That was an afternoon period in my college. I was explaining How an Aircraft wing generates lift to one of my friend who was absent last day. While explaining Bernoulli’s theorem, I had mentioned few limitations which I happened to read in the associated content and other aeronautical websites. Somebody told the instructor, Mr.Eldho sir about my doubts, and I had been compelled to explain my views in the class (afterwards I got a nick name- Bernoulli). Let me share my views here.
“If 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.” –I read this sentence in an article of an aircraft mechanic-Dave Jackson which made me think why he said so? Afterwards I tried to understand the Bernoulli’s principle deeper. It is normally considered as popular explanation.Bernoulli published his findings in"Hydrodynamica" in 1738. This theorem simply states that When the speed of a fluid increases the pressure decreases. Normally an aircraft wing is said to have an aerofoil shape which is convex on the top and flat below (camber). When the aircraft moves, the airflow will be divided to flow over and under the aerofoil (wing) which will create a pressure difference and thus a lift force. Most important thing is - Bernoulli’s principle itself says that the air traveling above the upper camber and below the lower camber will meet the trailing edge at the same time. It is too simple to understand. As it is having an equation based on conservation of energy, everybody took it blindly.
According to law of conservation of energy
Potential Energy + Kinetic Energy = Constant
PE + ½ mV¬2 = K
As we are considering only fluid or gas, static pressure is used to represent potential energy. The kinetic energy is a function of air motion and its density. Thus the Bernoulli’s equation became "Static Pressure plus Dynamic Pressure is a Constant".
Ps + ½ pV2 = K
In text books and colleges, many instructors used to teach this theorem pointing the venturi tube.
Ludwig Prandtl described how a fluid conforms to the shape of a container (known as the coanda effect). Wing can be considered as this container here. If the fluid takes the shape of this container, it has laminar flow. This flow is very essential to generate lift. “If this flow is replaced with its 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.”*.
Thus I came to know that something is missing in somewhere and you can not understand the theory completely unless you have completed a PG in mathematics and physics.
So far we discussed about the theorem. Now we shall take a look of its limitations. Unfortunately, the mathematics involved in calculating lift and circulations are truly horrific. Engineers need to be qualified enough to learn things completely. That might be the reason; pilots and engineers are being taught this principle for the simplification. “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.”
The main thing is that Bernoulli’s theorem is not applicable in the case of an inverted flight time. More over today there are some wings which are symmetrical in nature. Some aircrafts are having cambered lower surfaces also. Wind tunnel tests clearly shows that the up going air stream does not meet down going air stream at same time in the trailing edge. In fact it is lagging there. That means it does not obey the “principle of equal transit times”. This happens why because these two air particles have no "knowledge" of each other's presence at all, and there is no logical reason why these particles should end up at the rear of the wing at the same moment in time.
According to Nici Hinkel**, Bernoulli's equation is only applicable if the following four restrictions are true.
1. Flow is steady
2. Density is constant
3. Friction losses are negligible
4. The equation relates the states at two points along a single streamline, (not conditions on two different streamlines).
Once you go through the fluid mechanics of air, you can come to know that the above mentioned properties are not true in the case of different layers of air through which the aircrafts are normally operated.
However, one thing is sure that the aircraft wings generate lift due to the pressure difference. But nobody explains how this pressure difference occurs. Newton’s III rd Law of motion also plays an important role to explain lift. According to this law aircraft wing pushes the upcoming airflow down which results in a reaction force upward, thus lift. This can be truer than popular explanation. “A pilot can actually use the fuselage instead of the wing to create lift by flying sideways, with an appropriate angle of attack.”
After explaining this in the class, those who didn’t understand anything teased me a lot. They interpreted me as a fool who always try to criticize the conventional theorems. In my opinion, Bernoulli’s theorem must be defined as the total energy of an incompressible non-viscous liquid flowing from one place to another without friction is a constant. Its applications include venturimeter, Atomizer (used for getting a fine spray of perfume or insecticide), Magnus effect or swing bowling and flow of blood through artery which we study in our lower classes. I never said that Bernoulli’s theorem is wrong, but in this application (lift), it is creating a lot of doubts-that’s all. It is only a foundation, future theorems are built from here- afterwards only.
Valuable comments are most welcome.
Sreerajpathari
sreerajpathari@gmail.com
NB: - This is only a rough copy which I prepared to consolidate the points. Modified article has been published in an American online magazine.
Sources:-
*“How an Aircraft Wing Generates Lift” - Dave Jackson
**Deriving Bernoulli's Equation and How This Effects the Flight of Airplanes-Nici Hinkel
Bernoulli’s principle- From December 1943 Air Trails Magazine
Why aero planes fly: A physical description of lift-David Anderson& Scott Eberhardt
Aircraft Basic science
Aviation maintenance & AMT
Mechanics of flight, AC 65-9A, 15A
