# Rotary Derivatives in Yaw: Calculation by Lifting Plane Theory of the Rolling and Yawing Moments of a Wing Due to Rotary Motion in Yaw

ISSN: 0002-2667

Article publication date: 1 February 1951

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## Abstract

Calculations have been carried out on two elliptic wings, with ratios of major to minor axis 2·5 and 5 to 1 respectively, in order to demonstrate the use of vortex lattice theory in calculating lr and nr by lifting plane theory for wings of arbitrary plan form. Special tables of downwash, required in order to allow for the curvature of the wake, are included, and the origin of the formulae by which these are derived in a form applicable to linear theory is fully described. For the first wing, the calculated results for lr and nr and for local aerodynamic centre, load coefficients, and local lift coefficients are given for the Glauert‐Wieselsberger lifting line solution as well as for lifting plane solutions with three, six and nine control points respectively. The main work on the second wing is concerned with a six‐point lifting plane solution. The results show that there is not a serious difference between lifting line and lifting plane theory, excepting that the former does not give reliable values for the local a.c. For straight wings the six‐point lifting plane solution gives excellent accuracy. The method is applicable to wings of arbitrary plan, but the field of sweptback wings is unexplored and it should not be assumed without check that the relation of accuracy to number of control points is always the same. A further investigation is also required on the formula for nr when sweepback is present. The calculated value of lr for the 5 to 1 elliptic wing is in close agreement with the measured value for this wing obtained by Wieselsberger on a whirling arm. The report is concerned mainly with the calculation of spanwise load grading and local aerodynamic centre, and extension to detailed pressure distribution may require the use of more variables.

## Citation

Falkner, V.M. (1951), "Rotary Derivatives in Yaw: Calculation by Lifting Plane Theory of the Rolling and Yawing Moments of a Wing Due to Rotary Motion in Yaw", Aircraft Engineering and Aerospace Technology, Vol. 23 No. 2, pp. 44-54. https://doi.org/10.1108/eb031999

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