Math Brain Teaser - Rope Stretch Conversion

Status
Not open for further replies.
Jun 21, 2007
2,117
Hunter Cherubini 36_80-82 Sausalito / San Francisco Bay
For the engineer and math oriented types participating in this forum:

Running rigging rope specs include percent stretch against a percent of breaking strength. Between manufacturers, and even along different rope types of the same manufacturer, the basis isn't consistant. Example:

Type A = 2.4% stretch at 15% of the 6000 lbs breaking strength - 7/16"
Type B = 1.0% @ 20% 4600 lbs 3/8"
Type C = .79% @ 30% 6200 lbs 5/16"

Another factor, to calculate how many inches of stretch over a given length, I assume is the anticipated percent of breaking strength one might expect as normal for the given use. Say for a mainsheet halyard using a winch, say 300 lbs?

So for the given 300 lbs, how does one calculate the stretch of each rope?

I'm wanting to do the calculation in order to know how to compare whether a 7/16" Type A (above) at price X is a better or worse deal than a 3/8" Type B (above) at price Y.

I've worked out what I think is a solution, but probably its only an estimate since the stretch percentage I think wouldn't be linear with varying tension. Say for tension in the 1%-5% range of breaking strength stretch might be a neglible percent. But at the 15% of breaking strength, its the 2.4% in the case of Type A above. Or maybe the other way around, the tighter the tension the lower percentage of additional stretch?

Anyway, your thoughts? (Other than that I am over complicating things!)
 
Jun 2, 2004
425
- - Sandusky Harbor Marina, Lake Erie
Linear is a good assumption in the working range

It's only as you approach the breaking point that strange things begin to happen. With that assumption, the % stress per pound of strain on your three examples are:

A: 0.00267%
B: 0.00109%
C: 0.00042%

At 300 pounds of stress on a 50 foot halyard, their strain (stretch) would be:

A: 0.4 feet, or 4.8 inches
B: 0.16 feet or 2 inches
C: 0.06 feet, or 0.8 inches

Because (I think) line stress goes up as the cube of wind speed, 300 pounds is probably low for the high end of wind speeds on a 30 foot yacht.

David
Lady Lillie
 
Jun 21, 2007
2,117
Hunter Cherubini 36_80-82 Sausalito / San Francisco Bay
Thanks David : Noted

Thanks David: Your info noted. Now to make the decision.

regards,
Rardi
 
Status
Not open for further replies.