Abstract
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, pitching or other moments, 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.
Highlights
Minimizing drag in cruise is most important for aircraft emissions and economics since this is the longest phase of most flights, and where a large proportion of the total fuel is burnt
In a blended wing body (BWB) configuration, with control surfaces both on the centerbody and wing, there are multiple control surfaces; arises the question of which is the best combination of all available control surfaces to achieve pitch trim with least drag
The optimal Lagrange multiplier λ indicates how much the constraint of constant pitching moment M * penalizes the minimum drag D*, i.e. a large λ indicates a large effect on drag D* to achieve the required pitching moment M * and a small λ indicates a small effect on drag
Summary
Minimizing drag in cruise is most important for aircraft emissions and economics since this is the longest phase of most flights, and where a large proportion of the total fuel is burnt. The BWB offers superior lift-to-drag ratio over conventional configurations, promising lower fuel consumption; these benefits will be achieved more fully by minimization of any additional drag due to pitch trim in cruise [6-9] This is an instance of flight control and stability with multiple controls [10-17] that is relevant to novel aircraft designs like flying wing [18-39] and box-wing [40,41] aircraft. In order to have the starting values for the optimization procedure, the cruise condition of a flying-wing (FW) or Blended Wing Body (BWB) configuration is trimmed using the elevator alone (strategy A); the optimization method (strategy B) moves away from this initial condition and uses deflections of all five sets of control surfaces (section 5). The computational cost of the algorithm is small (seconds in a PC) and the iterations map a neighborhood of the optimum
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