Cálculo de distancia de cortina de luz de seguridad (Guía ISO 13855)

Safety light curtain distance calculation is the step that decides whether a guarded machine is actually safe or only looks safe. Mount the curtain too close to the hazard and a hand can reach the danger point before the machine finishes stopping. This guide works through the ISO 13855 formula S = (K × T) + C variable by variable, with three worked examples, a penetration-factor reference grid, the standards that govern it, and the changes introduced by ISO 13855:2024.

The Safety Distance Formula S = (K × T) + C: A Variable Decoder

A safety light curtain’s minimum safety distance, the smallest gap, or minimum distance, allowed between the detection plane and the nearest hazard, comes from the following formula in ISO 13855:

Each term answers a different question. The S = (K × T) + C Variable Decoder below is the fastest way to see where engineers actually get the number wrong.

Approach Speed (K): When to Use 2,000 vs 1,600 mm/s

K is a parameter, a fixed constant, that models how fast a body part travels toward the hazard. ISO 13855 gives two values for this parameter and one rule that catches people out.

A frequent audit finding on press brakes is a hand-reach distance computed with K = 1600 mm/s when 2000 mm/s applies. The shortfall reads as a rounding error on paper, yet it leaves the curtain roughly 20% too close, so an operator’s hand can reach the bend line before the ram halts. Picking the wrong constant is the quietest way to fail a safety distance calculation.

Q: What is the hand speed constant in ISO 13855?

The hand speed constant is K = 2000 mm/s. It applies whenever the light curtain resolves fingers or hands (detection capability d of 40 mm or finer) and the approach is perpendicular to the detection plane. If that calculation returns a distance of 500 mm or more, you recompute once with the walking-speed constant of 1600 mm/s, because over that range a full-body stride is the realistic motion.

Total Stopping Time (T): Add Up Every Delay, Then Measure It

T is the single largest lever in the calculation: at K = 2000 mm/s, every extra millisecond of system response adds 2 mm to the required distance, and every extra second of stopping time adds two full metres. It’s also the term people underestimate, because they count the light curtain alone.

Because the relay and contactor sit between the curtain and the motor, replacing a safety relay module with a slower one quietly increase your required distance. A QJKH ENT curtain contributes a t₁ from 6.0 ms that rises with beam count, more protective height means more beams, which means a slower response and a larger required distance, while the rest of the chain is yours to measure.

Detection Capability (d) and the Penetration Factor C Reference Grid

C accounts for how far a body part can travel into the detection field before it’s sensed. For a vertical curtain with d of 40 mm or finer, C = 8(d − 14) mm, never less than zero. For a body-detecting field (40 < d ≤ 70 mm), C is a flat 850 mm. The Penetration Factor C Reference Grid turns that into a lookup.

This grid is also a selection tool: a finer resolution lowers C, which lets you mount closer, but it raises curtain cost and nuisance trips. Choosing a 14 mm finger-detection light curtain only pays off if the application genuinely needs it. The 8(d−14) value is the long-established through-penetration term carried by every major manufacturer guide; ISO 13855:2024 refines how the over-, through- and under-reach distances combine into a single reaching term, which the final section covers.

Worked Examples: Three Real Calculations

Three perpendicular-approach cases using representative QJKH ENT response times (the ENT line runs from 6.0 ms, scaling with beam count). Run your own numbers in the ISO 13855 safety distance calculator once you follow the logic.

Mounting Orientation: Vertical, Horizontal, and Angled Approaches

Everything above assumes a vertical curtain a person walks toward. Mount the field horizontally, as an area guard in front of a machine, and both the penetration term and the height limits change under ISO 13855.

The orientation swap bites in the field. A palletizing cell that replaces a vertical access guard with a horizontal floor field, then reuses the old mounting distance, can discover its safe zone has quietly shrunk once C = 1200 − 0.4H is applied at floor height, a low detection plane drives C toward its 850 mm floor. Recompute the distance every time the mounting plane change, not just when the curtain does.

Q: How do you calculate safety distance for a horizontal light curtain?

For a horizontal field, swap the penetration term for C = 1200 − 0.4H, where H is the height of the detection plane above the floor, and never let C fall below 850 mm. The detection height itself is bounded: it must sit between 15(d − 50) mm and 1000 mm. A lower field need a finer resolution to stay valid, which is why area guarding often uses dense beam spacing.

The Safety-Distance Standard Matrix: ISO 13855 vs ISO 13857 vs ANSI B11.19

Each region answers the same physical question differently, and the device standards are separate again from the positioning standards. The ISO 13855-vs-ANSI B11.19 Safety-Distance Standard Matrix keeps them straight.

Three points trip people up. First, the penetration math differs: ISO uses 8(d−14), ANSI B11.19 uses ddt = 3.4(de−7), and the basic OSHA eTool formula Ds = 63 in/s × Ts carries no penetration term at all. Second, OSHA’s power-press rule is fuller than the eTool: 1910.217(h)(9)(v) gives the PSDI distance as Ds = Hs × (Ts + Tp + Tr + 2Tm) + Dp, where Dp is a penetration-depth factor. Third, choosing a Type 4 device under IEC 61496 does not by itself make the installation compliant, that standard governs how the curtain functions, not where it sits. The distance calculation is the application-level requirement.

Reach-Through, Over, Under, and Around: Exposure Checks That Change Your Distance

A curtain that passes the perpendicular formula can still be defeated by geometry. ISO 13855:2024 formalises this with a single reaching term, DDS, built from three directions. The Reach-Through / Over / Under / Around Exposure Check walks each one.

• ✓Reaching over (DDO): if a person can lean over the top of the field, add the over-reach distance from the hazard and field heights, then take the larger result.
• ✓Reaching through (DDT): the penetration term itself, the 2024 edition extends it with an additional formula for finer cases.
• ✓Reaching under (DDU): newly required in ISO 13855:2024. The 2010 edition only set a 300 mm lowest-beam value, leaving a one-arm gap; the new edition makes you calculate the under-reach.
• ✓Reaching around / reflection: keep the field clear of reflective surfaces that can bridge a broken beam, and block walk-around paths.

Field experience makes the under-reach concrete: leave a 150 mm gap beneath a vertical curtain and the required distance can start at 1.2 metres and grow from there. That’s the gap the 2024 reach-under requirement closes.

What Changed in ISO 13855:2024 (and What It Means for Your Distance)

ISO 13855’s third edition came into force in November 2024 and cancels and replaces the 2010 edition. If your last design referenced the 2010 text, several inputs to the distance calculation have moved: the reaching terms are restructured into over, through and under, reaching under the field becomes a required calculation, and the standard reaches toward moving robots with a dynamic distance concept. Here is what changed.

“We treat the calculated distance as the start of a sign-off, not the end. A number on a worksheet means nothing until the measured stopping time behind it has been re-checked on the actual machine, with the actual relay and contactor in the loop.”

QJKH Functional Safety Engineering Team, CCH Shanghai Sensing

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