Why Planes Stay in the Air: Gravity
A recent Scientific American article reported on a commonly confused phenomenon: flight. The authors, referencing experts in aerodynamics and a 2003 New York Times piece, discuss various flaws in the contemporary explanations for how wings produce lift. The article caught my attention when I recalled having personally been bemused by the explanations I encountered while researching the topic for a lecture on pressure back in 2015. Having thought about the notion for some time now, I thought I’d take a moment to demystify the notion. It’s my apprehension at this point that an important player has been left behind in the locker-room: that player is gravity.
In short, the usual explanation given for lift is that the cambered shape of the wing requires air above the wing to travel more quickly and this produces lower pressure in those regions with respect to higher pressure regions below the wing. This pressure-based argument was first developed by Daniel Bernoulli and so bears his name. Following from this theorem, in accordance with Newton’s observation that all reactions produce and equal but opposite reaction, the greater pressure below the wing forces the wing upward.
Failures cited for this explanation are threefold: First, there is no cause given by Bernoulli for high speed air to have a lower pressure. While it may be intuitive that a molecule of air must travel in the same time a greater distance above the wing with respect to below, this is actually not the case. The equal transit time is not apparent and even if it were could not account for the magnitude of the pressure differences observed. Second, Bernoulli’s explanation contradicts the apparent behavior of the high-speed (high temperature) gases studied in laboratories. High temp gases should produce increased pressure, not decreased as observed above wings during lift. This increased pressure of high temperature gases is evident in the production of steam power. Finally, it is noted that cambered wings can fly even when inverted, implying that the wing’s asymmetrical profile has little effect on the plane staying aloft. In fact, even non-cambered wings still produce regions of low pressure above and high below.
The equal-transit-time model for lift, traditionally offered in textbooks fails on numerous levels beginning with the fact that air does not in fact take equal times to travel each portion of the wind stream. Photo: wikimedia.
So what is happening with the air molecules and the wing that allows for lift? As with most confusions, the answer hides in the finer details. Bernoulli was certainly on the right track when he identified low-pressure regions above the wing. The reason this contradicts established theory on the speeds of gases with respect to pressure has to do with the directionality of the gaseous motion.
See, typically, gas behavior is modeled as chaotic and confined to some rigid container where all motion is accounted for by random collisions. Increased molecular speed in this context, can be best described as heat, which of course does apply more pressure to the container, since motion is constrained in all directions. However, in the context of a flying wing, air moves not at random but rather flows across the wing. The shape of the wing displaces the air upward and downward as well. But because the air is predominantly confined below by the ground, and not laterally or vertically, the air is more easily displaced in all directions except down. This is the case regardless of the shape of the wing.
In addition to air beneath the wing pressing against the ground, an additional impetus for the wing to move upward is supplied by the density gradient of air in the atmosphere: also, a product of gravity. Consider that each molecule of air is in some way connected and pulled by the multitude of atoms of the Earth downward. This allows for a greater density of air in the downward direction with respect to the upward. For this reason, any reciprocal pushing forces applied both upward and downward simultaneously by the air, as in the case of a symmetrical non-cambered wing, would be directed per Newton’s laws toward the path of least resistance: upward.
In summary, both Newton and Bernoulli were right and slightly incomplete. The dense, groundward-confined air will always offer more resistance, and hence pressure, when a wing forces air upward and downward with equal vigor. The result of these dynamics is a region of high pressure below the wing and a region of low pressure above, regardless of the cambered design. Of course, the camber can prove useful during take-offs and landings, when speeds are insufficient to part the air with appropriate force and so the design remains steadfast in most airfoils.
