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chairlift design questions
Started by sumit, Dec 06 2008 06:20 AM
6 replies to this topic
#1
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Posted 06 December 2008 - 06:20 AM
what are the factors consider while designing the rope of skilift or any ropeway i mean how can calculate the sag in the wire if i know the span . how can i clamp the wire with the sheaves? this question may sound very funny for those intellectuals on this site , i'm novice in this ropeway business but i'm learning very quickly and i hope u guys will help me ...
#2
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Posted 15 December 2008 - 10:11 AM
For most common terms you can check the glossary:http://www.skilifts.org/glossary.htm
Catenary is the technical term for the curve that you see in sag.
The definition comes from the Latin word for chain, but more than likely the word is derived from a shape from a rope suspended by its ends.
Early uses of catenaries suggest simple ropeways - foundation tie-offs can still can be found in the Himalayas and Andes mountains for simple rope spans for foot bridges.
Very early written references are found for Chinese suspension bridges.
Early correct but not the first equations (it’s very close in shape to a parabola) were produced by 4 mathematicians around 1691 as a challenge by one of the Bernoulli brothers.
Used the then new math of calculus along with trigonometry.
Gottfried Leibniz a German mathematician (probably the smartest and well-rounded of the bunch as he is compared to de Vinci and Galileo and Newton -invention of binary system etc.) I suspect he did the equation on the back of an envelope before breakfast…
But the rest of the bunch are no dummies either …
Christiaan Huygens a Dutch mathematician and lawyer (developed first pendulum clocks, discusses catenary problem in 1673)
David Gregory - Scottish mathematician did some early work on cassinian orbital models for stars and planets…also wrote a detailed paper discussing horizontal and vertical reactions, sag and tension of catenaries in 1690.
Johann Bernoulli a Swiss mathematician (his son was that Bernoulli of fluid dynamics).
Marc Seguin - builder of first documented suspension bridges 1700s - used the formula extensively for calculating actual suspension bridge catenaries and tension and load reactions on his bridges. By inference he would have used a construction ropeway to construct the bridges.
John Roebling uses same formulas for construction tramways used in his bridge building 100 years later.
The catenary formula is scalable: it also works for clothes lines, kite strings, rope tows, and power-lines
This formula is for a parabola which is easyer to understand and closely approximates a catenary of less than 1000’.
Sag = (Weight*length squared)/(8*Tension)
Here is a link that has some instructional applets.
http://www.math.ubc.ca/~cass/courses/m308/...th/catenary.htm
Catenary is the technical term for the curve that you see in sag.
The definition comes from the Latin word for chain, but more than likely the word is derived from a shape from a rope suspended by its ends.
Early uses of catenaries suggest simple ropeways - foundation tie-offs can still can be found in the Himalayas and Andes mountains for simple rope spans for foot bridges.
Very early written references are found for Chinese suspension bridges.
Early correct but not the first equations (it’s very close in shape to a parabola) were produced by 4 mathematicians around 1691 as a challenge by one of the Bernoulli brothers.
Used the then new math of calculus along with trigonometry.
Gottfried Leibniz a German mathematician (probably the smartest and well-rounded of the bunch as he is compared to de Vinci and Galileo and Newton -invention of binary system etc.) I suspect he did the equation on the back of an envelope before breakfast…
But the rest of the bunch are no dummies either …
Christiaan Huygens a Dutch mathematician and lawyer (developed first pendulum clocks, discusses catenary problem in 1673)
David Gregory - Scottish mathematician did some early work on cassinian orbital models for stars and planets…also wrote a detailed paper discussing horizontal and vertical reactions, sag and tension of catenaries in 1690.
Johann Bernoulli a Swiss mathematician (his son was that Bernoulli of fluid dynamics).
Marc Seguin - builder of first documented suspension bridges 1700s - used the formula extensively for calculating actual suspension bridge catenaries and tension and load reactions on his bridges. By inference he would have used a construction ropeway to construct the bridges.
John Roebling uses same formulas for construction tramways used in his bridge building 100 years later.
The catenary formula is scalable: it also works for clothes lines, kite strings, rope tows, and power-lines
This formula is for a parabola which is easyer to understand and closely approximates a catenary of less than 1000’.
Sag = (Weight*length squared)/(8*Tension)
Here is a link that has some instructional applets.
http://www.math.ubc.ca/~cass/courses/m308/...th/catenary.htm
www.ropetech.org
#3
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Posted 22 December 2008 - 07:10 AM
kelly i have one more problem , is it possible i can bend the wire rope at 30-40' angle (not exactly L shape but slight curvature in the rope) if it is? plz enlighten me on this riddle ,i will be deeply thankful to you..thnxs
This post has been edited by Kelly: 22 December 2008 - 02:54 PM
#4
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Posted 22 December 2008 - 11:16 AM
sumit, on Dec 6 2008, 07:20 AM, said:
what are the factors consider while designing the rope of skilift or any ropeway i mean how can calculate the sag in the wire if i know the span . how can i clamp the wire with the sheaves? this question may sound very funny for those intellectuals on this site , i'm novice in this ropeway business but i'm learning very quickly and i hope u guys will help me ...
Does this help?
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Number of downloads: 48
#5
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Posted 22 December 2008 - 02:55 PM
Amount of turn 0 – 360…bigger turns equal a bigger diameter sheave.
See Angled station topic which has some excellent picutures
http://www.skiliftfo...?showtopic=5634
dbl shows a pretty comprehensive formula for a catenary with fixed ends.
Notice the top formula (circled in red) is what I mentioned.
The rest of the formula is the trigonometry that establishes the angle reactions between stations, as you can imagine the sag gets less and less the steeper you go.
See Angled station topic which has some excellent picutures
http://www.skiliftfo...?showtopic=5634
dbl shows a pretty comprehensive formula for a catenary with fixed ends.
Notice the top formula (circled in red) is what I mentioned.
The rest of the formula is the trigonometry that establishes the angle reactions between stations, as you can imagine the sag gets less and less the steeper you go.
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Catenary_red.jpg (406.22K)
Number of downloads: 13
www.ropetech.org
#7
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Posted 23 December 2008 - 12:33 AM
Kelly, on Dec 22 2008, 02:55 PM, said:
Amount of turn 0 – 360…bigger turns equal a bigger diameter sheave.
See Angled station topic which has some excellent picutures
http://www.skiliftfo...?showtopic=5634
dbl shows a pretty comprehensive formula for a catenary with fixed ends.
Notice the top formula (circled in red) is what I mentioned.
The rest of the formula is the trigonometry that establishes the angle reactions between stations, as you can imagine the sag gets less and less the steeper you go.
See Angled station topic which has some excellent picutures
http://www.skiliftfo...?showtopic=5634
dbl shows a pretty comprehensive formula for a catenary with fixed ends.
Notice the top formula (circled in red) is what I mentioned.
The rest of the formula is the trigonometry that establishes the angle reactions between stations, as you can imagine the sag gets less and less the steeper you go.
thnxs kelly
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