Rod Moment of Inertia

Although I am not a physicist or an engineer I like to try to classify rods, particularity tenkara rods. As you are aware, the "standard" way to classify a tenkara rod is by where in the rod it begins to flex, or its point of flexure. This is often given in a ratio such as 5:5, 6:4, 7:3, etc. We've all seen this and we've all had issues with this system.

Other methods of trying to quantify rod action have been proposed. One such method is the Common Cents System (CCS). This uses simple tools, all readily available, that are then used to measure the flex of a rod. Step #1: The butt of the rod lays exactly horizontal and the length of the rod is measured. Step #2: This number is divided by 3. Step #3: A small, very lightweight bag is attached to the end of the rod. To this bag is added US pennies (specifically those minted after 1996) until the tip of the rod reaches the number calculated in step #2. The Common Cents System is easy to do, reproducible to within an acceptable error, and can be done quickly.  Chris Stewart of Tenkara Bum has a nice CCS database of common fixed-line rods already calculated.

One thing the CCS doesn't do is adjust for rod length. If one rod has a CCS of 18 pennies but its overall length is 270 cm, and another rod has a CCS of 18 pennies but its overall length is 400 cm I guarantee that do not feel the same when being cast. The 270 cm rod will feel pretty stiff, while the 400 cm rod will feel softer. So, to get length out of rod comparison, take the CCS (in pennies) and divide it by the length of the rod (in meters). This will give you (what I call) the Rod Flex Index (RFI). The smaller the RFI, the softer the rod. In our example above, the 270 cm rod will have an RFI of 6.67, while the 400 cm rod will have an RFI of 4.5. As you can readily see 6.67 and 4.5 are not the same number. Thus the RFI tells you that the 270 cm rod will be stiffer (faster) than the 400 cm rod (this is irregardless of the rod's 5:5, 6:4. 7:3 rating given by the company/manufacturer). The RFI will give you a better idea of how the rod will feel and how it compares to other rods than the CCS or the 5:5-6:4-7:3 system.

Although both the CCS and RFI give the user some idea of the rod's overall action and comparison to other rods they don't let you know how much force will be required to stop that rod in mid-air and change its direction (as in casting the rod). This is where Moment of Inertia (MOI) comes in. A rod that has a larger MOI will be more fatiguing over hundreds of casts than a rod that has a smaller MOI. The formula for MOI is: MOI=rod mass X radius^2 or I=m*r^2. Here is an easy online calculator to use. I use (g)m^2 as my units, where g=grams and m=meters.

From http://www.sexyloops.com/articles/swingweight.shtml

Another way to look at MOI as it pertains to fly rods is by what is called the "swingweight". Many sports use swingweight. These included tennis, baseball (the bat), squash, golf, etc. Basically any sport that uses a swinging tool uses swingweight. In these sports, the swingweight is the MOI around a predetermined point. For tenkara, the swingweight can be easily estimated by the MOI around the rod's center of gravity (or balance point from the rod butt) when the rod is fully extended.

Take for instance my Daiwa LT36S-F. This is a beefy 360 cm tenkara rod that is not as delicate as other rods. It has a mass of 82.4 g. When fully extended, it has a center of gravity (balance point) of 76.5 cm from the rod butt. This gives it a MOI or swingweight of 48.2 (g)m^2.  Now compare the Nissin Zerosum 360 7:3 which has a mass of 67 g and a center of gravity point at 72 cm. This give the Zerosum a MOI of 34.7. Therefore, the Zerosum has much less MOI than the Daiwa and will be less fatiguing over the course of fishing many hours. BTW, this is exactly what my personal experience with these two rods has shown!

Here is a better definition of MOI. This is from the calculator page: "The moment of inertia calculates the rotational inertia of an object rotating around a given axis. It represents how difficult it overcomed to change its angular motion about that axis. Moment of inertia of a same object will change against different axis. The more far away from the axis, the more moment of inertia the object has."

MOI doesn't take into account the overall length of a rod, but other formulas do. Personally, I find the other formulas too complicated. MOI is easy to calculate and rods can be easily compared to each other, particularly if they are approximately the same length (as in the LT36S-F and the Zerosum 360 7:3).

Here are some other rods that compare to those provided above:

Tenkara Times Try 360 6:4...............................MOI 32.9 (g)m^2
Nissin Zerosum 360 7:3.....................................MOI 34.7
Nissin Pro Spec 2-way 7:3.................................MOI 39.1 (at 360 cm)
Tenkara Times NEXT 360 5:5...........................MOI 42.1
Tenkara Rod Co Sawtooth.................................MOI 44.8
Daiwa LT36S-F................................................. Moi 48.2

Here's another 360 cm rod I have on hand, but I suppose it doesn't count when compared to those above -- because I wrapped the butt section with a tennis racket grip!! Its MOI is low however.

Suntech Suikei GM 39 Keiryu Special.................MOI 33.6 (at 360 cm)


So MOI is another rod comparison tool. Now you can get an idea of a rod's flex score (CCS), overall action and action comparison to other rods (RFI), and how fatiguing it will be (MOI) all without ever seeing or casting the rod! It's not perfect but it should help a lot when you want to know whether to spend your hard earned cash on that shiny new tenkara rod!! But remember: If you really want to know how a rod feels, casts, fights a fish you have to feel it, cast it and fight fish with that particular rod YOURSELF.

I'm sure I'll hear from you math brainiacs out there that I'm wrong and not to quit my day job, but what do you think? Would adding the MOI to my RFI rod comparison table be helpful?

Special thanks to David Walker for piquing my interest in MOI.