# Why do low pressure arrows point away from the surface if the pressure/air cannot pull/suck?

Pressure is always positive, so at the upper part of a wing pressure is positive as well, just lower than the free stream, but still PUSHes on wing surface, not PULLs.

Words like pull or suction don't exist in fluid reality, because this is not how fluids exert force on body.

Why do pressure arrows always point away from surface if pressure can't PULL?

(arrows at pictures below,are only tehnically correct if they represent direction of local net forces at airfoil surface)

I think pressure arrows must point always toward the wing surface and when wing produce lift, arrows must be longer at lower side of wing and shorter on upper side of wing because that is the way how pressure really works.

• It could be interesting (for us and/or for you) if you would draw the figure the way you think it should be drawn, show us your figure, and explain how to interpret it. Can someone easily see from your figure how much the pressure at each point on the airfoil's surface differs from the free-stream static pressure? Who knows, we might be surprised. Commented Aug 31, 2021 at 0:24

The arrows are drawn relative to 1atm. This is a convenient simplification because there is no meaningful difference between 'pulling' at the top surface against 1atm or 'not pushing' against a vacuum. And since most airplane fly in the atmosphere, this is a perfectly reasonable simplification (even though in reality, it's really the air inside the wing pushing the airfoil surface up).

Compare with the functionality of a straw. You might say you suck at a straw even though in reality you're just reducing the pushing of air inside the straw. But isn't it much more convenient to say you suck at the straw?

• The arrows are drawn relative to 1atm. Isnt arrows drawn relative to freestream pressure? Commented Aug 29, 2021 at 16:22
• Barometric pressure at which aircraft fly,usualy lower than 1atm Commented Aug 29, 2021 at 19:14
• Sure. So maybe 0.9 or perhaps 0.8atm. Still enough to "pull" I'd say. Commented Aug 29, 2021 at 20:05
• Fly an airplane with a fabric covered wing and watch how the fabric is bulging outward between the wing ribs on the upper surface. The air seems to pull the fabric up. What happens really is that the air inside the wing is pushing the fabric up. Still, "pull" is an appropriate term here. Commented Aug 29, 2021 at 23:52
• @LostinSpace You are, of course, technically correct. But practically speaking, it's much easier to think in terms of 'pulling' instead of 'not pushing'. Just as the concept of a 'fluid' is a practical approximation of 'a bunch of molecules bouncing around'. Commented Aug 30, 2021 at 6:50

## There is no such thing as "pressure arrow"

Pressure is a scalar quantity, i.e. a magnitude with no direction (NASA).

I believe the points you've raised deserve some attention. @Sanchises is right in that that's just a simplification, but it helps to understand what the author of the image is referring to.

Your image was adapted by Georgia State University from a book by Charles N. Eastlake where he talks about "surface pressure distribution" – even the original image caption reads, "Surface pressure." However, the adapted image says, "Pressure profile around airfoil", which is not as clear as the original caption:

[...] it is also clear that the surface pressure distribution will vary along the chord length of the airfoil, as illustrated in Fig. 3. [emphasis added]

— Eastlake, Charles N. "An aerodynamicist's view of Lift, Bernoulli, and Newton." The Physics Teacher 40.3 (2002): 166-173. (PDF)

## So, what are those arrows?

The arrows show the positive direction to/from the datum, and the arrow lengths are the magnitudes near the surface. (The datum of free-stream pressure being the envelope drawn around the airfoil.)

On the upper side the arrows point up towards that datum, meaning whatever is below that datum near the surface is a lower pressure. Similarly, on the lower side the arrows are above the datum, i.e. higher pressure. That drawing is nothing but trying to merge actual pressure distribution graphs (example below) with the shape of an airfoil as a means of explanation.

— Allen, H. Julian. "A simplified method for the calculation of airfoil pressure distribution." (1939).
(Click image to view)

## Actual force direction

Zoom in on air molecules, and they exert their pressure everywhere, unless they're right at a surface, in that case the force (pressure times the immediate area) felt by the surface will be down and normal (perpendicular) to the surface, as illustrated by NASA:

https://www.grc.nasa.gov/www/k-12/airplane/presar.html (I know, the force arrows above do not show the magnitude, but at least the direction is right.)

Given the magnitude of pressure difference on the upper side, lift is primarily achieved by reducing the down-pushing force on the upper side.

The arrows are drawn relative to the freestream static pressure, as mentioned on the diagram. (e.g. 1atm if testing at sea level).

Each vector indicates the relative air-pressure (after ambient pressure is subtracted) at that point on the surface. So we can look at relative arrows in different directions instead of small differences in the lengths of inward absolute-pressure arrows.

This subtraction always balances out because uniform air pressure won't push a stationary object in any direction, regardless of shape. (Buoyancy is negligible for wings). So these arrows do tell us which way the net air pressure differences will push / "pull" the wing.

(The arrows are not following the steepest pressure gradient or anything like that, so they're not telling you anything about the pressure field anywhere but at the wing surface. A pressure field diagram would usually have gradients shown with different colors, thanks @ymb1.)

• I started writing this as an edit to Sanchises's answer to mention freestream pressure, not assuming it was 1atm, but the part about being specific about the vectors was too much for an edit. ymb1 added a similar section to their answer while I was typing this. Commented Aug 30, 2021 at 16:18
• @ymb1: Thanks for noticing that inconsistency. Removed explicit mention of force so I don't have to say anything about pressure over units of area being force. And I'm tidying up comments under your answer now that I've included the interesting part about these arrows not being anything to do with the air not at the wing surface, despite the visual appearance of a boundary layer or something. Commented Aug 30, 2021 at 17:38