The Unsteady Forces on Finite Wings in Transient Motion. Part I. Initial Aerodynamic Forces Following a Sudden Change of Incidence. Part II. Transient Lift and Moment Functions for Rectangular and Delta Wings

Abstract

Part I. The forces and moments on wings of finite aspect ratio undergoing a sudden change of incidence are considered at the start of the unsteady motion. Linearized theory is used and the flow is assumed to be incompressible. The method adopted is only a slight extension of that suggested by R. T. Jones. Applications are made to rectangular and delta wings, but the method is suitable for many planforms. Spanwise and chordwise load distributions are given, and the position of the centre of lift is determined exactly in the case of a square wing. A comparison of the initial and final aerodynamic forces is made. Part II. Transient lift and moment functions are considered for the cases of (i) a sudden plunging motion, (ii) entry into a sharp-edged gust. Linearized theory is used and incompressibility of the fluid is assumed. For sudden plunging motion, the functions are calculated from the lift and pitching moment coefficients associated with wings in oscillatory plunging motion. Results are presented for rectangular and complete delta wings of aspect ratios 1, 2 and 4. Growth of lift functions due to gust entry are also calculated for these wings from knowledge of the corresponding functions due to sudden plunging motion. The method of analysis involves an application of a reverse flow theorem and an approximate relationship for the transient chordwise load distribution due to sudden plunging motion. It is uncertain whether the growth of pitching moment due to gust entry could be obtained accurately enough by a similar method. An alternative method is used to confirm the accuracy of the growth of lift function due to gust entry for a square wing. Calculations of this function by a simpler method for rectangular wings of high aspect ratio show reasonable agreement with those for aspect ratio 4; in addition, the exact solution for delta wings is derived for the limiting case of infinite aspect ratio.