## Pilot's Handbook of Aeronautical Knowledge Principles of Flight Theories in the Production of Lift

Pilot's Handbook of Aeronautical Knowledge

Preface

Acknowledgements

Appendix

Glossary

Index

 Figure 3-4. Air circulation around an airfoil occurs when the front stagnation point is below the leading edge and the aft stagnation point is beyond the trailing edge. This low-pressure area produces an upward force known as the Magnus Effect, the physical phenomenon whereby an object's rotation affects its path through a fluid, to include air. Two early aerodynamicists, Martin Kutta and Nicolai Joukowski, eventually measured and calculated the forces for the lift equation on a rotating cylinder (the Kutta-Joukowski theorem). To summarize the Magnus effect, an airfoil with a positive angle of attack (AOA) develops air circulation about the upper surface of the wing. Its sharp trailing edge forces the rear stagnation point to be aft of the trailing edge, while the front stagnation point falls below the leading edge. [Figure 3-4] Bernoulli's Principle of Differential Pressure A half-century after Newton formulated his laws, Daniel Bernoulli, a Swiss mathematician, explained how the pressure of a moving fluid (liquid or gas) varies with its speed of motion. Bernoulli's Principle states that as the velocity of a moving fluid (liquid or gas) increases, the pressure within the fluid decreases. This principle explains what happens to air passing over the curved top of the airplane wing. A practical application of Bernoulli's Principle is the venturi tube. The venturi tube has an air inlet that narrows to a throat (constricted point) and an outlet section that increases in diameter toward the rear. The diameter of the outlet is the same as that of the inlet. At the throat, the airflow speeds up and the pressure decreases; at the outlet, the airflow slows and the pressure increases. [Figure 3-5] Since air is recognized as a body and it is accepted that it must follow the above laws, one can begin to see how and why an airplane wing develops lift. As the wing moves through the air, the .ow of air across the curved top surface increases in velocity creating a low-pressure area. Although Newton, Magnus, Bernoulli, and hundreds of other early scientists who studied the physical laws of the universe did not have the sophisticated laboratories available today, they provided great insight to the contemporary viewpoint of how lift is created.

Figure 3-5. Air pressure decreases in a venturi tube.

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