Control line lateral-directional flight mechanics is (are?) pretty complicated. Lots of effects are in play. We use trial and error to pick a combination of values for wing asymmetry and other parameters that works. Various combinations work, some better than others. My Impact’s left wing is .624” longer than its right wing. My ciphering here is to show how the effect of wing asymmetry by itself varies with line length and wing shape for simple trapezoidal wings. All calculations assume a 60”-span wing of 700 square-inch area with no fuselage.

There are various ways of making asymmetric wings. Which one you pick depends on whether you’re starting with a stack of ribs, a top and bottom wing mold, a pair of templates for cutting foam wings, or a stack of foam wings that are already cut. For this analysis, I took a ratio of tip chord to root chord, a wing area of 700 square inches and span of 60 inches, then solved for root and tip chords. I used the same root and tip chords for all wing length calculations for a given taper ratio. To calculate asymmetry, I started with equal-length left and right wings, then iterated by lengthening the left wing and shortening the right wing the same amount until dCm/dα of the whole wing reached a target. For most cases, the target was the dCm/dα of a wing with taper ratio .7 and span difference of .624”. For fun, I also calculated asymmetry for a target of zero. Zero dCm/dα is where the wing rolling moment is balanced by offset alone. This is probably what folks calculated before the discovery of the miracle of tip weight.

I’m assuming that the left wing is the one toward the inside of the circle. Sign changes are left as an exercise to people who fly the other direction.

I used the Schrenk approximation to calculate wing loading. This looks kinda suspicious, but it seems to be pretty accurate for subsonic wings with little sweep and a reasonably high aspect ratio. The Schrenk approximation assumes that the air load on one side of a wing is proportional to the average of its actual planform and a quarter ellipse with the same area (figure 1). A further complication for control line airplanes—the reason for this exercise—is that airspeed varies along the wing, and the aerodynamic force at any point on the span is proportional to dynamic pressure (q), which is proportional to the square of the airspeed. I weighted the Shrenk “chord” for right and left wings by r^{2}/R^{2}, where r is the distance of a point on the span from the center of the flight circle, and R is the distance of the wing root from the center of the flight circle. Figure 2 shows the dynamic-pressure-weighted loading for a 60” total span, .7 taper-ratio wing of equal right and left lengths, with wing root 70 feet from the circle center.

Figure 3 shows how asymmetry of the 60” total span, .7 taper-ratio wing varies with distance of the wing root from the circle center. The red curve is for dCm/dα equivalent to my wing with .624” span difference at 70’ circle radius. The blue curve is for rolling moment balanced by wing asymmetry alone. The difference between the two is pretty constant at .704”.

Figure 4 looks peculiar. It says a constant-chord wing would need more offset than a tapered wing for a given dCm/dα. That’s what I think Serge said, but opposite of what I think Kees said. It’s not intuitively obvious to me, but I can’t find anything else wrong with my calculation.

Figure 5 shows the effects of both taper ratio and wing-root circle radius on the amount of asymmetry equivalent to that of my .7-taper-ratio wing with .624” span difference at 70’ circle radius.

Ken mentions flap effects, and thereby hangs a tale. We typically separate wing loading distribution into two parts: “basic distribution”, which is the part due to twist and camber, and “additional distribution”, the part that varies with angle of attack (p. 10 of Abbott and Costello, if you’d like to sing along). The stuff I did is for “additional distribution”. Basic distribution is zero for unwarped stunt or combat planes without flap deflection. Flap loading is generally part of basic distribution, but stunt flap deflection is related to angle of attack. Tip weight required, for example, is a function of both. To figure the effects of flaps, you’d need airfoil data vs. flap deflection all along the wing. We can get this now from programs like Javafoil, and it would be interesting, but it’s beyond the scope of this short monograph.