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10 April, 2012 Posted by Christopher Jenner Posted in Other engineering
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Subsonic Lift (Bernoulli’s Principle)

Subsonic Lift (Bernoulli’s Principle)

I just finished reading about current fighter design, one thing led to another and I ended up looking into lift mechanisms along with flow patterns over subsonic airfoils.

In subsonic incompressible flight the lift generated can be determined in terms of pressure using the Bernoulli’s principle and law of conservation of mass (Anderson, 2004). Figure 1 shows the streamlines around a 2d cross section of a subsonic airfoil. The upper streamlines representing tubes – also referred to as the up-wash – constrict as the flows moves around the top edge of the airfoil. From the law of conservation of mass the flow speed within the upper stream tube must increase due to the decrease in the stream-tube area. The area of the lower stream tube increases as per the law of conservation of mass and the flow speed within decreases. Therefore the particles on the top surface of the wing will reach the trailing edge (Figure 2) before the particles traveling on the lower surface of the wing (Figure 1).

 

Figure 1 – Subsonic Laminar flow Airfoil

Figure 2 – Components of the airfoil

In accordance with the Bernoulli equation the increase in airspeed relative to the upper surface of the airfoil will cause a decrease in pressure, while the decrease in airspeed relative to the lower surface of the wing will cause an increase in pressure (Anderson, 2004). The result is a net force with a component normal to the initial stream (lift) and a component parallel to the relative stream (drag). Changes to components of the airfoil like the chord, upper & lower camber, curvature and the angle of attack affect how lift is generated and to what degree, these changes and their effects fall into the same basic theory.

Anderson, J. (2004). “Introduction to Flight” (4th ed.). London: McGraw-Hill.

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