator Results and Indications

• EHT Setting: The target eye height over the threshold directly influences the nominal glide path angle. A higher EHT for a given DTP results in a steeper angle.
• DTP Placement: The distance of the PAPI from the threshold also defines the glide path angle and the point where the nominal glide path intersects the runway plane (aiming point).
• Angular Separation (S): This determines the vertical depth of the on-glide path zone (2W2R) and the slightly high/low zones. A smaller ‘S’ means a tighter, more precise glide path indication.
• Aircraft Distance (DFP): The vertical height window for each PAPI indication expands as the distance from the PAPI increases. The PAPI calculator shows this.
• Pilot’s Eye Height vs. Wheels: The PAPI is aligned for the pilot’s eye level. The aircraft’s wheels will be lower, and this difference varies between aircraft types.
• Visibility and Atmospheric Conditions: Haze, fog, or precipitation can affect the visibility range and clarity of the PAPI lights, although the PAPI calculator assumes clear visibility.
• PAPI Unit Serviceability: If one or more PAPI lights are unserviceable, the indication will be misleading. The calculator assumes all units are working correctly.
• Day/Night Conditions: PAPI intensity is adjustable for day and night, but the angles remain the same. The PAPI calculator deals with the geometry, not intensity.

Frequently Asked Questions (FAQ)

What do 4 reds mean when looking at the PAPI?

Four red lights (“all red”) indicate you are significantly below the correct glide path.

What if I see 3 whites and 1 red?

Three whites and one red indicate you are slightly above the correct glide path.

How accurate is PAPI?

PAPI is quite accurate, especially closer to the runway. The on-glide path sector (2 whites, 2 reds) is typically very narrow vertically (around 20-30 minutes of arc total).

Can PAPI be used in low visibility (bad weather)?

PAPI is a visual aid and requires the pilot to see the lights. In very low visibility (e.g., Category II/III ILS conditions), pilots rely primarily on instruments, but PAPI can be a useful supplement if visible.

What is the difference between PAPI and VASI?

VASI (Visual Approach Slope Indicator) is an older system, often with 2 bars of lights, providing fewer gradations of glide path information and sometimes a wider on-glide path zone. PAPI is more precise and is the ICAO standard.

How far out can I typically see the PAPI lights?

Under good visibility conditions, PAPI lights are typically visible from at least 5 nautical miles during the day and up to 20 nautical miles or more at night.

Is the PAPI glide path the same for all aircraft?

The angles are the same, but larger aircraft with higher cockpit positions will have their wheels lower relative to the pilot’s eyes. The PAPI is set for an average eye-to-wheel height group, but it provides safe guidance for a range of aircraft normally using that runway. The EHT used in the PAPI calculator should be representative of the aircraft type.

What if one of the PAPI lights is out?

If a light unit is out, the PAPI indication can be misleading. Pilots should be cautious and refer to NOTAMs (Notices to Airmen) for information on unserviceable airport lighting.

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