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One handed rod: test, length, action
and distance of casting  
The distance of bait casting ~ speed of its acceleration (see  "Spool and Distance of casting").
It is possible to accelerate a bait and by stake. But up to rather low-level speed.
The human muscles are powerful, but unfit to develop this power with major accelerations, speeds. "Muscles" of a rod rather feeble, but the elastic rod is capable to develop the power of straightening with huge accelerations and, in the issue, speed of a bait. At casting by a "normal" rod are present and stake-like acceleration, and investment of energy in curving a rod, and return by it of this energy.
It in ideal - all on-maxima. Actually is far from being everyone are capable to understand and to accept the rod, often it is simple on mismatch of its "inquiries" to properties of an organism of the owner. Not speaking that the abilities-properties of rods differ extremely  and  the abilities to stake-like qualities and "ejectional" (*) qualities always contradict one another.
Certainly, so everyone attempt (on-maxima), including by lengthy rods, with different techniques of casting. But, at first, is not always came to hand to have time just for "breaking" a rod on-maxima and to have time for receiving from it on-maxima; secondly, the "breaking" descends in a major degree not by mass of a bait, but by mass of a top of a rod plus by a heightened air resistance. And it is - useless expenditures of forces and time of casting, they in what are enclosed at "breaking", for that and will be spent at unbending. To bait from this part of energy nothing gets... In-general, the stake can add to casting, but can even and take away from it.
Specially notably it at a casting by one arm.
Mechanics of casting by two arms and one arm very much differ. At a casting by two arms more all acts the body on a hogging and shoulders, two shoulders. Work power, but the rather sluggish muscles (fig. see higher).
At a casting by one arm the operation by turn of body is essential and the operation by a forearm and hand is very much essential. The hand "picks up" the acceleration by turn of body, by a shoulder and forearm and is capable itself to add a rod rather high speed. But only if the inertance of a rod not too major - and first of all it means, that a rod is not lengthy. I shall remind, that the inertance of a rod at approximately roundabouts depends on masses of a bait and rod only linearly, and on length of a rod quadratically, i.e. approximately so: if the rod is twice longer, the inertance of tackle is higher approximately in four times. Plus a heightened air resistance. Total for acceleration of a bait by a rod-stake of twice greater length it is necessary to apply an effort in 5-6 times greater. And speed of the end of a rod (i.e. bait) thus will be higher only in 2 times.
Conclusion (and stimulant for further research): stake-similar component at a casting by one arm most likely only in a minus. And the "shooting" component should be saved at a level of lengthy rods... The short rod for one arm should be fast on straightening and "slow" on curving under a  working  load.
I score: all said concerns only to casting qualities of a rod and their usage. There is still operation of a rod on animation, retrieving, hookset and landing. Requests of good operation of a rod in all stages of fishing are contradictory, some compromise therefore is always searched. In-detail, for fast power landing of a large fish it is desirable to have a reserve in the "line test", and it just and evolves in partial stake-similar behaviour of a rod at casting (the presence of the tighter bottom of a rod, than it is necessary for casting of concrete baits).
So, stimulant: desire to find a construction of a rod for long-distance, but comfortable one-hand-held casting. Despite of losses in sense of operation on landing, bandwidth on mass of baits etc. In conditions of low probability of a picking of a large fish, when for catching even something should be much and far to bombard, it is expedient (with allowance for that a multiplicator with a strong line even on a feeble rod - in itself it is awesome weapons in a more-less skilful arms).
The compromise: always it is possible to use a rod with the higher bait test, than it is necessary. Distance and ease of casting are notably worsened, but "backbone" is magnified.
In due course will be and mathematical calculations, and reports of experimental results, and pictures-illustrations, and recommendations.
Now I can only say with confidence: it will be unusually and even surprisingly short rods.
(*)  The "ejectional", "shooting" qualities or component here in the sense that it is present and acts the mechanism accumulating our energy rather slowly and donating it in a useful work fast (catapult, bow, arbalest etc). Though alone mechanics of catapult etc. absolutely other.

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