Mechanical Efficiency

On 4/21/2017 11:13 PM, Jeff Liebermann wrote:
On Fri, 21 Apr 2017 20:03:26 -0400, Frank Krygowski wrote:

Not true, Jeff. The tension in the chain is a constant The load on
each pin in the free upper span is exactly the same, and it doesn't
change if the chain is longer, i.e. has more pins. A normal chain with
a 100 pound load has 100 pounds on each pin, no matter how long.

Argh. We went through this exercise a few years ago in this newsgroup
when I allegedly made the same mistake. Am I wrong again? (I just
hate it when that happens).

Well yes, you're wrong. I don't remember the previous discussion, so I
can't comment on the "again" part.


The way I look at it is that if I replace each link in the upper part
of the chain loop with a spring scale, methinks the deflection of each
spring (a measure of the force) would be the pulling load divided by
number of spring scales.

Nope. Each spring scale would measure the same. If you have two spring
scales at home, you can easily verify this.

Or, if we break the chain and put one spring scale between two
adjacent links, the measured force will be equal to the applied load.
However, if we break the chain in two places, methinks the measured
force will be half the applied load. If the force were equal to the
applied load on each link, I would expect the two spring scales to
also indicate a force equal to the applied load, which I don't believe
is the case.

I'll try a couple other explanations.

First, you can find tables of tensile strength for various sizes of
roller chain. You'll note that the tables don't specify length. That
tensile strength depends on several factors, but not length. If what
you're visualizing were true, they'd have to specify length.

Second, if what you visualize were true, let's take a chain with an
ultimate strength of (say) 5000 pounds. Would that apply to one link
(say, 1/2")? If so, would two links (say, 1") be able to hold 10,000
pounds? Would 10 inches of chain be able to hold 100,000 pounds? Would
100" of chain hold a million pounds? You see that it quickly becomes
absurd.

Under static and otherwise ordinary and reasonable conditions, the
length doesn't matter. Tension in a chain is constant over its length.
Same is true for ropes, cables, etc.


--
- Frank Krygowski