Bernoullis Principle of Lift

If only Daniel Bernoulli and Sir Isaac Newton were alive today. They would have been truly amazed to see an Airbus A380 rise off the runway and climb six miles into the sky. Great scientists as they were, a discussion about who’s ideas best explain the spectacle would surely have taken place. What an interesting discussion it would have been. Both men made enormous contributions to science, far beyond aviation. This article will speak for Mr. Bernoulli.

When Daniel Bernoulli died in 1782, heavier than air flight was science fiction. Many prominent scientists of the day claimed it would be a millennium before man would fly, if ever. The most serious research was aimed towards balloon technology. The first wind tunnel was constructed in 1871. Only thirty-two short years later the Wright brothers built an airplane in their bicycle shop and took to the air.

Bernoulli’s Principle proved that physics, at least in theory, allowed heavier than air flight. Previous designs based on flapping bird wings provided a dead end for aviation. The concept of a low pressure zone above a fixed wing put thinking on the right track. Applying this principle to the propulsion dilemma, the propeller, guaranteed eventual success. It’s widely understood that Bernoulli studied aerodynamics and developed his Principle of Lift to that end. Of course the field did not yet exist. But since the Bernoulli Principle can be applied to any fluid, it has relevance in many fields.

Bernoulli was working on his concept of conservation of energy when he discovered the inverse relationship between pressure and density. When the value of one increases, the other is required to decrease. Applying this relationship to fluids, he proved that a fast moving fluid must have a lower pressure than a slow moving fluid. This was a simple but profound realization and is the part of his principle that we use to describe lift. As air molecules pass over a wing they accelerate, spreading out more thinly. With fewer molecules the pressure becomes lower, just as the inverse relationship predicts.

He published his findings in “Hydrodynamica” in 1738. His father actually tried to steal the work, changing the title slightly. Needless to say, they did not enjoy a good relationship.

Giovanni Venturi’s venturi tube was used to demonstrate Bernoulli’s Principle. In aviation, a wing is often referred to as a “half venturi”. This entire concept is hotly debated in some circles.

A century passed before Ludwig Prandtl continued development of the physics of liquid flow. His concept of the viscous boundary layer, when combined with Bernoulli’s, would be very useful to the study of both aerodynamics and hydrodynamics. This describes how a fluid conforms to the shape of a container (known as the coanda effect). In aviation this container is the airfoil (wing). If the fluid, air, follows the shape of the “container” it has laminar flow. Laminar flow of air is required in the case of lift generation. If this flow is replaced with it’s opposite, turbulence, the wing has stalled.
In other words, the coanda effect has stopped working. The air is no longer adhering to and following the shape of the wing.
This part of the explanation of lift is quite correct. Circulation theory and Newton’s Laws also have a very large part to play however. Unfortunately, the mathematics involved in calculating lift and circulation are truly horrific. Only the most dedicated aeronautical engineers are interested enough or qualified to understand them fully. For this simple reason, students and pilots are normally taught a very simplified interpretation of Bernoulli’s Principle. This practice began shortly before world war two broke out. The urgent demand for pilots and maintenance crews justified a great deal of over simplification.

Personnel were taught that the shape of a wing is critical. The curved (cambered) shape of the upper wing must create a longer route for the air to travel. The upper airflow is forced to accelerate in order to catch up with the bottom airflow. The two streams must meet at the trailing edge at exactly the same time. Circulation theory, wing tip vortexes and the reaction forces described by Newton dropped out of the picture.

There is no explanation of why an aircraft can fly inverted or why many wings are completely symmetrical. Some modern wings actually have a cambered LOWER surface. If the new and simplified version of Bernoulli’s Principle was accurate, inverted flight would be suicidal and the other wings would generate no lift whatsoever.

Airflow does accelerate over the top of a wing. The low pressure zone does occur and it does cause the wing to generate lift. As aircraft speed increases, the pressure differential does increase. In fact, wind tunnel testing shows that airflow actually reaches the trailing edge before the lower airflow does. The “equal transit time” theory is quite incorrect for most situations.

Misconceptions about the required shape of a wing and the equal transit time theory of airflow are steadily eroding. Schools and newer textbooks are providing a more complete and accurate explanation of lift generation. I’m certain Mr. Bernoulli would be pleased with the progress. He never said a wing requires camber to generate lift. Or that air molecules above and below a wing must reach the trailing edge at exactly the same time. He never said anything about a wing for that matter. He just provided the future field of aerodynamics with a key principle: Accelerating a fluid will cause it’s pressure to drop.

If only he could stand on that runway with Newton and see what we did with their ideas.