Q:

All new airliner from Airbus (318-340) and Boeing (737-777) and all top class bizjets has got a wing which has almost flat upperside and it´s camber (lift bubble) below the wing. The Wings profile can be seen here:
http://amber.aae.uiuc.edu/~m-selig/ads/afplots/whitcomb.gif
New ”Non Bernoulli effect” wing on Airbus 330/340
http://aerodyn.org/HighSpeed/supercritical.html
How to apply Continuity Equation and Bernoulli Principle on this Wings? Best Regards

- Jan-Olov Newborg (age 18)

Sweden

- Jan-Olov Newborg (age 18)

Sweden

A:

Hi Jan-Olov,

Thanks for the new web links! For people interested in the analysis of wings and other airfoils, I’ll include here a link to your previous posting of many very nice links to detailed descriptions of how airfoils work.

.

Bernoulli’s principle isn’t wrong at all, but it is not a convenient way to describe lift, as your original sites correctly point out. Instead, wings turn airflow downwards, creating an action-reaction pair of forces, and there is suction on top of the wing. One talk I saw which nicely dismissed Bernoulli’s principle as a practical explanation of lift showed rather graphically the underside of an F-16’s wing, fully loaded with hanging fuel tanks and missiles. It really doesn’t matter much what you put on the bottom of the wing -- the top of the F-16’s wings was smooth and polished. Much of the flow turning comes from a vacuum created above the wing. So your postings I hope will help people think more about lift than the usual Bernoulli explanation.

In regards to your latest postings, these are great! However, here the usual Bernoulli’s principle as you may see it in introductory texts cannot be used at all because the flow is at least in places supersonic. This creates a shock wave which meets the wing. The design of wings for supersonic flight (and also wings for which some portion of the airflow around them might be supersonic) centers on minimizing the drag created by these shock fronts, while of course maintaining stability for safety. The simplest form of Bernoulli’s principle requires that the flow is incompressible, and a supersonic shock wave is a big compresson of the air. Of course there is the full version of Bernoulli’s equation which incorporates the heat function of the air (when you compress the air it has higher energy in the form of heat and the enthalpy is the right variable). The proper way to do all this is with numerical simulations using the Euler equation. The continuity equation also is more complicated for compressible flow. div(v) = 0 is no longer true -- div(rho*v) + d(rho)/dt = 0 where rho is the gas density and v is the velocity vector field and div is the divergence is the full continuity equation and applies whenver the total number of gas molecules remains constant (not true when there are chemical reactions or phase transitions -- liquid to vapor, for instance).

Tom

Thanks for the new web links! For people interested in the analysis of wings and other airfoils, I’ll include here a link to your previous posting of many very nice links to detailed descriptions of how airfoils work.

.

Bernoulli’s principle isn’t wrong at all, but it is not a convenient way to describe lift, as your original sites correctly point out. Instead, wings turn airflow downwards, creating an action-reaction pair of forces, and there is suction on top of the wing. One talk I saw which nicely dismissed Bernoulli’s principle as a practical explanation of lift showed rather graphically the underside of an F-16’s wing, fully loaded with hanging fuel tanks and missiles. It really doesn’t matter much what you put on the bottom of the wing -- the top of the F-16’s wings was smooth and polished. Much of the flow turning comes from a vacuum created above the wing. So your postings I hope will help people think more about lift than the usual Bernoulli explanation.

In regards to your latest postings, these are great! However, here the usual Bernoulli’s principle as you may see it in introductory texts cannot be used at all because the flow is at least in places supersonic. This creates a shock wave which meets the wing. The design of wings for supersonic flight (and also wings for which some portion of the airflow around them might be supersonic) centers on minimizing the drag created by these shock fronts, while of course maintaining stability for safety. The simplest form of Bernoulli’s principle requires that the flow is incompressible, and a supersonic shock wave is a big compresson of the air. Of course there is the full version of Bernoulli’s equation which incorporates the heat function of the air (when you compress the air it has higher energy in the form of heat and the enthalpy is the right variable). The proper way to do all this is with numerical simulations using the Euler equation. The continuity equation also is more complicated for compressible flow. div(v) = 0 is no longer true -- div(rho*v) + d(rho)/dt = 0 where rho is the gas density and v is the velocity vector field and div is the divergence is the full continuity equation and applies whenver the total number of gas molecules remains constant (not true when there are chemical reactions or phase transitions -- liquid to vapor, for instance).

Tom

*(published on 10/22/2007)*