It is not to difficult to calculate the theoretical maximum horizontal casting distance for any combination of: rod length, line length, height of the butt end of the rod, and angle of the rod. If you assume perfectly straight lines. The actual casting distance in practice would be shorter. To figure out the actual casting distance, accounting for line sag, would require a lot more information about line weight and a lot of dealing with centenary curves. More effort than most people would be interested in doing. Then on the stream wind would introduce new factors.
However, a lot of people, from time to time, do get interested in thinking about the idealized maximum casting distances. Or even the shortest and longest effective fishing range. And giving it a little thought can provide some insight into what changes to your system will really do for you. I myself got interested in this short of thing six years ago. I think one of my major insights was discovering a 2 foot longer rod, will not let you cast 2 foot farther away. You only gain about half the distance as the increase in rod length. For example a zoom rod going from 3.9m to 4.5m. Is about 24inch extension.
Here are a few links from people who have given this kind of thing some thought in the past.
tenkarakebari blog Line Lenght
The above webpage has this interesting table. But all the combinations of rod length and line length use lines longer than the rod. From 1.28x for the 5m rod + 6.4m line at a height (h) or 1 m. to 18x for the 3.5m rod + 6.3m line at h of 2m.
h = height of rod butt above ground. See the diagrams on the webpage.
Column 1 = Rod Length (竿長)
Center Column = Flying/Flight Distance (飛距離) , aka casting distance.
Right column = Line Length (ライン長)
Units (単位) = m, meters.
The most interesting thing is if you calculate the ratio of casting distance ÷ (rod length + line length). Almost all of them come out close to .71.
iow casting distance will be about 71% of the total length of rod length + line length.
Regardless for the h value. At least for all the combinations the author used. And notice that he increased line length as h increased.
The author also wrote something I am not sure I agree would work with other combinations of rod length + line length.
That casting distance or the horizontal distance on the water, (水平距離) = 1.414 * z + h.
Where z = rod length, and h = height of rod butt above ground. And 1.414 looks like the square root of 2 , to me. 1.41421
For example, on this next website, which sadly is now missing one diagram, the above formula doesn’t work. However he is using a 3.6m rod + 7.2m line. At an h of 1.5m. The above formula gives a horizontal distance of 6.59m, But his diagram shows 8.5m. Or 78% of the sum of rod length + line length. A little higher percentage that the previous table. Maybe this only happens when line length is 2x rod length. I doubt many people fish with a line that long. 1.375x is as long as I am comfortable fishing. Occasionally a little longer. But most often 1.25x.
And of course my own explorations from six years ago. Done in public where some people gave the same reaction that Gressak mentioned. wth?
TUSA Forum Daniel’s Article on long lines
One of the more interesting casting diagrams was on a website that has disappeared off the web. However, I can find it on web archive wayback. But it lacks the diagram, that included some practical considerations. Such as at what distance do you hit a red zone where the fishing efficiency would be poor due to too much line on the water making the kebari move unnaurally. Fortunately, I also saved the diagram. And my explanation or understanding of it.
archive of Master of Tenkara Line System
This diagram is intended to show the effective casting & fishing range when using a 3.6m rod with two different lengths of line, a 5.5m line and a 6.9m line. Assumes casting distance to surface of water, from full height of fisherman, ie not wading. So a more practical or common setup used by more people.
Rod height 1.7m (5’7”) with 3.6m ( 11’10”) rod.
Red/Blue diagram line for fising lines of either of two ratios, - total length of 5.3m ( 17’5”)
a) 3.6m line + 1.7m tippet = 5.3m ( authors preference is to use long tippet)
b) 4.5m line + .8m tippet = 5.3m ( author says a beginners set up )
Black dot or Red dot lines
Both are 6m ( 19’9”) + .9m ( 36” or 3’) tippet = total length 6.9m (22’9”)
Basic summary is you can effectively fish over a range of 2.25m ~ 7m ( 7’ 5” to 23’) when using a 3.6m rod + 5.3m line.
You can effectively fish a range of 5.5 ~ 8m ( 18” to 26’) when using a 3.6m rod + 6.9m line. But if you lower the rod to 10:00 , 30 degrees, with the same line you hit the red zone from 8m to 9m and the line will be to slack with to much line on the water , resulting in unnatural movement of the fly and you can not fish this range well with this set up, the fish will ignore the fly.
If using a 4.5m rod + 6.2m line the effective fishing range is longer, extending from 4.3m to 9.5m ( 14’ to 31’3.25”) The bottom rectangle box below the graph.
This is fun stuff only if you’re into this sort of thing. But not to long, Then there’s this
Some things are just not understandable.
After a while pondering, it is best to just go a fishing.