In this blog post, we’ll examine the principles behind how an airplane generates lift, focusing on Bernoulli’s principle and the Kutta–Joukowski theorem, and explore the actual process of flight.
Is the Principle of Lift We Know About Actually Correct?
For people living in the modern world, Icarus’s dream of flying freely through the sky has already become a reality. Now, going beyond that dream, an era is dawning where even commercial space travel is possible—provided one can afford it. The biggest reason these dreams have become a reality is undoubtedly the continuous advancement of aircraft technology—starting with the Wright brothers’ airplane—which has enabled machines capable of lifting humans into the sky.
However, most people do not understand the exact principles behind how airplanes—which play such a crucial role—actually fly. In fact, even though I majored in mechanical and aerospace engineering, I did not fully grasp the precise principles until I began studying aerodynamics in depth. So, let’s examine the differences between the commonly accepted explanations and the actual principles behind how airplanes fly.
Can the Bernoulli Principle Alone Explain It?
First, let’s look at the most widely known explanation: it is commonly believed that airplanes generate lift based on Bernoulli’s principle.
Looking at Bernoulli’s equation, the difference in altitude around the wing is very small and can therefore be ignored. In this case, the air above the wing flows along the upward-curving surface and accelerates, while the air below flows relatively more slowly. According to Bernoulli’s principle, as the speed of a fluid increases, its pressure decreases; therefore, the pressure on the upper surface of the wing is lower than that on the lower surface. Consequently, a force acts from the lower surface—where the pressure is higher—toward the upper surface—where the pressure is lower—and as a result, the airplane generates lift, which is an upward force. This has been the most widely accepted explanation for how airplanes generate lift.
However, this raises a question. Why should air suddenly flow faster simply because the upper surface of the wing is longer? Since the air isn’t gaining any special propulsive force, it’s difficult to conclude that its speed increases merely because it passes over a curved surface.
In fact, when computer simulations of airflow based on wing shapes are conducted, it is often found that the air flowing over the wing takes a longer path and therefore reaches the trailing edge later. In other words, the assumption that the air above and below the wing must start at the same time and arrive at the same time does not hold true. This means that the speed difference occurring above and below the wing cannot be explained by the wing’s shape alone, and that another principle is needed to account for this speed difference.
So, what exactly creates the pressure difference between the top and bottom of the wing that makes an airplane take off?
The Actual Principle of Lift Explained by the Kutta–Joukowski Theorem
This phenomenon can be explained by the Kutta–Joukowski theorem, which was established independently by the German mathematician Martin Wilhelm Kutta (1867–1944) and the Russian scientist Nikolai E. Zhukovsky (1847–1921).
According to this theorem, when air begins to flow around a wing, circulation is formed as the air wraps around the wing. Furthermore, as the aircraft moves, a vortex is created behind the wing. In actual aircraft, strong wingtip vortices occur at the wing tips, and a similar flow structure forms behind the wing as well.
These vortices move backward along the airflow, forming a starting vortex. Since total angular momentum must be conserved in the absence of external rotational forces, if the starting vortex rotates in one direction, a circulation in the opposite direction forms around the wing. This phenomenon can be explained by the law of conservation of angular momentum, also known as the law of conservation of torque.
The circulation formed in this way accelerates the airflow over the upper surface of the wing and reduces the relative speed on the lower surface. Ultimately, a difference in airspeed arises between the upper and lower surfaces of the wing, and lift is generated as a pressure difference forms according to Bernoulli’s principle. In other words, Bernoulli’s principle is not incorrect; rather, the process explaining why the difference in airspeed occurs had been omitted. The Kutta–Joukowski theorem explains precisely that cause.
The law of conservation of angular momentum states that in a system not subjected to external torque, the total angular momentum remains constant.
In particular, the Kutta–Joukowski theorem established that the magnitude of the lift generated is proportional to the magnitude of the circulation formed around the wing. This made it possible to quantitatively calculate the lift acting on an airplane and paved the way for modern aircraft design, where performance can be predicted through computer simulations and analysis before the actual aircraft is built.
Simply put, without the research of Kutta and Zhukovsky, aircraft design would have had no choice but to rely on countless trials and errors. The process would have continued with designers creating arbitrary wing shapes, conducting repeated test flights, adopting those that flew well, and redesigning those that did not. It is precisely because these aerodynamic theories were established that we can now design and manufacture large passenger aircraft, such as the A380 or the Boeing 777, with the high levels of safety and efficiency we see today.
Today, there is hardly anyone in South Korea who does not know what an airplane is. Airplanes have become such a familiar mode of transportation that if you look up at the sky even once a day, you’ll likely see one flying by. However, fewer people than you might think actually understand exactly how an airplane flies. Of course, it’s not necessary to know the underlying principles of every machine we use. But wouldn’t our perspective on the world broaden if we understood the basic principles of the technology we encounter so frequently in our daily lives?
