What can be approach of balancing canard glider model?

Question

There are a lot of instructions out there about balancing classic wing configuration glider models. The center of gravity should be approximately 25% to 30% from the front edge of the wing, which is easy to control. The next step is flight tests and adjustment by adding or removing weight or moving the wing forward or backward. Using this approach I constructed several gliders with stable horizontal flight.

But what can be approach for balancing canard configuration glider model? Is it the only recommendation for the canard wing to produce more pitch applied to the center of gravity then the main wing produces, is it possible to verify this somehow before testing flights?

Answer 1

Static longitudinal stability is defined as the tendency of the airplane to pitch down when it slows down and vice versa. In other words, when the lift coefficient goes up, the pitch moment coefficient must go down. This is expressed in equations like $$-\frac{c_{M\alpha}}{c_{L\alpha}} = \frac{x_N - x_{CG}}{l_\mu} = X\%$$ with X a positive number between 0.1 and 0.2. $x_N$ is the lengthwise coordinate of the neutral point, counted positive backwards, and $x_{CG}$ is the lengthwise coordinate of the center of gravity. The neutral point of both surfaces is at their respective quarter point and the combined neutral point sits between both, proportionally closer to the larger surface. Place the center of gravity X% of the mean aerodynamic chord $l_\mu$ ahead of this common neutral point and your stability is X. 0.2 is a rather high value and 0.1 makes for better performance but also less inherent stability.

Now all that is missing is that elusive neutral point of a canard. To explain what follows, it is the combination of the neutral point of both surfaces scaled by their area and corrected for the downwash of the forward wing which reduces angle of attack changes on the rear wing. Since only the inner wing will be hit by this downwash, we need to get a grip on the fraction of the wing which is exposed. This involves the span ratio of both wings $\frac{b_c}{b}$ and the taper ratio $\lambda = \frac{c_{outer}}{c_{inner}}$ of the main wing. $$x_{N_{canard}} = \frac{x_{N_{canard}}\cdot c_{l\alpha_{c}}\cdot S_{c}+x_{N_{wing+fuselage}}\cdot c_{l\alpha_{w+f}}\cdot S_{w+f}\cdot\left(1-\frac{\delta\alpha}{\delta\alpha_W}\right)\cdot\frac{2+(\lambda-1)\cdot\frac{b_c}{b}}{(1+\lambda)}}{c_{l\alpha_{c}}\cdot S_{c}+c_{l\alpha_{w+f}}\cdot S_{w+f}\cdot\left(1-\frac{\delta\alpha}{\delta\alpha_W}\right)\cdot\frac{2+(\lambda-1)\cdot\frac{b_c}{b}}{(1+\lambda)}}$$ In absence of a precise value, use 0.7 for the downwash factor $\left(1-\frac{\delta\alpha}{\delta\alpha_W}\right)$.

Answer 2

Exactly the same as a conventional wing/tail. You use the combination of lifting torques around the center of gravity to balance at the center of gravity. With some planes this is as easy as detaching the horizontal stabilizer from the back and putting on the front, with up lift instead of down force. Very appealing to the eye but ...

You now must evaluate stability, especially in pitch. Essentially, a canard reverses the role of tail and wing, you now have a much smaller fore wing, and the main wing (tail) must provide stability. With deltas, this is very practical, giving their large trailing edge area. With a straight wing, the results can be disasterous, as seen on the USAAF Ascender.

A lower aspect wing would be more stable with a canard, but the conventional high aspect wing sailplane design with a rear mounted horizontal stabilizer is hard to beat.