विषयवस्तु

  • General

    Author: Peter Higgins, PhD                                                                                                   Updated August 2023

    Keywords: aerodynamics, lift, wake turbulence, Bernoulli, flow equations, openFOAM, XFoil, JavaFoil

    Intended for students 14+

    Prerequisites: some basic science, but there are few equations here, whats really needed is curiosity and an interest in airplanes.

    Lift is explained as resulting from circulation, and is not the consequence of the widely held but the erroneous equal transit time hypothesis. Both wind tunnel observations and the author's own wing modeling in OpenFoam are used to explain what really happens. It is seen that the vortices that are a danger to following aircraft taking off behind jumbo-jets are also explained as a necessary result of lift generation. This lecture puts the Bernoulli equation in lift generation in proper perspective. The presence of lift in other atmospheres, such as found on Mars, is discussed.

    This lesson is intended for high school and lower university levels. It introduces students to the excellent book on the subject by Clancy. Hopefully, some will be inspired to learn computer modeling by looking at the results presented.


    Aerodynamic lift refers to the force pushing upwards that is generated on an airplane wing when it moves through the atmosphere. In short, lift keeps the airplane flying, without lift planes can not fly even with powerful engines. Rockets can, but that is another story.

    Lift can be understood by wind tunnel observations. When a wing is angled into the flow slightly upward, the flow is always faster flow over the top than under it. According to the principle of conservation of energy, such faster flow lowers the top surface pressure forcing (or sucking) the wing up. This principle was discovered by Daniel Bernoulli and will be discussed later.

    A question remains, however, why is the top flow faster when lift occurs? A common reason presented for this phenomenon is that the path over the top surface is longer than the path along the bottom surface so that flow over the top speeds up to join its counterpart at the trailing edge. This is wrong because as observed in wind tunnels, when flow recombines the top flow does not meet its counterpart that split at the front. The real reason is described in this lesson.

    Anticipating that some students will want to learn more about the performance of wings, known as airfoils, this lesson identifies three programs available for free that can be run by high school students to quantify lift for different airfoils. Airfoil shapes for different airplanes, like the Boeing 747, can be downloaded from the Internet. Analyzing wing performance could be a great Senior project.

    Lastly, since this lecture has been done with space exploration in mind, the lift of NASA's Martian helicopter is studied. It is noteworthy that it actually flew successfully because the Martian atmosphere is so thin compared to the Earth's. You can run the programs discussed in this lesson to see for yourself.


  • Bernouilli's equation

    For any point in a flow:

    Pressure/density + gravitational constant · height + Velocity squared/2 = constant

    Each of these terms is an energy: the first is called flow energy, the second, potential energy, the third is kinetic energy. According to conservation of energy the sum these three terms at any point in the flow equals the sum of these terms at any other point. As a consequence, if the velocity increases from point 1 to point 2, the pressure must decrease at point 2. Daniel Bernoulli is credited with this discovery.

    Daniel Bernoulli came from a famous family of scientists; he was a mathematician and a Doctor. In his medical practice, he pioneered the measurement of blood pressure by inserting glass tubes in patient’s arms noting the height reached by the blood in the tube– if the patient’s blood was flowing normally, this height was low, but, if the height was high, the blood wasn’t flowing well.  But, Bernoulli never published the equation above that is attributed to him, it was his father’s student, the brilliant Leonhard Euler who did some years later. According to Euler,  along any streamline the sum of energies resulting from fluid pressure, height and velocity must be the same. When the fluid slows down at the same height, the pressure goes up, and vice-versa. It is now known that this relationship comes from conservation of energy. P/ρ is the flow energy, gz is potential energy and v2/2 is the flow's kinetic energy. By conservation of energy the sum of these values is the same anywhere in a non viscous flow. It is left to the student to show the units of each term equate to energy.