Newton, Bernoulli, Wings, and LiftHOW THEY ALL ACT TOGETHER TO MAKE AN AIRPLANE FLY

Andy Foster, CFI-S, BAE

©𝑊𝑖𝑙𝑙𝑖𝑎𝑚 𝐴 𝐹𝑜𝑠𝑡𝑒𝑟 2020

There are lots of explanations…and many of them are wrong!

u Early explanations of how a wing creates lift centered exclusively on the use of Bernoulli’s equations….

X

XP1V1

P2V2

pressure

velocity

• When air speeds up or slows down, it affects the static and dynamics the pressures in the flowfield.

• A scientist named Daniel Bernoulli studied this in 1738. He used Isaac Newton’s Second Law (F=ma where F=force, m=mass, and acceleration) to calculate the relationship between velocity and pressure for an air particle moving along a streamline.

P1>P2V1<V2

𝑃 + 𝜌𝑉2/2 = constant𝑃= static pressure𝜌 = 𝑑𝑒𝑛𝑠𝑖𝑡𝑦𝑉 = 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦

Bernoulli’s Equation

𝜌𝑉2

2𝑖𝑠 𝑐𝑎𝑙𝑙𝑒𝑑 “𝑑𝑦𝑛𝑎𝑚𝑖𝑐 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒”

𝑎𝑛𝑑 𝑖𝑠 𝑜𝑓𝑡𝑒𝑛 𝑟𝑒𝑓𝑒𝑟𝑟𝑒𝑑 𝑡𝑜 𝑎𝑠 “𝑞”𝑜𝑟 “𝑞 − 𝑏𝑎𝑟”. Thisis the pressure measured in the direction ofthe flow (i.e. hitting you in the face).

P or static pressure is pressure measured in a direction perpendicular to the flow.

X

XP1V1

P2V2

pressure

velocity

P1>P2V1<V2

It’s mostly right…

l Use of Bernoulli’s is accurate in that the pressure and velocity relationships can be used to understand and calculate the lift a wing section is creating.

l Lift on a wing section in a wind tunnel can be calculated by measuring the pressure at multiple points above and below it, plotting them, and then using calculus to calculate the area of the enclosed curves which equates to the Lifting force. (Beginning aerospace engineering student exercise.)

l You get the right answer for simple flows but it doesn’t fully explain or capture all the fluid mechanics of what’s going on.

• LIFT is simply the difference between the forces created by the larger low-pressure area on the top of the airfoil and the higher-pressure area underneath. This creates a force imbalance that pushes the airfoil in the opposite direction of the major downward defection of the air (top and bottom).

• PRESSURE (always a push) is the ONLY thing the airfoil “feels”.

• To help us understand how air flowing around an object acts, I’ve referred to “streamlines”.

• Streamlines are lines drawn along the direction of velocity of the flow.

• This graphic shows the streamlines created by air flowing from left to right around a smooth, non-moving ball.

• So, let’s look at an airfoil (i.e., a cross-section of a wing) and talk about what happens when air moves past it.

• We’ll use an airfoil that has the same curvature on the top as the bottom. This is called a “symmetrical airfoil” because its upper and lower halves are the same.

• At zero angle to the airstream, the shape of the airfoil causes the air above and below the airfoil to move (speed up) the same amount. This means the pressure drops above and below the airfoil are the same. There is also no downward deflection of air, so there is no “lift”.

• But if we incline the same airfoil 9° to the airflow. (As an example).

Streamlines bunch together indicating higher velocity and lower static pressure.

Streamlines don’t curve as much and spread out a little, indicating lower velocity and higher pressure.

Representative path of the air flowing over the top of the airfoil.

The airfoil deflects the air downward over its top a lot more than on its bottom (but there, also)!

Modified Screenshot from NASA FoilSim

• The downward deflection of the air shows that the lifting action is in accordance with Newton’s Third Law which says “For every action, there is an equal and opposite reaction.”

• When most people think about Newton’s Third Law, they think about rockets. The principle is the same; but the physical mechanisms are different.• This is where many explanations get it wrong about how

Newton’s Third Law is associated with the creation of lift.

VELOCITY

THRUST

LIFTAn airfoil only feels the pressure of the air around it. The pressure imbalance created from the pressure and velocity changes and the downward deflection of air in the flow field around the wing creates is what creates lift.

DOWNWARD TURNS

• The nature of the flowfield around the airfoil is dependent on the physical processes described by both Bernoulli’s equation and Newton’s Second an and Third Laws, (i.e., the changes in velocity, pressure and conservation of momentum) and the presence of the airfoil, are very complex, and interdependent (i.e., they feed each other).

• Better to think and understand them as a SYSTEM!• Our simpler explanations and equations are correct but don’t shed a

strong or complete light on the complex physics (fluid mechanics) in the background.

If we plot the static pressure over the streamlines (with – for lower static pressure and + for higher, we’d get something that looks like this.

There is a diffuse velocity-pressure field created for some distance around the airfoil, with the strongest effects at its surface.

ex. L= ½ ρCL𝑉2

• So far, we have been talking about an airfoil. • Airfoils form the cross section of a wing.

• An airfoil is 2 dimensional.• A wing is 3 dimensional.

• That extra dimension introduces a change in the airflow.

• Air flows from high pressure to low.• The high-pressure air under the wing swirls around the wingtips,

creating an effect like two horizontal tornadoes spinning toward the fuselage.

• This swirling air combines with the air flowing OVER the wing and changes its flow slightly.

• This illustration shows how it affects the velocity of the air, the angle of attack, and the aerodynamic forces the wing creates.

Lift acts perpendicularly to the Relative Wind (i.e. velocity vector).

The airflow around the wingtips causes a decrease in the angle of attack which rotates the lift vector rearward. This decreases LIFT and increases DRAG.

This drag due to lift is called induced drag.

The wingtip vortices are inhibited when an airplane is within a half-wingspan of the ground. This can allow a too heavy airplane to get airborne but not be able to climb away. This is “ground effect”.

• What we call “downwash” is a result of a wing creating lift. (Not vice versa!)

• The strength of its vorticity is directly proportional to the aircraft’s weight.

• Downwash decreases lift and increases drag, which is why engineers try to minimize it.

Image from FAA-H-8083-25B, p. 5-7https://www.grc.nasa.gov/www/k12/airplane/winglets.html

• In 2002, some physics teachers1 published an article in “The Physics Teacher” that Bernoulli’s was the incorrect way to teach aerodynamics, and only Newton’s Laws need to be used.• As previously stated, Bernoulli’s equations are derived by using

Newtons’ second law. Bernoulli’s can be used by itself to calculate the lift created by simple flows.

• One can also use momentum exchange (Newton’s laws) to calculate the forces (including lift) in a wing-airflow system by itself to do so.

• The best mathematical way to calculate complex aerodynamics flows is the use of a version of the Navier-Stokes equations.

• They use conservation of mass, momentum, and energy of fluid particles (air) to solve for complex mathematical solutions.

• Today’s Computational Fluid Dynamics approaches are based on this.

• WAY BEYOND the simplified explanations we’re seeking to explain lift!!

In trying to infuse Newton’s laws into the explanation for lift..

u It started a competition and argument” about which was correct (not among engineers and aerodynamicists)…u Most lay explanations completely ignored Newton’s Second Law but correctly

seized on Newton’s Third Law and grabbed the wrong mechanics:u The public’s familiarity with Newton’s Third Law with the science of rocketry led to trying to

reconcile it with one of two false mechanisms:

u A reaction to air hitting on the bottom of the airfoil

u Streamlines around an airfoil show the air is flowing parallel to the bottom (except at the boundary layer where the surface velocity is actually “zero”)

u A reaction to the “downwash” associated with wingtip vorticity

u Downwash due to wingtip vorticity REDUCES lift and INCREASES DRAG!

u Confused with the airfoil’s overall downturn of air…

Summary• Air moves in response to pressure changes or mechanical action.• As air accelerates, its static pressure decreases and its dynamic pressure

increases; and vice versa.• An airfoil can only feel and respond to pressure. Pressure is always a

“push”.• Lift occurs from a pressure imbalance an airfoil creates with an envelope

of air that causes velocity and pressure changes and a downward deflection of the air.

• Bernoulli’s Principle and Newton’s Third Law are both in action, reciprocal, and needed for an airfoil to produce lift.

• Downwash is product (not a cause) of a wing producing lift. Downwash decreases lift and increases drag.

• A heavy aircraft may get airborne in ground effect but not be able to climb higher.

• If you want more, see “Aerodynamics for Pilots” video.

Misconceptions and Myths about Creating Lift• Bernoulli’s Principle and Newton’s Third Law are mutually exclusive or

competitive when talking about the production of lift.• Air at the top of the airfoil goes faster over the top of the airfoil

because it has to get there at the same time as the air on the bottom. (Equal Transit Theory)• Untrue. See: https://www.youtube.com/watch?v=e0l31p6RIaY.• Air moves because of the pressure gradient and air over the top

arrives first (larger pressure drop; faster velocity). Which raises a question; what came first: the velocity gain or pressure drop?

• Newton’s Third Law is illustrated by: (1) the wing reacting to the air bouncing off its bottom, or (2) as a reaction to downwash.• (1) What do the streamlines show along the bottom? (2) This is

confusing downwash with the downward deflection of air on top and bottom of the airfoil.

• The Coanda Effect is involved in the creation of lift.• Untrue. We explained the generation of lift without it. The

Coanda Effect is dependent upon a focused high stream jet of air close to an object, which does not act the same as freestream air close to an object.

QUESTIONS?