Bernoulli or Newton's Laws for Lift?

Which is best for describing how aircraft get the needed lift to fly? Bernoulli's equation or Newton's laws and conservation of momentum? This has been an extremely active debate among those who love flying and are involved in the field. If the question is "Which is physically correct?" then the answer is clear -- both are correct. Both are based on valid principles of physics. The Bernoulli equation is simply a statement of the principle of conservation of energy in fluids. Conservation of momentum and Newton's 3rd law are equally valid as foundation principles of nature - we do not see them violated. This physical validity will undoubtedly not quell the debate, and this treatment will not settle it. But perhaps it can at least indicate the lines of the discussion.

Those who advocate an approach to lift by Newton's laws appeal to the clear existance of a strong downwash behind the wing of an aircraft in flight. The fact that the air is forced downward clearly implies that there will be an upward force on the airfoil as a Newton's 3rd law reaction force. From the conservation of momentum viewpoint, the air is given a downward component of momentum behind the airfoil, and to conserve momentum, something must be given an equal upward momentum. Those who prefer to discuss lift in these terms often invoke the Kutta-Joukowski theorem for lift on a rotating cylinder. The lift on a spinning cylinder has been clearly demonstrated, and its discussion includes a vortex in the circulating air. Many discussions of airfoil lift invoke such a vortex in the effective circulation of air around the moving airfoil. Conservation of angular momentum in the fluid requires an opposite circulation in the air shed from the trailing edge of the wing, and such vortex motion has been observed.

Those who advocate the Bernoulli approach to lift point to detailed measurement of the pressures surrounding airfoils in wind tunnels and in flight. Such pressure measurements are typically done with Pitot tubes. Correlating the pressures with the Bernoulli equation gives reasonable agreement with observations.

Those who argue against modeling the lift process with the Bernoulli equation point to the fact that the flow is not incompressible, and therefore the density changes in the air should be taken into account. This is true -- the ideal gas law should be obeyed and density changes will inevitably result. This does not render the Bernoulli equation invalid, it just makes it harder to apply. But the pragmatic success of modeling the lift with Bernoulli, neglecting density changes, suggests that the density changes are small. Pragmatic difficulties exist also for those who would model the lift from Newton's third law -- it is difficult to measure the downward force associated with the downwash because is is distributed in the airstream leaving the trailing edge of the airfoil. Detractors from the Bernoulli approach often make calculations using the Kutta-Joukowski theorem (see Craig).

Flying Upside-Down

Part of the fascination of an aerobatics display is that with loops and upside-down flight. If the greater curvature on top of the wing and the Bernoulli effect are evoked to explain lift, how is this possible? The illustrations below attempt to show that an increase in airstream velocity over the top of the wing can be achieved with airfoil surface in the upright or inverted position. It requires adjustment of the angle of attack, but as clearly demonstrated in almost every air show, it can be done.

Similar sketches can show the conditions for lift on a symmetric airfoil. While the typical asymmetric shape of an airfoil make increase efficiency of lift production in its upright position, the asymmetry of the airfoil is not essential for producing lift.

Airfoil Terminology

Based on Eastlake, Charles N., "An Aerodynamicist's View of Lift, Bernoulli, and Newton", The Physics Teacher 40, 166 (March 2002).

It is useful to be aware of some of the terms used in the aerodynamic field when discussing airfoil lift. Critical to lift is the angle of attack, which is the angle between the relative velocity and the chord line of the airfoil. The chord line is the straight line from the leading edge to the trailing edge of the airfoil. Although the relative velocity is shown as horizontal in the illustration, that is for level flight only. If the aircraft is ascending or descending, the relative velocity will not be horizontal, but the angle of attack would still be defined as the angle between the relative velocity of the air and the chord line of the airfoil. The mean line of the airfoil is the line equidistant from the lower and upper surfaces, measured perpendicular to the chord line. The camber of the airfoil is the maximum distance between the chord line and the mean line and is usually a few percent of the length of the chord. Aerodynamicists usually measure angles relative to the relative velocity of the air, sometimes referred to as the "relative wind". Lift and drag are then measured perpendicular and parallel to the relative wind, respectively. In that context, "lift" is not generally vertical, and not generally perpendicular to the chord of the wing -- it is the component of force perpendicular to the relative velocity of the air or the "relative wind".

The general shape of the airfoil above is patterned after the NACA 2412 airfoil. According to Eastlake, this airfoil has been used on most single-engine Cessna aircraft since the 1940s. It is likely the most widely used airfoil in the world, so it has been thoroughly studied.