Papi Calculation

Precision Approach Path Indicator – Calculate Your Glide Path Angle

Understanding PAPI (Precision Approach Path Indicator)

The Precision Approach Path Indicator (PAPI) is a visual aid system installed at most airports to help pilots maintain the correct glide path during approach and landing. This sophisticated lighting system provides immediate visual feedback about whether an aircraft is too high, too low, or on the correct approach path to the runway.

Did You Know? PAPI systems replaced the older VASI (Visual Approach Slope Indicator) systems and are now the international standard for approach path guidance at most airports worldwide.

How PAPI Works

A PAPI system consists of four light units positioned beside the runway, typically on the left side. Each unit projects a beam of light that appears either red or white depending on the pilot's viewing angle. The combination of red and white lights tells the pilot their position relative to the ideal glide path.

The Four PAPI Light Configurations

• Four White Lights: Aircraft is significantly high – more than 3.5° above the glide path. Pilot should reduce altitude immediately.
• Three White, One Red: Aircraft is slightly high – between 3.2° and 3.5° above the glide path. Minor descent required.
• Two White, Two Red: Aircraft is on the correct glide path – typically 3° angle. This is the ideal approach position.
• One White, Three Red: Aircraft is slightly low – between 2.5° and 2.8° below the glide path. Minor altitude correction needed.
• Four Red Lights: Aircraft is dangerously low – less than 2.5° below the glide path. Immediate climb required to avoid terrain or obstacles.

PAPI Calculation Mathematics

The PAPI calculation involves determining the actual glide path angle based on the aircraft's altitude, runway elevation, and horizontal distance from the threshold. The fundamental formula uses basic trigonometry:

Glide Path Angle Formula

Glide Angle (degrees) = arctan(Height Above Runway ÷ Horizontal Distance)

Where:

• Height Above Runway: Aircraft altitude minus runway threshold elevation (in feet)
• Horizontal Distance: Distance from runway threshold (converted to feet from nautical miles)

Step-by-Step Calculation Example

Let's calculate the PAPI indication for an aircraft on approach:

• Runway threshold elevation: 500 feet MSL
• Aircraft altitude: 1,500 feet MSL
• Horizontal distance: 3 nautical miles (18,228 feet)
• Target glide path: 3.0 degrees

Step 1: Calculate height above runway
Height = 1,500 – 500 = 1,000 feet

Step 2: Convert nautical miles to feet
Distance = 3 × 6,076 = 18,228 feet

Step 3: Calculate actual glide angle
Angle = arctan(1,000 ÷ 18,228) = arctan(0.05486) = 3.14 degrees

Step 4: Determine PAPI indication
Deviation = 3.14° – 3.0° = +0.14° (slightly high)
PAPI shows: Three White, One Red

Standard Glide Path Angles

While PAPI systems can be set to different glide path angles depending on terrain and obstacle clearance requirements, the international standard glide path angle is 3 degrees. This angle provides:

• Adequate obstacle clearance in the approach corridor
• Comfortable descent rate for most aircraft types
• Sufficient runway remaining for landing and rollout
• Optimal approach speed and configuration management

Important: Some airports use steeper glide paths (up to 3.5°) due to terrain or noise abatement procedures. Always check the airport's approach procedures and NOTAMS before landing.

Converting Distance and Altitude Units

PAPI calculations require consistent units. Here are the essential conversion factors:

• 1 nautical mile = 6,076 feet = 1,852 meters
• 1 statute mile = 5,280 feet = 1,609 meters
• 1 foot = 0.3048 meters
• 1 meter = 3.28084 feet

Practical Applications in Aviation

1. Visual Approach Guidance

PAPI systems are essential during visual approaches, especially in challenging conditions such as night operations, hazy weather, or approaches over water or featureless terrain where depth perception is compromised.

2. Backup for Instrument Approaches

Even during instrument approaches with electronic glideslope guidance (ILS), PAPI provides visual confirmation that the aircraft is on the correct path during the critical final approach phase.

3. Training and Proficiency

Student pilots learn to use PAPI indications to develop proper glide path awareness and altitude management skills essential for safe landings.

PAPI vs. ILS Glideslope

While both systems provide glide path guidance, they differ significantly:

• PAPI: Visual system, works in VMC, provides discrete indications, installed beside runway
• ILS Glideslope: Electronic system, works in IMC, provides continuous deviation information, requires cockpit instrumentation
• Accuracy: ILS typically more precise (±0.1°) vs. PAPI (±0.5°)
• Range: ILS effective from 10+ miles, PAPI visible from 3-5 miles

Factors Affecting PAPI Accuracy

Environmental Conditions

• Visibility: Reduced visibility from fog, rain, or snow limits PAPI effectiveness
• Sun Position: Direct sunlight can wash out PAPI lights, especially during sunrise/sunset
• Precipitation: Rain or snow on the windscreen can distort light perception

Aircraft-Specific Factors

• Eye Height: Pilot's eye position varies with aircraft type, affecting perception angle
• Approach Speed: Faster approaches require earlier recognition and correction
• Aircraft Configuration: Gear and flap position affects drag and descent rate

Descent Rate Calculations from PAPI

Pilots can calculate required descent rate using the glide path angle and groundspeed:

Descent Rate (feet per minute) = Groundspeed (knots) × Glide Angle (degrees) × 101.27

For a typical 3° glide path:

• At 120 knots groundspeed: 120 × 3 × 101.27 ÷ 60 = 608 feet per minute
• At 140 knots groundspeed: 140 × 3 × 101.27 ÷ 60 = 710 feet per minute
• At 160 knots groundspeed: 160 × 3 × 101.27 ÷ 60 = 811 feet per minute

Safety Considerations

Critical Safety Points:

• Never descend below the glide path (four red lights) – risk of terrain or obstacle collision
• PAPI provides lateral guidance for approach path – maintain runway centerline separately
• Monitor airspeed during glide path corrections to prevent stall or excessive speed
• In unstabilized approach conditions, execute a go-around immediately

Obstacle Clearance

PAPI systems are surveyed to provide adequate obstacle clearance throughout the approach corridor. Flying below the glide path (more than two red lights) significantly reduces obstacle clearance margins and may result in collision with terrain, buildings, or approach lighting systems.

International PAPI Standards

The International Civil Aviation Organization (ICAO) sets standards for PAPI installations:

• Light unit spacing: 9 meters (approximately 30 feet)
• Installation distance: 300-400 meters from runway threshold
• Lateral distance: 15 meters from runway edge
• Light intensity: Must be visible in daylight and darkness
• Transition angles: Precisely calibrated for ±0.5° indication bands

Using This PAPI Calculator

This calculator helps pilots, students, and aviation professionals understand the relationship between altitude, distance, and PAPI indications:

Input Parameters

• Runway Threshold Elevation: Enter the published elevation of the runway landing threshold in feet MSL (Mean Sea Level)
• Aircraft Altitude: Enter your current altitude in feet MSL from your altimeter
• Horizontal Distance: Enter your distance from the threshold in nautical miles (use DME or GPS)
• Target Glide Path: Enter the published glide path angle (typically 3.0 degrees, check airport data)

Interpreting Results

The calculator provides:

• Your height above the runway in feet (altitude AGL)
• Your actual glide path angle in degrees
• Deviation from the target glide path (positive = high, negative = low)
• Expected PAPI light configuration you would see
• Visual representation of the four PAPI lights
• Recommended action based on your position

Common PAPI Scenarios

Scenario 1: Normal Approach

Aircraft at 1,800 feet MSL, runway elevation 300 feet, 4 nautical miles out, target 3° glide path:

• Height above runway: 1,500 feet
• Distance: 24,304 feet
• Actual angle: 3.53 degrees
• PAPI: Three white, one red (slightly high)
• Action: Slight increase in descent rate

Scenario 2: High Approach

Aircraft at 2,500 feet MSL, runway elevation 500 feet, 3 nautical miles out, target 3° glide path:

• Height above runway: 2,000 feet
• Distance: 18,228 feet
• Actual angle: 6.26 degrees
• PAPI: Four white lights (dangerously high)
• Action: Immediate corrective descent or go-around

Scenario 3: Low Approach

Aircraft at 1,100 feet MSL, runway elevation 400 feet, 3 nautical miles out, target 3° glide path:

• Height above runway: 700 feet
• Distance: 18,228 feet
• Actual angle: 2.20 degrees
• PAPI: Four red lights (dangerously low)
• Action: Immediate climb to safe altitude

Advanced Topics

Temperature Effects on PAPI

Extreme temperatures can affect altimeter readings due to pressure altitude errors. In cold weather, true altitude may be lower than indicated, causing pilots to fly below the glide path even when PAPI shows correct indications. Apply temperature corrections in accordance with aviation regulations and aircraft operating manuals.

Multiple PAPI Systems

Some airports with multiple runways have different PAPI angles for each runway due to terrain, obstacles, or operational requirements. Always verify the correct glide path angle for your specific runway before approach.

PAPI Maintenance and Reliability

PAPI systems require regular maintenance and calibration. Pilots should check NOTAMs for PAPI outages or malfunctions. A malfunctioning PAPI may show incorrect indications, so cross-reference with other approach guidance systems when available.

Conclusion

Understanding PAPI calculations and indications is fundamental to safe approach and landing operations. This calculator provides a mathematical foundation for interpreting PAPI lights and maintaining proper glide path throughout the approach. Whether you're a student pilot learning visual approaches, an experienced aviator brushing up on fundamentals, or an aviation enthusiast exploring approach procedures, mastering PAPI principles enhances flight safety and proficiency.

Remember: PAPI is a visual aid that supplements, but does not replace, proper altitude awareness, airspeed management, and adherence to published approach procedures. Always maintain situational awareness and be prepared to execute a go-around if the approach becomes unstabilized.