Jack Rego - Thank you for your investigation into the validity of my Table of Wrap Strengths [
www.rodbuilding.org], and for your analysis of the system using a Pulley Model. I very much appreciate your comments and input. The system is a line guide being strapped down to a rod blank by winding the thread around the rod blank and across the guide feet. And the thread’s tensile strength or the thread’s tension certainly plays a role in holding a line guide in place on the rod blank. … However, I am not 100% sure that a pulley model applies to the guide wraps quite as you are asserting. I'm gonna try not to get too bogged down in that argument / discussion. … Lots of Luck!… Here comes my explanation. … Put on your chest waders! And grab something to wet your whistle.
Jack - So you can understand my model, my view of the tensile strength was that of a series of individual HOOPS of thread holding the guide foot in place. If I exceed the tensile strength, the thread will pop. Period. There is no multiplier effect because of going 360+ degrees around the rod blank. One winding provides a strapping force equal to the tensile strength of a single strand of thread. As I see it.
I also viewed the situation as a series of individual inverted U-shaped tie-downs, like holding a canoe down on a car-top rack. There is no multiplier affect in that situation either. All I am doing is changing the direction of the force as the thread passes over the guide foot. The thread is continuous and not moving. If you've ever tried to use a pulley with a frozen bearing, I think you'll agree that the multiplier effect that is possible with a good pulley system has been nullified, plenty pronto. The benefits of or analogy to anything near an IDEAL pulley system have been lost.
[A pulley system can multiply or lower FORCE. BUT it does NOT multiply WORK. Work equals a (FORCE) times the (DISTANCE) over which that force is sustained or exerted. ENERGY is the ability to do WORK. The First Law of Thermodynamics is the Conservation of Energy and Matter: Neither energy nor matter can be further created nor destroyed. That prevents multiplication of energy in our wrap system. Remember that in a multiple pulley system, you have to pull a longer length of rope that is inversely proportional to the lower force required. The work done is equal, regardless. This type of mechanical work calculation is usually path-dependent, and is not a state- function, as in many thermo-chemical systems.]
The coefficient of static friction around the rod blank is very high, and this friction acts as an anchor for the thread. So I thought of the underside of the rod blank as acting as an anchor to hold the “over-the-top†tie-down threads in place. After all, the thread is NOT free to roll over any sort of an imaginary or virtual pulley at the top of or at the bottom of the rod blank. So I chose a model for analysis which deals with the 180 degree arc on the top half of the rod blank, and simultaneously ignored any pulley effect from a 540+ degree wrap-around view of the subject. Which again, I believe rapidly degenerates to the trivial case of the thread in a 180 degree arc. Here again, one winding provides a strapping force equal to the tensile strength of a single strand of thread. As I see it.
The LOAD on the thread may be distributed over the two halves of the thread which lie on either side of the guide foot. But since the thread is CONTINUOUS, at the point in the thread which lies directly at the top of the guide foot, the two forces of thread tension are pulling the thread apart in opposite directions, and the thread’s tensile strength could not be exceeded. If the tension in the thread exceeds the tensile strength of the thread, then the thread would pop. The whole wrap would unravel, because FRICTION has been holding the entire system in stasis to begin with. Friction from the underside of the rod blank is acting as a static anchor. As I see it.
Another way to view this system is to put aside the pulley model, and use an analysis based on STATICS. Describe the balance of the static forces that hold the guide foot in place. (Unfortunately, we don’t have a chalk board between us, so words will have to do.) The two halves of the thread each carry one-half the TENSION in the thread, and the resultant sum of those strapping forces creates a normal force perpendicular to the rod blank that drives the bottom of the guide foot straight down into the top of the rod blank. These two forces are DEPENDENT, and if the sum of them exceeds the tensile strength, the thread will pop.
The semicircular curvature of the rod blank somehow integrates the angle of exertions to have a net resultant force vector that drives the guide straight down into the rod blank. It does not spin around because of the direction in which we wound the thread. As soon we lay the thread down in the wrap, and take off our externally imposed tension force, then all the tension forces internal to the thread RE-ORIENT their direction to hold the guide in place, pulling laterally and downward. (Not in a rotary fashion, as in a pulley). The HUMP formed by the guide foot is the source of this new tension force. It is like a WEDGE (an inclined plane) pulling the thread up and toward the 12 o’clock position. But the internal molecular stretching of the thread is like a spring trying to recoil, and it is exerting an equal but opposite net resultant vector that is in static balance with the wedge-like force exerted by the body of the guide foot.
In this Statics method of analysis, there is no multiplier effect, and the maximum tension in the thread is its tensile strength. And the tension in the thread generates the normal force perpendicular to the rod blank, at any point around the circumference of the rod, thus providing the compressive force that holds the guide in place. I can postulate that the normal force equals the thread tension, but I don’t know enough calculus to integrate the force vectors around the rod blank to derive or prove that.
On a Cave-man level, I offer the following examples of a model for our system: If you wound a rope a couple times around my neck, and started pulling me toward you, the force strangling my throat would equal your pull (tension). IMO, plain and simple. End of story. Since you won’t get to do that, you could wrap a string around your finger. Pull on it. Convinced? I think you’ll soon agree that the normal or compressive force would equal your pulling (tension) force multiplied by the number of winds of thread. The multiplier effect to this force is proportional to the number of windings, not the number of legs of thread. If you use a 2-legs of thread model, then each leg’s LOAD is always ONE-HALF the tension. When summed, that puts us right back to what I said in the first place:
Compression = Tension.
Once we start sticking our sensory body parts into this model for the rod blank or for the guide foot, I don’t think we will need Newtonian calculus and integration to derive a useful mathematical description of the system. Calculus & geometry may be the best way to PROVE what I have proposed. But for now, I’m just presenting it as a hypothesis based on a decent knowledge of statics and some simple physics.
Notice that in this STATICS model of the system, we have considered this system in its entirety, and haven’t said much about any kind of a pulley, or counting ropes. (But the longer I think about it, even by the Pulley Model, there is only ONE “UP†rope for each winding of this system anyway, so it seems that my formula would still be a valid conclusion.
Compression = (Tension) x (# Windings) . )
Which is why my formula takes (the tensile strength) times (the number of winds per centimeter) and reports that value as the thread wrap band-width strength.
Wrap Strength = (Tensile Strength) * (Number of Thread Winds)
Wrap Strength = per unit width of guide wrap = Pounds / Centimeter
Wrap Strength = 10 x (Tensile Strength in Pounds) /
(Thread Diameter in Millimeters)
In a discussion that took place during Hurricane Frances last Fall 2004 with other RBOers (see Appendix), the suggestion was made that some sort of vector analysis and calculus integration around the 360 degrees of the rod blank would prove the validity of this formula. But after thinking about this at great length, it all seemed to culminate in the simple formula proposed above. That the sum of all the micro-tangents to the rod blank would exert an integrated force of compression onto the guide foot and normal to the rod blank equal to the tension under which the thread was wrapped. It just seemed like a postulate or a sound hypothesis or an inevitable result. And, for a guide being pulled STRAIGHT OFF the rod blank at a 90 degree angle, that tension would be equal to the TENSILE strength of the thread. …
Now – IF the direction of pull were PARALLEL to the rod blank, then the TENSION under which the thread was wrapped would be the operative force. And that tension would, of necessity, always be less than or equal to, but never greater than, the TENSILE strength. And that FRICTIONAL force would equal the coefficient of static friction (close to 1.00 in this case) times the effective normal force (the thread TENSION).
Frictional force = (coefficient of friction) * (normal force)
Frictional force = (coefficient of friction) * (thread TENSION) * (# of windings)
[Note: In physics, the “normal†force is the resultant force or pressure exerted onto a flat surface at a 90 degree angle. If the surface is curved, then the normal force is perpendicular to a tangent to that curved surface.]
I realize this may seem like a confusing distinction between two different restrictive forces: a FRICTIONAL force that prevents the guide from SLIDING around on the rod blank; verses a TETHERING force that prevents the guide from RIPPING away from the rod blank.
But think of it this way: If the thread is wound slightly loosely over the guide foot, you can still slide the guide around or up or down the rod blank somewhat easily. The thread TENSION is near zero. But you are unable to pull a double- footed guide straight off the rod blank, at a 90 degree angle to the rod blank, because it is the thread’s TENSILE strength that is restraining the guide. That is NOT a frictional force; now it is a TENSILE issue. But with low-tension in the thread, the COMPRESSIVE (normal) force driving the guide foot into the rod blank is low. Since the compressive force is low, therefore the normal force is low, and therefore the strapping force restricting the guide movement from rocking or sliding is also low. The guide will move around, but not really get ripped off the guide blank. …
Everyone who wraps their line guides on loosely enough to align them slightly after they are finished wrapping all the guides has utilized this principle and distinction between these two very different restrictive capacities of the band of thread holding down the guide foot. Again, whether you are aware of it or not. And, yes, math is involved here, like it or not, and some high school physics, too.
Jack – One thing that should NOT be in dispute is that I did say that those Tabulated values are RELATIVE and INTERNALLY CONSISTENT. As you, or anybody else who is facile in arithmetic, run the numbers yourself, you will see that the formulas are actually very simple, as shown above. And the calculations are performed consistently. So your implication, Jack, that an error exists merely means that the Wrap Strengths could all be exactly off by a factor (of 2.00). Which would not change the RELATIVE RESULTS or the COMPARISON of Strengths. Or the conclusions I would draw from those comparisons. … But I do appreciate your bringing this Pulley Model of the situation into view. I know that the system LOOKS LIKE it fits a Pulley Model, but it does not seem TO ACT like a Pulley.
And I think that I have made a fairly good argument to support my assertion that even by using a Pulley Model, we would arrive at the same results and conclusions as when using the Statics Model.
Wrap Strength = (Tensile Strength) * (# Windings)
Jack - I am open to amending my model and analysis, or putting some new factor into the equation-calculation if you, or anybody else, can offer further explanation for why my model or my equations need correction. My background relevant to this discussion is a college course in non-calculus physics, a course in engineering statics, and lots of systems analysis from thermo-dynamics in chemical engineering. From that standpoint, or from someone who has actually measured the forces involved, I am open to correction. (See Appendix)
Sincerely, Cliff Hall, Gainesville, FL-USA+++
cmkmhall@ufl.edu
P.S. – And, Yes, Mr. Tom Kirkman, I do concede your comment that A-size thread is strong enough to hold the guide, and that greater abrasion resistance is about the only reason that requires a heavier thread. As I recall, you and others have repeatedly said that it takes at least 30+ pounds of straight pull directly on the ring of a single-foot guide to begin removing it from under any decent thread wrap. And that the guide frame seriously deforms before the foot is pulled free. My Table of Wrap Strengths shows that even the weakest (NCP-A) has AT LEAST 125 pounds of tensile holding capacity for a 1.00 cm guide foot. And even SILK-2/O has 160# per cm. Regular Nylon-A also has 160# per cm. Therefore, any of these sizes and styles of thread (Gudebrod) would be several (3 to 5) times stronger than required to hold the guide. … Therefore, I will re-iterate my original comment (to Ken Saums) that a single overwrap of any size thread is sufficient.
But given that Jack Rego questioned the validity of the CALCULATIONS and the THEORY in my Table of Strengths, that took this discussion into an analytical, rather than an applicational, direction. Thank you for your indulgence, Tom K.
–Cliff Hall+++
APPENDIX: For a look at a seminal Post on this subject, read:
Thread Tension Measuring Device ?? Ken Driedger 09-07-04 [
www.rodbuilding.org] . In this day and age of digi this and digi that, is there a simple inexpensive measuring device that measures relative thread pressure/tension/around a cylinder, such as a rod blank, or a fly-fishing hook, by a pre-test around the device? -Ken Driedger.
IMO, the comments of Robert Huisman and of Steve Daley (excerpted below) support the formulas and analyses which I have made above. -Cliff Hall+++.
Re: Thread Tension Measuring Device ?? Robert Huisman 09-07-04 19:58
The measure of tension would be a tangent at any point on the circumference of the rod. Again if you took some scales and measured around the circumference, you would find that one pound of tension produced one pound of tension at any point. -Robert Huisman.
Re: Thread Tension Measuring Device ?? Steven Daley 09-07-04 22:55
It seems as if you want to know the resultant force from wrapping, rather than the tensile force from "pulling", the thread around a cylinder. The force is applied tangent to the cylinder. The only real shear forces inherent to wrapping is by squeezing / stretching the thread to wrap it. It then reaches an equilibrium. (Like putting a rubber band around something. If you stretch it, and then just place it around an object at intervals, with one end pinned. It will strangle it with the same force as if you put tension on it to stretch it out while winding.) -Steve Daley.
Edited 3 time(s). Last edit at 11/12/2005 10:52AM by Cliff Hall.
