Basic Statistical Properties of the Knot Efficiency
A knot is the weakest point of every rope, and the <i>knot efficiency</i> measures the portion of original rope strength taken away by the knot. Despite possible safety implications, surprisingly little attention has been paid to this life-critical quantity in research papers. Knot effic...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/9/1926 |
| _version_ | 1797481874696699904 |
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| author | Ján Šimon Branislav Ftorek |
| author_facet | Ján Šimon Branislav Ftorek |
| author_sort | Ján Šimon |
| collection | DOAJ |
| description | A knot is the weakest point of every rope, and the <i>knot efficiency</i> measures the portion of original rope strength taken away by the knot. Despite possible safety implications, surprisingly little attention has been paid to this life-critical quantity in research papers. Knot efficiency is directly immeasurable and the only way to obtain it is by calculation from rope breaking strength. However, this complication makes room for a wide spectrum of misleading concepts. The vast majority of authors do not treat knot efficiency as a random variable, and published results mostly suffer from incorrect statistical processing. The main goal of the presented paper is to fix this issue by proposing correct statistical tools needed for knot efficiency assessment. The probability density function of knot efficiency <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ψ</mi><mo>(</mo><mi>η</mi><mo>)</mo></mrow></semantics></math></inline-formula> has been derived in general, as well as for normally distributed breaking strength. Statistical properties of knot efficiency PDF have been discussed, and a less complex approximation of knot efficiency PDF has been proposed and investigated. |
| first_indexed | 2024-03-09T22:20:48Z |
| format | Article |
| id | doaj.art-09e374f5fb36421480b11965375c7e4d |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T22:20:48Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-09e374f5fb36421480b11965375c7e4d2023-11-23T19:13:21ZengMDPI AGSymmetry2073-89942022-09-01149192610.3390/sym14091926Basic Statistical Properties of the Knot EfficiencyJán Šimon0Branislav Ftorek1Faculty of Mechanical Engineering, University of Žilina, Univerzitná 8215/1, 010 26 Žilina, SlovakiaFaculty of Mechanical Engineering, University of Žilina, Univerzitná 8215/1, 010 26 Žilina, SlovakiaA knot is the weakest point of every rope, and the <i>knot efficiency</i> measures the portion of original rope strength taken away by the knot. Despite possible safety implications, surprisingly little attention has been paid to this life-critical quantity in research papers. Knot efficiency is directly immeasurable and the only way to obtain it is by calculation from rope breaking strength. However, this complication makes room for a wide spectrum of misleading concepts. The vast majority of authors do not treat knot efficiency as a random variable, and published results mostly suffer from incorrect statistical processing. The main goal of the presented paper is to fix this issue by proposing correct statistical tools needed for knot efficiency assessment. The probability density function of knot efficiency <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ψ</mi><mo>(</mo><mi>η</mi><mo>)</mo></mrow></semantics></math></inline-formula> has been derived in general, as well as for normally distributed breaking strength. Statistical properties of knot efficiency PDF have been discussed, and a less complex approximation of knot efficiency PDF has been proposed and investigated.https://www.mdpi.com/2073-8994/14/9/1926knot efficiencyprobability density functioncumulative distribution functionstatistical properties |
| spellingShingle | Ján Šimon Branislav Ftorek Basic Statistical Properties of the Knot Efficiency Symmetry knot efficiency probability density function cumulative distribution function statistical properties |
| title | Basic Statistical Properties of the Knot Efficiency |
| title_full | Basic Statistical Properties of the Knot Efficiency |
| title_fullStr | Basic Statistical Properties of the Knot Efficiency |
| title_full_unstemmed | Basic Statistical Properties of the Knot Efficiency |
| title_short | Basic Statistical Properties of the Knot Efficiency |
| title_sort | basic statistical properties of the knot efficiency |
| topic | knot efficiency probability density function cumulative distribution function statistical properties |
| url | https://www.mdpi.com/2073-8994/14/9/1926 |
| work_keys_str_mv | AT jansimon basicstatisticalpropertiesoftheknotefficiency AT branislavftorek basicstatisticalpropertiesoftheknotefficiency |