An Evaluation of the Measurement Requirements for an In-Situ Wake Vortex Detection System

Results of a numerical simulation are presented to determine the feasibility of estimating the location and strength of a wake vortex from imperfect in-situ measurements. These estimates could be used to provide information to a pilot on how to avoid a hazardous wake vortex encounter. An iterative algorithm based on the method of secants was used to solve the four simultaneous equations describing the two-dimensional flow field around a pair of parallel counter-rotating vortices of equal and constant strength. The flow field information used by the algorithm could be derived from measurements from flow angle sensors mounted on the wing-tips of the detecting aircraft and an inertial navigation system. The study determined the propagated errors in the estimated location and strength of the vortex which resulted from random errors added to theoretically perfect measurements. The results are summarized in a series of charts and a table which make it possible to estimate these propagated errors for many practical situations. The situations include several generator-detector airplane combinations, different distances between the vortex and the detector airplane, as well as different levels of total measurement error. Nomenclature b det span of the detecting aircraft, ft. b gen span of the generating aircraft, ft. b sep separation distance between the vortex pair, ft. C numerical method cost function (see Eqn. 7), deg. M Measurement magnitude of flow field values (see eqn. 8), deg. r radius from the center of a vortex to the point of calculation (eqn. 3A), ft. R radius from the center of a vortex dipole to the point of calculation, ft. V gen velocity of the generating aircraft, ft./sec. V det velocity of the detecting aircraft, ft./sec. v θ tangential velocity component at radius (r) of a vortex, ft./sec. v horizontal velocity component of the vortex flow field (eqn. 4), ft./sec. or deg. v ideal theoretical horizontal velocity component of vortex flow field, ft./sec. W gen weight of the generating aircraft, lb. w vertical velocity component of the vortex flow field (eqn. 3), deg. w ideal theoretical vertical velocity component of vortex flow field, ft./sec. y horizontal position of the detecting aircraft, ft. z vertical position of the detecting aircraft, ft. α angle of attack at one wing tip due to one vortex, radians β angle of sideslip on one wing tip due to one vortex, radians ∆α differential angle of attack across span of detector airplane due to vortex, …