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Measure the Catenary Depth of Your Bait

October 17, 2010

The St. Louis Arch is probably the most familiar example of a catenary curve to Americans.

Catenaries are important to the troller because it is the basic shape that a trolled line takes on if it has some kind of terminal tackle, such as a lead weight and a lure, attached. If you imagine a heavy weight at the end of your line, and a fair amount of line out, the line will take on a steep curve at the weight, gradually becoming a shallower curve near the boat. You see than that the depth increase per foot of line out is greatest near the weight, and continues to diminish as more and more line is let out.

The way an engineer would solve the problem of depth vs line out, is to calculate a formula for the curve by the looking at the basic laws of classical mechanics to determine the fundamental drivers; in this case the unit weight of the line, its diameter, and the towing +- the current speed. He or she would then perform a series of manipulations and calculations to get the depth at any point on the curve. I will be publishing a set of tables like that in the next week or so, but I cannot possibly cover every possible combination of leader length, line time, blades or no blades, lure or live bait, etc.. So I am going to present here a way to measure the depth of your presentation that relies strictly on measurements that can be taken from the boat using simple carpenter’s tools, a pencil, paper, and some addition and some way to measure the line out. You can mark your line with a tape measure and spray paint if you want to keep strictly in the realm of carpenters tools, or you can use a line counting reel. This is an extension of my post regarding the “Guestimator Tool,” which only works on lead core line with a minimal type of terminal tackle.

The important thing to remember is that this curve keeps roughly the same shape, no matter how much line is out, as long as you don’t hit the bottom 😉 Imagine a sheet of paper covering the image, level, and revealing the curve as you slide the paper from bottom to top. The curve as it is revealed will be the curve as the line enters the water.

Your task is to measure the angle of the line at different points as the line goes out, creating a series of triangles, for which you have the angle and the approximate hypotenuse. From this you can calculate the depth gained from each section of line using trig. Add them up, and you have a decent measure of the depth of the end tackle. If you are using a long leader, do the measurements for the leader as well. This technique will only work if you use a neutrally-buoyant, weighted, or diving bait. If you want to run a Jitterbug on the end, you are on your own.

Make up whatever kind of angle measurement apparatus you can with the stuff in your tool box, or from the local hardware store to measure the angle of the line in degrees as accurately as you can. Use the following table to estimate the depth increase (Factor) for the section of line you let out.

Angle Factor Angle Factor Angle Factor Angle Factor
90 1 67.5 0.92388 45 0.707107 22.5 0.382683
87.5 0.999048 65 0.906308 42.5 0.67559 20 0.34202
85 0.996195 62.5 0.887011 40 0.642788 17.5 0.300706
82.5 0.991445 60 0.866025 37.5 0.608761 15 0.258819
80 0.984808 57.5 0.843391 35 0.573576 12.5 0.21644
77.5 0.976296 55 0.819152 32.5 0.5373 10 0.173648
75 0.965926 52.5 0.793353 30 0.5 7.5 0.130526
72.5 0.953717 50 0.766044 27.5 0.461749 5 0.087156
70 0.939693 47.5 0.737277 25 0.422618 2.5 0.043619

Make up a table for your measurements, using the example as a guide:

Line Out Length Angle Factor Depth Running Total
10 10 50 .76 7.6 7.6
20 10 40 .64 6.4 14
30 10 30 .5 5 19
40 10 20 .34 3.4 22.4

Use the running total to get the depth at 10, 20, 30, and 40 ft. The smaller the sections the more accurate, in theory, but measurement error will probably erase any gains by trying to get too cute. If you do this once, or better yet, a few times for each rig and take the averages for each speed or set of conditions you wish to know the table, you can have a create a set of personalized depth charts for your gear. Laminate them, and keep them on your boat. The beauty of this method is that it takes into account local conditions. Any pre-calculated tables would inevitably ignore many factors to make the math workable, like doing the measurements on a cold, still, lake. When our like is “cold and still”, we are fishing through the ice.

This technique will also work for divers, which create the same kind of curves

Good luck.

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