Introduction
To properly place a PIR sensor, you need to understand its field of view (FOV) and how it translates to actual coverage area. This article provides the formulas and calculations needed.
Basic Parameters
- Horizontal FOV (θ_h): The angle the sensor covers side-to-side (typically 90-180°).
- Vertical FOV (θ_v): The angle top-to-bottom (typically 60-90°).
- Mounting Height (H): Distance from sensor to floor.
- Tilt Angle (α): Angle sensor is aimed downward from horizontal (0° = straight ahead, 90° = straight down).
- Maximum Range (R_max): The farthest distance the sensor can detect (specified by manufacturer).
Coverage Area Geometry
The sensor’s detection pattern is roughly conical or pyramidal. The actual coverage on the floor depends on mounting height and tilt.
For Wall-Mounted Sensor (Typical)
The detection pattern projects onto the floor as a truncated sector. Key distances:
- Near Limit (D_near): The closest point on the floor that is detected.
- Far Limit (D_far): The farthest point detected (limited by range).
- Width at distance D: W(D) = 2 × D × tan(θ_h/2).
Calculations
Near Limit Calculation
For a sensor mounted at height H, tilted downward by angle α, the near limit is:
D_near = H × tan(90° – α – θ_v/2) (if result is negative, coverage starts at the wall).
Far Limit Calculation
The far limit is the smaller of:
- R_max (sensor’s maximum range)
- Distance to where the top of the vertical FOV hits the floor: D_top = H × tan(90° – α + θ_v/2)
Example Calculation
Given: H = 2.5m, θ_v = 80°, α = 20°, θ_h = 100°, R_max = 10m.
- D_near = 2.5 × tan(90° – 20° – 40°) = 2.5 × tan(30°) = 2.5 × 0.577 = 1.44m.
- D_top = 2.5 × tan(90° – 20° + 40°) = 2.5 × tan(110°) = 2.5 × (-2.747) negative → no top floor intersection, so far limit is R_max = 10m.
- Width at 5m: W = 2 × 5 × tan(50°) = 10 × 1.192 = 11.92m.
Coverage Maps
For precise work, you can generate a coverage map by calculating the detection boundaries at various distances. This helps identify blind spots.
Ceiling-Mounted Sensors (360°)
For ceiling-mounted sensors, coverage is typically circular:
- Radius: r = H × tan(θ/2) where θ is the total coverage angle (often 90-110°).
- Example: H = 3m, θ = 100°, r = 3 × tan(50°) = 3 × 1.192 = 3.58m. Coverage diameter ≈ 7.2m.
Lens Effects
Note that the Fresnel lens creates discrete detection zones, not a continuous field. The above calculations give the envelope within which zones exist. Actual detection may have gaps.
Software Tools
Several manufacturers provide coverage calculation tools:
- Panasonic: PaPIRs Sensor Selection Tool
- Bosch: Detector Coverage Tool
- Honeywell: Coverage Calculator
Conclusion
Understanding FOV calculations ensures you place sensors correctly, avoiding blind spots and maximizing coverage efficiency.