How far can I cast when using long lines? Or fun with trigonometry.
How far can I theoretically cast using the 3 lengths of line Daniel listed in his Tenkara Long Lines article.
Trigonometry used to be as familiar to me as doing simple addition but I found it took me a while to re-awaken those skills. But, once stirred up a bit with the first couple of calculations all the rest rolled along quickly.
I wondered what casting distances I could expect if using lines with total lengths, including tippet of 19’, 24’ & 29’ (5.77m, 7.29m & 8.81m). The distances calculated are idea distances. That is no compensation for curl in the line, or for the catenary sag. I just ignored the presence of gravity. These are laser straight casting distances. Not real on the stream distances that will be a bit shorter.
The assumptions were height of the butt end of the rod were at 1.25 m or at 1.5m (49.375” and 59.35”). The rod length used was 3.9 m, = the length of the Ayu or Ito at its shorter length. The rod angle was at the 2 O’clock (30 degrees) or at the 1 O’clock (60 degrees) angle. The TCD, total casting distance, is the horizontal distance from a point directly below the butt end of the rod to the location of the kebari, as if the rod and line were laser line straight. You have to imagine you are standing on a stone in the middle of the stream and the top of the stone is at the water’s surface. The kebari is just at the water surface level.
I thought the results rather interesting.
Rods at 30-degree angle, 2 O’clock, handle height at 1.25 m. (49 3/8 “)
Line length -- > ..... 19’ (5.77m)...... 24 ‘(7.29m)..........29’(8.81m)
TCD .........................8.18m................9.93m.................11.59m
TCD ......................... 26’ 11”...............32’ 8”.................38’ 1.65”
Rods at 60-degree angle, 1 O’clock, handle height at 1.25m. (49 3/8 ”)
Line length -->..... 19’ (5.77m)..........24 ‘(7.29m)..........29’(8.81m)
TCD .........................5.40m................7.58m.................9.44m
TCD ........................ 17' 9.2”..............24’ 11.5”...............31’ 1”
Note; raising the angle shortens the distance about 2.42m, (8’)
Rods at 30-degree angle, 2 O’clock, handle height at 1.5m (59 11/32”)
(25 cm or about 9 7/8” higher handle height)
Line length -- >..... 19’ (5.77m)........24 ‘(7.29m)..........29’(8.81m)
TCD .........................8.00m................9.79m.................11.48m
TCD ....................... 26' 4”................ 32’ 3.0” ............... 37’ 9.4”
Edited : to correct mistake in last TCD numbers. The correct base number to be added is 3.3775m. By mistake the base number used previously to determine the TCD of the lines with the rod held at a height of 1.5m was 3.770m . A difference of .3925 m ( 15.5") .
Due to that error the previously entered distances were 8.395m (27' 7.6") , 10.3m ( 33' 6.5") , and 11.88m ( 39' 1" ). All incorrect and too long. And a mystery since I knew the distances should have been shorter not longer if the rod where held higher.
With the TCD now corrected for a rod held at a height of 1.5 m and at a 60-degree angle. The TCD distances for the rod held 25 cm higher now makes sense. The distances are shorter than before by 15.5", 16.2" and 15.9".
New Conclusion: Shorter people cast farther than taller people.
I did not do the calculations for the rod at the 1 O’clock , 60-degree angle and with the handle height at 1.5m. This was enough to satisfy my curiosity.
Last – line length vs. Rod Length, RL
Line length -- >..... 19’ (5.77m)...... 24 ‘(7.29m)..........29’(8.81m)
RL ........................ x 1.48............... x 1.87................... x 2.26

For those who don't like numbers. Well I guess just ignore this. I have worked in engineering for 40 years, numbers on mechanical things mean stuff to me.

If you have been casting a 4.0m line which is approximately equal to the length of Ayu/Ito then the farthest you have been able to cast the kebari is about 5.78m ( 19ft) at most. Which as you can see is several feet shorter than could be cast using any of Danie's suggested longer lines. Just trying to create a sense of reach. I know my family room is 30' x 16'. When I image casting from the door to the kitchen to the wood stove 30 feet way. I'm impressed.

Edited 2/15 to correct 60-degree TCD, they were to long by about 17' on average.