Safety Distance Calculation


Hazards must come to a safe state prior to an operator reaching the hazard. For the safety distance calculation, there are two groups of standards that have proliferated. In this chapter, these standards are grouped as follows:

ISO EN: (ISO 13855 and EN 999)

US CAN (ANSI B11.19, ANSI RIA R15.06 and CAN/CSA Z434-03)


The minimum safety distance is dependent on the time required to process the Stop command and how far the operator can penetrate the detection zone before detection. The formula used throughout the world has the same form and requirements. The differences are the symbols used to represent the variables and the units of measure.

The formulas are:

ISO EN:S =K x T+ C

US CAN: Ds =K x(Ts + Tc + Tr + Tbm) + Dpf


Ds and S are the minimum safe distance from the danger zone to the closest detection point.

Directions of Approach

When considering the safety distance calculation where a light curtains or area scanner is used, the approach to the detection device must be taken into consideration. Three types of approaches are considered:

Normal: an approach perpendicular to the detection plane

Horizontal: an approach parallel to the detection plan

Angled: an angled approach to the detection zone.

Speed Constant

K is a speed constant. The value of the speed constant is dependent on movements of the operator (i.e. hand speeds, walking speeds, and stride lengths). This parameter is based on research data showing that it is reasonable to assume a 1600 mm/sec (63 in./s) hand speed of an operator while the body is stationary. The circumstances of the actual application must be taken into account. As a general guideline, the approach speed will vary from 1600 mm/s (63 in./s) to 2500 mm/sec (100 in./s). The appropriate speed constant must be determined by the risk assessment.

Stopping Time

T is the overall stopping time of the system. The total time, in seconds, starts from the initiation of the stop signal to the cessation of the hazard. This time can be broken down to its incremental parts (Ts, Tc, Tr and Tbm) for easier analysis. Ts is the worst stopping time of the machine/equipment. Tc is the worst stopping time of the control system. Tr is the response time of the safeguarding device, including its interface. Tbm is additional stopping time allowed by the brake monitor before it detects stop-time deterioration beyond the end users’ predetermined limits. Tbm is used with part revolution mechanical presses. Ts + Tc + Tr are usually measured by a stop-time measuring device if the values are unknown.

Depth Penetration Factor

The Depth Penetration Factors is represented by the symbols C and Dpf. It is the maximum travel towards the hazard before detection by the safeguarding device. Depth penetration factors will change depending on the type of device and application. Appropriate standard must be checked to determine the best depth penetration factor. For a normal approach to a light curtain or area scanner, whose object sensitivity is less than 64 mm (2.5 in.), the ANSI and Canadian standards use:

Dpf = 3.4 x (Object Sensitivity – 6.875 mm), but not less than zero.

For a normal approach to a light curtain or area scanner, whose object sensitivity is less than 40 mm (1.57 in.), the ISO and EN standards use:

C = 8 x (Object Sensitivity – 14 mm), but not less than 0

Figure 107 shows a comparison of these two factors. These two formulas have a cross over point at 19.3 mm. For object sensitivity less than 19 mm, the US CAN approach is more restrictive, as the light curtain or area scanner must be set back further from the hazard. For object sensitivities greater than 19.3 mm, the ISO EN standard is more restrictive. Machine builders, who want to build one machine for use throughout the world, must take the worst case conditions from both equations.

Click to enlarge - Fig 5.1 Minimum Object Sensitivity
Figure 107: Depth Penetration vs. Object Sensitivity

Reach Through Applications

When larger object sensitivities are used, the US CAN and ISO EN standards differ slightly on the depth penetration factor and the object sensitivity. Figure 108 summarizes the differences. The ISO EN value is 850mm where the US CAN value is 900 mm. The standards also differ in the object sensitivity. Where the ISO EN standard allows for 40 to 70 mm, the US CAN standard allows up to 600 mm.

Click to enlarge - Fig 5.2 Reach Through Apps
Figure 108: Depth Penetration Factors for Reach-Through Applications

Reach-Over Applications

Both standards agree that the minimum height of the lowest beam should be 300 mm, but differ with respect to the minimum height of the highest beam. The ISO EN states 900 mm, whereas the US CAN states 1200 mm. Figure 109 summarizes the differences.

The value for the highest beam seems to be moot. When considering this to be a reach-through application, the height of the highest beam will have to be much higher to accommodate an operator in a standing position. If the operator can reach over the detection plane, then the reach over criteria applies.

Click to enlarge - Fig 5.3 Reach Over Apps
Figure 109: Depth Penetration Factors for Reach-Over Applications

Single or Multiple Beams

Single or multiple separate beams are further defined by the ISO EN standards. Table 5.1 shows the “practical” heights of multiple beams above the floor. The depth penetration is 850 mm for most cases and 1200 mm for the single beam usage. In comparison, the US CAN approach takes this into account by the Reach-Through requirements. Getting over, under or around the single and multiple beams must always be taken into consideration.

No. of Beams Height Above the Floor [mm (in.)] C [mm (in.)]
1 750 (29.5) 1200 (47.2)
2 400 (15.7), 900 (35.4) 850 (33.4)
3 300 (11.8), 700 (27.5), 1100 (43.3) 850 (33.4)
4 300 (11.8), 600 (23.6), 900 (35.4), 1200 (47.2) 850 (33.4)
Table 7: Single and Multiple Beam Heights and Depth Penetration Factor

Distance Calculations

For the normal approach to light curtains, the safety distance calculation for the ISO EN and U.S. CAN are close, but differences do exist. For the normal approach to vertical light curtains where the object sensitivity is a maximum of 40 m, the ISO EN approach requires two steps. First, calculate S using 2000 for the speed constant.

S = 2000 x T + 8 x (d -1 4)

The minimum distance that S can be is 100 mm.

A second step can be used when the distance is greater than 500 mm. Then the value of K can be reduced to 1600. When using K=1600, the minimum value of S is 500 mm.

The U.S. CAN approach uses a one step approach:

Ds = 1600 x T * Dpf

This leads to differences greater than 5% between the standards, when the response time is less than 560 ms. Figure 110 shows the minimum safety distance as a function of the total stopping time for 14 and 30 mm object sensitivity. A combination of both approaches needs to be examined to achieve the worst case scenario for globally designed machines.

Click to enlarge - Fig 110 Safety Distance Comparisons
Figure 110: Safety Distance Comparisons

Angled Approaches

Most applications of light curtains and scanners are mounted in vertical (normal approach) or horizontal (parallel approach). These mountings are not considered angled if they are within ±5° of the intended design. When the angle exceeds ±5°, the potential risks (e.g. shortest distance) of foreseeable approaches must be taken into consideration. In general, angles greater than 30° from the reference plane (e.g. floor) should be consider normal and those less than 30 considered parallel. This is depicted in Figure 111.

Click to enlarge - Fig 5.5 Angular Approach
Figure 111: Angle Approach to the Detection Field

Safety Mats

With safety mats, the safety distance must take into account the operators pace and stride. Assuming the operator is walking and the safety mats are mounted on the floor. The operator’s first step onto the mat is a depth penetration factor of 1200 mm or 48 in. An example arrangement is shown in Figure 112.

Click to enlarge - Fig 5.6 Safety Mat on Floor
Figure 112: Safety Mat mounted on Floor

If the operator must step up onto a platform, then the depth penetration factor can be reduced by a factor of 40% of the height of the step (see Figure 113).

Click to enlarge - Fig 5.7 Step up Approach
Figure 113: Step Up to Safety Mat Mounted on a Platform


Example: An operator uses a normal approach to a 14 mm light curtain, which is connected to a monitoring safety relay which is connected to a DC powered contactor with a diode suppressor. The safety system response time, Tr, is 20 + 15 + 95 = 130 ms. The machine stopping time, Ts+Tc, is 170 ms. A brake monitor is not used. The Dpf value is 1 inch, and the C value is zero. The calculation would be as follows:

Dpf = 3.4 (14 - 6.875) = 24.2 mm (1 in) C = 8 (14-14) = 0
Ds = K x (Ts + Tc + Tr + Tbm) + Dpf S = K x T + C
Ds = 63 x (0.17 + 0.13 + 0) + 1 S = 1600 x (0,3) + 0
Ds = 63 x (0.3) + 1 S = 480 mm (18.9 in)
Ds = 18.9 + 1  
Ds = 19.9 in (505 mm)  

Therefore, the minimum safe distance the safety light curtain must be mounted from the hazard is 508 mm (20 in.) for a machine to be used anywhere in the world.