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 This has been an extremely active debate among those who love flying and are involved in the field. If the question is Which is !hysically correct? then the answer is clear "" both are correct. Both are based on valid !rinci!les of !hysics. The Bernoulli equation is equation is sim!ly a statement of the !rinci!le of conservation conservation of energy in energy in fluids. #onservation of momentum and momentum and Newton's Newton's $rd law are law are equally valid as foundation !rinci!les of nature " we do not see them violated. This !hysical validity will undoubtedly not quell quell the debate% and this treatment will not settle it. But !erha!s it can at least indicate the lines of the discussion.
Bernoulli conce!ts +eferences ,astlae
#raig
N--erodynamic s
Those who advocate an a!!roach to lift by Newton's laws a!!eal to the clear existance of a strong downwash downwash behind behind the wing of an aircraft in flight. The fact that the air is forced downward clearly im!lies that there will be an u!ward force on the airfoil as a Newton's $rd law reaction force. &rom the conservation of momentum view!oint% the air is given a downward com!onent of momentum behind the airfoil% and to conserve momentum% something must be given an equal u!ward momentum. Those who !refer to discuss lift in these terms often invoe the (utta")ouowsi theorem for theorem for lift on a rotating cylinder. The lift on a s!inning cylinder has been clearly demonstrated% and its discussion includes a vortex in the circulating air. *any discussions of airfoil lift invoe such a vortex in the effective circulation of air around the moving airfoil. #onservation of angular momentum in momentum in the fluid requires an o!!osite circulation in the air shed from the trailing edge of the wing% and such vortex motion has been observed.
Those who advocate the Bernoulli a!!roach to lift !oint to detailed measurement of the !ressures surrounding airfoils in wind tunnels and in flight. uch !ressure measurements are ty!ically done with /itot tubes. #orrelating the !ressures with the Bernoulli equation gives reasonable agreement with observations. Those who argue against modeling the lift !rocess with the Bernoulli equation !oint to the fact that the flow is not incom!ressible% and therefore the density changes in the air should be taen 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 0ust maes it harder to a!!ly. But the !ragmatic success of modeling the lift with Bernoulli% neglecting density changes% suggests that the density changes are small. /ragmatic 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. 1etractors from the Bernoulli a!!roach often mae calculations using the (utta")ouowsi theorem 2see #raig3. Illustration of different angles of attac
4y!er/hysics55555 *echanics 55555 &luids
R Nave
6o Bac
Flying Upside-Down /art of the fascination of an aerobatics dis!lay is that with loo!s and u!side"down flight. If the greater curvature on to! of the wing and the Bernoulli effect are evoed to ex!lain lift% how is this !ossible? The illustrations below attem!t to show that an increase in airstream velocity over the to! of the wing can be achieved with airfoil surface in the u!right or inverted !osition. It requires ad0ustment of the angle of attac% but as clearly demonstrated in almost every air show% it can be done.
Index Bernoulli conce!ts +eference ,astlae
imilar setches can show the conditions for lift on a symmetric airfoil. While the ty!ical asymmetric sha!e of an airfoil mae increase efficiency of lift !roduction in its u!right !osition% the asymmetry of the airfoil is not essential for !roducing lift.
4y!er/hysics55555 *echanics 55555 &luids
R Nave
6o Bac
Airfoil Terminology
Based on ,astlae% #harles N.% -n -erodynamicist's 7iew of 8ift% Bernoulli% and Newton% The /hysics Teacher 9:% ;<< 2*arch =::=3. It is useful to be aware of some of the terms used in the aerodynamic field when discussing airfoil lift. #ritical to lift is the angle of attac% 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. -lthough the relative velocity is shown as hori>ontal in the illustration% that is for level flight only. If the aircraft is ascending or descending% the relative velocity will not be hori>ontal% but the angle of attac 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 u!!er surfaces% measured !er!endicular 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 !ercent of the length of the chord. -erodynamicists usually measure angles relative to the relative velocity of the air% sometimes referred to as the relative wind. 8ift and drag are then measured !er!endicular and !arallel to the relative wind% res!ectively. In that context% lift is not generally vertical% and not generally !er!endicular to the chord of the wing "" it is the com!onent of force !er!endicular to the relative velocity of the air or the relative wind.
Index Bernoulli conce!ts +eferences ,astlae
The general sha!e of the airfoil above is !atterned after the N-#- =9;= airfoil. -ccording to ,astlae% this airfoil has been used on most single"engine #essna aircraft since the ;9:s. It is liely the most widely used airfoil in the world% so it has been thoroughly studied.
