Detailed mathematical analysis of RD-03D sensor coverage in a rectangular room.
Room Dimensions: 7 meters (width) × 10 meters (depth)
Sensor Position: Center of 7m short wall
Mounting Height: 1.5-2 meters (recommended)
| Specification | Value |
|---|---|
| Maximum Range | 8 meters |
| Minimum Range | ~0.6 meters |
| Horizontal Angle | ±60° (120° total) |
| Vertical Angle | ±30° (60° total) |
| Range Resolution | 0.75m |
| Range Accuracy | ±0.15m |
| Frequency | 24 GHz ISM band |
| Optimal Range | 0-6 meters |
Sensor Position: (3.5m, 0m) [x = width center, y = short wall]
Position: (3.5m, 10m)
Distance = √[(3.5-3.5)² + (10-0)²]
Distance = √[0 + 100]
Distance = 10 meters ❌ (Exceeds 8m maximum)
Position: (0m, 10m)
Distance = √[(3.5-0)² + (10-0)²]
Distance = √[12.25 + 100]
Distance = √112.25
Distance ≈ 10.6 meters ❌ (Far beyond range!)
Position: (7m, 10m)
Distance = √[(7-3.5)² + (10-0)²]
Distance = √[12.25 + 100]
Distance = √112.25
Distance ≈ 10.6 meters ❌ (Far beyond range!)
Position: (0m, 5m)
Distance = √[(3.5-0)² + (5-0)²]
Distance = √[12.25 + 25]
Distance = √37.25
Distance ≈ 6.1 meters ✅ (Good coverage)
Position: (7m, 5m)
Distance = √[(7-3.5)² + (5-0)²]
Distance = √[12.25 + 25]
Distance = √37.25
Distance ≈ 6.1 meters ✅ (Good coverage)
At 8m distance, lateral width:
x = 8 × tan(60°)
x = 8 × 1.732
x ≈ 13.86 meters
Since room width is 7m:
→ Left wall FULLY covered ✅
Same calculation for right side:
→ Right wall FULLY covered ✅
Result: Side walls are completely within coverage, but depth is the limiting factor.
- Area: ~28 m² (room width × 4m)
- Coverage: 100%
- Characteristics: All sensor features work optimally
- Use Cases: Entry area, seating area
- Area: ~14 m² (room width × 2m)
- Coverage: 95%
- Characteristics: Very reliable
- Use Cases: Room center
- Area: ~14 m² (room width × 2m)
- Coverage: 70%
- Characteristics: May occasionally miss targets
- Use Cases: Back area (if not critical)
- Area: ~14 m² (room width × 2m + corners)
- Coverage: 0%
- Characteristics: Cannot detect
- Problem: Opposite wall and corners
Total Room Area: 70 m² (7m × 10m)
Excellent Coverage: 28 m² (40%) ✅
Good Coverage: 14 m² (20%) ✅
Fair Coverage: 14 m² (20%) ⚠️
No Coverage: 14 m² (20%) ❌
Total Usable: 56 m² (80%)
Blind Spots: 14 m² (20%)
- Position: (0m, 8m-10m)
- Area: ~3.5 m²
- Distance: 9.4m - 10.6m
- Reason: Both range and angle limit exceeded
- Position: (7m, 8m-10m)
- Area: ~3.5 m²
- Distance: 9.4m - 10.6m
- Reason: Both range and angle limit exceeded
- Position: (1m-6m, 9m-10m)
- Area: ~7 m²
- Distance: 9-10m
- Reason: Range limit exceeded only
New Position: (3.5m, 2m)
Opposite wall center: (3.5m, 10m)
New distance = √[(3.5-3.5)² + (10-2)²]
= √[0 + 64]
= 8 meters ✅ (At maximum range)
Top left corner: (0m, 10m)
New distance = √[(3.5-0)² + (10-2)²]
= √[12.25 + 64]
= √76.25
= 8.7 meters ⚠️ (Slightly better)
Advantages:
- Opposite wall becomes 8m (just within range)
- Excellent coverage area increases
- No additional cost
Disadvantages:
- Creates 2m blind spot behind sensor
- If door is at back, could be problematic
Coverage: ~90% ✅
New Position: (0m or 7m, 5m) [Middle of long wall]
Farthest corner: (7m, 10m) [sensor at (0m, 5m)]
Distance = √[(7-0)² + (10-5)²]
= √[49 + 25]
= √74
≈ 8.6 meters ⚠️ (Borderline)
But angle check:
tan⁻¹(7/5) = 54.5° ✅ (Within 60°)
Advantages:
- All areas within ~8.6m
- Better balanced coverage (~95%)
- More uniform detection
Disadvantages:
- Longer cable run required
- Side wall mounting position
Coverage: ~95% ✅
Position: (3.5m, 5m, 2m height) [Room center, ceiling]
Corner distance: (0m, 0m, 0m) [sensor at (3.5m, 5m, 2m)]
Distance = √[(3.5-0)² + (5-0)² + (2-0)²]
= √[12.25 + 25 + 4]
= √41.25
≈ 6.4 meters ✅ (Excellent!)
Opposite corner: (0m, 10m, 0m)
Distance = √[(3.5-0)² + (10-5)² + (2-0)²]
= √[12.25 + 25 + 4]
= √41.25
≈ 6.4 meters ✅
Advantages:
- 100% coverage - no blind spots!
- Maximum distance only 6.4m (safe margin)
- Utilizes vertical angle (±30°)
- Can see behind furniture
Disadvantages:
- Ceiling installation required
- More complex cable management
- Higher difficulty level
Coverage: 100% ✅✅✅
This is the optimal solution!
Positions: (1.75m, 0m) and (5.25m, 0m)
Advantages:
- 100% coverage guarantee
- Redundancy (if one fails, other works)
- More precise tracking
Disadvantages:
- Cost doubles
- Requires two ESP32 units (or dual UART)
- More complex configuration
Coverage: 100% ✅
| Option | Coverage | Cost | Difficulty | Recommendation |
|---|---|---|---|---|
| Current Position | 80% | - | ✅ Easy | |
| Move 2m Forward | 90% | - | ✅ Easy | ✅ Good |
| Long Wall Mount | 95% | - | ⭐ Medium | ✅ Good |
| Ceiling Center | 100% | - | ⭐⭐⭐ Best | |
| Dual Sensor | 100% | 💰💰 2x | 💡 Luxury |
Vertical angle impact: Minimal
Coverage: Near horizontal plane
Advantage: Easy installation
Vertical angle: ±30° utilized
Coverage: Wider area
Advantage: Can see behind furniture
Vertical angle: Fully utilized
Coverage: Maximum
Advantage: Full room view
Disadvantage: Installation difficulty
- ❌ Furniture (couches, cabinets, etc.)
- ❌ Metal objects (reflection)
- ❌ Glass surfaces (partial reflection)
- ❌ Wall thickness (signal attenuation)
- ✅ Open areas
- ✅ Flat walls
- ✅ Higher mounting
- ✅ Proper calibration
⚠️ Cannot see opposite wall and corners- ✅ 80% of room has excellent coverage
⚠️ Top 2 meters depth is blind zone
🎯 CEILING MOUNT AT CENTER (2m height)
- 100% coverage
- No blind spots
- Can see behind furniture
- Optimal solution
💰 MOVE SENSOR 2M FORWARD (to position 3.5m, 2m)
- 90% coverage
- No additional cost
- Easy installation
- Acceptable blind spots
-
Test Before Permanent Install:
- Place sensor on table/stand
- Test different positions
- Find optimal location
- Then permanent mount
-
Mark Blind Spots:
- Identify on floor plan
- Ensure critical areas covered
- Plan furniture placement
-
Height Adjustment:
- Test between 1.5-2m
- Consider furniture height
- Optimize viewing angle
-
Calibration:
- Required after installation
- Test in empty room first
- Fine-tune position
Distance = √(X² + Y²)
Where:
X = Horizontal offset (mm)
Y = Depth offset (mm)
Result in cm: Distance / 10.0
Angle = atan2(Y, X) × 180 / π
Result in degrees: -180° to +180°
Left = negative
Right = positive
For circular sector:
Area = (π × r² × θ) / 360°
Where:
r = range (8m)
θ = angle (120°)
Result ≈ 67 m² (theoretical)
| Point | Distance | Status |
|---|---|---|
| Opposite wall center | 9.5m | ❌ Out of range |
| Top left corner | 10.3m | ❌ Out of range |
| Top right corner | 10.3m | ❌ Out of range |
| Left wall center | 6.1m | ✅ Good |
| Right wall center | 6.1m | ✅ Good |
| First 4 meters | 0-4m | ✅✅✅ Excellent |
- Hardware Setup Guide - Wiring and mounting
- Troubleshooting Guide - Common issues
- Coverage Map HTML - Interactive visualization
- Home Assistant Automations - Usage examples
- Use trigonometry for custom rooms
- Consider furniture and obstacles
- Account for mounting height
- Interactive Coverage Map - Open in browser for animated view
- Floor plan software (SketchUp, etc.)
- Home Assistant floor plan integration
Success! 🎉
You now have complete mathematical understanding of RD-03D coverage in your room!