. Conclusion

A simple approach to design a small remote control glider or airplane has been presented. It is based on a hierarchy of computer models, that help with the sizing of the wing, using a rapid prototyping code, estimating the take-off velocity with input and best estimate of rolling conditions, and finally, an equilibrium code that analyzes the equilibrium in various phases of the flight, from take-off to cruise and descent and provides the flight envelop in which the airplane is controllable with the tail as a function of the static margin. The design of winglets that contribute to improved efficiency by decreasing the induced drag, is also discussed along with trimming the glider for maximum distance or maximum duration. Lastly, it is shown that with a classic configuration, the wing and tail sizing and the center of gravity location can be found to make the tail a lifting tail at take-off, which is desirable for a heavy lifter airplane.

11.4 Problems

Aerodynamic Center of the Glider

Derive the formula

from the linear aerodynamic model of Sect. 11.2.

Equilibrium Equation for the Moment

Show that the equilibrium equations can be combined to eliminate CW from the moment equation to give

Xca

Cm о +—- a (CL cos в — CD sin в + CT sin(a + в + т)) cos(a + в) = 0

Iref

Global Aerodynamic Coefficients of a Glider

A glider has the following lift and moment characteristics in terms of the geometric angle of attack a (rd) and the tail setting angle tt (rd):

CL(a, tt) = 5.0a + 0.5tt + 0.5, CM, o(a, tt) = —1.3a — 0.4tt — 0.1

Find the effective aspect ratio AR of the glider (wing+tail) assuming ideal loading and

dCL 2n

d a 1 + 2/AR

Give the definition of the aerodynamic center.

Find the location xa. c./ lref of the aerodynamic center.

Find the location xc. a./ lref of the center of gravity, given a 6 % static margin of stability SM = 6.0.

Derive the expression for the moment about the aerodynamic center as a function of tail setting angle tt, i. e. CM, a.c.(tt).

Find an expression for the moment about the center of gravity CM, c.a.(a, tt). Which condition holds for the moment about the center of gravity at equilibrium? Find the equilibrium condition aeq (tt) and CL, eq (tt) for the glider.

If the glider take-off lift coefficient is CL = 1.5, find the equilibrium angle of attack aeq and corresponding tail setting angle tt.

Explain and sketch under which condition the tail can create positive lift at take-off.

Acknowledgments One of the authors (JJC), acknowledges that part of the material in this chapter was originally published in the International Journal of Aerodynamics, Ref. [4].

References

1. Bertin, J. J., Cummings, R. M.: Aerodynamics for Engineers, 5th edn., pp. 653-656 (2009)

2. Munk, M. M.: The Minimum Induced Drag of Aerofoils. NACA, Report 121 (1921)

3. Chattot, J.-J.: Low speed design and analysis of wing/winglet combinations including viscous effects. J. Aircr. 43(2), 386-389 (2006)

4. Chattot, J.-J.: Glider and airplane design for students. Int. J. Aerodyn. 1(2), 220-240 (2010). http://www. inderscience. com/jhome. php? jcode=ijad