How to Calculate Safety Distance for Light Curtains: ISO 13855 Formula Explained
Calculating the correct safety distance between a light curtain and the nearest hazard is the most critical step in any machine guarding installation. This guide explains the ISO 13855 formula in plain language with real-world examples.
The ISO 13855 Formula: S = (K x T) + C
S = (K x T) + C
| Variable | Meaning | Unit | Typical Value |
|---|---|---|---|
| S | Minimum safety distance | mm | Calculated result |
| K | Approach speed toward hazard | mm/s | 2,000 or 1,600 |
| T | Total system stopping time | seconds | 0.1 - 0.3 |
| C | Intrusion distance before detection | mm | 0 - 850 |
Parameter K: Approach Speed
- K = 2,000 mm/s: For finger/hand detection (resolution d ≤ 40 mm)
- K = 1,600 mm/s: For body detection (40 < d ≤ 70 mm)
Crucial: If S ≥ 500 mm with K = 2,000, you must recalculate using K = 1,600 mm/s. This mandatory step is frequently overlooked.
Parameter T: Total Stopping Time
| Element | Example Value |
|---|---|
| Light curtain response time | 6 - 30 ms |
| Safety relay processing | 10 - 30 ms |
| Contactors | 10 - 40 ms |
| Machine mechanical stop time | 50 - 500 ms (measure, don't assume!) |
Critical: Measure actual stopping time with a calibrated device. Take 10 readings and use the maximum.
Parameter C: Intrusion Distance
| Resolution (d) | Body Part | K (mm/s) | C (mm) |
|---|---|---|---|
| 14 mm | Finger | 2,000 | 0 |
| 20 mm | Finger | 2,000 | 48 |
| 25 mm | Hand | 2,000 | 88 |
| 30 mm | Hand | 2,000 | 128 |
| 40 mm | Arm | 2,000 | 208 |
| 50+ mm | Body | 1,600 | 850 |
For d ≤ 40 mm: C = 8 x (d - 14). For 40 < d ≤ 70 mm: C = 850 mm.
Worked Example A: Finger Detection
14mm curtain, response 10ms, machine stop 100ms.
C = 8(14-14) = 0 mm. T = 0.010+0.100 = 0.110 s.
S = 2,000 x 0.110 + 0 = 220 mm. (No recalc needed)
Worked Example B: Hand Detection
30mm curtain, response 15ms, machine stop 150ms.
C = 8(30-14) = 128 mm. T = 0.015+0.150 = 0.165 s.
S = 2,000 x 0.165 + 128 = 458 mm. (No recalc needed)
Worked Example C: The Recalculation Trap
25mm curtain, response 12ms, machine stop 250ms.
C = 8(25-14) = 88 mm. T = 0.012+0.250 = 0.262 s.
First: S = 2,000 x 0.262 + 88 = 612 mm. (S ≥ 500 mm, recalc needed!)
Recalc: S = 1,600 x 0.262 + 88 = 507 mm.
Mistake avoided: Without recalc the safety distance would be 612mm — 105mm more than necessary, wasting factory floor space.
Common Calculation Mistakes
- Wrong K value — using 1,600 for hand detection (should be 2,000)
- Incomplete T — ignoring relay and machine stopping time
- Missing recalc — not re-running with K = 1,600 when S ≥ 500 mm
- Confusing ISO 13855 and ISO 13857
- Wrong installation orientation — horizontal vs vertical C formula
- Ignoring circumvention — top/side penetration distances
DADISICK Free Engineering Consultation
DADISICK offers free safety distance calculation support. With 20 years of industrial safety experience and thousands of installations, our engineers guide you from risk assessment through commissioning.
