## A closed-form trim solution yielding minimum trim drag for airplanes with multiple longitudinal-control effectorsNational Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Division, 1989 - Mathematics - 24 pages |

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### Contents

LOTS for TwoLiftingSurface ThrustVectoring Airplane | 11 |

Appendix ASurface Deflections | 18 |

References | 24 |

### Common terms and phrases

aerodynamic center aerodynamic surfaces aft tail airplane with s.m. airplane with thrust angle of attack appendix body reference line canard Cm,o Configuration lift coefficient cos(a cruising flight deflected thrust downwash drag coefficient drag equation drag over nonlinear effective trim drag equations eqs estimated example airplane example three-surface airplane flight condition hoc methods induced drag induced lift influence coefficients influence matrix influence terms influence-coefficient matrix Lagrange formulation Lagrange multipliers Langley Research Center lift coefficient Figure lift forces linear optimum trim longitudinal load distribution Mach number minimum trim drag moment-trim equations Nondimensionalized nonlinear optimization routine nonlinear optimum solution nonlinear programming optimum trim solution Percent of increase percent stable simplex algorithm sin(a solution for example static margin supercirculation surface deflections surface lift coefficients techniques three-lifting-surface airplane three-surface solution thrust coefficient thrust deflection angle thrust loss thrust recovery thrust-vectoring airplane trim surfaces trim-drag reductions trim-error reduction Two-Lifting-Surface variable vectoring Vertical trim wing