To : Howard's #12 and Larry's #13 -
Thanks for adding things learned since!
I may have to dig back into the relevant threads to get a clearer view of the sideslip action...
Please keep in mind I first played with these things in the mid-1970's, when few people applied the full-scale aerodynamic, and even space-age, technologies as we do today for our toy airplanes. I just used the theoretical g that
would be needed IF we flew a 5' radius. Bill Netzeband eventually wound up agreeing with the 17 to 20 g some have observed. He admitted he wasted a lot of effort trying to achieve that 5' radius...
The formulas I used were very basic - Lift, Induced Drag, CF, etc., etc. And, no, Larry there is no universal magic number for line rake or leadout separation... I suspect you knew that
Each model's dimensions, including CG location, were used. I even came up with a solution for the theoretical panel length difference. Approached this way:
All forces applied to the model in flight have lines of action. If a force's line of action does not pass through that hypothetical point, the CG, it forms a torque tending to rotate the model until the force
does pass through the CG.
The aerodynamic performance across the wingspan is affected by the gradually increasing velocity from the inboard tip to the outboard tip. Lift, in other words, is not centered at the physical mid-point of the span.
The CG is usually within the fuselage, spanwise, or very nearly so when the model is neither connected to the lines nor moving in its basic circular orbit at flight speed. Differing lift between the physical half-spans means that its theoretical center point is somewhat outboard.
That's where it seems sensible to hang the fuselage, AT the dynamic mid-point of the wing's lift in flight. The weight of the fuselage, engine and
empennage, ahem... would not be off center, causing a torque trying (unsuccessfully) to roll the model until it lines up.
This involves the shift of lift AND tip weight... Simplest starting point to find the needed tipweight is to balance half the weight of the flying lines. Trim to perfection from there; you'll have enough for a safe first flight. The idea is that in the neutral condition, low, level, steady flight, the flier carries half the lines' weight and the model carries the other half.
The shift of lift, in a simplified reduction, should be close to the (ready?) cube root of the average of the cubes of the dynamic radii. Lift's dynamic radius? The actual radius to the point lift is equal to the inside and to the outside as the model flies in that neutral condition. It includes some of the length of the flier's arm, of the line connector overhang, the eye-to-eye line length, the distance from the connectors at the inboard wingtip and the span to the outboard tip.
Would an example help?
Arm: 24" from center of rotation to handle
Handle Overhang: from 2" to however long the cable is to the flying line connectors. We'll use 6".
Flying lines: 60' (720")
Wing leadouts to "last airfoiled rib": say another 6"
Span: 48"
So, we have the inboard tip term: (24+6+720+6) and outboard tip term(24+6+720+6+48).
Cube each and average them.
Find the cube root of the average.
Subtract that from the outboard tip term to get the dynamic spanwise lift center location measured from that tip, or subtract the inboard tip term from the dynamic spanwise lift center. Either way finds the intended location.
So, these two factors try to reduce a 'mass' imbalance due to tip weight, and to try to place the fuselage and assorted bits ON the center of the wing's lift in flight.
Line pull is one of the major forces on the model, and it provides a large stabilizing factor. Somewhere in the neighborhood of 3g is a generally acceptable SWAG. For a 4 lb model, that's 12 lbs. The various shifts from perfectly aligned trim due to maneuvering are immediately countered by the way they tend to aim pull force away from the CG. ...creates a restoring torque ...trim is quickly restored. Is even takeoff thrust as much as 12 lbs?
Now, let's see what word was posted while I was typing...