Harmonic Analyzer Appendix A

Use of Natural Resonant Vibrational Frequencies And Resonant Vibrational Mode Shapes To Measure Performance Characteristics of Fishing Rods There are two theories that form the basis for this technology: • That the natural resonant vibrational frequencies of a fishing rod precisely describe the stiffness of the rod as it is used – in a dynamic setting. • That, when a fishing rod is vibrated at its higher natural frequencies, the locations of the “nodes” or points of minimal motion, precisely describe the stiffness distribution of the rod as it is used – dynamically. Frequency Theory It is a well-developed fact that two structures with the same weight, weight distribution and stiffness will have the same natural resonant vibrational frequencies. If the weight and weight distribution are held constant but the stiffness is increased, the natural resonant frequencies of the structure will increase also. The simpler the structure, the more direct the relationship between the stiffness change and the frequency changes. This theory was applied to golf shafts by Dr. Joseph Braly in 1977 (US Patent 4,122,593). In this application, the first natural vibrational frequency of a golf shaft is used to measure its stiffness.

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Sketch of Dr. Braly’s Frequency Measuring Device

Fishing rods are even simpler structures than golf shafts, since they have virtually no requirement to resist torsional loads. The current method of measuring the stiffness of a fishing rod is to mount the fishing rod horizontally, held only at the grip. A weight is then placed on the tip, and the tip is allowed to deflect. The relative distance of the deflection compared to other rods is used to determine the rod’s stiffness rating. There are no standards for the method of gripping the butt section, the mass of the weight used, or the amount of deflection for different standard terms used to describe rod stiffness.

D

W Current Method of Measuring Fishing Rod Stiffness

Node Theory Most structures have more than one natural resonant vibrational frequency. For the simplest structures (the strings of a violin or guitar) the frequencies are simple mathematical multiples (harmonics) of the lowest resonant frequency. A fishing rod is only slightly more complex: it is held at only one end, and the stiffness is not the same throughout the rod. The rod is considerably stiffer at the butt than at the tip. The distribution of stiffness varies greatly from one rod to another, depending on how it is intended to be used. If a fishing rod is vibrated at any of its higher natural frequencies, vibrational “lobes” will form. These lobes will have a roughly sinusoidal shape, and there will be small concentrated areas between lobes where the fishing rod is virtually stationary. These points are called “nodes.” Node 2

Node 1

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Rod Vibrated at Its 3rd Natural Resonant Frequency, Showing Lobes and Nodes

There is a very strong relationship between the distribution of stiffness in the rod and the location of these nodes. For example, compare three rods that have the same stiffness at the butt and tip, but have different stiffness distributions between, as shown below.

Rod B

S tiffn ess

Rod A

Rod C

Butt

Tip Three Different Rod Stiffness Profiles

If Rods A, B and C are all vibrated at their third natural resonant frequency, the lobe sizes and node locations will be very different. The nodes on Rod A will be closest to the tip, followed by the nodes for Rod B, and lastly Rod C. Rod A Node Locations

Rod B Node Locations

Rod C Node Locations

The current method of measuring the stiffness distribution of a fishing rod is purely judgmental. A rod like with a stiffness distribution like Rod A would be called a “Fast” rod; one like Rod B would be called “Moderate;” and one like Rod C would be called soft or “Parabolic.” These terms have no thresholds or values associated with them. Theories Combined If Frequency Theory and Node Theory are combined, we now have two tools that give us the capability to describe the overall stiffness and stiffness distribution of a fishing rod with a high degree of precision. We also have a method for distinguishing between two rods that are each suited for different species, sizes of fish and methods of presentation. Using the method currently employed in the market, sensitive 6-ft walleye-specific rod with a stiffness distribution like Rod B above would probably be called a 6-ft medium rod. However, a 6-ft rod intended for bass fishing, with a stiffer action and a stiffness distribution like Rod A would also be called a 6-ft medium rod. These rods would be sold in different markets, and the rating only has meaning within the sub-market, species and presentation techniques at hand. On the other hand, the Frequency/Node system would give a more meaningful description of the two rods. The walleye rod might be a 6-ft 30-Hz rod with nodes at 4 and 22 inches. The bass rod could be a 6-ft 42-Hz rod with nodes at 3½ and 18 inches.

Implementation of Frequency Matching Technology In Fishing Rods First of all, I think it would be useful to explain the similarities and to draw some distinctions between the Frequency Matching technology we have licensed from Royal Precision Golf and the technology I am proposing here. •

The Frequency Matching technology for golf clubs and shafts was originally patented by Dr. Joe Braly in the late 1960’s. Only one patent is currently in force. There are two elements to the technology: 1. Frequency is a better way to measure the stiffness of a golf shaft in play than static deflection (simple bending with a weight). 2. There is a natural progression of stiffness for virtually all golfers - as clubs get shorter, they need to get stiffer in a linear relationship.

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•

The technology that we have developed agrees with Dr. Braly’s first conclusion – frequency is a better way to measure the dynamic stiffness of a golf club… or a fishing rod. Node 2

Node 1

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1. 2. 3.

• The technology we have developed goes beyond Dr. Braly’s patents and ideas in several areas: Dr. Braly’s technology is only concerned with the first natural frequency (“cpm”) of a golf club. We look at a minimum of two higher natural resonant frequencies. Dr. Braly’s technology is not concerned about the stiffness distribution in the shaft. We are – very much. Dr. Braly’s patents rely on a single deflection of the club, and measures only the first natural frequency as the shaft’s vibration damps down. We excite the rod continuously and look for resonances.

•

Our technology was developed independently of any activity by Royal Precision Golf. It is derived from our patented Mode Sync golf club technology. Technology Implementation There are three levels at which we can implement this technology. Each can be implemented separately, all can be implemented together, or the three could be implemented sequentially in stages. The three separate levels of implementation are…

• • •

In design and verification of the performance of our designs As a new way of assuring that our rods are consistent As a new way of describing rod action and power for the consumer

At this point, we have only filed a disclosure statement on this technology. We are in position to move forward with one or more patents, but it is not urgent to protect our position.

Each of these levels has benefits and costs associated with implementation. The paragraphs below describe what we have already done, and what would be required to implement the technology at each level. Design & Design Verification This process is already implemented in PI. We use this technology especially when we have a “target” rod that we are trying to equal or surpass. Using the 2 separate pieces of analysis equipment we constructed in 1997, we can find the natural frequencies and node locations of the target rod. Then we design and build our prototype, and test it side-by-side with the target, modifying the patterns, the mandrel, even the guide type and spacing, until we have the desired frequencies and node points. We have found that we can pass the “golden-elbow” test far more consistently using this technique than simply building to a deflection profile. The open questions are if/how we market this, or do we keep it a trade secret? I recommend that we keep this specific application of the technology a trade secret as long as it is the only level we have implemented. Even with patents, this application of the technology would be virtually impossible to defend, because it would be practiced in the back labs of our competitors. There are no obviously measurable product characteristics that we could use to prove that a competitor is in violation. Implementation as a Production Quality Assurance Tool Perhaps the highest level of benefit would come from using frequency matching and node locations as a quality assurance check. To maximize the benefits and minimize the cost impact, the test should be done on blanks prior to painting. The current production method used by Maibor on golf shafts would make sense. The blanks are frequency tested after the mandrel is extracted, the tape is stripped and the blank has been cut to length. This frequency should be slightly higher than the final frequency. The difference between this “raw” frequency and the target frequency can be used to determine the amount of material to be removed in sanding. The node locations of the raw blank will determine where the material needs to be removed. There are four things that need to be done to implement this technology for quality assurance: 1. We need to build a version of our “rod shaker” that is more production friendly. For example, we need • a faster clamping method that is set up for blanks instead of complete rods, • a simpler way of getting the unit tuned to a desired frequency, • simpler power controls, and • a “ruggedized” way of shaking the rod (maybe heavy duty speakers, maybe an electric motor). None of these are difficult challenges. A machine suitable for manufacturing use could be developed and tested for $7,500 to $10,000 in about 90 days. Depending on the complexity of the waveform generator required and the method of shaking the rod, these machines should cost between $1,500 and $3,500 each.

2. We need to develop a system of tolerances for frequency and node location. This would require some work at the factory… • looking at current production batches of blanks, • determining what tolerances the factory are typical now for frequency and node locations at different quality levels, and • correlating these to distinguishable differences in rod “feel.” Starting this process would require 2-3 weeks, and could be integrated with the training program for the technicians that would be using the machine in production. Afterward, the factory technicians would have to participate in collecting additional statistical data to substantiate early conclusions and sharpen our estimates. 3. We need to set in-process sample rates for the factory to determine what percentage of the blanks and/or complete rods would be checked at each level of quality. For Techna AV fly rods, we might want to inspect 100%; lower levels could be set for other fly rods and lower yet for saltwater and freshwater actions. These levels need to be set in conjunction with the Quality Assurance staff here and in Asia, and including the input of the factory engineers. 4. We need to work with the factories to develop a cost impact for implementing this technology. This cost will include the cost of doing the test, plus some predicted change in blank scrap rate as a result of the test. This would be determined from the statistical data the factory collects after the system is set up in the factory. From the limited data we have, we project that implementation of this technology in production would have the effect of raising the “feel” consistency of our fly rods above the Sage rods we have tested. We would also have a much better story than they do. If we want to implement this level of the technology in a Fenwick fly rod series for the May ’00 sales meeting, we need to move forward on the project immediately after the May ’99 sales meeting. At that time, PI would have to begin immediate development of a production-friendly rod frequency-analysis machine. The development should be complete not later than August ’99. At that time, we would ship the machine to OTG-DG and spend 2-3 weeks there evaluating blanks, developing tolerances, training OTG-DG technicians in use of the machine, and starting the negotiation of the cost impacts of implementation. This should put OTG-DG in position to receive a new rod design based on this technology in September or October, with enough development and production test time to support a May ’00 introduction. Implementation in the marketplace would require an effort similar to but not quite as complex or complete as the implementation of a whole new rod rating system. Many of the elements overlap, but we would not have to impose a whole new numbering system on the public at the beginning. From a public perception standpoint, the rating system could follow this implementation, and would be a natural outgrowth of it. At the end of the first year (or two), the consumer should be asking, “How does Fenwick make their rods so consistent?” The answer would come in the next year: “Because they are using Frequency Matching to test their rods, and now they’re going to share that knowledge with you.” It is a multi-year campaign that must be on-message consistently from throughout the campaign for it to stick in the consumers’ minds. This is patentable technology.

A New Consumer System for Rating Rod Performance & Behavior The current systems that our competitors and we use to describe the performance and behavior of a rod do not do the job. As a result, we leave the consumer confused about what rod to buy, and why one rod is better or more expensive than the next. There are three problems with the current systems used to describe rod action and power to consumers. The Fenwick Action/Power concept was an improvement, but it is not understood widely and suffers from some of the same problems listed below. •

•

•

The ratings are descriptive but are not quantitative – there is no specific value for what “Medium” means or how much different it is from “Medium-Heavy.” The fly rod line-weight rating system is slightly better, but it still suffers from a second problem that most other systems also have: the issue of “Fast” vs. “Moderate.” How fast do you have to be to be “Fast?” Where does “Fast” end and “Extra Fast” begin? They’re arrived at by subjective human judgements – I call it the “golden elbow” system. The problem with it is that Barry Day’s elbow and Vic Cutter’s elbow have different opinions of what a Medium is… at least they usually do on Tuesdays. On Wednesdays, they usually are closer together, unless Barry has lunch at the L.C. Stadium Lounge. Then you have to factor in… • the difference in gravity between Spirit Lake and Huntington Beach, • the barometric pressure, • wind chill factor, • hours of sleep the night before. On several occasions we have given each of these great fishermen the same rod on two different days, and we have gotten two different opinions of the action of that rod. Not to pick on them – they are more consistent than anyone I know. The bottom line is that no human is consistent enough. The systems are all based on static measurements of deflection and bend profile, but rods are used in a dynamic way. A 6’6”MH Hank Parker crankbait rod and a Techna AVC66MH baitcasting rod have close to the same deflection, but they sure don’t feel the same. Dynamically, they aren’t even close.

There are four technical aspects that need to be in place to make Frequency Matching useful to the angler: 1. He needs to understand that frequency is a better way to express the stiffness of a rod. Golfers understand this about their clubs, so there is some history that it can be done, as well as how. 2. He needs to understand that the node locations are a much more precise and descriptive way to express exactly how “fast” or “moderate” a rod really is. 3. He needs to know that there are “ideal” frequency ranges and node-location ranges for each different style of fishing and rod length. For example… • The ideal frequency for a 6’6” crankbait rod is between 30 and 35 Hz, regardless of what it is made of.

•

The ideal node locations are around 4” from the tip and 22” from the tip. A 6’6” topwater rod should be much higher frequency – above 50 Hz – and the nodes should be closer to the tip – 3½” to 3¾” and 19½”. • Fly rods are a little more rational, probably because they have to be able to keep a standard-weight line in the air, and that requires a specific frequency response to loading. A good 5# rod (regardless of length!) has a frequency around 19 Hz ±1; a 6# is in the 22 Hz ±1 range. Node locations vary with the “speed” of the rod, but the first node is around 7½” to 8½” and the second node is between 40” and 44”. A very sophisticated fisherman could get to the point that he knew what frequencies and node locations within these ranges work best for him. 4. We would need to start including the design frequency and node location data in the variable copy on our rods. Some further technical work - an absolute maximum of 3 months - would be needed to identify “ideal” frequency and node-location ranges for some casting & presentation styles we haven’t already analyzed. With an expenditure in the range of $5,000 - $10,000, we should be able to get some academic backup from Dr. Ken McConnell at Iowa State. He was the key resource in the development of Mode Sync technology for Fenwick Golf. By far the most costly and difficult aspect is the communication of the system to the angler. It would require a complex thrust including PR/press relations, some advertising, consumer shows and grassroots work with store managers and clerks. The sports and outdoor writer group would be particularly important in the promotion of this system, because a consumer is more likely to read a long explanation by a theoretically unbiased writer than from us. PI would have to distill this complex theory down to understandable concepts, and would have to be available for extensive interviews by writers. It would take time and money – how long and how much are questions I do not have the knowledge to answer, but a plan could be developed with Marketing and Sales as team members. This technology is patentable, and a patent should be pursued if we choose to take this approach.