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Re: Pulleys (Spanish rig?)

Chuck,

Are you possibly thinking of a posting by Donald Simanek, describing the Spanish
Burton? I found that interesting and saved a copy, which I'll paste in below.
It's easy to delete if this is not what you wanted.

Charles Crook

Chuck Britton wrote:

Some YEARS ago Leigh Palmer posted an ascii sketch of an unusual
arrangement of pulleys.

I BELIEVE that he referred to it as some 'Spanish' variant of the
more usual block and tackle.

Anyway you could dredge it up again, Leigh?

My mail from those years is on another machine.
-. .-. .-. .-. .-. .-. .-. .-. .-. .-
\ / \ / \ N / \ C / \ S / \ S / \ M / \ / \ /
`-' `-' `-' `-' `-' `-' `-' `-' `-'
Chuck Britton Education is what is left when
britton@ncssm.edu you have forgotten everything
North Carolina School of Science & Math you learned in school.
(919) 286-3366 x224 Albert Einstein, 1936

* * * * * ARCHIVED MESSAGE FOLLOWS * * * * *

From: "Donald E. Simanek" <dsimanek@eagle.lhup.edu>
Subject: Re: Pulleys
To: PHYSHARE@LISTS.PSU.EDU
Date: Wed, 2 Dec 1998 08:51:53 -0500

On Tue, 1 Dec 1998, Peter G. Bruecken wrote:

I used to do pulley exercises in physical science class. As I recall, the
most difficult part of making measurements is synchronizing the effort
distance with the resistance distance. It is easily checked by dividing the
effort distance by the resistance distance. This ratio should be equal to
the number of support strands. If not, the synchronization was not correct.

Again, this is true only for the block and tackle pulley system. It is not
true, for example, in this system, called the "Spanish Burton" . The
system is one of many shown in Leonardo daVinci's notebooks and was
apparently common in his day:

____________________
| | | | |
| | | | |
| | | | |
| | | | /|\
| | | | | o |
| | | | |\_/|
| | | | | | SPANISH BURTON
| | | | _ | |
| | | |/ \| |
| | | | o | |
| | | \|/ |
| | | | |
| | | _ | |
| | |/ \| |
| | | o | |
| | \|/ \|/
| | |
| | _ | F
| |/ \|
| | o |
| \|/
| |
| _ | Obviously these systems work better
|/ \|
| O | with round pulleys :-)
\|/
|
---
/ \
/ L \
-------

This is quite instructive. If one pulls at F, through a distance y, the
load lifts y/16. The displacement ratio is 16. The upper limit on
mechanical advantage is 16 (ignoring friction and pulley mass). One gets
the same result with equlibrium free-body diagrams for each pulley,
ignoring pulley weight and friction, i.e. the "idealized mechanical
advantage" is 16, the result for frictionless, weightless pulleys. A good
exercise in correctly using free-body diagrams.

How many strings support the load? There are only four strings in the
problem. How many segments support the load? There are only 9 string
segments in the problem, and only 8 of them could be judged "supportive".
Clearly the "number of strings supporting the load" isn't clear-cut here,
and is in no way equal to the displacement ratio or the idealized
mechanical advantage. That "strings supporting the load" only applies to a
particular type of pulley system--the block and tackle. Why place so much
emphasis on just one of the many pulley systems which are useful?

Problem 1: What's the mechanical advantage of this system if there's no
friction, and each pulley weighs L/10 and one is lifting the load? What is
it if one is lowering the load? What's the efficiency in each case?
Careful with that last question, for there's no friction, so.... This
reminds us that "efficiency" is often defined in different (and strange)
ways. To ask "how much mechanical energy is lost to friction" is a
fundamentally different type of question from "what's the ratio of output
to input work." The latter forces you to define what's "input" and what's
"output" and whether the weight of the pulleys should be included in one
or the other, or both. Are they part of the load being lifted, or part of
the lifting force? Or are they merely contributors to inefficiency? If you
aren't willing to take the time to deal with these issues, you'd better
not even mention pulley systems.

Problem 2 (Advanced): What's the mechanical advantage of this system if
each pulley weighs L/10 and the friction in each pulley is 5% of the load
on the axle of that pulley. Do this for two cases: lifting the load, and
lowering the load.

Obviously the Spanish Burton may have more, or fewer, pulleys. Also,
pulley systems are designed for heavy loads, heavy in comparison to the
"effective" weight of the pulleys in the system. If the displacement ratio
is high enough (easily obtained) one can tolerate the inefficiencies due
to friction in the pulleys, and even the reduction of mechanical advantage
due to weight of the pulleys. Efficiency isn't the primary criterion of
the usefulness of a pulley system. For example, consider the differential
chain hoist, often used in auto service shops to lift engines out of cars.
There's so much friction in it that when the load is lifted, friction
alone may be sufficient to keep it lifted without falling back down.
That's a desirable (though inherent) feature of the system. We keep a
small version of differential chain hoist to demonstrate this point to
students.

Pulley systems are fascinating examples of old-fashioned physics. To call
them "simple" is a misrepresentation. To limit oneself to block and
tackles takes all the fun (and instructive value) out of the subject.

As always we must ask whether we are doing this lab, or demonstrating the
systems, in order to gain understanding of physical principles, or merely
to "make measurements and calculate and answer".

-- Donald

.....................................................................
Dr. Donald E. Simanek Office: 717-893-2079
Professor of Physics FAX: 717-893-2048
Lock Haven University of Pennsylvania, Lock Haven, PA. 17745
dsimanek@eagle.lhup.edu http://www.lhup.edu/~dsimanek
.....................................................................