An Assessment Of The Strength Of Knots And Splices Used As Eye Terminations In A Sailing Environment, Sports Engineering (2006)

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911 Sports E77 McLaren 27706 238 pm Page 1 An assessment of the strength of knots and splices used as eye terminations in a sailing environment KA Milne and AJ McLaren Department of Mechanical Engineering University of Strathclyde Glasgow UK Abstract Research into knots splices and other methods of forming an eye termination has been limited despite the fact that they are essential and strongly affect the performance of a rope The aim of this study was to carry out a comprehensive initial assessment of the breaking strength of eye ter minations commonly used in a sailing environment thereby providing direction for further work in the field Supports for use in a regular tensile testing machine were specially developed to allow indi vidual testing of each sample and a realistic spread of statistical data to be obtained Over 180 break tests were carried out on four knots the bowline double bowline figureofeight loop and perfection loop and two splices threestrand eye splice and braidonbraid splice The factors affecting their strength were investigated A statistical approach to the analysis of the results was adopted The type of knot was found to have a significant effect on the strength This same effect was seen in both types of rope construction threestrand and braidonbraid Conclusions were also drawn as to the effect of splice length eye size manufacturer and rope diameter on the breaking strength of splices Areas of development and further investigation were identified Keywords break knot rope sailing splice strength Introduction such as guard rails which are present for reasons of safety The running rigging is used to hoist andor Ropes are widely exploited in sailing Their use on control the sails Halyards are used to hoist the sails yachts may be broadly divided into two categories into position sheets are attached to the sails and are namely the standing and running rigging Standing used primarily to control the angle of the sails to the rigging consists of the structural components that boats centreline and therefore the wind The running support the mast and spars together with equipment rigging will also generally include ropes that are used to control the position of moveable components of the Correspondence address boat which are used for fine adjustment of the sails Dr AJ McLaren Many different methods have evolved that allow Department of Mechanical Engineering one rope to be attached to another to a fixed point or University of Strathclyde to a sail One common method is to create an eye with Glasgow UK a knot or a splice or by binding or stitching the end of Tel 44 0 141 548 3104 the rope to the standing part with twine This last Email method is called seizing A knot is defined as a way of 2006 isea Sports Engineering 2006 9 113 1911 Sports E77 McLaren 27706 238 pm Page 2 The strength of knots and splices KA Milne and AJ McLaren joining or securing lengths of rope thread or other strand is discussed by Saitta et al 1999 This is more strands by tying the material together or around of interest to the polymer scientist due to the micro itself A splice is defined as a way to join ends of ropes scopic scale of the fibres in question Wu 1993 by intertwining strands Unlike knots a specific splice considered friction and slippage between the strands is suitable only for a specific type of rope of polymeric ropes and made some observations con The ropes used in sailing are similar in appearance cerning slippage in end terminations to those utilised by climbers but the materials used A particular method for forming an eye termination are different Climbing ropes are designed to absorb might be selected because it is easy to form or release shock loads in the event of a fall and are of relatively because it holds securely because it is compact and low stiffness By contrast sailing ropes need to have will slide over apparatus easily or because it is consid high stiffness to preserve precise control by minimis ered relatively strong The presence of the eye ing elastic extension Whereas it is generally accepted termination can have a significant effect upon the that climbing ropes do not fail either at a knot or fatigue life of a line its response under dynamic generally unless loaded over an edge Schubert 2002 loading and its static breaking load While much Bailie 2000 sailing ropes are subject to failure par experimental and analytical work has been conducted ticularly near the ends where high degrees of wear and upon synthetic ropes knowledge about eye termina chafe are possible during extended use In addition tions is limited Advice on how to create eye sailing ropes are subjected to high static loadings terminations is generally based upon oneoff tests or upon which considerable dynamic fluctuations are tradition There is no definitive guide about which superimposed These ropes are also prone to ultra knot to choose or how to form a splice in order to get violet attack due to prolonged exposure in the marine the highest splice efficiency which is defined as the environment ratio of the breaking strength with the eye to the rope A wealth of information has been published con strength cerning the suitability of the various methods of Limited mathematical modelling has been carried forming a loop termination This information is out Maddocks Keller 1987 propound the available in books specifically dedicated to knots and mechanics of some simple hitches while Leech 2003 splices eg Jarman 2000 Shaw 2004 and Pawson models the stresses in some commonly used splices 2001 It may also be found in standard sailing However such models are founded upon numerous textbooks Cunliffe 2000 Recent articles in the assumptions and although they help to understand sailing press demonstrate the continuous development the mechanics involved they do not provide accurate of ropes and splicing techniques James 2003 predictions of the breaking loads or the effect of Pawson 2005 changing one of the huge number of variables such as The published research on polymeric ropes is the maker of the eye referred to hereafter as the man somewhat limited Manes 2002 has reviewed work ufacturer rope type eye size length of the working carried out on the structure of ropes for rock climbing end or the type of loading This project has attempted Leech 2002 considers the hierarchical structure built to carry out an assessment of the static strength of up from individual strands bundles and subropes to knots and splices used in a sailing environment and the make the overall cable He also considers the frictional factors that affect this strength load transfer between the elements of the rope Pan The aim of this study was to carry out a compre Brookstein 2002 have reviewed the recent work that hensive preliminary assessment of the static breaking has been carried out on the modelling of polymer strength of several common eye terminations These ropes included four knots the bowline double bowline The theory of knots has stimulated some interest in perfection loop and figureofeight loop and two the mathematics community This is typified by the splices the threestrand eye splice and the braidon Fields Medal winning work of Vaughan Jones as braid splice The effect of various factors upon the reviewed by King 1986 At a fundamental level the breaking strength of the line was investigated and the effect of a knot on the strength of a single polymer practical relevance of the results discussed 2 Sports Engineering 2006 9 113 2006 isea911 Sports E77 McLaren 27706 238 pm Page 3 KA Milne and AJ McLaren The strength of knots and splices Experimental procedure threestrand eye splice was manufactured from the prestretched rope while a braidonbraid splice was This section describes the programme of experimental manufactured from the braidonbraid rope The eye work First the determination of the initial baseline size was defined as the inside length of the eye strength of each rope type and diameter is described measured with a flexible tape The working end is the Secondly the preparation of knots and the method by unloaded end of the rope which eye splices were prepared using the specific All knot and splice samples were finished in the method appropriate to each rope type is discussed same manner A mark was made 13 m along the Thirdly the apparatus used to test the loops is standing part of the rope measuring from the crotch detailed Finally the procedure used to test the of the eye The rope was whipped either side of the strength of the knots and splices and the means by mark cut and the end sealed by melting which data were recorded is reviewed Knots Determination of rope strength The four knots investigated were the bowline double Two different commercially available types of rope bowline figureofeight loop and perfection loop were used to make the knots and splices Both rope shown in Fig 1 Each sample was prepared with a types were manufactured by Liros Ropes Ltd 100 mm working end and a 150 mm internal eye size Germany The first was a 16plait braidonbraid polyester rope sold as the LIROS Top Cruising rope Threestrand eye splice The second was a threestrand twisted prestretched polyester rope sold as the LIROS Prestretch rope In The eye splices were manufactured as shown in Fig 2 the course of the project ropes of 6 8 and 12 mm Jarman 2000 gives a stepbystep guide of how to do diameter were used this The standard eye splice had four tucks and a The breaking loads of all diameters of threestrand 15 cm internal eye size It was manufactured from an rope were found Only the breaking load of the 8 mm 8 mm diameter rope by the author Once the splice braidonbraid rope was found due to the limitations was completed the working ends were cut to a length of the project The rated breaking load was taken for of about 5 mm The splice was rolled under foot three the 6 and 12 mm braidonbraid ropes The testing times to settle it was carried out by Marlow Ropes now part of Bridon The following factors were varied during the study International Ltd on an AJT horizontal tensile test to find their effect on spice efficiency machine as specified in BS EN 919 1995 For each number of tucks sample set three samples were tested and the mean manufacturer static break load was calculated The results are shown eye size in Table 1 rope diameter The factors were varied one at a time to allow direct Sample preparation comparison of the results This method did not The knots were made using both types of 8 mm rope however allow of the factors to be Splices are specific to the type of rope construction A studied Splices with two three four and eight tucks were Table 1 Average breaking load for the four types of rope tested by tested Samples were prepared by three different man Marlow Ropes now part of Bridon International Ltd ufacturers two adult males and one adult female all of Type of rope Diameter mm Average break load kN whom had little previous experience of making splices 3strand 6 922 The different eye sizes tested were 8 15 and 25 cm 3strand 8 1256 8 cm was the smallest eye that could pass over the 3strand 12 2923 shackle used in the test rig Rope diameters of 6 8 and Braidonbraid 8 1442 12 mm were tested 2006 isea Sports Engineering 2006 9 113 3911 Sports E77 McLaren 27706 238 pm Page 4 The strength of knots and splices KA Milne and AJ McLaren a b c d Figure 1 Knots investigated in the current work a bowline b double bowline c figureofeight loop d perfection loop Figure 2 Sequence of operations involved in the manufacture of an eye splice in threestrand prestretched rope After Jarman 2000 Braidonbraid eye splice Again eye sizes of 8 15 and 25 cm and rope The braidonbraid splices were manufactured as diameters of 6 8 and 12 mm were tested Variation of shown in Fig 3 Again the reader is referred to Jarman the splice length for a braidonbraid splice was more 2000 for detailed instructions difficult Unlike the threestrand eye splice the The factors considered for this splice were internal construction of the braidonbraid splice shown in Fig 4 has an infinite number of possible splice length variations Dimension OA dictates the final length of eye size the splice Dimension DE dictates the length for rope diameter which the sheath passes through the core Dimension 4 Sports Engineering 2006 9 113 2006 isea911 Sports E77 McLaren 27706 238 pm Page 5 KA Milne and AJ McLaren The strength of knots and splices CD is critical in the construction of the splice as it extended Seven different splice constructions were dictates the amount of sheath that is pushed back If it tested These are labelled as Types I to VII Type I is is too short it becomes very difficult to milk the sheath the standard as described in Jarman 2000 Type II over the splice from O to A Dimension CD could varied the relative length of CD to OA Type III varied therefore have an effect upon the breaking strength of the absolute length of the splice Types IV to VII the rope If it is very short the sheath has to be strained varied the amount of core overlap in the internal con excessively to make it pass over the splice This struction The variations are summarised in Table 2 process involves a lot of abrasion and Fig 5 Fid implies the length of one Swedish fid Initially just two samples were tested for each the hollow tool shown in Fig 3 which is approxi variation in splice length Where differences in mately 14 cm For accuracy the length was measured breaking load were significant the sample sets were with a tape measure B B E D C A O A B O E A D B D C Figure 3 Sequence of operations involved in the manufacture of a braidonbraid splice The fid referred to in the text and in Table 2 is the metal needle approximately 14 cm in length shown in the Figure After Jarman 2000 Table 2 Splice constructions for braidonbraid splices Here the geometry is characterised by the lengths of rope between the significant points labelled in Figs 3 and 4 Fid refers to the length of a Swedish fid the 14 cm long splicing needle shown in Fig 2 Splice length OA DE CD Type I 1 fid 2 3 fid 1 fid Type II 1 fid 1 3 fid 1 fid Figure 4 Internal construction of the braidonbraid splice showing Type III 1 2 fid 1 3 fid 1 2 fid significant points in the structure The distances between these Type IV See Fig 5 points define the geometry of the splice in Table 2 Type V See Fig 5 Type VI See Fig 5 Type VII See Fig 5 2006 isea Sports Engineering 2006 9 113 5911 Sports E77 McLaren 27706 238 pm Page 6 The strength of knots and splices KA Milne and AJ McLaren Figure 5 Internal construction of Type IV to VII splices showing significant points in the structure The distances between these points define the geometry of the splice in Table 2 Test apparatus Three rope manufacturers were contacted to determine the method by which eye splice strengths are currently measured The companies concerned were Location of New England Ropes Fall River MA USA T stopper knot DaCosta Liros Ropes Lichtenberg Germany K Rosenberger Marlow Ropes Hailsham UK T Scofield now part of Bridon International Ltd The current method for testing eye terminations in industry involves creating a line with an eye in each end The eyes are then looped over pins in a tensile testing machine and the line is loaded at a constant crosshead velocity until failure occurs The line will always fail at its weakest point Pan 1996 which if To knot or the rope has been manufactured correctly should lie at spice one of the eye terminations The major limitation of this test method is that the breaking load of the weaker eye is invariably measured Statistically then a set of data obtained from this test will be inherently flawed The method adopted for this work an adaptation of the support used to drop test dynamic moun taineering ropes BS EN 892 1996 allowed each Figure 6 Upper support Utilised in the present work for the individual eye termination to be tested The eye ter attachment of the standing part of the rope to the tensile testing mination was looped over a shackle that was attached machine The position of the stopper knot and eye are indicated 6 Sports Engineering 2006 9 113 2006 isea911 Sports E77 McLaren 27706 238 pm Page 7 KA Milne and AJ McLaren The strength of knots and splices to the moving crosshead of a tensile testing machine The breaking load was defined as the highest load As illustrated in Fig 6 the standing part of the rope reached in the rope prior to complete failure In a real was wrapped around a 100 mm diameter drum passed life situation the load would not be relaxed after the through a clamp and then a stopper knot was tied in initial failure and having reached the maximum the end The stopper knot prevented the rope from supported load catastrophic failure would follow For slipping through the clamp under tension The upper the threestrand prestretched rope the maximum and lower supports were carefully designed such that supported load was attained just before the first strand neither presented a greater weakness in the rope than broke After this initial failure relaxation of the twisted the eye termination itself there were no sharp edges structure occurred and the load in the line reduced and the rope did not follow any tight bends over the significantly The other two strands would subse supports Furthermore to prevent failure at the quently break at much lower loads In comparison in stopper knot the rope was wrapped at least twice the braidonbraid splices the core of the rope failed around the drum thereby reducing the tension in the first The sheath finally failed at an even higher load rope at the clamp A test was considered valid when An analogue plotter a dial gauge and a computer the rope broke at the eye termination program which took measurements at 3 second The disadvantage of this method was that as the intervals logged the breaking load and elongation rope could not be totally constrained at the drum it The data obtained from the computer is given here did not allow accurate measurement of the elongation These measurements were the most precise to the The measured value of elongation included the strain nearest 001 lb or 022 N but data was captured only for the entire length of rope from the eye termination once every three seconds meaning that the maximum to the clamp and any slack that had existed in the set breaking load recorded was marginally lower than the up Beddingin loading of the sample prior to the actual maximum breaking load All values were main run to a value well below its breaking strength verified against those obtained from the analogue was used to take up the slack and thereby limit the plotter and the dial gauge extent of this problem Results and analysis Sample testing The samples were tested in a Tinius Olsen 81000 This section presents an analysis of the results of the vertical tensile testing machine with a load capacity of tests carried out First a description of the statistical 200 000 lb 4325 kN and a maximum stroke of 2 m techniques utilised is presented Secondly a comparison in order to find their breaking load A mark was made between the strengths of the four knots is discussed on each sample 300 mm from the crotch of the eye Next the factors that affect the strength of threestrand The standing part of the sample was wrapped twice eye splices are analysed Finally the variation in around the drum and the mark was aligned with its strength of braidonbraid eye splices is described horizontal longitudinal axis The standing part was then passed through the clamp and a stopper knot was Statistical analysis tied in the end The upper support was clamped into The inherent variance in the breaking strength of position in the tensile testing machine The eye termi ropes is significant Ropes are discontinuous struc nation was threaded through a shackle attached to the tures manufactured by the twisting or braiding of moving crosshead yarns of fibre The tensile strength of a given length of The samples were beddedin by increasing the load rope is dependent upon many factors including the to 10 of the ropes rated breaking load three times chemistry of the fibres the manufacturing method except for Type VII braidonbraid splices where the the number of slack and damaged fibres present from failure load was too unpredictable Each sample was manufacture Phoenix 1979 and the type of rope then loaded until failure by applying a constant construction Further variability is introduced by crosshead speed of 1 mms The experiment was human error when an eye termination is made in a repeated at least five times for each sample set rope There are also errors in the testing technique 2006 isea Sports Engineering 2006 9 113 7911 Sports E77 McLaren 27706 238 pm Page 8 The strength of knots and splices KA Milne and AJ McLaren These factors are difficult to control The conse ANOVA assumes that the population distribution is quence is that no two samples will be exactly the same normal that the observations are independent and and there will be random variance in the measured that except for variance caused by the factor variance breaking loads One alternative is to try to control is the same at each treatment level each level of these factors However within the limits of this variation of the factor These assumptions were project this was impracticable Further on the basis verified by examining plots of the residuals The that such errors would exist in any eye termination analysis was carried out using the MINITAB created in the real world it was decided that it was in computer programme fact essential to include these variations so that the real significance of any results could be demonstrated However drawing conclusions from data sets with Knots such a degree of variance can become very difficult A The standing part of the rope as it exits an eye will statistical approach was therefore adopted carry the entire load The working or free end will The sample mean and so the average knot or splice carry no load The load is transferred from the efficiency were calculated for each sample set Only the standing part to the working part through the knot or efficiency is quoted here Knot efficiency is defined as splice until the load is shared equally at the crotch Load transference occurs through friction and contact line strength with knot knot efficiency between the different parts of the rope In a knot line strength because of the complex geometry the load decreases The sample standard deviation was also calculated in suddenly where parts of the rope come into contact order to find the estimated standard error ESE of the Maddocks and Keller 1987 data The ESE indicates how representative the sample The mechanisms of failure in an eye are extremely mean is of the population mean The highest ESE for complex In any length of rope the shortest fibres will any sample set was calculated as 451 of the average initially take the entire load and fail first The load will breaking load however this was for a particularly then redistribute and can be increased further until the unpredictable sample set The next highest ESE was longer fibres start to fail Failure occurs catastrophi 544 most of the errors were around 3 It was cally when a certain number of fibres have failed In an concluded that the sample mean was a sufficiently eye the fibres fail due to stress created by contact accurate point estimate of the population mean friction or bending or by abrasion Abrasion occurs as The effect of varying a factor was initially analysed the knot tightens fibres both slide over one another by comparing the means and spreads of sample data and move across one another at an angle in a cutting Even though trends appeared it was difficult to state action Leech 2003 objectively whether the factor had an effect due to the The position of failure of the knots was observed degree of variance in the results A oneway analysis of with the aid of a highspeed camera Both the figure variance ANOVA was carried out in these cases to ofeight loop and the perfection loop failed just where allow an objective decision to be made the standing part enters the body of the knot as shown Montgomery et al 2001 give a detailed explana in Fig 7 The position of failure of the bowline and tion of ANOVA and hypothesis testing The null double bowline was not clear It appeared to fail at the hypothesis posed was that changing the factor had no first bend after the standing part enters the knot effect Using a statistics programme the Pvalue However failure occasionally occurred in other 0P1 for the sample set was calculated In general if positions Failure where the standing part enters the the Pvalue is small then the evidence against the null knot makes sense the entire standing part of the rope hypothesis is very strong It can be concluded that the will see the entire load but at the point of entry factor in question does affect the breaking load of the stresses due to contact and friction are superimposed rope If the Pvalue is large then the evidence for the As shown in Table 3 the general trend in the null hypothesis is strong It can be concluded that the breaking load was the same for both the threestrand factor does not affect the breaking load of the rope and the braidonbraid rope the figureofeight loop 8 Sports Engineering 2006 9 113 2006 isea911 Sports E77 McLaren 27706 238 pm Page 9 KA Milne and AJ McLaren The strength of knots and splices Figure 7 The ellipses indicate the observed positions of failure of the four knots These are from left to right bowline double bowline figureofeight loop perfection loop was the strongest by a significant margin the perfec to the clew of sails by using a single bowline as it is tion loop the weakest and there was little difference easy to tie and untie quickly During sail changes speed between the bowline and the double bowline Analyses is important so strength and security are sacrificed In of variance were carried out to see if changing the knot rock climbing circles the figureofeight loop is the had any significant effect upon the breaking load The knot of choice for climbers when they attach the rope difference between the bowline and the double end to their harness In this case they clearly value bowline was found to be statistically insignificant with security and strength above all other considerations a Pvalue of 0346 for knots made in threestrand rope and a Pvalue of 0365 for braidonbraid rope the Threestrand eye splice knots are practically In a splice unlike a knot the load transference will In general then it was the knots with tighter bends occur continuously along its length For both of the and more numerous crossovers that proved to be the splices observed failure occurred at the very end of weakest The figureofeight loop is considerably the splice Many of the splices had efficiencies greater stronger than the others Sailors generally attach sheets than 1 suggesting that the presence of the splice increases the strength of the rope However it was Table 3 Results of breaking strength tests on knots formed in the concluded that this could not be the case as the rope threestrand prestretched and braidonbraid rope invariably failed at the splice rather than at any other In each case knot efficiency is defined as breaking strength of the point Splice efficiencies greater than 1 must be knot breaking strength of the rope alone anomalous The rope used to determine the rope Knot type Threestrand rope Braidonbraid strength was purchased almost a year after the bulk of Knot efficiency Knot efficiency the knot and splice testing was carried out The low Bowline 066 062 rope strength may simply be a result of the variance in Double bowline 063 064 rope strength between different batches If the study Perfection loop 060 055 were to be repeated the rope strength of the original Figureofeight loop 076 084 batch would be tested at the outset 2006 isea Sports Engineering 2006 9 113 9911 Sports E77 McLaren 27706 238 pm Page 10 The strength of knots and splices KA Milne and AJ McLaren Variation of the number of tucks the point of failure would therefore depend upon the The splices with three four or eight tucks failed by geometry rather than the splice length breaking The splices with only two tucks failed by slipping This observation was reflected in the calcu Variation of the manufacturer lated splice efficiencies listed in Table 4 The longer The results for variation of the manufacturer ie the splices all had extremely high efficiencies with very person making the splice are presented in Table 5 An little variance between them whereas a twotuck analysis of variance was carried out which showed that splice could support only 73 of the ropes rated the breaking loads are independent of the splice man breaking strength This is only comparable to the ufacturer P 0641 It is noted that all the strength of the stronger knots It is a measure of the manufacturers had little experience of splicing and relative security afforded by splicing as compared to therefore it is suggested that further testing be carried knots that even twotuck splices are of similar strength out perhaps involving professionals It is thought to the best knot tested However again it is noted that unlikely however that a professionals splice would be a knot is often preferred for ease of tying and untying stronger than that of an amateur so long as the splice Failure by slipping probably occurs due to dilation geometry was correctly formed in both cases This is of the rope during loading Most continuous materials significant since it indicates that any reasonably exhibit a Poissons ratio effect when loaded In ropes competent person can make threestrand splices that the fibres not only contract radially but they move achieve the maximum possible strength together changing the shape of the strands to use up the least possible space If this effect is not comple Variation of the eye size mented by an increase in the resisting frictional forces The results for variation of the eye size are presented then the splice can simply unravel The fact that this in Table 6 A trend was apparent an increase in eye occurs below a certain number of tucks implies the size appeared to cause a slight decrease in splice effi existence of a critical splice length ciency ANOVA of the data did not strongly support It was hypothesised that above this critical splice the existence of a trend The Pvalue was 0277 There length an increase in the number of tucks had no effect is therefore a possibility that breaking load varies with upon the breaking load An analysis of variance was eye size but not substantially More extensive testing at carried out on the splice data for three four and eight more treatment levels would need to be carried out tucks The resulting Pvalue was 0693 supporting the before a strong conclusion could be made It is not hypothesis This seems logical The splices that fail by obvious why the eye size would affect the splice effi breaking do so at the top of the splice At this point the ciency as the angle of entry of the first tuck does not rope strands are carrying the full line tension very little affect the geometry of the developed splice load transference to the splice strands has occurred Furthermore the presence of the splice strands distorts the rope geometry so that the tension in the strands at Variation of the rope diameter this point is greater than that in the undisturbed line Variation of the rope diameter gave unexpected results above the splice Leech 2003 The loads developed at These are summarised in Table 7 The 8 mm 4 tuck Table 4 Effect of variation of number of tucks on the splice Table 5 Effect of variation of manufacturer the individual making efficiency of threestrand prestretched ropes the splice on the splice efficiency of threestrand prestretched ropes Number of tucks Splice efficiency Splice efficiency computer analogue plotter Manufacturer Splice efficiency Splice efficiency computer analogue plotter 2 073 074 3 107 109 Female 1 108 110 4 108 110 Male 1 106 108 8 110 112 Male 2 106 107 10 Sports Engineering 2006 9 113 2006 isea911 Sports E77 McLaren 27706 238 pm Page 11 KA Milne and AJ McLaren The strength of knots and splices Table 6 Effect of variation of eye size on the strength of splices in Table 7 Effect of variation of rope diameter on the strength of prestretched threestrand ropes splices in threestrand prestretched ropes Rope densities per unit length for each diameter are also shown Eye size cm Splice efficiency Splice efficiency computer analogue plotter Rope diameter Splice efficiency Splice efficiency Rope density per mm computer analogue plotter unit length kgm2 8 111 113 15 108 110 6 063 065 113882 25 105 107 8 104 110 126328 12 083 084 114945 splice had an efficiency of 104 but 4 tuck splices Table 8 Effect of variation of splice length on the efficiency of braidonbraid splices made from the 6 mm and 12 mm ropes were both con siderably weaker with splice efficiencies of 63 and Splice length Splice efficiency Splice efficiency 83 respectively It was expected that if the splice computer analogue plotter geometries the pitch ratio of fibre diameter to rope Type I 098 098 diameter and number of fibres per strand for different Type II 103 104 diameters of rope were identical then the splice effi Type III 100 102 ciency would be the same However as this was not the Type IV 097 101 case and the same diameter fibres are used to manufac Type V 099 100 ture all diameters of rope it was expected that the rope Type VI 082 084 Type VII 015 024 diameter might have an effect upon the breaking load However there is no obvious trend in these results The packing ratio of a rope is defined as the ratio of that changing length CD may affect the splice effi the rope density to the material density Leech 1987 ciency as discussed in the sample preparation section It was assumed that the material density was constant but testing of more samples at more lengths of CD The rope densities per unit length were calculated for would be required the 6 8 and 12 mm diameter ropes and are listed in One of the five Type VI samples failed by slipping Table 7 alongside the splice efficiencies An increase in one failed by breaking and the remaining three failed by packing ratio corresponds to an increase in splice effi a combination of slipping and breaking In the latter ciency This is in agreement with the results predicted case the core failed at point A shown in Fig 4 and the by Leech 2003 for the Admiralty splice However the sheath slipped out Despite the different failure modes effect here is far more pronounced More extensive the failure load was consistent the mean splice effi testing would be required to fully understand the effect ciency was 82 compared to around 100 for Types I and of various factors to V splices with an estimated standard error of 458 All Type VII samples failed by slipping at consider Braidonbraid splice ably lower loads Interestingly the variance in failure Variation of splice length load for these samples was large the estimated The results of changing the splice length are reported standard error as a percentage of the mean rope in Table 8 As with the threestrand splices two breaking load was 45 different failure modes were observed Types I to V Only the splices with the shortest internal overlap Fig 4 and Fig 5 failed by breaking at the top of the failed by slipping It is obvious then that the overlap is splice At this point the load in the rope is highest and essential for both maintaining the geometry of the amplified by the disturbance in the rope geometry splice and developing friction that resists slippage The ANOVA for Types I to V give a Pvalue of 0365 upon loading The length OA appears to be more suggesting that the variation of the splice construction critical in preventing slippage reducing the length of has no effect on the breaking load core threaded through the eye as was done for Type An ANOVA for Types I and II splices alone was IV and V splices has little effect on its own A combi carried out giving a Pvalue of 0147 This suggests nation of a short OA and a short overlap in the eye as 2006 isea Sports Engineering 2006 9 113 11911 Sports E77 McLaren 27706 238 pm Page 12 The strength of knots and splices KA Milne and AJ McLaren with Type VII splices invariably results in failure Conclusions through slipping at very unpredictable loads When considering methods of making eye termina In general then the braidonbraid splice behaves tions for a sailing environment it is very unlikely that similarly to the threestrand splice Above a certain an improvement of a few percent in the breaking load splice length the sample fails by breaking and the will be sufficient to encourage the adoption of breaking load is independent of the construction different manufacturing practices This is particularly Below a certain splice length the sample fails by true when general variance due to the rope itself can slipping In this case the failure load is more unpre far outweigh such a small gain It is therefore inadvis dictable than for the threestrand rope possibly able to spend excessive amounts of time determining because of the more continuous nature of the splice whether the eye size for example definitely affects the Variation of eye size average breaking load of a threestrand eye splice The results of variation of eye size are shown in Table especially when the eye size is to a large extent 9 The ANOVA carried out on the data for variation dictated by the purpose of the eye termination anyway of the eye size gave strong evidence to support the null From this point of view the most interesting results hypothesis ie it has no effect upon breaking load of the investigation have been This splice geometry is radically different from that The demonstration that there is no difference in for the threestrand rope The eye size in this case strength between the single and double bowline almost certainly has no effect upon the load state at despite traditional opinion the point of failure The difference in breaking load between knots If strength alone were considered the figure of eight Variation of rope diameter knot would be the obvious choice this and its The results for varying the rope diameter shown in security make it a common preference in climbing Table 10 are almost identical to those for the three However other issues such as the length of rope strand splice The 8 mm Type I splice gave an required and the ease of tying and untying means efficiency of 98 Splices in the 6 mm and 12 mm that the bowline may be preferred The perfection rope gave efficiencies of 63 and 75 respectively loop is not recommended it is weak complex to tie These results raise the same issues noted previously and uses a lot of line The fact that the trends for both rope types are the The manufacturer ie the individual making the same is curious especially as the two splice geometries splice has no effect upon the strength of three are so dissimilar strand splices As discussed if further testing Again the rope densities per unit length were calcu demonstrates that employment of a professional lated for the 6 8 and 12 mm diameter ropes and are splice maker does not improve the splice efficiency listed in Table 10 alongside the splice efficiencies then no advantage is gained by paying a more expe The highest splice efficiency corresponds to the rienced person to do the splicing for you highest rope density but that is where the correlation The existence of a critical number of tucks or splice ends Again more testing would be required to under length was demonstrated Below this length the stand the of the factors Table 10 Effect of variation of rope diameter on the efficiency of Table 9 Effect of variation of eye size on the efficiency of braidon braidonbraid splices braid splices Rope diameter Splice efficiency Splice efficiency Rope density Eye size cm Splice efficiency Splice efficiency mm computer analogue plotter per unit length computer analogue plotter kgm2 6 098 100 6 061 063 106103 8 098 098 8 098 098 111408 12 100 101 12 073 075 104334 12 Sports Engineering 2006 9 113 2006 isea911 Sports E77 McLaren 27706 238 pm Page 13 KA Milne and AJ McLaren The strength of knots and splices failure mode was different and the splice considerably Jarman C 2000 Knots in Use Adlard Coles Nautical weaker and in the case of the braidonbraid splice London UK King CC 1986 Vaughan Jones and knot theory a New the failure load was highly unpredictable Above this Zealand mathematician unravels a new invariant which length an increase in length or the number of tucks links diverse sciences in an unforeseen thread New caused no variation in the breaking load Zealand Mathematical Society Newsletter 37 2832 Different diameter ropes have totally different splice Leech CM 1987 Theory and numerical methods for the efficiencies 8 mm rope appears to give the highest modelling of synthetic ropes Communications in Applied splice efficiencies However it is noted that a 12mm Numerical Methods 3 407413 Leech CM 2002 The modelling of friction in polymer spliced rope is still significantly stronger even if the fibre ropes International Journal of Mechanical Sciences efficiency is lower 44 621643 Leech CM 2003 The modelling and analysis of splices Future work used in synthetic ropes In Proceedings Mathematical Physical and Engineering Sciences Royal Society London The present work has concentrated on knots and 459 16411659 simple splices on standard polyester ropes of two con Maddocks JH Keller JB 1987 Ropes in equilibrium structions Future work is needed to examine the Siam Journal on Applied Mathematics 47 11851200 Manes A 2002 Analysis of a Textile Rope with strength of splices in more exotic materials commonly Analytical Models in Nylon and Ropes for Mountaineering used in yacht racing Pawson 2005 These materials and Caving 89 March 2002 Turin Italian Alpine while of higher performance than standard ropes Club Technical Committee Online at provide significant challenges in the formation of splices and knots due to their high material stiffness Montgomery DC Runger GC Hubele NF 2001 The formation of eye terminations by stitching and Engineering Statistics John Wiley Sons New York US whipping needs to be investigated together with the Pan N 1996 Fiber interactions in a twisted fiber effect of wear chafe and UV attack on the security of structure under tension Oceans Conference Record IEEE knots and splices 1 138143 Pan N Brookstein D 2002 Physical properties of twisted structures II Industrial yarns cords and ropes Journal of Applied Polymer Sciences 83 610630 The authors gratefully acknowledge Marlow Ropes Pawson D 2001 Pocket Guide to Knots and Splices for the baseline rope tests and New England Ropes Chartwell Books Pawson D 2005 Rope Yarns Yachts and Yachting 1513 and LIROS for information provided on rope testing 4246 techniques Thanks are also due the Laboratory Phoenix SL 1979 Statistical theory for the strength of Technicians at the Department of Mechanical twisted fiber bundles with applications to yarns and Engineering University of Strathclyde and in partic cables Textile Research Journal 49 407423 ular to Mr A Crockett who patiently assisted Saitta AM Soper PD Wasserman E Lein ML throughout the testing 1999 Influence of a knot on the strength of a polymer strand Nature 398 No 6731 4648 Shaw S 2004 The Directory of Knots Grange Books References Rochester UK Bailie M 2000 Ropes dont break Summit 17 17 Schubert P 2002 A Number of Rope Failures amongst BS EN 892 1996 Mountaineering equipment Dynamic German and Austrian Mountaineers and Climbers since mountaineering ropes Safety requirements and test 1968 in Nylon and Ropes for Mountaineering and Caving methods 89 March 2002 Turin Italian Alpine Club Technical BS EN 919 1995 Fibre ropes for general service Committee Online at Determination of certain physical and mechanical properties Wu HC 1993 Frictional constraint of rope strands Cunliffe T 2000 The Complete Yachtmaster Adlard Coles Journal of the Textile Institute 84 199213 Nautical London UK James H 2003 Splice up your life Yachts and Yachting 1460 4249 2006 isea Sports Engineering 2006 9 113 13911 Sports E77 McLaren 27706 238 pm Page 14

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