# Explaining lift on a wing via forces

Consider the bottom of a wing.

Air below the wing is deflected downwards by the wing. Hence by Newton's 3rd Law the wind must exert an equal and opposite force on the wing. Hence lift, and this makes logical sense.

What becomes confusing, is explaining how lift is created at the top of the wing. Air once again moves down the top of the wing. However, now it doesn't make sense to say the wing is exerting a downwards force on the wind, because clearly it is below the wind. How do we get around this?

Bernoullis principle, visocity, and pressure can all explain this, but how do we do this soley in terms of forces? What force is causing the wind to move downwards at the top?

• Air above the wing is also deflected downward. Commented Mar 28 at 22:10
• "Lift on top of a wing" seems just a figure of speech to describe the effect of lowered pressure on top of the wing. There is no actual force of air acting on top of a wing which would pull the wing up (except for the small friction force at the front curved part of the cutting edge of the wing). Most of the lift force on the wing is due to pressure forces, so lift comes from pressure force at the bottom face being greater than pressure force acting on top face of the wing. Commented Apr 11 at 23:22
• very poor question, starting from English and ending with Physics Commented Apr 12 at 7:14

What force causes the wind to move downwards at the top of a wing?

The phenomenon known as the "no-slip condition" explains that a fluid flowing past a solid surface tends to adhere to it. For instance, if you hold your finger under a gently running tap, the water will cling to your finger and flow down along it.

Similarly, for an airplane wing, the air above it adheres to the surface and follows its contour until the separation point. The wing's curvature acts as a guide, directing the airflow downwards.

The misconception that "the wing exerts a downward force on the wind above it" likely stems from a misunderstanding of the no-slip condition.

How can we explain this solely in terms of forces?

In terms of forces, the air above the wing is deflected downwards by the wing. Consequently, by Newton's third law, the wind must exert an equal and opposite force on the wing.

In terms of viscosity: Viscosity alone cannot explain this phenomenon.

In terms of pressure: As the air streamlines above the wing are directed downward, the streamlines above must descend to fill the vacated space, resulting in a low-pressure zone above the wing and thus generating lift.

Regarding Bernoulli's principle: The assumption that fluid must flow faster over the wing to match the transit time of the wind below is a misconception. Instead, the streamline curvature theorem provides a more accurate explanation of aerodynamic lift. More

As the wing moves forwards, it creates void of empty space behind it, on the topside of the wing. This is a low-pressure zone, which then pulls the air above the wing downwards.

To see the full explanation search for ‘Newton explains lift’ on www.researchgate.net

The airflows created by the topside of the wing can be observed from a balloon that was seen to cross in front an A-380 airliner on approach to landing.

The video is on youtube: Airbus A380 vs Balloon; YouTube channel: 3 Minutes of Aviation; Mar 8, 2023; https://youtu.be/ir06S6ntbyk

To understand this, remember that air is a continuous medium in which every part exerts pressure forces on all the surrounding parts. In the absence of an aircraft wing, higher up air is pushing downwards on the layer of air beneath, and that lower layer is meanwhile pushing upwards on the layer above. When the wing comes along it deflects away the lower layer, so the upper layer has nothing to support it. It is meanwhile pushed downwards by layers higher still, so it accelerates downwards.

The vertical components of the forces directly on the wing are also primarily pressure forces.

The downward deflection of air by a wing can provably exert an upward force on the aircraft. This is because aerobatic aircraft with a symmetrical cross sectional profile can quite happily fly upside down. In a fact a skilled pilot can maintain altitude upside down in a an aircraft that is upside down and the curvature of the wing is in the wrong direction in this case.

When a well designed wing has a positive angle of attack, the airflows generally stay attached to the wing and flow smoothly over it. When the angle of attack is excessive, the upper flow detaches and this is a condition called stall which is to be avoided. When the air is flowing smoothly over the curved wing surface, both the lower and upper bodies of air are directed downward and this mass of downward moving air has a momentum and there is a corresponding upward reaction force on the aircraft.

The total real forces on a wing are complicated and subtle and of course includes such things as pressure differences due to Bernoulli's principle and the rotation of the block of air around the wing and in fact lift can be interpreted in many different ways.

What force is causing the wind to move downwards at the top?

On a properly designed wing, the leading edge is nicely curved and this allows air to smoothly follow the curvature of the top surface of the wing which is a natural result of how fluids behave when they pass over a curved surface. If the air flow leaves this surface they leave a pocket of reduced pressure and the greater pressure of the surrounding air directs the flow back to following the surface.

If the wing is a barn door at a high angle of attack, the wind passing over the top can basically continue in a straight line, leaving a vacuum above the wing, which might seem like a good thing as far as providing lift is concerned, but this huge difference in pressure between the surface of the wing and the surrounding air cause air to circulate backwards towards the wing and the momentum of this back circulating wind hitting the top of the wing can cause a downforce and the extra drag due to not having a smooth flow, all conspire to destroy the lift of the wing significantly and cause instability, so not such a good thing.

What allows airplanes to fly is not straightforward, and trying to break down fluid dynamics into simple parts as this question is trying to do may not give you any new knowledge.

That said, the top part of the flow sticks to the surface of the airfoil due to the Coanda effect.

The Coandă effect (/ˈkwɑːndə/ or /ˈkwæ-/) is the tendency of a fluid jet to stay attached to a convex surface.

This phenomenon makes your tea spill over the cup while trying to pour it into a saucer. I know, this answer is just naming the phenomenon you asked about, rather than explaining why it happens. I am sorry that I don't have the expertise to comment on this, probably someone else on this site would help you out. But searching along this line could lead you to the answer you are looking for.

I need a bit of interpretation of your question. If you don't feel comfortable with the idea that the flow on the top of an airfoil can be deviated downwards, you're probably forgetting the role of pressure, or better pressure gradient. To add some details, it's possible to recast Navier--Stokes equations in a Lagrangian formulation (following the trajectory of a material particle)

$$\rho \mathbf{a} = \rho \mathbf{g} + \nabla \cdot \mathbb{T} \ ,$$

being $$\mathbb{T}=-p\mathbb{I}+\mathbb{S}$$ the stress tensor splitted as the sum of pressure and viscosity contributions.

Now, it's possible to project this vector equation onto a Frenet bases (tangential, normal and binormal vectors):

$$\begin{cases} \rho a_t & = \mathbf{\hat{t}} \cdot \left( \rho \mathbf{g} + \nabla \cdot \mathbb{T} \right) \\ \rho \frac{v^2}{R} & = \mathbf{\hat{n}} \cdot \left( \rho \mathbf{g} + \nabla \cdot \mathbb{T} \right) \\ 0 & = \mathbf{\hat{b}} \cdot \left( \rho \mathbf{g} + \nabla \cdot \mathbb{T} \right) \ , \\ \end{cases}$$

being $$\rho \frac{v^2}{R}=a_n$$ the normal acceleration, with $$v$$ velocity, and $$R$$ the local radius of curvature of the trajectory, and the bi-normal component of acceleration $$a_b=0$$ by kinematics.

Working with high-$$Re$$ flows outside the (thin) boundary layer over an airfoil at small AOA, viscous stresses are negligible, so that the stress tensor becomes $$\mathbb{T}=-p\mathbb{I}$$ and the equations (neglecting volume forces as well) read

$$\begin{cases} \rho a_t & = - \mathbf{\hat{t}} \cdot \nabla P \\ \rho\frac{v^2}{R} & = - \mathbf{\hat{n}} \cdot \nabla P \\ 0 & = \mathbf{\hat{b}} \cdot \nabla P \ , \\ \end{cases}$$

As you can see from the tangential component of the vector equation,

• the opposite of the derivative of the pressure field along the trajectory is proportional to the tangential acceleration (and thus it makes the absolute value of the velocity increase)

• the opposite of the derivative of the pressure field in the normal direction is proportional to the "normal" centripetal acceleration. As a simple example of a flow where you can easily find this contribution, you can think at any 2D-flow with circular trajectories, either rotational or irrotational. Even more qualitatively, like the flow of a tornado swirling around a low-pressure central point.

Short remark about signs. Focusing on the normal component, Frenet basis is defined with the normal vector pointing "inwards" towards the center of curvature of a line, here the trajectory. On the LHS we have a positive term (density, absolute value of the velocity squared, radius of curvature all positive), thus the derivative of pressure field along the $$\mathbf{\hat{n}}$$-direction must be negative to make the RHS positive, i.e. pressure "decreases towards the center of curvature".

On the other hand, if I have to re-interpret the title of your question as "explaining lift as a sum of elementary forces", the only answer I'd feel to give starts from the expression of the force acting on a solid body surrounded by a fluid,

$$\mathbf{F} = \oint_{S_{solid}} \mathbf{t_n} \ .$$

Simply put, it is because when the wing moves forward, a low-pressure area is formed at the top of the wing. Due to this low-pressure area, the air at the top of the wing is pushed down by distant atmospheric pressure, resulting in downward movement of the air above the wing. This is similar to the air at the bottom of the wing being pushed down.