Re: Block & Tackle vs. Spanish Burton

["John S. Denker" <jsd@MONMOUTH.COM>]

At 08:34 PM 2/27/01 -0500, Chuck Britton wrote:

> That was EXACTLY what I was trying to dredge up. I suppose I just didn't
> quite hit the right search criterion in the archives.

No amount of skill in searching the phys-l archives would have helped,
because the article of interest isn't there.  Instead, it's in the PHYSHARE
archives at
  http://lists.psu.edu/cgi-bin/wa?A2=ind9812&L=physhare&P=R1386

> This is much more effective than using the same number of pulleys in
> the block & tackle arrangement. I join Donald in wondering why the
> block & tackle gets so much more 'press'.

Answer:  This alleged "effectiveness" is more theoretical than
practical.  The block and tackle is incomparably more practical in ordinary
situations.  If there is even modest stretch in the ropes, the 4th-order
Spanish Burton (as shown in the article cited above) could well have ZERO
effectiveness.

> (well, the amount of 'headroom' that it requires IS greater than for the B&T.)

That's one way of saying it.  An even stronger statement is that the
block&tackle can lift the load nearly 100% of the way to the attachment
point, whereas the Spanish Burton is much more limited.  If it has a
mechanical advantage of N, it can only lift 1/Nth of the way.  This problem
can be alleviated only with considerable complexity and inconvenience.

The root of this problem should be fairly easy to see:  If you want to get
exponentially large mechanical advantage, N = 2^M, using the Mth-order
Spanish Burton, conservation of energy tells us you need to pull an
exponentially long distance.  Since the rig doesn't contain an exponential
amount of rope, you've got a problem.

In practice, if you want a huge mechanical advantage, you can use a
differential chain hoist.  This satisfies conservation of energy, allowing
you to pull for a very long distance, because it recycles the chain.

If you insist on using only pulleys, then a 4th-order Spanish Burton
(advantage = N = 16) is still less practical than a luff-on-luff system (*)
using a lightweight jigger (N=4) to pull the fall of a beefier block&tackle
(also N=4).  And to be really practical, you would want to have TWO
jiggers, so you could use one to hold the fall while you set up the other
for the next stage of the pull.

(*) Reference:  Clifford W. Ashley, _The Ashley Book of Knots_, entry #3257
(page 528).