# Is pressure lower than ambient on the pressure (bottom) side of an airfoil? [duplicate]

I've been reading about this for quite some time and thought I understood it. Then somewhere someone mentions that air under the wing has higher velocity than ambient thus a lower pressure than ambient. I couldn't find any other reference to this so here I am.

What this means is that, in a purely hypothetical situation, without the upper part of the wing generating a lower pressure zone the airplane would actually be pulled down because the pressure on top would be ambient thus higher pressure than the bottom.

This makes sense since hitting air molecules with the wings will cause them to accelerate and suddenly move faster than ambient, thus have lower pressure.

How accurate is this?

Picture version:

• That's why flying too fast would tear a aircraft apart, because outside the skin is fast moving air and inside is non-moving air, so the inside has a higher pressure. – user3528438 Mar 28 '18 at 14:58
• @Sanchises: No, a thick airfoil at low angle of attack has also suction on the bottom, only less than on the top. This question requires a longer answer. – Peter Kämpf Mar 28 '18 at 18:17
• @Peter Enlighten us! ;) – Sanchises Mar 28 '18 at 18:27
• – Peter Kämpf Mar 28 '18 at 18:29

If the airfoil generates lift, pressure on the upper side has to be lower than on the bottom. Still, there can be suction (less pressure than ambient) on both sides.

For an extreme example, take the airfoil from US patent application 2004/0094659 A1 by Dan Somers. It tries to stabilize the boundary layer over the first 80% by creating an increasing suction over chord. The picture below is shamelessly copied from this application.

Ambient pressure is at a pressure coefficient c$_p$ of zero, and negative values denote suction, i.e. lower than ambient pressure.

All lift is generated by the highly cambered flap while the forward wing will only start to contribute lift once the angle of attack is increased from the current value of -2°. Note that airfoils for high subsonic speed show the same philosophy of a rooftop pressure distribution over their forward part with high rear loading. Such airfoils exhibit a high pitching moment and require a larger tail surface for stability, which blunts their advantage of low drag a bit. The plot below is taken from US patent 3,952,971 by Richard Whitcomb and shows just such a transsonic airfoil with a weak shock on its upper side.

This plot shows the speed difference ∆v compared to ambient, and again higher speeds which equal more suction are positive.

All those airfoils will develop a suction peak at the forward end of the upper surface and a corresponding pressure increase on the lower side once the angle of attack is increased. Now a Birnbaum-type pressure distribution will be added and at high angle of attack, this effect will dominate the pressure distribution and will ensure higher than ambient pressure on the lower side. This effect will be the more pronounced the thinner the airfoil is - a thick airfoil exhibits a stronger displacement effect which adds a little suction on both sides.

hitting air molecules with the wings will cause them to accelerate

Not exactly hitting - it is air molecules flowing around the wing which will contribute a speed increase and hence a lower local pressure. This can best be seen by the pressure distribution around symmetrical airfoils at zero angle of attack. Note in the plot below that suction is on both sides and growing with airfoil thickness. Of course at that angle of attack those airfoils do not generate lift, but when an angle of attack is added, they will, and it will need a higher angle to push the bottom side of the thicker airfoil into the pressure region of negative c$_p$ values.

Inviscid pressure distribution of symmetrical NACA airfoils (picture source).

Ambient pressure is higher than any wing pressure

Not quite: Note that all plots show a pressure peak at the nose and a pressure recovery to slight overpressure at the trailing edge. While most of the pressure around a thick airfoil at low angle of attack is indeed lower than ambient, the stagnation point will always ensure that this is not true for all of the airfoil.

• I think the first word should be ‘yes”, not ‘no’, because both drawings in the question show the pressure being lowest on top and the question is just whether the pressure on bottom is still lower than ambient, which you confirm. – Jan Hudec Mar 28 '18 at 19:40
• @JanHudec: Initially I wanted to write "it depends". You are right, a No is clearly misleading. But the new understanding is also wrong - there is always a stagnation point. – Peter Kämpf Mar 28 '18 at 19:46
• @JanHudec and PK: The first part I wrote was air hitting a random object. The second part (moving wing): on the pressure side at a positive AoA, the air is accelerated forward, right? Accelerated air loses pressure, bunching up forward gains pressure, so the overall will be like the answer to the proposed duplicate: pressure close to ambient, is that correct (in the subsonic envelope)? In other words, Not exactly hitting is confusing me because I keep recalling the two images here -- with the air indeed moving forward. – ymb1 Mar 28 '18 at 19:55
• @ymb1: It all depends on the point of reference. If the wing is stationary, the molecules flowing towards the stagnation point will be decelerated and slowed down. If the point of reference is stationary and the wing moves, the wing will add some energy to the stagnation point flow and increase pressure. And yes, the air will be accelerated forward first, backwards after that in the suction region and slowed down again when it leaves the airfoil. – Peter Kämpf Mar 28 '18 at 19:59
• @PeterKämpf I tried explaining the frame of reference point on a question about static ports a year or two ago and got a ton of down votes, people just can get past thinking about the aircraft as stationary and the air flowing at speed. It could help your answer if you explained more how positive Cp's are higher than free stream static pressure. – OSUZorba Mar 29 '18 at 1:55