Тематический план

  • Общее

    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.


  • How is lift studied

    There are two ways to study lift: the first is observation of flow around models in wind tunnels, the second is by simulation with computer programs.


    Wind tunnel testing


    A blue glider is shownin a wind tunnel, tethered to its sides.


    Wind tunnels can be very impressive facilities with huge tubes containing an instrumented  test chamber. Air is blown into the tubes by enormous fans then the tubes get smaller to further speed up the flow.. Baffles straighten the flow into parallel streams. The object being tested can be a wing or a model airplane as shown in this figure.

    Wind tunnel flow results


    Air flow captured by cameras through ports in the test chamber shows that for a slightly inclined wing (the inclination is called angle of attack) the flow splits into a portion which flows up over the top of the wing and into a portion which flows under the wing.  However, if the angle of attach is too great, the wing stalls and flow over the top separates from the wing and does not join with flow from the bottom. In this case lift is destroyed, gravity takes over, and the plane nosedives.

    When lift happens, two observations are always made:


    bluepanel1

    1 Airflow is faster on the top of the wing than it is under the wing.

    2 The airflow from the top is not from the same air volume that split in the front.

    Observation 1 is important for  understanding lift because when flow is faster its pressure is lower. Observation 1 is the same as stating that the pressure on the top of the wing is lower than the pressure on the bottom. This pressure difference forces the wing upward opposing gravity. We would be done understanding lift if we understood why the top flow was faster.

    Observation 2 is critical in understanding lift. A popular, but incorrect theory claims that the faster flow on the top surface is the result of the top path being longer compared to the bottom path, and because the two paths are crossed by the split fluid parcels in equal time. This theory depends on the notion that the flow volumes that split at the front have to recombine with themselves as if this was the consequence of conservation of mass.  It isn't, and by placing dye markers in the upstream flow it's clear to any observer that this recombination constraint doesn't happen. This incorrect theory has a name: the equal transit time fallacy.

    Without the equal transit time theory, there is no apparent reason to explain the faster flow. There must be another mechanism to explain it.

    Returning to observation 1: the inverse relationship between flow speed and flow pressure is widely attributed to Daniel Bernoulli.