# Minimum Clearance Distance in Fall Arrest Systems with Energy Absorber Lanyards

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{max}+ w + 1

_{max}is the EAL maximum extension during the fall (m); w is the distance between the harness attachment (chest or back) and the user’s feet (m); 1 is the safety distance equal to one meter. It includes harness extension, body deformation and tall users.

_{max}maximum extension (S

_{max}) has an elastic (S

_{e}) and a plastic (S

_{p}) component Equation (2), both of them are relevant in MCD [21,22].

_{max}= S

_{e}+ S

_{p}.

_{p}) obtained in the test due to the difference between the length at rest after the test and the initial length. The standards methodology [18,23,24,25,26] deem elastic elongation (S

_{e}) to be a negligible value, which, a priori, is not necessarily true. An error in predicting this elastic elongation means that the MCD is underestimated and that the accident victim could reach the floor level.

_{EN355}should be Arrest Distance (H) plus one meter (standards include a safety distance). H is defined as the vertical distance, expressed in meters, between the initial position (start of free fall) and the final position (balance after arrest) of the mobile point of the connection subsystem that supports the load, not counting elongations of the fall arrest harness and its attachment element [28]. The definition and methodology used in EN 355 show that it only takes plastic elongation (S

_{p}) into account.

_{EN355}≥ H + 1

_{p}.

_{EN355}Equation (3), to be equivalent, necessarily L = S

_{e}+ w. On the other hand, for the formula proposed by EN 355 to be on the safe side, the condition L ≥ S

_{e}+ w must be fulfilled. Taking into account that w is not defined and that S

_{e}is not known, compliance with this equation is not guaranteed. Therefore, it is necessary to establish a method to measure S

_{e}and establish a value for w.

_{MAN}in their instruction manuals, as shown in Table 2. The distance provided is based on the tests included in the standards, which, as already mentioned, neglect elastic elongation. The MCD value obtained experimentally is compared with the data provided by manufacturers (MCD

_{MAN}) and with the MCD

_{EN355}value obtained by applying standard method Equation (3). These checks are useful for determining the reliability of Equation (3) established in EN 355 [18] and, on the other hand, to ensure that the data provided by the manufacturer guarantees that the user will not hit the ground, or an obstacle, in a hypothetical fall. More important is to determine the reliability of the data provided by the manufacturers and by EN 355.

_{max}due to impact. A real value should be obtained through tests on each EAL prior to commercialization. Unfortunately, manufacturers do not provide information about this parameter or about tests performed on equipment that they commercialize. Given the lack of information in this regard, both from manufacturers and in the specialized literature [29], this study proposes the performance of experimental tests in order to measure the maximum elongation of the equipment (S

_{max}), plastic plus elastic elongation in the worst scenario that the EAL provides. Therefore, reliably obtain the MCD.

## 2. Materials and Methods

_{MAN}, the plastic component of EAL elongation (S

_{p}), and the distance from the feet to the attachment point of the user’s harness (w) shown in Table 2 are those included in the instruction manuals of the different manufacturers. It should be noted, from the outset, that the values provided by the manufacturers do not fulfill Equation (1).

_{p}), and, in three cases, the data provided corresponds to the maximum allowed by the standard (1.75 m in Europe), which raises doubts about its veracity. On the other hand, it should be noted that there is no unified criterion regarding the value of w, which is required to calculate the MCD Equation (1). Either the data are not provided or a value between 1.5–2 m is applied arbitrarily. Manufacturer B determines that it is the user who takes the value of w that he/she sees fit as a function of his/her own height. Given this dispersion of criteria, it is difficult for the user to be clear about MCD, and it is therefore probable that he/she does not know the minimum distance from an obstacle (the ground) at which an anchorage may be installed safely for the use of an FAS with an EAL.

_{m}) of the results were obtained directly using the software indicated above. To determine the Average Force (F

_{a}), the values between the first and last time that the value 3.3 kN appears in the curve [24] were taken.

_{p}is solved, it is substituted in Equation (4) and the Arrest Distance H is obtained.

_{f}= L + S

_{p}.

_{p}, it is possible to solve S

_{e}(elastic deformation) of Equation (6) (Figure 5).

_{e}= 4100 − 470 − D − L − S

_{p}.

## 3. Results

#### 3.1. Forces

_{a}Exp.) and maximum forces (F

_{m}Exp.). Shown also are the initial length of the equipment (L) and the final length (Lf) of the same measured at rest before and after impact, respectively.

_{a}) can be solved. The table shows the average theoretical unstitching force (F′

_{a}), calculated according to Equation (8):

^{2}); L is the length of the EAL (m); F′a is the average theoretical deployment force (N); S

_{p}is plastic elongation (m); S

_{e}is elastic elongation (m); S

_{max}is total elongation (m).

_{m}value above 6 kN, exceeding the injury threshold assumed by EN355 [18]. Test IX is deemed to be at the safety limit. These two items of equipment should not be available on the market because they do not meet the requirements of EN355 [18] and are, therefore, presumed to not comply with Regulation (EU) 2016/425 [37].

_{m}is, for example, 6.5 or 4.5 kN. The descriptive statistics for F

_{a}(8 samples) are: minimum, 4.127, first quartile, 4.207, median, 4.281, mean, 4.474, third quartile, 4.694, and maximum, 5.177 N. The Wilconxon test [39] can be used as an alternative to the parametric Student’s t-test. The Wilconxon test allows us to determine whether the median is equal to a known theoretical value. Table 5 shows the results obtained by applying the Wilcoxon test to our data, for the different null hypotheses of F

_{m}, from which it can be concluded that the median F

_{m}is lower than 5 kN with a significance of 5%. This follows from the p-value (0.0017) in this case, being the probability of obtaining test results at least as extreme as the observed ones. Therefore, the probability that the F

_{m}is 5 or higher is 0.0117. The text continues here.

_{a}Exp. data obtained in the laboratory with the Theoretical F′

_{a}(Equation (8)), the difference between them has been taken, since the data were two measurements from the same test and see whether there are significant differences. Table 6 shows the data that were the object of the study.

_{a}–F

_{a}Exp. are: minimum, −0.0540, first quartile, 0.2972, median, 0.3345, mean, 0.4228, third quartile, 0.4228, and maximum, 1.2370 N. In order to analyze this sample, it is interesting to know whether the distribution of the values of the mean forces obtained follow a normal distribution. Figure 8 compares the probability distributions of our sample with the normal distribution. Now, let us see if it is acceptable that the sample comes from a normal population.

_{a}–F

_{a}Exp. is significantly greater than zero, with a significance value less than 0.01.

_{a}and F

_{a}Exp. By quantifying the difference between F′

_{a}and F

_{a}Exp., it is concluded that F′

_{a}is valid for calculating F

_{a}Exp. F′

_{a}explains 90% of the variability present in F

_{a}Exp. (Linear regression of F′

_{a}and F

_{a}Exp. R-squared: 0.9077; F-statistic: 58.98; p-value: 0.000255).

_{m}, F

_{a}Exp. and the free fall height in each case, it is confirmed that there is no linearity between the two variables and that there are manufacturers that achieve lower impact forces at higher fall heights. The data have been ordered by free fall height for easier visual understanding.

#### 3.2. Elongations

_{p}in Table 7) is found in all cases below the 1.75 m, maximum allowable extension (X), required by EN 355 [18]. In the majority of the equipment, elastic deformation accounts for approximately 18% of the total, significantly less than plastic deformation; therefore, a test and regulatory requirement based solely on plastic elongation seem, at first glance, to be adequate.

_{max}is linear, the correlation between the two measurements being 0.85 (10 samples). The fall distance (free fall) explaining 72% of the variability observed in the S

_{max}. The adjustment coefficient between the two sets of data was 0.333 (the slope of the regression line), therefore, it can be concluded that the S

_{max}represents a third of the fall distance.

#### 3.3. Minimum Clearance Distance below Anchorage (MCD)

_{MAN}is the required distance according to the equipment manufacturer and MCDen355 is the required distance calculated according to EN 355.

_{EN355}, the real length (L) of the EAL’s measured in the laboratory was taken into account, not the one declared by the manufacturer. In order to unify criteria regarding the distance from the feet of an operator to the harness attachment point (w), the anthropometric data of the Spanish working population [40] published by the National Institute for Health and Safety at Work (INSST), were consulted. The parameter w was taken as the vertical distance from the support surface of the feet to the highest point of the acromion for a 99th percentile. The highest point of the acromion corresponds to the attachment point of the harness. Therefore, w is 1588 mm, this value being in line with Small (2011) [29]. The results from following the indications of EN 355 [18] and calculating MCD

_{EN355}according to Equation (2) are shown in Table 8.

_{MAN}. The non-parametric Wilkinson test supports the hypothesis that manufacturers are conservative, in other words, MCD < MCD

_{MAN}, with a significance level below 5%.

_{MAN}) with the distance calculated using the HSC (MCD) it is demonstrated that the distance provided by the manufacturer is insufficient to arrest the fall without the operator hitting the ground.

_{EN355}, is calculated and compared with the real one, MCD, obtained in the laboratory using an HSC as described in Equation (1), it can be seen that, in six out of the ten cases studied, the standard is removed from reality, putting the user of the equipment at risk. The standard calculation displays a difference, from a lack of safety perspective, of up to 928 mm, which would put the user at risk of hitting the ground or another obstacle. It is necessary that the standard reformulates the way of calculating MCD for FF 2 falls with a mass of 100 kg. In a practical way, it can be established that one meter must be added to the distance obtained in the application of EN 355. Therefore, MCD

_{EN355}+ 1 = MCD.

_{m}below 6 kN. For the equipment of tests II and VII, safety depends on the user installing the anchorage taking w (a distance between the harness attached to the user’s feet greater than 1363 mm and 903 mm, respectively).

## 4. Discussion

_{a}was calculated based on clause 4.1.102.2 of ANSI/ASSP Z359.13 [24] which establishes that the values between 2.2 kN be taken the first and second time they appear on the force-time graph, these values being for type E4 [19] low capacity absorbers, used for FF 1 falls and an F

_{m}below 4 kN [43]. In the case that concerns us, for FF 2 falls and assuming certain linearity, for F

_{m}(6 kN), values above 3.3 kN must be taken. The F

_{a}range thus obtained spans from 3.7 to 4.5 kN, higher than to be expected from those of the American Standards, which are between 2.67 and 3.6 kN described in Z259.16 and Z359.6 referring to E4. This is similar to the 3.2 to 4.7 kN range calculated by Goh [19] for absorbers according to AS/NZS 1891.1:2007 [25]. The F

_{a}calculated based on the principles of energy conservation differ by 12% from the experimental one. This could be influenced by the effects of heterogeneous tearing and by the absorption of energy of other components such as the tapes and connectors of the EAL’s, which has a slight effect on the Energy Conservation equation Equation (2) from a safety perspective. Therefore, in the absence of data provided by manufacturers, it can be used to calculate the F

_{a}. The F

_{a}is required, for example, to estimate the opening of an EA and to determine the obstacle-free distance below the anchoring in a FAS Equation (8).

_{max}) that ranges from 17 to 274%, which is an exaggeratedly wide range.

## 5. Conclusions

_{m}exceeds the threshold for injury established at 6 kN. For the rest of the equipment, it is around 5 kN or below. The forces obtained theoretically Equation (8) are 12% higher than those obtained experimentally. Therefore, Equation (8) is a good tool for calculating the F

_{a}with EAL’s certified under EN 355 [18].

_{a}) ranges from 3.7 to 4.5 kN, somewhat higher than in previous studies [19,38,41,43]. As expected, the fall height and the arrest force do not present linearity, in line with other studies [12,30,31,32]. At the same FF, the intrinsic characteristics (type and location of stitching) of each EAL have a significant influence on the arrest force value.

_{EN355}obtained according to EN 355 [18], by applying Equation (2). The authors propose not using this formula based solely on plastic elongation and the length of the equipment.

_{m}, F

_{a}, S

_{max}, S

_{p}and S

_{e}. With these data, a prevention technician charged with procuring the equipment can assess the purchase according to the safety and versatility offered by the equipment. An Engineer could perform the calculations required to determine the clearance distance below anchorage. At present, the data offered by the manufacturers do not allow a choice to be made based on the safety of the equipment.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**Frame corresponding to the maximum stretch moment for experiment VIII. Some auxiliary lines in the ground help to locate the point to measure the distance from it to the bottom of the ballast.

Standard | Test Mass m (kg) | Free Fall Distance h (m) | X (m) | F_{m} (kN) |
---|---|---|---|---|

ISO 10333-2:2000 TYPE1 | 100 | 1.8 | 1.2 | 4 |

NSI/ASSE Z359.13-2013 | 128 ^{1} | 1.83 | 1.2 | 8 |

ANSI/ASSE Z359.13-2013 | 128 ^{1} | 3.66 | 1.5 | 8 |

ISO 10333-2:2000 TYPE 2 | 100 | 4 | 1.75 | 6 |

AS/NZS 1891.1 2007 | 100 | 4 | 1.75 | 6 |

Z259.11.17 | manufacturer | manufacturer | 0.7~0.95 (X_{MAN} ^{2}) | 8 |

EN 355:2002 | 100 | 4 | 1.75 | 6 |

^{1}Conversion factor 1.1 is being used comparing rigid test weight to the human body (140 kg);

^{2}Maximum elongation that manufacturer declares.

Code | Type | Manufacturer | Connectors | L (m) | MCD_{MAN} (m) | S_{P} (m) | w (m) |
---|---|---|---|---|---|---|---|

I | Rope + EA | A | No | 2 | 5 | 1.75 | 1.5 |

II | Rope + EA | B | Yes | 2 | 4.75 + w ^{2} | 1.75 | - |

III | Rope + EA | C | No | 1 | 4.4 | - | - |

IV | Rope + EA | D | Yes | 1.1 | 4.2 | - | - |

V | Adjustable rope + EA | D | Yes | 2 | 6.2 | 1.2 | 2 |

VI | Adjustable rope + EA | D | Yes | 2 | 6.2 | 1.2 | 2 |

VII | Webbing + EA | B | Yes | 1.5 | 4.25 + w | 1.75 | - |

VIII | Elastic webbing | F | No | 1.7 | 6.5 | - | - |

IX | Elastic webbing + EA | D | Yes | 2 | 6.2 | 1.2 | 2 |

X | Wire + EA | D | No | 2 | 3 ^{1} | - | - |

^{1}The manufacturer of this equipment contemplates a use as a fall arrest device limited by the installation system to factor 1 falls (FF = 1). However, it has been tested under the same conditions as the rest of the devices.

^{2}w is the distance between harness attachment and the user’s feet.

Test | L (mm) | Lf (mm) | F_{m} Exp. (kN) | F_{a} Exp. (kN) | F′_{a} (kN) |
---|---|---|---|---|---|

I | 1770 | 2690 | 7156 | 4493 | 4439 |

II | 2030 | 3180 | 4237 | 3823 | 4121 |

III | 989 | 1152 | 4169 | 3951 | 4347 |

IV | 880 | 1263 | 5177 | 4504 | 5155 |

V | 1960 | 3130 | 4326 | 3795 | 4099 |

VI | 2010 | 3250 | 4220 | 3863 | 4001 |

VII | 1520 | 2390 | 4127 | 3820 | 4185 |

VIII | 1660 | 2470 | 4622 | 4172 | 4768 |

IX | 1430 | 1770 | 5995 | 5075 | 5372 |

X | 2070 | 2910 | 4911 | 4342 | 5579 |

Statistic | p-Value | |
---|---|---|

Kruskal–Wallis | 4.3636 | 0.03671 |

Hypothesized Median | Alternative Hypothesis | Statistic | p-Value | Value Null Hypothesized at 5% Sig | Value Null Hypothesized at 1% Sig |
---|---|---|---|---|---|

6 | <6 | 0 | 0.0039 | Reject | Reject |

5 | <5 | 2 | 0.0117 | Reject | Accept |

4.5 | <4.5 | 16 | 0.4219 | Accept | Accept |

Test | I | II | III | IV | V | VI | VII | VIII | IX | X |
---|---|---|---|---|---|---|---|---|---|---|

F_{a} Exp | 4.493 | 3.823 | 3.951 | 4.504 | 3.795 | 3.863 | 3.820 | 4.172 | 5.075 | 4.342 |

F′_{a} | 4.439 | 4.121 | 4.347 | 5.155 | 4.099 | 4.001 | 4.185 | 4.768 | 5.372 | 5.579 |

F′_{a}–F_{a} Exp | −0.054 | 0.298 | 0.396 | 0.651 | 0.304 | 0.138 | 0.365 | 0.596 | 0.297 | 1.237 |

Test | D (mm) | S_{p} (mm) | S_{e} (mm) | S_{max} (mm) | X (mm) | S_{e}/S_{max} × 100 |
---|---|---|---|---|---|---|

I | 705 | 920 | 235 | 1155 | 1750 | −20.35 |

II | 105 | 1150 | 345 | 1495 | 1750 | −23.08 |

III | 2033 | 563 | 45 | 607 | 1750 | −7.25 |

IV | 2282 | 383 | 85 | 468 | 1750 | −18.16 |

V | 315 | 1170 | 185 | 1355 | 1750 | −13.65 |

VI | 185 | 1240 | 195 | 1435 | 1750 | −13.59 |

VII | 1065 | 870 | 175 | 1045 | 1750 | −16.75 |

VIII | 1025 | 810 | 135 | 945 | 1750 | −14.29 |

IX | 1090 | 340 | 770 | 1110 | 1750 | −69.37 |

X | 610 | 840 | 110 | 950 | 1750 | −11.58 |

Test | MCD | MCD_{MAN} | MCD_{EN355} | Difference MCD_{MAN}−MCD | Difference MCD_{EN355}−MCD |
---|---|---|---|---|---|

I | 5513 | 5000 | 5460 | −513 | −53 |

II | 6113 | 4750 + w | 6210 | w ≥ 1363 | 97 |

III | 4184 | 4400 | 3541 | 216 | −643 |

IV | 3936 | 4200 | 3143 | 264 | −793 |

V | 5903 | 6200 | 6090 | 297 | 187 |

VI | 6033 | 6200 | 6260 | 167 | 227 |

VII | 5153 | 4250 + w | 4910 | w ≥ 903 | −243 |

VIII | 5193 | 6500 | 5130 | 1307 | −63 |

IX | 5128 | 6200 | 4200 | 1072 | −928 |

X | 5608 | 6000 | 5980 | 392 | 372 |

Test | S_{p} | S_{max} | EN 355 | % S_{p} | % S_{max} |
---|---|---|---|---|---|

I | 920 | 1155 | 1750 | 90 | 52 |

II | 1150 | 1495 | 1750 | 52 | 17 |

III | 563 | 607 | 1750 | 211 | 188 |

IV | 383 | 468 | 1750 | 357 | 274 |

V | 1170 | 1355 | 1750 | 50 | 29 |

VI | 1240 | 1435 | 1750 | 41 | 22 |

VII | 870 | 1045 | 1750 | 101 | 67 |

VIII | 810 | 945 | 1750 | 116 | 85 |

IX | 340 | 1110 | 1750 | 415 | 58 |

X | 840 | 950 | 1750 | 108 | 84 |

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## Share and Cite

**MDPI and ACS Style**

Carrión, E.Á.; Ferrer, B.; Monge, J.F.; Saez, P.I.; Pomares, J.C.; González, A.
Minimum Clearance Distance in Fall Arrest Systems with Energy Absorber Lanyards. *Int. J. Environ. Res. Public Health* **2021**, *18*, 5823.
https://doi.org/10.3390/ijerph18115823

**AMA Style**

Carrión EÁ, Ferrer B, Monge JF, Saez PI, Pomares JC, González A.
Minimum Clearance Distance in Fall Arrest Systems with Energy Absorber Lanyards. *International Journal of Environmental Research and Public Health*. 2021; 18(11):5823.
https://doi.org/10.3390/ijerph18115823

**Chicago/Turabian Style**

Carrión, Elena Ángela, Belén Ferrer, Juan Francisco Monge, Pedro Ignacio Saez, Juan Carlos Pomares, and Antonio González.
2021. "Minimum Clearance Distance in Fall Arrest Systems with Energy Absorber Lanyards" *International Journal of Environmental Research and Public Health* 18, no. 11: 5823.
https://doi.org/10.3390/ijerph18115823