Module 5 - Thin Aerofoil Theory Flashcards
What assumptions are made in Thin Aerofoil Theory?
- Thin aerofoil (aerofoil shape approximated by camber)
- Camber is streamline of flow
- Potential flow (incompressible, irrotational - inviscid)
- Small AoA
- Small camber line slope
- Small camber such that vortex sheet can be approximated as on the chord
In what component of velocity is there a discontinuous change across a vortex sheet? What is this change equal to?
- Tangential
- Vortex sheet strength
What is the primary statement of the Kutta condition?
- circulation obtains a value such that flow leaves smoothly at the trailing edge
How is the Kutta Condition different for finite trailing edge vs a cusped trailing edge?
Finite: TE is stagnation point
Cusped: velocity is finite and equal in magnitude and direction at TE
Either way the vortex sheet strength is 0 at TE
How is circulation developed for an aerofoil?
Starting vortex: vortex produced at trailing edge when aerofoil accelerated from rest - large V gradient produces vorticity which rolls up into a CCW vortex
What is Kelvin’s circulation theorem?
The circulation around a closed curve is the same at steady flight as when it is at rest, meaning the circulation within the curve containing the aerofoil and starting vortex is zero at flight conditions - takeaway is that the starting vortex induces circulation around aerofoil
What are some reasons it is dangerous to take off right after another plane?
- Downwash in wake of leading aircraft
- Starting vortex of leading aircraft can make following aircraft unsteady
Where is the vortex sheet placed in thin aerofoil theory?
It is approximated as being on the chord line
What (in words) is the fundamental equation of thin aerofoil theory stating?
The sum of the normal component of the free stream velocity and the component of velocity normal to the camber line induced by the vortex sheet is zero at any given point on the vortex sheet
What is the transformation used in thin aerofoil theory?
ξ = (c/2)(1-cos(θ))
Upon which coefficients does the moment coefficient about c/4 rely on?
A1, A2
What is the predicted lift slope from thin aerofoil theory?
2π rad-1
Where is the aerodynamic centre located based on thin aerofoil theory?
Quarter chord point
Where is the predicted centre of pressure of a symmetric aerofoil from thin aerofoil theory?
Quarter chord point
Can thin aerofoil theory predict stall?
No, stall is the result of boundary layers (viscous phenomena) separating from the surface and thin aerofoil theory assumes inviscid flow
