The effect of large bending deformations on the aerodynamic lift of an elliptical aircraft wing

Naloga obravnava spremembo usmeritve sile vzgona na upognjenem krilu, ki se jo med praktičnimi izračuni pogosto zanemari, saj se krilo večinoma obravnava v okviru majhnih deformacij. S to teorijo pa ni mogoče natančno izračunati upogiba in usmeritve sile vzgona na močno deformiranih krilih. Zato smo v nalogi izpeljali teorijo, ki temelji na nelinearnem Euler-Bernoullijevem modelu nosilca. Izpeljava je prikazana za močno upognjeno eliptično krilo, ki ima obliko in zato porazdelitev vzgona, značilno za jadralna letala. S programom za določevanje aerodinamičnih lastnosti krila XFLR5 smo preverili porazdelitev vzgona vzdolž celotnega krila, ki smo jo izračunali sami. Enačbe upogibne deformacije krila smo izračunali numerično in upoštevali, da obremenitev sledi deformaciji. Na podlagi kota zasuka v vsaki točki krila, smo tako dobili dejansko porazdelitev vzgona, ki jo imamo v realnosti. Napisali smo kodo, ki lahko pod pogoji naših predpostavk reši problem deformabilnosti krila za vsak tip letala. S tem programom lahko uporabnik sam izračuna in presodi, ali je pojav za obravnavano letalo v določenem manevru zanemarljiv ter tako upošteva našo teorijo za pridobitev bolj natančnih rezultatov.The thesis deals with the change of direction of the lift force on a bent wing, which is often neglected in practice, since the wing is usually calculated with the small deformation theory. However, with this theory it is not possible to determine the deflection and direction of the lift force on strongly deformed wings accurately. Therefore we have derived a theoretical procedure based on a nonlinear Euler-Bernoulli beam model. The procedure is intended for a strongly bent elliptical wing, whose shape and thus the lift distribution is typical for gliders. Our calculations of the lift force along the entire wing were verified with XFLR5, a program for calculating the aerodynamic properties of the wing. The bending deformation equations were calculated numerically, taking into account that the load follows the deformation. Based on the angle of inclination at each point of the wing, we obtain the actual lift distribution as can be seen in reality. We have written a computer code that can solve the problem of the wing deformability for any type of aircraft under the conditions of our assumptions. With this code, any user can calculate and decide if the deformations are large enough for a given aircraft maneuver, and use our theory to get more accurate results