"Turning the corner" is the trickiest part of a single, and IMHO the reason it's so hard for people to learn it thoroughly. It certainly was for me.
It doesn't help that it's so similar to a switch, yet so different - most casters do many times more switches to singles in their practice routines. It's so close in mental and physical concepts that we tend to attempt a switch cast with a change of direction instead of a single spey. Although one could argue that the single spey IS a switch with a change, conceptually true but the differences between the two are distinct and the key to success lies in these differences. The devil is indeed in the details.
I know of three ways of turning the corner worth covering in my class. The first is the basic turn with a dip, the second is the more advanced method of using no dip and regulating applied power and body turn (advanced single per Gawesworth), and the third is a slight variation of the advanced single spey but broken down into a 'carry and coerce' sequence, which is my preferred method for mid to long belly lines.
This topic warrants it's own thread, images and even videos. Written word can not do it justice... however I am working on a new edition of my class handouts so will give it a shot as it might help that cause to try to describe it purely through words...
First and foremost, in spey casting I believe the body accomodates the arms, the arms do not accomodate the body. This is something I find myself saying a lot during classes, because I think it's human nature to use fulcrum motions of top/bottom hands to prevent the body from turning, moving, etc. We are efficient that way in conserving body movement, but that does not load the rod properly. The body must move fluidly with the sweep so that rod maintains a full and stable load as it turns the path of the line around the corner.
Case in point:
If we started with the body facing the dangle and tried to complete the cast without moving the body, we'd be twisted like a pretzel by the time the d-loop was ready.
Conversely, if we started with the body in final d-loop position and left the body stiff we'd be better off, but would have to use our arms with a lot of top and bottom hand travel during the lift and sweep to keep the rod loaded properly, which is difficult and unnecessary. The chances of being consistent using a stiff body and lots of arm travel are very low unless using a very short head where it doesn't matter. With mid, long or extended belly lines this is hard work and problematic for most if not all casters.
It's much more effective to coordinate the turning of the hips to accomodate the position of the arms and thus the rod load, held stable as the corner is turned. The objective is to load the rod smoothly and evenly over it's entire length and hold that load captive in the blank as you turn the corner.
How much rotation?
I am a strict believer that the body should begin facing the dangle (or at least the point where the lift is transitioned into the sweep), then turn in concert with the loaded rod like the spindle of a compass until the desired casting angle is reached - through the sweep.
In other words, for a 90 degree change where 12 o'clock is the target angle, the pickup (left bank) begins at a 9 o'clock dangle and the stop of the rod tip occurs around 5 o'clock to the rear. That's a 225 degree rotation of the rod tip.
The hips however only need to rotate from 9-ish to 12 o'clock (or whatever the target angle). During the sweep the loaded rod and hips should turn together until the hips are square to the target (12 o'clock). That's only a 90 degree rotation of the hips.
Stand up and try it. (yes, they all do think we're nuts)
Once hip-square the shoulders and arms continue around leaving the hips behind at 12 o'clock. The rod tip continues all the way to about a 5 o'clock in order to align the d-loop straight ahead. This does not mean my arms rotated to 5 o'clock, it just means that if you drew a line through both hands that line would point to 5 o'clock if my body were the spindle. In fact the rod does exactly that, form a line through both hands.
In the left-bank right-up single spey my bottom hand ends up out in front of my right armpit or thereabouts (depending on desired stroke length).
The right hand is up and out to the side as if I were a valet holding a tray of martinis in a crowded aisle - resulting in the rod being in the proper angle for a good load when the d-loop forms.
The coersion of the d-loop is done using the energy that was held in the rod during the hip-rotation, which by the way originated all the way back in the lift. The load is continuous throughout. A little (keyword little) bottom hand goes a long way here.
Can the hips rotate more?
Sure but they don't really need to. The only advantage I see is a possible elongation of the casting stroke by incorporating a reaching drift.
Breaking this down...
So the lift is the lift is the lift, and in a switch cast we can transition directly into the shoulder/arm powered d-loop movement because our hips start square and remain square to the target the entire time.
BUT in a single spey, one must add a coordinated rotation of the body/rod after the lift and before the d-loop turning the hips from dangle to target. During this rotation the rod should keep the load intact and deliver it to the d-loop once the hips are square to target. This movement where the hips are turned in concert with the loaded rod is what I have coined "the carry" of the line between the lift and the d-loop.
If you can 'carry' a tight line 180 degrees, even 360 degrees while the line follows in an smooth tight elongated curve, you know you have got it going right. At that point simply stop the hips and allow the shoulders and arms to coerce the d-loop at a 5 o'clock attitude to the target and you know the rest from there.
Some casters will allow the energy in the rod to fluctuate from lift to sweep to d-loop. In other words, the lift flexes the rod, recoils, then the sweep re-flexes the rod, then the d-loop is pushed back with an entirely separate recoil motion. The key to smooth effortless change of direction is to blend the lift flex into the carry flex into the d-loop flex... for that matter right into the forward cast. I believe when we watch a very experienced old timer doing his spey poetry on the water, that continuity is what we are observing. Every ounce of energy in one move is leveraged into the next.
Often casters will push/pull the two hands during the lift or sweep. Some will argue that this is fine and is a matter of style and indeed some do it well however I believe such fulcrum movements are best reserved for the forward cast and not the lift and carry.
With very short scandi/underhand style lines we can get away with maneuvers made with nothing more than a bottom hand pivot on a small axis but this is not realistic for mid-belly and long-belly lines.
Line (/rod) length matters:
Shorter spey lines can be brought around the corner with just about any method you choose. I recall fishing very short Skagit-style heads in the late 80's that I could stop, tie my shoe, and finish the cast between the set and the cast on a 15ft rod. Not so with a long belly line, the timing window and margin for error while turning all that moving line around a corner is small. Elongating the line through maximum tension helps by keeping the longer heads aloft and manageable in a horizontal plane.
About the dip:
I broke from tradition a bit and purposely left the dip out of the discussion until the end. In an ideal world we would be able to learn how to single spey without it. But the dip does make it easier to turn the corner, here's why:
We all know by now that when there is a dip in the rod movement the line loses it's steam in the original direction. This is pretty easy to envision if we are pulling a streamer in our hand as we run and let the hand dip downward, making the rest of the line follow the downward turn, then slowly come back into line. The dip releases some tension in the most critical point, the front nearest the rod.
It's easier to turn a corner when there is a dip introduced for this very reason. A slight dip takes the leading tension out of the line for a moment so that the line can be pulled in another direction and the corner can be turned.
However the dip must be very slight to avoid side effects like upriver bloody-L's and crashing anchors, and it trades-off some energy for an easier direction change.
I'll cover that in detail later... the important thing about the dip is to keep it slight, shallow and small, only what you need to turn the corner. With practice, that can be none at all.
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