27:
36:
20:
2625:
2296:
108:
A holding capstan is a ratchet device that can turn only in one direction; once a load is pulled into place in that direction, it can be held with a much smaller force. A powered capstan, also called a winch, rotates so that the applied tension is multiplied by the friction between rope and capstan.
983:
supercarriers (97,000 tons each, but for the baby it would be only a little more than 1 kg). The large number of turns around the capstan combined with such a high friction coefficient mean that very little additional force is necessary to hold such heavy weight in place. The cables necessary
1489:
1302:
44:
524:
2412:
2133:
2124:
30:
An example of when knowledge of the capstan equation might have been useful. The bent white tube contains a cord to raise and lower a blind. The tube is bent 40 degrees in two places. The blue line indicates a more efficient
1579:
1680:
1333:
1157:
1185:
202:
587:
It is important that the line is not rigid, in which case significant force would be lost in the bending of the line tightly around the cylinder. (The equation must be modified for this case.) For instance a
976:
For instance, the factor "153,552,935" (5 turns around a capstan with a coefficient of friction of 0.6) means, in theory, that a newborn baby would be capable of holding (not moving) the weight of two
1965:
398:
113:
a holding capstan and a powered capstan are used in tandem so that a small force can be used to raise a heavy sail and then the rope can be easily removed from the powered capstan and tied off.
2700:
Metzger, Andreas; Konyukhov, Alexander; Schweizerhof, Karl (2011). "Finite
Element implementation for the EULER–EYTELWEIN problem and further use in FEM-simulation of common nautical knots".
2620:{\displaystyle T_{0}e^{-\mu _{\tau }ks\,{\sqrt {\cos ^{2}\alpha -\sin ^{2}\alpha /\mu _{g}^{2}}}}\leq T\leq T_{0}e^{\mu _{\tau }ks\,{\sqrt {\cos ^{2}\alpha -\sin ^{2}\alpha /\mu _{g}^{2}}}}.}
1037:
2407:
643:
333:
558:
390:
363:
259:
232:
1826:
2376:
2291:{\displaystyle \omega =\mu _{\tau }{\sqrt {k_{n}^{2}-{\frac {k_{g}^{2}}{\mu _{g}^{2}}}}}=\mu _{\tau }k{\sqrt {\cos ^{2}\alpha -{\frac {\sin ^{2}\alpha }{\mu _{g}^{2}}}}},}
1729:
1325:
1180:
950:(a rope to the loose side of a sail) wound more than three turns around a winch. The force gain would be extreme besides being counter-productive since there is risk of a
1086:
1885:
582:
303:
1905:
1703:
97:
Because of the interaction of frictional forces and tension, the tension on a line wrapped around a capstan may be different on either side of the capstan. A small
2325:
2019:
1853:
279:
2349:
1992:
1779:
1057:
965:
It is both ancient and modern practice for anchor capstans and jib winches to be slightly flared out at the base, rather than cylindrical, to prevent the rope (
969:
or sail sheet) from sliding down. The rope wound several times around the winch can slip upwards gradually, with little risk of a riding turn, provided it is
2026:
1039:
is a function of the total angle subtended by the rope on the capstan. On the verge of slipping, this is also the frictional force, which is by definition
1484:{\displaystyle {\frac {dT_{\mathrm {load} }(\varphi )}{d\varphi }}=\mu T_{\mathrm {load} }(\varphi ),\qquad T_{\mathrm {load} }(0)=T_{\mathrm {hold} },}
1500:
1604:
2736:
1297:{\textstyle \delta R(\varphi )\approx T_{\mathrm {load} }(\varphi )\sin(\delta \varphi )\approx T_{\mathrm {load} }(\varphi )\delta \varphi }
1091:
1705:
is the angle (in radians) between the two flat sides of the pulley that the v-belt presses against. A flat belt has an effective angle of
145:
984:
to support this weight, as well as the capstan's ability to withstand the crushing force of those cables, are separate considerations.
2810:
1912:
519:{\displaystyle F=T_{\text{load}}-T_{\text{hold}}=(e^{\mu \varphi }-1)~T_{\text{hold}}=(1-e^{-\mu \varphi })~T_{\text{load}}}
2927:
2676:
2912:
2646:
2885:
2762:
338:
For dynamic applications such as belt drives or brakes the quantity of interest is the force difference between
26:
2384:
995:
607:
with the coefficient of friction, the number of turns around the cylinder, and the angle of contact. Note that
282:
68:
1745:
For the same power transmission, a V-belt requires less tension than a flat belt, increasing bearing life.
305:
is the total angle swept by all turns of the rope, measured in radians (i.e., with one full turn the angle
1742:
tends to wedge into the mating groove in a pulley as the load increases, improving torque transmission.
617:
308:
2840:
1754:
596:
536:
368:
341:
237:
210:
1786:
2740:
2354:
1708:
2866:
2717:
2328:
1307:
1162:
1062:
604:
560:
is the maximum load that one can hold. Smaller loads can be held as well, resulting in a smaller
80:
2858:
1863:
567:
288:
1890:
1688:
71:), relates the hold-force to the load-force if a flexible line is wound around a cylinder (a
2932:
2848:
2709:
2651:
970:
35:
2303:
1997:
1831:
1749:
Generalization of the capstan equation for a rope lying on an arbitrary orthotropic surface
955:
2792:
1739:
947:
264:
19:
2844:
105:
force on the other side; this is the principle by which a capstan-type device operates.
47:
An example of holding capstans and a powered capstan used to raise sails on a tall ship.
43:
2334:
1977:
1764:
64:
2119:{\displaystyle T_{0}e^{-\int _{s}\omega \,ds}\leq T\leq T_{0}e^{\int _{s}\omega \,ds}}
1042:
16:
Relates the hold-force to the load-force if a flexible line is wound around a cylinder
2921:
2870:
2721:
2641:
133:
117:
589:
1574:{\displaystyle T_{\mathrm {load} }(\varphi )=T_{\mathrm {hold} }e^{\mu \varphi }}
951:
592:
is to some extent rigid and doesn't obey the principles of the capstan equation.
1675:{\displaystyle T_{\text{load}}=T_{\text{hold}}e^{\mu \varphi /\sin(\alpha /2)}}
977:
125:
91:
87:
2862:
129:
110:
2853:
2828:
2713:
954:, result being that the sheet will foul, form a knot and not run out when
2902:
Arne
Kihlberg, Kompendium i Mekanik för E1, del II, Göteborg 1980, 60–62.
2886:"Introduction to Computational Contact Mechanics: A Geometrical Approach"
1152:{\textstyle \delta R(\varphi )=R(\varphi +\delta \varphi )-R(\varphi )}
72:
1753:
If a rope is lying in equilibrium under tangential forces on a rough
1735:
1595:
966:
197:{\displaystyle T_{\text{load}}=T_{\text{hold}}\ e^{\mu \varphi }~,}
1907:
are satisfying the following criteria for all points of the curve
121:
76:
42:
34:
25:
18:
261:
is the resulting force exerted at the other side of the capstan,
959:
529:
Several assumptions must be true for the equations to be valid:
609:
the radius of the cylinder has no influence on the force gain
1757:
surface then all three following conditions are satisfied:
2378:
is a coefficient of friction in the tangential direction.
645:
based on the number of turns and coefficient of friction
1304:. Combining these and considering infinitesimally small
86:
It also applies for fractions of one turn as occur with
973:(loose end is pulled clear), by hand or a self-tailer.
1960:{\displaystyle -\mu _{g}<\tan \alpha <+\mu _{g}}
1310:
1188:
1165:
1094:
1045:
998:
2415:
2387:
2357:
2337:
2306:
2136:
2029:
2000:
1980:
1915:
1893:
1866:
1834:
1789:
1767:
1711:
1691:
1607:
1503:
1336:
1065:
620:
570:
539:
401:
371:
344:
311:
291:
267:
240:
213:
148:
2632:
This generalization has been obtained by
Konyukhov.
1590:
Generalization of the capstan equation for a V-belt
946:From the table it is evident why one seldom sees a
2791:Moradmand, Jamshid; Marcks, Russell; Looker, Tom.
2619:
2401:
2370:
2343:
2319:
2290:
2118:
2013:
1986:
1959:
1899:
1879:
1847:
1820:
1773:
1723:
1697:
1674:
1573:
1483:
1319:
1296:
1174:
1151:
1088:. By simple geometry, the additional normal force
1080:
1051:
1031:
637:
576:
552:
518:
384:
357:
327:
297:
273:
253:
226:
196:
101:force exerted on one side can carry a much larger
2829:"Contact of ropes and orthotropic rough surfaces"
603:It can be observed that the force gain increases
533:The rope is on the verge of full sliding, i.e.
1781:is positive for all points of the rope curve:
120:this effect allows a lighter person to hold (
8:
2833:Journal of Applied Mathematics and Mechanics
285:between the rope and capstan materials, and
39:Schematic of quantities for capstan equation
2786:
2784:
2654:, a device that exploits the capstan effect
1159:when increasing the angle by a small angle
614:The table below lists values of the factor
1032:{\textstyle T_{\mathrm {load} }(\varphi )}
2852:
2670:
2668:
2604:
2599:
2590:
2578:
2559:
2553:
2552:
2540:
2535:
2525:
2502:
2497:
2488:
2476:
2457:
2451:
2450:
2438:
2430:
2420:
2414:
2402:{\displaystyle \omega ={\text{constant}}}
2394:
2386:
2362:
2356:
2336:
2311:
2305:
2275:
2270:
2253:
2246:
2231:
2225:
2216:
2199:
2194:
2184:
2179:
2173:
2164:
2159:
2153:
2147:
2135:
2107:
2098:
2093:
2083:
2061:
2052:
2044:
2034:
2028:
2005:
1999:
1979:
1951:
1923:
1914:
1892:
1871:
1865:
1839:
1833:
1803:
1788:
1766:
1710:
1690:
1659:
1642:
1635:
1625:
1612:
1606:
1562:
1542:
1541:
1509:
1508:
1502:
1462:
1461:
1429:
1428:
1395:
1394:
1348:
1347:
1337:
1335:
1309:
1263:
1262:
1212:
1211:
1187:
1164:
1093:
1064:
1044:
1004:
1003:
997:
634:
625:
619:
569:
544:
538:
510:
488:
466:
441:
425:
412:
400:
376:
370:
349:
343:
324:
310:
290:
266:
245:
239:
218:
212:
179:
166:
153:
147:
2678:The Mechanics of Friction in Rope Rescue
2021:are satisfying the following inequality
1855:is a normal curvature of the rope curve.
651:
2664:
1971:Limit values of the tangential forces:
2681:. International Tech Rescue Symposium
7:
1974:The forces at both ends of the rope
234:is the applied tension on the line,
2827:Konyukhov, Alexander (2015-04-01).
2675:Attaway, Stephen W. (1999-11-01).
1552:
1549:
1546:
1543:
1519:
1516:
1513:
1510:
1472:
1469:
1466:
1463:
1439:
1436:
1433:
1430:
1405:
1402:
1399:
1396:
1358:
1355:
1352:
1349:
1273:
1270:
1267:
1264:
1222:
1219:
1216:
1213:
1014:
1011:
1008:
1005:
638:{\displaystyle e^{\mu \varphi }\,}
14:
1860:Dragging coefficient of friction
1594:The belt friction equation for a
1327:yields the differential equation
2351:is a curvature of a rope curve,
1761:No separation – normal reaction
328:{\displaystyle \varphi =2\pi \,}
1423:
553:{\displaystyle T_{\text{load}}}
385:{\displaystyle T_{\text{hold}}}
358:{\displaystyle T_{\text{load}}}
254:{\displaystyle T_{\text{hold}}}
227:{\displaystyle T_{\text{load}}}
1821:{\displaystyle N=-k_{n}T>0}
1667:
1653:
1531:
1525:
1451:
1445:
1417:
1411:
1370:
1364:
1285:
1279:
1252:
1243:
1234:
1228:
1201:
1195:
1146:
1140:
1131:
1116:
1107:
1101:
1075:
1069:
1026:
1020:
500:
475:
456:
434:
1:
2647:Frictional contact mechanics
2371:{\displaystyle \mu _{\tau }}
1724:{\displaystyle \alpha =\pi }
1320:{\textstyle \delta \varphi }
1175:{\textstyle \delta \varphi }
2913:Capstan equation calculator
2735:Mann, Herman (5 May 2005).
2702:PAMM Proc. Appl. Math. Mech
1081:{\displaystyle R(\varphi )}
2949:
2809:Slocum, Alexander (2008).
392:. The formula for this is
958:(by slacking grip on the
881:
824:
778:
742:
716:
690:
685:
682:
679:
676:
673:
670:
667:
659:
654:
2811:"FUNdaMENTALS of Design"
2793:"Belt and Wrap Friction"
1880:{\displaystyle \mu _{g}}
1182:is well approximated by
660:Coefficient of friction
577:{\displaystyle \varphi }
298:{\displaystyle \varphi }
124:) a heavier person when
2884:Konyukhov, A.; Izi, R.
2761:Johnson, K. L. (1985).
1900:{\displaystyle \alpha }
1698:{\displaystyle \alpha }
1059:times the normal force
283:coefficient of friction
69:Johann Albert Eytelwein
61:Euler–Eytelwein formula
2854:10.1002/zamm.201300129
2714:10.1002/pamm.201110116
2621:
2403:
2372:
2345:
2321:
2292:
2120:
2015:
1988:
1961:
1901:
1881:
1849:
1822:
1775:
1725:
1699:
1676:
1575:
1485:
1321:
1298:
1176:
1153:
1082:
1053:
1033:
639:
578:
554:
520:
386:
359:
329:
299:
275:
255:
228:
198:
57:belt friction equation
48:
40:
32:
23:
2622:
2404:
2373:
2346:
2322:
2320:{\displaystyle k_{g}}
2293:
2121:
2016:
2014:{\displaystyle T_{0}}
1989:
1962:
1902:
1882:
1850:
1848:{\displaystyle k_{n}}
1823:
1776:
1726:
1700:
1677:
1576:
1486:
1322:
1299:
1177:
1154:
1083:
1054:
1034:
640:
579:
555:
521:
387:
360:
330:
300:
276:
256:
229:
199:
46:
38:
29:
22:
2928:Equations of physics
2413:
2385:
2355:
2335:
2304:
2134:
2027:
1998:
1978:
1913:
1891:
1864:
1832:
1787:
1765:
1709:
1689:
1605:
1501:
1334:
1308:
1186:
1163:
1092:
1063:
1043:
996:
992:The applied tension
618:
568:
537:
399:
369:
342:
309:
289:
274:{\displaystyle \mu }
265:
238:
211:
146:
128:, and also produces
2845:2015ZaMM...95..406K
2609:
2507:
2331:of the rope curve,
2280:
2204:
2189:
2169:
2617:
2595:
2493:
2399:
2368:
2341:
2329:geodesic curvature
2317:
2288:
2266:
2190:
2175:
2155:
2116:
2011:
1984:
1957:
1897:
1877:
1845:
1818:
1771:
1734:The material of a
1721:
1695:
1672:
1571:
1494:whose solution is
1481:
1317:
1294:
1172:
1149:
1078:
1049:
1029:
635:
574:
550:
516:
382:
355:
325:
295:
271:
251:
224:
194:
49:
41:
33:
24:
2764:Contact Mechanics
2610:
2508:
2397:
2344:{\displaystyle k}
2283:
2281:
2207:
2205:
1987:{\displaystyle T}
1774:{\displaystyle N}
1628:
1615:
1382:
1052:{\textstyle \mu }
944:
943:
547:
513:
505:
469:
461:
428:
415:
379:
352:
248:
221:
190:
174:
169:
156:
2940:
2890:
2889:
2881:
2875:
2874:
2856:
2824:
2818:
2817:
2815:
2806:
2800:
2799:
2797:
2788:
2779:
2778:
2776:
2774:
2769:
2758:
2752:
2751:
2749:
2748:
2739:. Archived from
2732:
2726:
2725:
2697:
2691:
2690:
2688:
2686:
2672:
2652:Torque amplifier
2626:
2624:
2623:
2618:
2613:
2612:
2611:
2608:
2603:
2594:
2583:
2582:
2564:
2563:
2554:
2545:
2544:
2530:
2529:
2511:
2510:
2509:
2506:
2501:
2492:
2481:
2480:
2462:
2461:
2452:
2443:
2442:
2425:
2424:
2408:
2406:
2405:
2400:
2398:
2395:
2377:
2375:
2374:
2369:
2367:
2366:
2350:
2348:
2347:
2342:
2326:
2324:
2323:
2318:
2316:
2315:
2297:
2295:
2294:
2289:
2284:
2282:
2279:
2274:
2265:
2258:
2257:
2247:
2236:
2235:
2226:
2221:
2220:
2208:
2206:
2203:
2198:
2188:
2183:
2174:
2168:
2163:
2154:
2152:
2151:
2125:
2123:
2122:
2117:
2115:
2114:
2103:
2102:
2088:
2087:
2069:
2068:
2057:
2056:
2039:
2038:
2020:
2018:
2017:
2012:
2010:
2009:
1993:
1991:
1990:
1985:
1966:
1964:
1963:
1958:
1956:
1955:
1928:
1927:
1906:
1904:
1903:
1898:
1886:
1884:
1883:
1878:
1876:
1875:
1854:
1852:
1851:
1846:
1844:
1843:
1827:
1825:
1824:
1819:
1808:
1807:
1780:
1778:
1777:
1772:
1730:
1728:
1727:
1722:
1704:
1702:
1701:
1696:
1681:
1679:
1678:
1673:
1671:
1670:
1663:
1646:
1630:
1629:
1626:
1617:
1616:
1613:
1580:
1578:
1577:
1572:
1570:
1569:
1557:
1556:
1555:
1524:
1523:
1522:
1490:
1488:
1487:
1482:
1477:
1476:
1475:
1444:
1443:
1442:
1410:
1409:
1408:
1383:
1381:
1373:
1363:
1362:
1361:
1338:
1326:
1324:
1323:
1318:
1303:
1301:
1300:
1295:
1278:
1277:
1276:
1227:
1226:
1225:
1181:
1179:
1178:
1173:
1158:
1156:
1155:
1150:
1087:
1085:
1084:
1079:
1058:
1056:
1055:
1050:
1038:
1036:
1035:
1030:
1019:
1018:
1017:
940:
939:
936:
933:
926:
925:
922:
915:
914:
911:
904:
903:
896:
895:
877:
876:
873:
866:
865:
862:
855:
854:
847:
846:
839:
838:
820:
819:
812:
811:
804:
803:
796:
795:
774:
773:
766:
765:
652:
644:
642:
641:
636:
633:
632:
595:The line is non-
583:
581:
580:
575:
559:
557:
556:
551:
549:
548:
545:
525:
523:
522:
517:
515:
514:
511:
503:
499:
498:
471:
470:
467:
459:
449:
448:
430:
429:
426:
417:
416:
413:
391:
389:
388:
383:
381:
380:
377:
364:
362:
361:
356:
354:
353:
350:
334:
332:
331:
326:
304:
302:
301:
296:
280:
278:
277:
272:
260:
258:
257:
252:
250:
249:
246:
233:
231:
230:
225:
223:
222:
219:
203:
201:
200:
195:
188:
187:
186:
172:
171:
170:
167:
158:
157:
154:
59:, also known as
53:capstan equation
2948:
2947:
2943:
2942:
2941:
2939:
2938:
2937:
2918:
2917:
2909:
2899:
2897:Further reading
2894:
2893:
2883:
2882:
2878:
2826:
2825:
2821:
2813:
2808:
2807:
2803:
2795:
2790:
2789:
2782:
2772:
2770:
2767:
2760:
2759:
2755:
2746:
2744:
2737:"Belt Friction"
2734:
2733:
2729:
2699:
2698:
2694:
2684:
2682:
2674:
2673:
2666:
2661:
2638:
2574:
2555:
2536:
2531:
2521:
2472:
2453:
2434:
2426:
2416:
2411:
2410:
2383:
2382:
2358:
2353:
2352:
2333:
2332:
2307:
2302:
2301:
2249:
2248:
2227:
2212:
2143:
2132:
2131:
2094:
2089:
2079:
2048:
2040:
2030:
2025:
2024:
2001:
1996:
1995:
1976:
1975:
1947:
1919:
1911:
1910:
1889:
1888:
1867:
1862:
1861:
1835:
1830:
1829:
1799:
1785:
1784:
1763:
1762:
1751:
1740:serpentine belt
1707:
1706:
1687:
1686:
1631:
1621:
1608:
1603:
1602:
1592:
1587:
1585:Generalizations
1558:
1537:
1504:
1499:
1498:
1457:
1424:
1390:
1374:
1343:
1339:
1332:
1331:
1306:
1305:
1258:
1207:
1184:
1183:
1161:
1160:
1090:
1089:
1061:
1060:
1041:
1040:
999:
994:
993:
990:
937:
934:
931:
929:
923:
920:
918:
912:
909:
907:
901:
899:
893:
891:
874:
871:
869:
863:
860:
858:
852:
850:
844:
842:
836:
834:
817:
815:
809:
807:
801:
799:
793:
791:
771:
769:
763:
761:
656:
621:
616:
615:
566:
565:
540:
535:
534:
506:
484:
462:
437:
421:
408:
397:
396:
372:
367:
366:
345:
340:
339:
307:
306:
287:
286:
263:
262:
241:
236:
235:
214:
209:
208:
175:
162:
149:
144:
143:
139:The formula is
17:
12:
11:
5:
2946:
2944:
2936:
2935:
2930:
2920:
2919:
2916:
2915:
2908:
2907:External links
2905:
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2903:
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2892:
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2839:(4): 406–423.
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1133:
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1121:
1118:
1115:
1112:
1109:
1106:
1103:
1100:
1097:
1077:
1074:
1071:
1068:
1048:
1028:
1025:
1022:
1016:
1013:
1010:
1007:
1002:
989:
986:
942:
941:
927:
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905:
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883:
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624:
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593:
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564:contact angle
543:
527:
526:
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502:
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244:
217:
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193:
185:
182:
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165:
161:
152:
65:Leonhard Euler
15:
13:
10:
9:
6:
4:
3:
2:
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2802:
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2787:
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2781:
2766:
2765:
2757:
2754:
2743:on 2007-08-02
2742:
2738:
2731:
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2723:
2719:
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2693:
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2669:
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2650:
2648:
2645:
2643:
2642:Belt friction
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2633:
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2605:
2600:
2596:
2591:
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2053:
2049:
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2041:
2035:
2031:
2023:
2022:
2006:
2002:
1981:
1973:
1972:
1970:
1952:
1948:
1944:
1941:
1938:
1935:
1932:
1929:
1924:
1920:
1916:
1909:
1908:
1894:
1872:
1868:
1859:
1840:
1836:
1815:
1812:
1809:
1804:
1800:
1796:
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1790:
1783:
1782:
1768:
1760:
1759:
1758:
1756:
1748:
1746:
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1741:
1737:
1732:
1718:
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1712:
1692:
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1660:
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1650:
1647:
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1639:
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1632:
1622:
1618:
1609:
1601:
1600:
1599:
1597:
1589:
1584:
1566:
1563:
1559:
1538:
1534:
1528:
1505:
1497:
1496:
1495:
1478:
1458:
1454:
1448:
1425:
1420:
1414:
1391:
1387:
1384:
1378:
1375:
1367:
1344:
1340:
1330:
1329:
1328:
1314:
1311:
1291:
1288:
1282:
1259:
1255:
1249:
1246:
1240:
1237:
1231:
1208:
1204:
1198:
1192:
1189:
1169:
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1143:
1137:
1134:
1128:
1125:
1122:
1119:
1113:
1110:
1104:
1098:
1095:
1072:
1066:
1046:
1023:
1000:
987:
985:
982:
981:
974:
972:
968:
963:
962:(free end)).
961:
957:
953:
949:
928:
917:
906:
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880:
868:
857:
849:
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833:
830:
827:
823:
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781:
777:
768:
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754:
751:
748:
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741:
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734:
731:
728:
725:
722:
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715:
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708:
705:
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696:
693:
689:
666:
663:
653:
650:
648:
629:
626:
622:
612:
610:
606:
605:exponentially
598:
594:
591:
586:
571:
563:
541:
532:
531:
530:
507:
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492:
489:
485:
481:
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463:
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445:
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438:
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373:
346:
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321:
318:
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284:
268:
242:
215:
191:
183:
180:
176:
163:
159:
150:
142:
141:
140:
137:
135:
134:lead climbing
131:
127:
123:
119:
118:rock climbing
114:
112:
106:
104:
100:
95:
93:
89:
84:
82:
78:
74:
70:
66:
62:
58:
54:
45:
37:
28:
21:
2879:
2836:
2832:
2822:
2816:. pagea 5–9.
2804:
2773:February 14,
2771:. Retrieved
2763:
2756:
2745:. Retrieved
2741:the original
2730:
2705:
2701:
2695:
2683:. Retrieved
2677:
2631:
1752:
1744:
1733:
1684:
1593:
1493:
991:
979:
975:
964:
945:
661:
646:
613:
608:
602:
590:Bowden cable
561:
528:
337:
206:
138:
115:
107:
102:
98:
96:
85:
60:
56:
52:
50:
2708:: 249–250.
1755:orthotropic
1738:or multi-V
967:anchor warp
952:riding turn
92:band brakes
88:rope drives
2922:Categories
2747:2013-02-23
2659:References
1887:and angle
988:Derivation
126:top-roping
2871:122410452
2863:1521-4001
2722:119597604
2597:μ
2588:α
2585:
2572:−
2569:α
2566:
2542:τ
2538:μ
2519:≤
2513:≤
2495:μ
2486:α
2483:
2470:−
2467:α
2464:
2440:τ
2436:μ
2432:−
2389:ω
2364:τ
2360:μ
2268:μ
2263:α
2260:
2244:−
2241:α
2238:
2218:τ
2214:μ
2192:μ
2171:−
2149:τ
2145:μ
2138:ω
2105:ω
2096:∫
2077:≤
2071:≤
2059:ω
2050:∫
2046:−
1949:μ
1939:α
1936:
1921:μ
1917:−
1895:α
1869:μ
1797:−
1719:π
1713:α
1693:α
1657:α
1651:
1640:φ
1637:μ
1567:φ
1564:μ
1529:φ
1415:φ
1388:μ
1379:φ
1368:φ
1315:φ
1312:δ
1292:φ
1289:δ
1283:φ
1256:≈
1250:φ
1247:δ
1241:
1232:φ
1205:≈
1199:φ
1190:δ
1170:φ
1167:δ
1144:φ
1135:−
1129:φ
1126:δ
1120:φ
1105:φ
1096:δ
1073:φ
1047:μ
1024:φ
978:USS
630:φ
627:μ
572:φ
562:effective
496:φ
493:μ
490:−
482:−
451:−
446:φ
443:μ
419:−
322:π
313:φ
293:φ
269:μ
184:φ
181:μ
130:rope drag
111:tall ship
2888:. Wiley.
2636:See also
2396:constant
1828:, where
657:of turns
2933:Winches
2841:Bibcode
597:elastic
281:is the
132:during
103:loading
99:holding
81:capstan
73:bollard
63:(after
31:design.
2869:
2861:
2720:
2685:23 Nov
2300:where
1736:V-belt
1685:where
1596:v-belt
980:Nimitz
971:tailed
655:Number
504:
460:
207:where
189:
173:
109:On a
2867:S2CID
2814:(PDF)
2796:(PDF)
2768:(PDF)
2718:S2CID
2409:then
2327:is a
2130:with
956:eased
948:sheet
122:belay
79:or a
77:winch
2859:ISSN
2775:2011
2687:2022
1994:and
1942:<
1930:<
1813:>
1627:hold
1614:load
1598:is:
960:tail
691:0.5
686:0.7
683:0.6
680:0.5
677:0.4
674:0.3
671:0.2
668:0.1
546:load
512:load
468:hold
427:hold
414:load
378:hold
365:and
351:load
247:hold
220:load
168:hold
155:load
75:, a
67:and
51:The
2849:doi
2710:doi
2576:sin
2557:cos
2474:sin
2455:cos
2381:If
2251:sin
2229:cos
1933:tan
1648:sin
1238:sin
938:281
935:321
932:553
924:935
921:552
919:153
913:624
910:635
902:751
900:286
894:392
888:535
875:631
872:702
864:026
861:540
853:751
851:286
845:228
837:881
831:152
818:503
816:537
810:612
802:392
794:881
788:286
782:6.6
772:661
764:881
758:535
755:152
746:3.5
738:81
726:6.6
723:3.5
720:1.9
709:6.6
706:4.8
703:3.5
700:2.6
697:1.9
694:1.4
335:).
116:In
90:or
83:).
55:or
2924::
2865:.
2857:.
2847:.
2837:95
2835:.
2831:.
2783:^
2716:.
2706:11
2704:.
2667:^
1731:.
892:12
885:23
882:5
870:43
843:23
828:12
825:4
808:81
800:12
785:43
779:3
752:43
749:12
743:2
735:43
732:23
729:12
717:1
712:9
649:.
611:.
136:.
94:.
2873:.
2851::
2843::
2798:.
2777:.
2750:.
2724:.
2712::
2689:.
2615:.
2606:2
2601:g
2592:/
2580:2
2561:2
2550:s
2547:k
2533:e
2527:0
2523:T
2516:T
2504:2
2499:g
2490:/
2478:2
2459:2
2448:s
2445:k
2428:e
2422:0
2418:T
2392:=
2339:k
2313:g
2309:k
2286:,
2277:2
2272:g
2255:2
2233:2
2223:k
2210:=
2201:2
2196:g
2186:2
2181:g
2177:k
2166:2
2161:n
2157:k
2141:=
2112:s
2109:d
2100:s
2091:e
2085:0
2081:T
2074:T
2066:s
2063:d
2054:s
2042:e
2036:0
2032:T
2007:0
2003:T
1982:T
1953:g
1945:+
1925:g
1873:g
1841:n
1837:k
1816:0
1810:T
1805:n
1801:k
1794:=
1791:N
1769:N
1716:=
1668:)
1665:2
1661:/
1654:(
1644:/
1633:e
1623:T
1619:=
1610:T
1560:e
1553:d
1550:l
1547:o
1544:h
1539:T
1535:=
1532:)
1526:(
1520:d
1517:a
1514:o
1511:l
1506:T
1479:,
1473:d
1470:l
1467:o
1464:h
1459:T
1455:=
1452:)
1449:0
1446:(
1440:d
1437:a
1434:o
1431:l
1426:T
1421:,
1418:)
1412:(
1406:d
1403:a
1400:o
1397:l
1392:T
1385:=
1376:d
1371:)
1365:(
1359:d
1356:a
1353:o
1350:l
1345:T
1341:d
1286:)
1280:(
1274:d
1271:a
1268:o
1265:l
1260:T
1253:)
1244:(
1235:)
1229:(
1223:d
1220:a
1217:o
1214:l
1209:T
1202:)
1196:(
1193:R
1147:)
1141:(
1138:R
1132:)
1123:+
1117:(
1114:R
1111:=
1108:)
1102:(
1099:R
1076:)
1070:(
1067:R
1027:)
1021:(
1015:d
1012:a
1009:o
1006:l
1001:T
930:3
908:6
859:3
835:1
792:1
770:6
762:1
662:μ
647:μ
623:e
599:.
584:.
542:T
508:T
501:)
486:e
479:1
476:(
473:=
464:T
457:)
454:1
439:e
435:(
432:=
423:T
410:T
406:=
403:F
374:T
347:T
319:2
316:=
243:T
216:T
192:,
177:e
164:T
160:=
151:T
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