# Capstan Equation

#### theTreeSpyder

I need help please, as this math is beyond me
For capstan , bollard frictions.
I even have trusted document that has let me make sense and understand many things of knots and bollard frictions.
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Jrre.org/att_frict.pdf
gives .25 coefficient for nylon rope on aluminum pipe for brake force.
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I have made this chart, the paper shows brake force same on larger pipe, friction by degrees of contact.

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I am seeking to mostly fill in 180° on to table assuming same coefficient to show pattern.
But , would also like to show 90°, 360°, 720° please.
Wouldn't mind knowing how to calc or some tool even.
This would help immensely to define more about working knots and rigging, thank-you!
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#### Woody

If you have Microsoft Excel available to you,
try placing the data into a graph and fitting an exponential trend-line through the data.
This will give you an equation fitting the data.

However I doubt that, in practice, the actual friction is as precisely matched to the theoretical friction, as this table suggests.

For a practical estimate of the friction, I would suggest that a simple linear interpolation (straight line between the adjacent points in the table) will suffice.

Having said that, the gap between 5pi and 7pi is a bit large,
which will result in a simple linear estimate being less than ideally accurate.
If data in this region is vital, then the more accurate exponential fit is indicated.

#### theTreeSpyder

Figured out what i was doing wrong, thanx.
.
For my usage, the focus is the brake force yield for controlled lowering of heavy wood, mostly. Was amazed at what a small 2" pipe could do, then to find the secret was degrees, rather than inches of contact. Then can also see how this must play out inside of knots, and then also the other side of the coin of that gives the control on the grabbed host; especially useful in a special class of sliding knots called 'friction hitches'.
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Thus, larger host drum/pipe/branch/capstan would be for strength and softer arc deformity of rope around arc
>> NOT brake force by size of branch/pipe etc. eye may say but rather brake force is determined by the amount of half turns
extending to inside of knots, friction hitches (knot internals and friction hitch rope on rope grabs) etc.
.
i never went to school for this, but can joyfully report the numbers do define what have been witnessing and feeling thru these systems. This is my take on a simplification for others like me; to focus on the degrees/radians once round friction co-efficient (pi x coefficient) and exponential growth realized:
.

.
Cracking the code
>>and so by extension can fill in the blanks:
(otherwise known as mebbe i don't get out enough cuz find this exciting)
.

.
But, i do have other questions; of small blanks to fill in.
And hope this is the proper place!

#### theTreeSpyder

Figured out what i was doing wrong, thanx.
.
For my usage, the focus is the brake force yield for controlled lowering of heavy wood, mostly. Was amazed at what a small 2" pipe could do, then to find the secret was degrees, rather than inches of contact. Then can also see how this must play out inside of knots, and then also the other side of the coin of that gives the control on the grabbed host; especially useful in a special class of sliding knots called 'friction hitches'.
.
Thus, larger host drum/pipe/branch/capstan would be for strength and softer arc deformity of rope around arc
>> NOT brake force by size of branch/pipe etc. eye may say but rather brake force is determined by the amount of half turns
extending to inside of knots, friction hitches (knot internals and friction hitch rope on rope grabs) etc.
.
i never went to school for this, but can joyfully report the numbers do define what have been witnessing and feeling thru these systems. This is my take on a simplification for others like me; to focus on the degrees/radians once round friction co-efficient (pi x coefficient) and exponential growth realized:
.

.
Cracking the code
>>and so by extension can fill in the blanks:
(otherwise known as mebbe i don't get out enough cuz find this exciting)
.

.
But, i do have other questions; of small blanks to fill in.
And hope this is the proper place!