Even the Ancient Greeks Dealt with Turbulence

There's very little difference between the definitions of Plutarch and Google.

Technicalities
The earliest known reference to turbulence may be in a biography of the Roman general and statesman Titus Quinctius Flamininus.Philippe Lechien

My mother, who fortified herself for any aerial voyage with either Miltown or Chivas Regal, would later revisit with perverse relish each “air pocket” the plane had encountered. I’m not sure what she believed an air pocket consisted of, but I suppose it was something like the “region of low pressure causing an aircraft to lose altitude suddenly” that you still find if you Google the phrase today.

You would not suppose that awareness of air pockets could much precede the Wrights, but in fact, the earliest reference I have encountered is in a biography of the Roman general and statesman Titus Quinctius Flamininus, who in 197 B.C. liberated a number of Greek city-states from Macedonian control. Writing some 250 years after the event, the author, Plutarch, describes how a large gathering of Greeks gave out such a shout of joy at the announcement of their emancipation that passing crows fell from the sky.

He pauses in his narrative to ponder this remarkable event. “The disruption of the air must be the cause of it. For the voices, being numerous, and the acclamation violent, the air breaks with it, and can no longer give support to the birds, but lets them tumble, like one that should attempt to walk upon a vacuum. ... It is possible, too, that there may be a circular agitation of the air, which, like marine whirlpools, may have a violent direction of this sort given to it.”

The mixture of credulity and careful analysis is characteristic of ancient authors; we, or at least the irreligious among us, simply dismiss implausible stories of long-past events as mere fables. But it is also interesting to see that a first-century Greek, who was a newborn babe as far as the mechanisms of flight and the behavior of air are concerned, nevertheless came pretty close to describing what today we would call “loss of lift” and “turbulence.”

Despite the passage of 2,000 years, Google’s “region of low pressure” is scarcely an improvement upon Plutarch’s “disruption of the air.” There are, indeed, regions of low pressure in the atmosphere, but they are hundreds or thousands of miles wide and in no sense “pockets.” Besides, pressure has nothing to do with it; if a deficit of something caused an airplane or a crow to drop, it would be density, not pressure.

In fact, what causes an airplane to drop or to surge upward is not a change in the quality of the air. It is a change in its motion — indeed, a sort of “agitation.” What you perceive as bumps are differences in the direction and velocity of airflow as you pass rapidly from one region of the air mass to another. Bumps feel more sharp-edged and percussive in a fast airplane than in a slow one because the transition from one region to another is quicker.

The airplane cannot instantly re-trim itself for each swirl and eddy through which it passes, and so the wing experiences transitory changes in angle of attack and airspeed. The lift force therefore changes, and the airplane rises or sinks accordingly.

There is a connection between weight, speed and turbulence that pilots learn but do not necessarily understand. We are taught that the safe speed for turbulence penetration gets lower as an airplane gets lighter. This seems counterintuitive; why would a lightly loaded airplane not be better rather than worse equipped to sustain a given gust loading?

The reason has to do with angle of attack and lift coefficient — and this may be why it is not more easily understood.

When an airplane encounters a gust, the change in angle of attack is the result of combining the speed of the airplane with the relative direction and speed of the gust. For example, if an airplane traveling at 300 feet per second (about 180 ktas) encounters a vertical gust of 20 feet per second, its angle of attack changes by nearly 4 degrees (that is, a 15-to-1 slope).

How the airplane responds to that change has to do with both its speed and its wing loading. The higher an airplane’s wing loading, the higher its lift coefficient at a given speed. The lower its speed, the higher its lift coefficient at a given weight.

Now we come to the bumpy part of the trip.

Lift coefficient is a measure of how much of a wing’s lifting capacity is being used. Its range in normal flight is from 0.1 to about 1.5 with flaps up. The lift coefficient of a wing at an angle of attack of zero depends on the camber of its airfoils, but each change of 1 degree of angle of attack results in a change of about one-tenth of a unit of lift coefficient. This relationship has the following result: If the lift coefficient is 0.2 at an angle of attack of 1 degree, it will be 0.4 at an angle of attack of 3 degrees. But if it is 0.4 at 1 degree — that is, the wing loading is higher or the airplane is moving more slowly — it will be 0.6 at 3 degrees. In the first case, the lift force increases by 100 percent and the airplane experiences an acceleration of 2 G; in the second, although the change in angle of attack is the same, it increases by only 50 percent and the acceleration is 1.5 G.

If you ponder this relationship, you will see that it has two important consequences. One is that airplanes with higher cruising lift coefficients — generally, ones with higher wing loadings or flying at higher altitudes, or heavy airplanes flying at lower indicated airspeeds — experience lower accelerations in turbulence. The other, which is the more consequential, is that by slowing down, and therefore increasing your angle of attack and lift coefficient, you reduce the effects of turbulence. This is true in spite of the fact that as you slow down, the change in angle of attack for a given gust gets larger.

Pilots sometimes ask why, if an airplane is lightly loaded, its allowable G-loading doesn’t go up. Surely an empty cabin puts less strain on the wing spar than a full one. The reason is that the entire structure of the airplane — not just the wing spar, but the engine mounts and battery box and gear up-locks and fuel tanks and what have you — are designed for the 3.8 G limit load required by the FARs, and so parts other than the wing are still vulnerable to overstress. That’s why it is always wise to slow down for turbulence — even if it is merely anticipated turbulence, and even if your airplane is lightly loaded.

But just to be super safe, heed old Plutarch and don’t fly over any rock concerts or bowl games. Those people can really yell.