Journal of Theoretical
and Applied Mechanics
5, 3, pp. 347-383, Warsaw 1967
and Applied Mechanics
5, 3, pp. 347-383, Warsaw 1967
Stateczność dynamiczna podłużna szybowca w zespole holowniczym
W pracach związanych z zagadnieniem holowania szybowców nie rozpatrywano stateczności zespołu holowniczego, tzn. stateczności zespołu składającego się z samolotu holującego na linie szybowiec i szybowca. Rozpatrywano wyłącznie stateczność szybowca, traktując samolot jako ciało o nieskończenie wielkiej bezwładności. Przedmiotem niniejszej pracy jest przypadek holowania sztywnego szybowca przez sztywny samolot za pośrednictwem ciężkiej, wiotkiej i sprężystej liny holowniczej, obciążonej siłami aerodynamicznymi. Otrzymane wyniki wskazały wzajemne oddziaływanie na siebie samolotu i szybowca w czasie holowania, co wyraziło się w niemożności rozprzęgnięcia równań ruchu układu. Rozwiązanie układu równań sprowadzono do zagadnienia znajdowania wartości własnych macierzy niesymetrycznych (dowolnych) czternastego stopnia (w omawianym przypadku). Na podstawie obliczeń numerycznych wykonanych dla jednego z szybowców wyczynowych i obecnie stosowanego samolotu holującego zbadano, jak wpływa na stateczność szybowca położenie względem samolotu holującego i prędkości holowania.
DYNAMIC LONGITUDINAL STABILITY OF A TOWED SAILPLANE
The problem of longitudinal dynamic stability of the rigid glider towed behind the rigid aircraft with heavy and flexible towing rope affected by aerodynamic forces, has been considered. Before the disturbance had occurred the aircraft as well as the glider performed horizontal, straightlinear, steady flight. Using the second kind Lagrange’s equations, differential equations of motion have been derived. After the linearization had been performed, the system consisted of seven ordinary, second order differential equations with constant coefficients. The solution of the system consists in finding out the eigenvalues of asymmetric (arbitrary) matrices, which were of the fourteenth order in the case considered. By means of numerical calculations, the influence of the reciprocal location of the typical aircraft and the high-performance typical glider on the stability of the glider, has been investigated. The results are as follows: 1. Since it is possible to reach the critical angle of attack first at the glider and afterwards at the aircraft, the minimum towing velocity should be determined. 2. The stability of the glider increases with increasing the towing velocity. 3. The order to increase the stability, the glider should fly in the line of- or below the aircarft. 4. In all cases the towed glider is slightly unstable and even at higher velocities there exist some divergences of the aperiodic motions, calling the intervention of pilot.
DYNAMIC LONGITUDINAL STABILITY OF A TOWED SAILPLANE
The problem of longitudinal dynamic stability of the rigid glider towed behind the rigid aircraft with heavy and flexible towing rope affected by aerodynamic forces, has been considered. Before the disturbance had occurred the aircraft as well as the glider performed horizontal, straightlinear, steady flight. Using the second kind Lagrange’s equations, differential equations of motion have been derived. After the linearization had been performed, the system consisted of seven ordinary, second order differential equations with constant coefficients. The solution of the system consists in finding out the eigenvalues of asymmetric (arbitrary) matrices, which were of the fourteenth order in the case considered. By means of numerical calculations, the influence of the reciprocal location of the typical aircraft and the high-performance typical glider on the stability of the glider, has been investigated. The results are as follows: 1. Since it is possible to reach the critical angle of attack first at the glider and afterwards at the aircraft, the minimum towing velocity should be determined. 2. The stability of the glider increases with increasing the towing velocity. 3. The order to increase the stability, the glider should fly in the line of- or below the aircarft. 4. In all cases the towed glider is slightly unstable and even at higher velocities there exist some divergences of the aperiodic motions, calling the intervention of pilot.