Why Planes Can Fly Upside Down
A couple of years ago, I read with great interest an article titled No One Can Explain Why Planes stay in the Air. It was sent to me by no less than four newsletters (and a fifth recently- almost two years later). Even after reading the article, I assumed this was just surprising trolling from Scientific American. The article was not suggesting all flight was a mystery but that engineers could not agree on how an airfoil designed for upright flight could function upside down. I refreshed my memory of college physics and sought additional sources from as many angles as I could imagine. When I found a deep rabbit hole on the NASA website for the Glenn Research Center, I was driven to distraction. What I found was a lot of math founded on empirically derived coefficients. How could such fundamental behavior with so many observable effects not be reasonably explained by a more straightforward physical model?
The Basics
Like many students, powered flight was explained to me as a balance of four forces- thrust, lift, drag, and gravity. The picture presented showed the forces working in oppositional couplets- drag retarding thrust and lift countering gravity- in orthogonal fashion. Scientists found Bernoulli and then Navier-Stokes to explain the more complex fluid mechanics, but I was still hoping for a conceptually accessible version.
Fundamentally, an object is lifted into the air when either force is applied by the body on the surrounding air (such as by a propeller) or the body rapidly expelling mass, causing movement in reaction (such as by a jet engine). If all you need is Newtonian force, why is an airfoil important? Additional forces are introduced by the movement of air over surfaces in flight that make things like paper airplanes stay aloft longer than a ball of paper.
Imagine a right triangular prism in a wind tunnel with one side parallel to the air flow and one perpendicular. In place of a static fixture, this prism could be on a track that only allowed vertical movement with a vertex resting on the ground in still air.
Now place a barrier that shields the top half of the tunnel, Newtonian behavior will cause the prism to rise assuming the force of the fan creates enough momentum in the air to overcome the mg of the prism as the force of the air is split with some amount reflected and some directed downward by the angle. This makes clear intuitive sense as the same would happen if you sent a rush of water. Even pushing the surface with your finger in a parallel vector will suffice for the same reason. If the surface were not angled, no vertical movement would be observed.
The effect of gravity could even by isolated by rotating the apparatus ninety degrees and observing horizonal forces. That does not feel like lift. That feels like conservation of momentum. In the same way that a turbine or propeller channels air to create thrust, air pushes back as a wind load. There is no difference between movement of the air creating that force or the movement of the body through static air. You could hypothesize an increase in pressure under the leading edge, but since any parallel force can produce the same effect (flowing sand, for instance) this is just a fine reasoning.
If we instead isolate the top surface by placing the barrier in the bottom have of the tunnel, the wind rushing past the top parallel surface will also cause the prism to rise. If you are unfamiliar with Bernoulli or Venturi, this may come as a surprise, but anyone that has seen a sheet of plywood lifted off the ground by a gust of wind should expect that result. The movement of unbounded air creates a non-ideal situation that reduces pressure. A lifting force is created by the atmospheric pressure remaining constant on the opposing side.
For a more intuitive version, imagine a wind tunnel with a hose and a vacuum drawing air. If a seal was created the hose would suction to the prism and lift assuming the reduction in pressure within the hose multiplied by the cross-sectional area of the hose is greater than the mg of the prism.
The force applied by the vacuum draws the air within the hose leaving the atmospheric pressure of 760 mm Hg at sea level pressing the hose end of the hose to the prism through conservation of momentum.
Even without a seal, the flow of air over the surface creates a drop in pressure. That same principle will cause the prism to rise. The faster the air, the greater the drop. A higher volume of air is required to move at a higher velocity, but the remaining surfaces continue to experience the force created by atmospheric pressure along a perpendicular vector. This is true whether the fan pushes air, or the fan is placed behind the prism, and air is drawn. Conveniently, in a closed system (like a pneumatic piston) measuring the electrical load of the fan would provide the force calculation for raising a surface under these conditions.
In each case, the mechanism at work is the need for gaseous molecules to equilibrate. Pressure either increases or decreases locally until the prism moves to accommodate the imbalance. The various currents and eddies created in the process may impact the change at the margins, but they are not required to explain lifting action. The prism may settle at a fixed elevation with a constant flow, but the interaction between the movement of the air and gravity is ongoing.
If all of that is generally understood, where is the debate? The implication in the article is that by turning our theoretical prism upside down, none of these explanations hold true- which is true if the prism has no independent agency.
Force and Flight
Scaling up the thought experiment, helicopters produce lift and acceleration in general harmony. The shape of the rotor provides downward force. Angling the plane of rotation directs force ahead or behind the center of mass, and the body moves laterally. Most airplanes rely on a fixed vector of thrust across the body and control surfaces that adjust the angles of air resistance to change direction. Dramatic oversimplification aside, you could model an airplane as helicopter flying horizontally. Mechanically, nothing would make sense, but the visual gets to the heart of my original confusion and frustration. Everyone accepts that thrust propels all manner of objects in all directions, but somehow an airplane requires a mysterious “lift factor” to remain in the air.
From the perspective of an airfoil in a wind tunnel, moving a profile through static air is physically the same as moving air over the object. The boundary conditions and other local behaviors are identical. From the perspective of an aircraft moving through space, the two arrangements are significantly different. A strong enough wind can topple a parked aircraft, but an object in flight due to impulse or continuous thrust has momentum that interacts with the airflow. Under circumstances with a high angle of attack (i.e. take off) the oppositional force of the air creates lift. Under regular flight, the air serves more as a porous surface along which the object is propelled. There are nuances like entrainment and the Coanda effect, but the basis for a plane staying in the air- even upside down- is somewhat simpler. Planes stay in the air because of a simple resolution of x (thrust) and y (gravity) vectors. Added mathematical complexity is about efficiency and stability of a lifted body- not whether it can remain in the air.
Looking from the perspective of the air, in an ideal state the Universal Gas Law makes a neat summary of behavior (PV = nRT) that relates pressure, volume, quantity, and temperature. In aggregate, this applies whether the volume is a jar or the entire atmosphere. An object moving through a gas however creates a temporarily bounded volume resulting in non-linear, non-ideal behavior. For example, the faster you attempt to swing a tennis racquet, the greater the air resistance becomes. That resistance is one component of lift- which is one reason that even mathematical predictions of airfoil shape do not call for a sharp leading edge to reduce drag.
In other words, an airplane in flight has more in common with a snow machine motoring across the surface of a river or a puck on an air hockey table than with a helicopter or hot air balloon. That is true regardless of scale. Inversion of an airfoil may require additional thrust and adjustment to the vector of thrust to stay aloft, but if the power to weight ratio can handle the maneuver the airframe will continue in the direction of travel buoyed slightly by the surrounding fluid. Perhaps the most compelling demonstration of this is the improved fuel economy at higher altitudes. If proper airfoil interactions with the surrounding air were required for flight, the thinner air would require additional thrust to compensate. Instead, the reduction is drag is far more beneficial for long flights even when the reduced engine efficiency is considered.
I wrote this for the same reason I write most things- to help me understand. I hope this has sparked more interest than argument. If there is enough interest I will continue with a second part that elaborates further.
