On the minimization of cruise drag due to pitch trim
A blended-wing-body is an example of an aircraft configuration with multiple control surfaces. The most effective use of these control surfaces, e.g. to minimize cruise drag due to pitch trim, or to maximize pitching moment at low speed in an engine-out condition, leads to optimization problems. This kind of control optimization problems can be addressed by the method of Lagrange multipliers; this allows for multiple constraints, e.g. constant lift, each associated with one multiplier. The value of the multiplier is a measure of the severity of the constraint, e.g. the drag penalty of imposing pitch trim at constant lift. The estimates of the Lagrange multipliers for different control surfaces also indicate the evolution of the iterative process to find the optimum. Three distinct initial conditions to start the iterative process are considered. The method is applied to multiple control surfaces, taking into account their mutual interactions and also the influence of shifts of center of gravity. It is shown in a particular case that it is possible to achieve pitch trim in cruise with drag reduction relative to the untrimmed case. The minimization of cruise drag with pitch trim and unchanged lift, i. e. same airspeed and altitude, is considered for a flying-wing configuration, using several strategies from part A plus a few additional ones for a total of eight. Of the four non-optimal strategies, only strategy II of using the centerbody elevator alone leads to drag reduction, albeit with a large deflection and increased angle-of-attack. There is drag increase for the strategies: (I) of equal deflection of all control surfaces; (III) preferential deflection of inner control surfaces with an aeroelastic limit of 7.5º; (IV) equal contribution to lift for all control surfaces. The two optimal strategies V using Lagrange multipliers after a few interactions give: (VA) a drag reduction for a good initial condition like strategy II; (VB) a drag increase for a poor initial condition like strategy I. A sub-optimal strategy VI of using multiples of optimal deflections, with a multiplication factor determined by lift equilibrium, requires a larger angle-of-attack, and thereby increases drag. The strategy VII of deflecting all control surfaces in two groups to minimize trim drag, leads to a larger angle-of-attack, and thereby increases drag. The strategy VIII of using the two most effective control surfaces with opposite drag slops gives the best compromise: (i) lift balance with unchanged angle-of-attack; (iii) second best drag reduction with small control deflections. The latter justify the use of linear aerodynamics and reduce the risk of adverse aeroelastic effects.