Light Curtain Safety Distance

What is modelled

A person walks toward a hazard on a conveyor. A light curtain detects the hand, the safety PLC reads the trip on its next scan, writes the output on the following scan, the relay drops out and the belt brakes to a stop. The person keeps moving all that time, so the curtain must be far enough away that the hand has not reached the hazard when the belt stops.

Equations

• Total stop time T = t1 + t2, with response t1 = tcurtain + 2 tscan + trelay (worst case) and braking time t2 = v / a.
• Belt stopping distance s = v² / (2a).
• Minimum distance in the style of ISO 13855 S = K T + C, with approach speed K and the penetration depth C = 8 (d − 14) mm (not below 0) for beam resolution d up to 40 mm.

Checks run in the page

• A time-stepped simulation finds the same minimum distance as the formula.
• Integrated belt braking against v²/(2a) and v/a.
• Monte Carlo PLC latency: mean 1.5 scans, maximum 2 scans.
• Finite-difference sensitivities dS/dK = T and dS/d(scan) = 2K.

Honest simplifications

The formula keeps the structure of the standard but this page is an educational model, not a machine-safety calculation and not a substitute for the standard, a risk assessment or a safety-rated design. It ignores approach direction, reaching over or around the curtain, stopping-time measurement tolerance, braking wear and the supplementary distance for body parts other than the hand.

• Choose Too close: the curtain is shorter than the minimum distance and the hand reaches the hazard before the belt stops.
• Choose Fast conveyor: a longer braking time pushes the minimum distance out.
• Raise the PLC scan time and see that each millisecond adds two millimetres, in the third plot.