A Journey into Rotational Moment and a Bespoke ESZ Rivermaster Z2 4.5

Article by Gary Mineart

In late summer 2023, the Driftless Region was characterized by exceptional drought and low water levels in the spring-fed limestone creeks comprising the bulk of the prime target trout habitat. I found myself heading out to previously unexplored locations including the confluence of cold water creeks with their larger downstream waterways. In these areas where the shiryu transitions to the honryu, micro-habitats form as summer trout in the relatively warm river water tend to congregate immediately downstream of the creek mouth where cold water from the tributary mixes into the main flow. Some of the trout here are surprisingly large compared to their small creek counterparts. These confluence areas also include relatively unobstructed casting space and the perceived need for a bit more reach into the main river.

I was happy with my modest personal stable of four-meter rods as my go-to “big” tenkara rods, but became intrigued by some of the new honryu rods making their way to the retail market. When the ESZ Rivermaster Z2 4.5 meter (m) hit the street earlier in the year, the specifications seemed to scratch a lot of my itches. The 92 grams (g) weight was in Shimano and Nissin territory. I liked the continuity and robustness of its longer rod blanks with their anti-stiction rings. The advertised 4.5 Rod Flex Index, 6:4 action, and “reasonable” Rotational Moment (RM) of 9.1 all seemed to be in my desired wheelhouse. The price for the Z2 was less than half of a River Peak Kiwami Honryu 45. So I took the plunge.

My enthusiasm waned once I got the rod out for its initial field test. Initial reviews and a few subsequent YouTube posts claiming good balance, an attribute that certainly applies to the Rivermaster Z1 and the 390 centimeter (cm) version of the Z2, seemed wildly overstated for their 450 cm sibling. Within the first 20 minutes arm fatigue became problematic, akin to one-arm casting a keiryu rod. It felt surprisingly tip heavy and took considerable effort to cast while holding the short, cylindrical cork grip. I subsequently tried casting while holding the rod blank above the cork grip with the base of my palm against the winding check. This reduced the rotational resistance but quickly resulted in major discomfort in the smaller fingers of my casting hand. I simply could not zero in on a comfortable technique to fish the rod effectively.

Savvy tenkara rod reviewers almost always qualify their reviews by stating the only way to know a rod’s true performance is to fish with it. Sage advice, but quantitative tenkara rod specifications are ubiquitous these days and shared with the expressed purpose of facilitating comparisons with other rods and complementing subjective on-the-water reviews when they’re available. In my experience with the Rivermaster Z2 4.5, the available quantitative specifications fell short of a full representation of the rod’s performance, at least in my hands.

A Closer Look at Moment of Inertia

Dr. Tom Davis of Teton Tenkara renown and contributing Tenkara Angler author has discussed this topic on several occasions. His early 2013 thoughts on moment of inertia engendered a wave of follow-up interest. In 2022 he introduced his readership to the concept of RM, an index adopted by the Japanese company Gamakatsu for basic rod comparisons that remains in wide use today. RM is calculated by multiplying the weight of the rod in kilograms (kg) times the distance in cm from the butt of the rod to its center of gravity (CG; often called the rod’s balance point) with the rod fully extended in its “fishing” configuration (i.e., no tip plug). While technically having units of kg-cm, RM values in tenkara rod specifications are usually presented as unitless indices.

Although a bit dated by evolution of the tenkara industry since its publication in 2019, Dr. Paul Gaskell’s article Your Tenkara Guide to The Good, The Bad, and The Ugly (available on Discover Tenkara) remains one of the best web-based descriptions of tenkara rod development history and measures of rod performance. In the final section of this article, Dr. Gaskell relates an observation regarding RM when discussing his work in helping to create the Hakusan zoom rod. Using RM concepts alone, if one counterbalanced a rod by adding weight to the butt end, one might expect little if any improvement in rotational resistance since any shift in CG toward the butt of the rod would be offset by the increase in the total weight of the rod.

What Dr. Gaskell observed during his participation in the Hakusan development was that this weight-to-balance assumption was an oversimplification. A heavier rod can actually feel lighter in the hand when casting, depending on the grip configuration and the rod’s weight distribution. He deemed this observation counterintuitive and characterized it as “weird.” Anyone who has had the pleasure of fishing Masami Sakakibara’s Oni Type-I understands this enigma. While not the lightest four-meter rod on the planet, its balance may be unmatched. As Linda Richmond of Saturday Night Live Coffee Talk fame would say, it feels and casts “like butter.”

To Dr. Davis’ credit, he recognized and reported in his 2022 article that a moment of inertia calculation would be more accurate but considerably more cumbersome, making adoption of RM more straightforward, easy to calculate, and useful as a specification for rod-to-rod comparisons. He shared the mathematical derivation for moment of inertia shown below (humorously and self-effacingly stating it made his brain hurt):

What is interesting about this equation is that it represents the moment of inertia about the end of a uniform rod. In other words, if other real-world variables are set aside for a moment (e.g., uniformity, thickness, flex, etc.) this represents the rotational resistance due to inertia if one could somehow pivot a uniform rod of negligible thickness at the focal point coincident with its end (for a tenkara rod, by its butt cap).

Now examine the moment of inertia derivation about the CG of a uniform rod:

Note how the moment of inertia changes linearly for a uniform rod of negligible thickness, and the factor of four change in the magnitude of I from the rod end to the CG. Thus, it is four times easier to “swing” the uniform rod about its CG than at its end. Instinctively this makes sense. If you perform an experiment by grabbing a dowel at its center and rotating it by twisting your wrist, the force needed to overcome the at-rest inertia is much less than if you held the dowel at its end. Given that the CG for a uniform rod would be found at its midpoint (i.e., L/2) it logically follows there would be a point between the CG and the end where I = 1/6 ML² and at that point of rotation, it would be twice as easy to overcome static inertia when compared to the rod end and twice as hard compared to the CG.

To be fair, tenkara rods do not have negligible thickness nor are they uniform along their length. If one makes a gross approximation of a tenkara rod of non-zero thickness but uniformly tapered and of uniform density, some interesting qualitative comparisons with the uniform rod are possible.

First, the CG location of the tapered rod (A) is shifted to the right compared to the uniform rod due to the gradually increasing mass (dm) resident in each differential segment (dr) of the rod as one moves from left to right. Second, the intermediate point (C) is also shifted to the right; however, note the length of A to C for the tapered rod is greater than the length of C to B, again due to the differential mass (dm) for each differential segment (dr) of the rod on either side of C. The moment of inertia is no longer changing linearly along the rod but exponentially. Selecting an axis of rod rotation at a point further to the left of B appears to be equally if not more important in economizing the moment of inertia than shifting A (the CG) to the right through alteration of the mass distribution of the tapered rod (i.e., counterbalancing).

The composition and weight distribution along an actual tenkara rod are complex and variable. Drawing calculable conclusions from the tapered rod example would be a stretch and likely a bridge too far. The example does illustrate a contributing factor that may already be intuitively obvious—the grip position on the rod and its location relative to the rod’s CG and axis of rotation rival the magnitude of the standalone RM specification in providing insight into a rod’s rotational resistance.

Tenkara rod grips come in an almost limitless number of lengths, girths, shapes, weights, and configurations. Tenkara anglers have a wide range of preferences regarding where and how they hold those grips, especially for shorter and lighter rods (those with an RM < 6). It would be nearly impossible to define a universal specification for these rods that captures the axis of rod rotation as a function of hand position. Furthermore, the rod’s axis of rotation is dependent on an individual’s casting style. A big arm swing moves the axis of rotation closer to the butt of the rod. For a wrist-dominated cast, the axis shifts back in the direction of the CG.

Is it possible to simplify the situation for tenkara rods with a relatively large RM? For starters, unless one has an arm like Dwayne Johnson or is just plain masochistic, one might conclude most honryu and keiryu rods, when casted one-handed, are usually grasped with the index finger somewhere in the vicinity of the winding check rather than with the palm near the butt of the grip. Also, presuming a somewhat “normal” casting motion, the stronger muscles in the arm will involuntarily come to the rescue of the wrist while casting a tip-heavy rod. The axis of rotation naturally settles in a location somewhere near or below the base of the palm.

Recognizing the inherent variability, I nonetheless settled on a grip position with the tip of my forefinger on the winding check and identified a presumed, notional location of the axis of rotation at the base of my palm. I measured the distance from the winding check to this point of rotation, and for the scale of my hand this measurement was approximately 16 cm. This result led to a personalized rod specification (RM’) defined as the weight of the rod in kg times the distance (r’) in cm between the rod’s CG and the location of the theoretical axis of rotation resulting from the aforementioned notional grip position. It seemed plausible that relative RM’ values might add insight into the expected balance and “feel” among these longer, bigger rods.

Table I provides calculated RM and RM’ values for a representative subset of honryu-class tenkara rods with the Oni Type-I also included for contrast. The rods are listed in order of increasing RM value. The data were obtained from manufacturer’s websites, reputable online rod reviews, and physical in-situ measurements. Rod weights are rounded to the nearest g with length measurements to the nearest millimeter.

TABLE I.  RM and RM’ Values for a Subset of Tenkara Rods

Rod	Weight (kg)	r (cm)	RM	Grip Length (cm)	r’ (cm)	RM’
Oni Type I (4m)	0.086	63.5	5.2	30.0	49.5	4.3
Shimano Honryu Tenkara NP44	0.084	94.0	7.9	30.1	78.0	6.6
Nissin Air Stage Honryu 450	0.083	102.4	8.5	30.5	86.4	7.2
Nissin Zerosum Oni Honryu 450	0.098	88.8	8.7	30.5	74.3	7.3
ESZ Rivermaster Z2 4.5	0.092	99.0	9.1	22.0	93.0	8.6
Tenkara USA Ito (14.7′)	0.108	89.8	9.7	30.5	73.8	7.8
River Peak Kiwami 45	0.105	101.6	10.7	29.2	88.4	9.3
Wasatch Tenkara T-Hunter 450	0.130	97.7	12.7	30.0	81.7	10.6
Tenkara Rod Co. Rocky (14.5′)	0.133	102.3	13.6	35.6	86.3	11.5

Several conclusions can be drawn from the data in Table I. One immediate observation is that the RM’ specification for the Rivermaster Z2 4.5 no longer fits within the ascending order of associated RM values. Even with its relatively light weight, its short grip length is an outlier among the listed rods. The small difference between r and r’ (6 cm) results in greater perceived tip heaviness even with its overall weight advantage. It is also interesting that save for the Z2 and the Tenkara Rod Co. Rocky, the grip lengths fall within a relatively small window around 30 cm.

The grip length of the River Peak Kiwami 45 is only marginally shorter than its peers, but this difference combined with the location of its CG results in a relatively large r’ of 88.4 cm. Recall Michael Agneta’s April 2023 Tenkara Angler review of the Kiwami 45 where he characterized the rod as suffering from “short grip syndrome.” His observation lends subjective support to the tapered rod conclusion made earlier; i.e., that fairly small changes in the location of the axis of rotation in the fat part of the rod can have considerable impact on its perceived rotational resistance.

One might say these conclusions are an overly complicated way of declaring that longer grips are better for longer, heavier rods. That may be true, but certainly the distribution of weight along the length of the rod and its contribution to the CG are important factors as well. The CG should be sufficiently close to the gripping location regardless of the length of the grip. This applies to tenkara rods of all lengths and weights. The ridiculously small r value of 63.5 cm for the Oni Type-I is a testimonial to this claim.

Modifying the Rivermaster Z2 4.5

Many design and environmental factors contribute to a rod’s rotational resistance (e.g., uniformity, thickness, flex, wind resistance, line weight, fly weight, grip position, casting motion and speed, etc.). These variables complicate the ability to use RM and RM’ for comparisons between dissimilar rods. Thankfully, most of them are negligible when discussing physical modifications to one rod for one angler. Thus, armed with the additional insight above, we can return to the original discussion regarding my personal Rivermaster Z2 4.5 experience. Undeterred by the challenges, I decided this rod had too many good qualities to just abandon it. I wanted to improve its performance and believed I could do so by moving the CG closer to the butt of the rod (through counterbalancing) and moving my grip position closer to the CG (by modifying the grip).  

The counterbalancing component was easy. Experienced tenkara anglers have previously explored techniques for adding weight to the butt of the rod. Affixing coins to the inside of the butt cap is a great solution for fine-tuning, but for my application the multiple coins needed to achieve the necessary weight would be onerous. The slip-over silicon butt caps on the market could easily be weighted, but they all seemed cumbersome in bulk and downright ghastly in aesthetics.

Fortunately (for me) these ESZ rods share a design feature with Tenkara USA (and perhaps some other brands) that I considered prior to this rod modification to be the single most useless element ever designed into a tenkara rod. Of course, I’m referring to the butt cap receptacle used for storing a tip plug. (What salt-worthy tenkara angler out bushwhacking in the brush wouldn’t snag and lose their tip plug within the first 10 minutes?) To tackle the counterbalancing effort on my Z2, I took advantage of this superfluous feature by layering #9 lead shot and resin within the butt cap receptacle and topped it with a final coat of polyurethane. The result was an additional 9 g of weight and a total butt cap weight of 12.2 g.

Modifying the rod grip was a bit more involved. It’s common for tenkara anglers to employ tennis racket wrap, bicycle handlebar tape, or analogous materials to shape and optimize the effectiveness and comfort of their rod grips. Others have reshaped cork grips using a lathe or sander to better fit their hand. I remembered my involuntary tendency to grasp the Rivermaster Z2 above the winding check during my initial efforts to fish with it. In my mind’s eye I pictured a massive, nightmarish wad of tape balled up on the rod blank above the cork, a clump of dead weight, and a transformation of the rod’s appearance into a modern day Frankenstein’s monster. I had no intention of dishonoring the rod in this fashion. A more refined approach was necessary.

It was my good fortune to have local tenkara aficionado and friend Dre Fornasiero refer me to Chris Wasta of Wasta Workshops as a possible source. Chris is renowned throughout the Driftless for his high quality handcrafted split cane fly rods. He is an avid trout angler and active in the Iowa Driftless Chapter of Trout Unlimited. He is also accomplished at the vise and hosts engaging fly tying socials every month at his rustic workshop in the rugged limestone bluffs of northeast Iowa. I contacted Chris and to my delight, he agreed to take on the work of upgrading my grip as a one-time favor for a local Driftless colleague.

Chris removed the winding check, added length to the grip with multiple cork rings above the preexisting grip, shaped the upper portion of the grip on a lathe into a classic hyotan gourd (using the top half of a DRAGONtail HELLbender grip as a template), then smoothed the cork surface and re-affixed the winding check. The modified grip is 34 cm in length and adds 1.9 g to the handle section. The fit and finish is what one would expect from a master craftsman of quality fly rods. I was overjoyed with the result and am indebted to Chris for his fine work.

Quantitative Results

Table II compares the rod weights, length variables, and RM and RM’ values for the stock, original equipment Rivermaster Z2 4.5 (same values as in Table I) and the modified Rivermaster Z2 4.5 with counterbalancing and grip modifications.

Table II. RM and RM’ Values for Stock and Modified ESZ Rivermaster Z2 4.5

Rod	Weight (kg)	r (cm)	RM	Grip Length (cm)	r’ (cm)	RM’
ESZ Rivermaster Z2 4.5	0.092	99.0	9.1	22.0	93.0	8.6
Modified ESZ Rivermaster Z2 4.5	0.103	84.6	8.7	34.0	66.6	6.9

Despite adding almost 11 g to the total weight of the rod, the modified weight distribution alone reduces the standard RM value by 0.4 compared to the stock rod. The revised RM of 8.7 is identical to the frequently lauded Nissin Zerosum Oni Honryu 450. Though this reduction in RM is marginal, it is interesting to see the positive change in the face of the added weight. The CG moves a full 14.4 cm closer to the handle and, when coupled with the 34 cm grip length, the resulting r’ value is 66.6 cm—the best of all the honryu rods itemized in Table I. With an RM’ of 6.9 (presuming this measure of effectiveness is credible) and based on numbers alone, the “feel” of the modified Rivermaster Z2 4.5 trails only the Shimano Honryu Tenkara NP44. Only one question remained: how would these attractive numbers translate to on-the-water performance?

Qualitative Results

Not long after completing the rod modifications I was able to exercise the finished product on a local Iowa Driftless creek. The video log of that trip is available below.

I might be accused of seeing the outcome through rose-colored glasses but the transformation of the rod’s rotational resistance was unambiguous and striking. Arm fatigue was no longer an issue. After nearly five hours of continuous fishing, I felt as if available daylight was my only constraint. Did the rod “disappear” in my hand? Certainly not, and I doubt any honryu-class rod ever would. A rod this long and beefy will always have noticeable wind resistance. The Rivermaster Z2 4.5 will gift the user with a bit of mid-rod wobble if one tries to overpower it, but casts beautifully once the operator finds the proper rhythm. All other comparisons being equal, I can state with confidence that my modified version of the rod is superior to the factory original as a fishing tool, and by a considerable margin.

If you own a Rivermaster Z2 4.5, I strongly recommend you consider a counterbalancing strategy. It’s easier to accomplish than the grip modification and provides an immediate improvement in performance. The majority of the reduction I achieved in RM (from 9.1 to 8.7) was through counterweighting alone. The grip extension makes a huge difference in casting quality too and it’s unquestionably a worthwhile endeavor, but the work involved may not appeal to everyone.

This deeper dive into moment of inertia and its application to tenkara gave me an entirely new perspective on the complexity of a rod’s dynamics and how it affects the fishing experience. It reinforced my belief that specifications are valuable for comparing the performance of certain families of rods but may not tell the whole story on their own. The tenkara wizards are right—the only sure method of characterizing a rod’s performance is to fish with it. Lastly, I’m happy the improved performance promised by my analysis actually materialized. I now have a honryu rod I won’t hesitate to use when the conditions warrant. It sure beats the alternative of the rod finding a home among the dormant tubes collecting dust in the corner of the garage.

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Gary Mineart is a retired Earth Scientist and Space Systems Engineer, a native of Iowa’s Driftless Region, and a tenkara devotee. He shares a video log of his local experiences in previously unexplored trout habitat in the YouTube channel Tenkara in the Iowa Driftless.

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