Airfoil Terminology, Its Theory and Variations As Well As Relations with Its Operational Lift Force and Drag Force In Ambient Conditions
Author Names: Dr V.N. Bartaria (H.O.D Mechanical engineering LNCT Bhopal) Shivani Sharma (B.E. Mechanical engineering Pursuing M.tech)
Abstract: It is a fact of common experience that a body in motion through a fluid experiences a resultant force which, in most cases is mainly a resistance to the motion. A class of body exists, However for which the component of the resultant force normal to the direction to the motion is many time greater than the component resisting the motion, and the possibility of the flight of an airplane depends on the use of the body of this class
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It was devised by German-American mathematician Max Munk and further refined by British aerodynamicist Hermann Glauert and others in the 1920s. The theory idealizes the flow around an airfoil as two dimensional flows around a thin airfoil. It can be imagined as addressing an airfoil of zero thickness and infinite wingspan.
Thin airfoil theory was particularly notable in its day because it provided a sound theoretical basis for the following important properties of airfoils in two-dimensional Flow:
(1) On a symmetric airfoil, the center of pressure and
Aerodynamic center lies exactly one quarter of the chord
Behind the leading edge
(2) On a cambered airfoil, the aerodynamic center lies exactly
One quarter of the chord behind the leading edge
(3) The slope of the lift coefficient versus angle of attack
Line is 2π units per
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4 Derivation of thin airfoil theory
The airfoil is modeled as a thin lifting mean-line (camber line). The mean-line, y(x), is considered to produce a distribution of vorticity (s) along the line, s. By the
Kutta condition, the vorticity is zero at the trailing edge. Since the airfoil is thin, x (chord position) can be used instead of s, and all angles can be approximated as small. From the Biot–Savart law, this vorticity produces a flow field w(x) where
Where x is the location where induced velocity is produced, x′ is the location of the vortex element producing the velocity and c is the chord length of the airfoil.
Since there is no flow normal to the curved surface of the airfoil, w(x) balances that from the component of main flow V , which is locally normal to the plate – the main flow is locally inclined to the plate by an angle α-dy/dx. That is:
4 DERIVATION OF THIN AIRFOIL THEORY From top to bottom:
• Laminar flow airfoil for a RC park