I was recently reading this very helpful string What is the physical meaning of circulation found in Kutta condition? and it explained very nicely potential flow around an airfoil. My question then is this: what happens to circulation around a cambered airfoil at a small, negative angle of attack which is producing lift, but is also producing upwash. How do we reconcile Kutta-Жуковский theorem with this observation?

  • $\begingroup$ For lift to exist, a net downwash has to be present too, because action and reaction are opposite and equal... $\endgroup$
    – xxavier
    Jul 24, 2021 at 12:26
  • $\begingroup$ Well okay sure. But Lift is equal to ρvΓl where gamma is circulation, rho is density, l is length (of chord) and v is of course velocity. Impulse accounts for only half this and is caused by the turning of the flow (which is caused by adding the circulation into a streamline mathematical model). So yes. But also. As per A. Bowers et al (in ‘On Wings of the Minimum induced drag: Spanload implications for aircraft and birds’) such airfoils do exist in nature and do produce lift if very little. $\endgroup$ Jul 24, 2021 at 20:59
  • $\begingroup$ You can't have lift without downwash. It's a physical impossibility... $\endgroup$
    – xxavier
    Jul 25, 2021 at 8:54
  • $\begingroup$ There is always upwash and downwash. The only impact of a negative attack angle is that the circulation will be opposite and the lift will go downwards instead of upwards. $\endgroup$ Jul 25, 2021 at 13:06
  • $\begingroup$ If circulation is opposite it means г is negative and lift is not produced. Lift IS produced no matter what is said by xxavier. I agree with them we have no idea how but I am certain that Al Bowers is correct and further experiments by amateurs confirm his experimental, and analytical evidence. There has to be positive circulation or a new nuance to the theorem of lift. $\endgroup$ Jul 26, 2021 at 9:46

2 Answers 2


Don't know if you're still on this, but I think that your doubt arises from a misunderstanding in terms: the angle of attack we are normally discussing about is the geometric one, i e. the AoA which is referred to the line connecting the leading edge with the trailing edge of the airfoil. This line has no real aerodynamic meaning (unless the airfoil is symmetrical: in that case it coincides with the line of zero lift). The AoA that separates positive lift and negative lift is the aerodynamic one and it's measured in respect to the line of zero lift.

For a not symmetrical airfoil (aka cambered airfoil) the line of zero lift is normally negative, just like in your example:

think about cambered airfoils, some of them have a zero lift angle at around -5°, so if you held one at -3°, you would have lift but negative AoA

Yes, you would have lift at negative geometric AoA but positive aerodynamic AoA.

The geometric AoA is normally used because the line connecting leading and trailing edge is easy to draw and not mistakable, even if that can lead to an airfoil producing positive lift at negative AoA: but that's not against physics, it's just a convention.

what happens to circulation around a cambered airfoil at a small, negative angle of attack which is producing lift, but is also producing upwash

Hopefully now it's clear that a positive lift is produced if and only if the circulation is positive too (and viceversa). That the (geometric) AoA is negative has nothing to do with the sign of the circulation and of the lift.

By the way, since we are dealing here with potential flow around a 2D airfoil, please note that the net downwash around the airfoil is always zero.

  • $\begingroup$ Thanks, I do still check this. I get that geometric AoA isn’t a very useful measure, and aerodynamic AoA is more relevant so let me rephrase. Is it possible to have an airfoil at positive aerodynamic AoA, producing upwash past the trailing edge. This appears to be what ‘On Wings of the Minimum Induced Drag: Spanload Implications for Aircraft and Birds’ suggests. $\endgroup$ Jul 11 at 12:51
  • $\begingroup$ @AeroDude12: wait, you're mixing up airfoil with wing. Airfoil is a 2D shape which has no (or infinite) span. The only circulation involved is the one that you see for example in the picture of this answer. A wing is a 3D object with a much more complex circulation environment, as visible for example in this picture from this answer. There you see that all the vortices shed from the trailing edge coalesce in two vortices, one behind each wingtip... $\endgroup$
    – sophit
    Jul 11 at 13:31
  • $\begingroup$ ... Those two vortices (called tip vortices) have an upward component which is used by birds when the fly in formation. $\endgroup$
    – sophit
    Jul 11 at 13:31
  • $\begingroup$ I understand gamma and circulation in 2D aerodynamics, and the kelvin theory leading to both wingtip and starting vortices. But it is unlikely to be the case that the wingtip vortex is what birds use. If you look at the studies done on it they often have to appeal either to incorrect flying by birds or wake contraction (which is totally unobserved) to explain why they appear to fly in a different region than predicted with greater standard deviation. The reason, as outlined in the above paper, freely available on the NTRS server, and by a thesis by Lukacovic is upwash before the wingtip. $\endgroup$ Jul 12 at 20:01
  • $\begingroup$ ntrs.nasa.gov/api/citations/20160003578/downloads/… Here is the NASA paper by Bowers et Al. digitalcommons.calpoly.edu/cgi/… And that’s the thesis (it’s very long I’m sorry). $\endgroup$ Jul 12 at 20:04

The forward top part of a cambered wing will always create upwash if it is lifting. Momentum (mass of air molecules) plays a key role in creating the lifting low pressure area above the wing.

Reynolds number also plays a key role, particularly velocity. "Top lift" can only be created if velocity is sufficient (literally) for the wing chord to pass before the low pressure area collapses$^1$. This tendency for the air to "bend" back towards the wing is the downwash.

if only the front top of the wing pushes air up, and the rest of the top is bending air down, the net effect is lift$^2$ $^3$

Lower Reynolds number wings cannot create top lift, and must rely on "surfing" the air (action/reaction) off the bottom of the wing. These wings will not create lift at negative angles of attack.

Top lift has a much lower drag penalty. This is why thin undercambered wings fell out of favor as airspeeds of early planes began to exceed 100 km/hr.

$^1$ angle of attack is also a critical factor
$^2$ this can happen even at a slightly negative AoA.
$^3$ similar to leverage, the longer distance/time, of downwash zone creates more lifting force than the upwash takes away


You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .