Due to the unbounded nature of the situation, the only way to get enough constraints to actually find a solution requires turning to the ultimate hammer of fluid dynamics, the Navier—Stokes equations. This is a set of complex equations that involves inertia and viscosity of air, both essential properties for generating lift. Inviscid flow does not produce any lift as can be tested in liquid helium. Massless flow wouldn't produce any either, but unfortunately there are no massless fluids to test it with.
You still have to throw in conservation of energy, i. Bernoulli's equation, along with conservation of mass actually, they are both considered part of the Navier-Stokes set , and for larger pressure differences also the ideal gas equation and the equation for adiabatic process to get enough equations to restrict all the free variables. The result is a set of partial differential equations that don't have any useful analytical solutions and need to be numerically integrated over sufficiently large volume of space surrounding the wing and sufficiently long time period.
Now you'll have huge dataset describing the flow at each point in space and time with some granularity. If you plot the total lift over sufficient set of boundary conditions, and try to fit a simple equation to it, you'll get the famous lift equation.
Approximately—it is just fitting to a bunch of points! Bernoulli's principle does contribute to the explanation by holding in the situation.
You wouldn't have enough constraints to get a unique solution otherwise. But there is no way to specify what the contribution meant in the resulting equation.
All you can say is that it is needed to calculate the exact points that can be approximated with the lift equation. Note: there are decent qualitative explanations of the phenomena described by the Navier-Stokes equations, but you've already seen them as it is the answer you linked in the question. No point in repeating them here. The statement "Because of continuity, so the air that flows in from the left side must flow out at the right, the upper flow must get there at the same time.
But because that line is curved, air has to go faster to get there at the same time. See Chapter 3. He demonstrates that air above and below the wing do not arrive at the same time.
The book also discusses quite well in my opinion how downwards airflow at the back of the wing really contributes to the lift created, more so than any low pressure area above the wing. The old "opposite and equal reaction". Lift is hard. There is simply no simple way of explaining lift. Why would there be? It is only fair that you need quite some math to figure out the pressure distribution, which is the pressure field around an arbitrary body in airflow, and as you can imagine, that is no easy task.
Who gets to say that just because lift is essential to flight , it must be readily understandable? A more accurate portrayal of lift is most easily achieved by simplifying the airflow first to 2D-potential flow , i. But perhaps the way that provides the most insight into lift generation is through a conformal mapping , i.
There are three kinds of basic solution to the flow around the cylinder: rectilinear, vortex and doublet. And per the linearity of the Laplace equation, any superposition of the three solutions is also a solution. Note that just like I said, there are three basic solutions, the pressure shown above is the result of changing the coefficient of combining the solutions. A most useful result of this approach is a direct proof of Kutta—Joukowski theorem.
This tool, not the Bernoulli's principle, is the real workhorse of aerodynamicists. This is a stronger version of Bernoulli's Law , implicit in the Newton's second law.
Please do notice I have only mentioned lift under the ideal circumstance of inviscid potential flow , and the solution given by this theory deviates from real life in a significant way. For example, you can tell from experience that there is no way a cylinder can stand in water flow and not feel any drag , yet the solution to flow around cylinder says so. This is called d'alembert paradox. The answer to this paradox is viscosity of water. The viscosity of water prevents a full pressure recovery on the rear half of the cylinder, and the flow would separate near the top and bottom of the cylinder.
Bernoulli came from a family of mathematicians. In other words, the theorem does not say how the higher velocity above the wing came about to begin with. There are plenty of bad explanations for the higher velocity. Because the top parcel travels farther than the lower parcel in a given amount of time, it must go faster. The fallacy here is that there is no physical reason that the two parcels must reach the trailing edge simultaneously.
And indeed, they do not: the empirical fact is that the air atop moves much faster than the equal transit time theory could account for. It involves holding a sheet of paper horizontally at your mouth and blowing across the curved top of it. The page rises, supposedly illustrating the Bernoulli effect. The opposite result ought to occur when you blow across the bottom of the sheet: the velocity of the moving air below it should pull the page downward.
Instead, paradoxically, the page rises. On a highway, when two or more lanes of traffic merge into one, the cars involved do not go faster; there is instead a mass slowdown and possibly even a traffic jam.
That lower pressure, added to the force of gravity, should have the overall effect of pulling the plane downward rather than holding it up. Moreover, aircraft with symmetrical airfoils, with equal curvature on the top and bottom—or even with flat top and bottom surfaces—are also capable of flying inverted, so long as the airfoil meets the oncoming wind at an appropriate angle of attack. The theory states that a wing keeps an airplane up by pushing the air down. The Newtonian account applies to wings of any shape, curved or flat, symmetrical or not.
It holds for aircraft flying inverted or right-side up. The forces at work are also familiar from ordinary experience—for example, when you stick your hand out of a moving car and tilt it upward, the air is deflected downward, and your hand rises.
But taken by itself, the principle of action and reaction also fails to explain the lower pressure atop the wing, which exists in that region irrespective of whether the airfoil is cambered. It is only when an airplane lands and comes to a halt that the region of lower pressure atop the wing disappears, returns to ambient pressure, and becomes the same at both top and bottom.
But as long as a plane is flying, that region of lower pressure is an inescapable element of aerodynamic lift, and it must be explained. Neither Bernoulli nor Newton was consciously trying to explain what holds aircraft up, of course, because they lived long before the actual development of mechanical flight.
Their respective laws and theories were merely repurposed once the Wright brothers flew, making it a serious and pressing business for scientists to understand aerodynamic lift. Most of these theoretical accounts came from Europe. In the early years of the 20th century, several British scientists advanced technical, mathematical accounts of lift that treated air as a perfect fluid, meaning that it was incompressible and had zero viscosity.
These were unrealistic assumptions but perhaps understandable ones for scientists faced with the new phenomenon of controlled, powered mechanical flight. These assumptions also made the underlying mathematics simpler and more straightforward than they otherwise would have been, but that simplicity came at a price: however successful the accounts of airfoils moving in ideal gases might be mathematically, they remained defective empirically. In Germany, one of the scientists who applied themselves to the problem of lift was none other than Albert Einstein.
Einstein then proceeded to give an explanation that assumed an incompressible, frictionless fluid—that is, an ideal fluid. If the difference of pressure causes the force to fly, no plane should be able to fly upside down, but stunt planes do. If a Cessna plane is considered, the equation will have the following numbers:.
The speed is about kilometers per hour, the weight kilograms, the wings about 30 feet long and 6 feet wide, with a total area of about 18 square meters. The velocity is about 60 meters per second on the bottom and 62 meters per second on the top.
The force Pascals, or Newtons per meter squared, which is the unit of pressure. Thus, the upward force to the wing is Newtons, and the weight downward force is 10, Newtons. There is a huge lack of force to lift the plane when the equation is used. Consequently, it cannot explain how planes fly. To explain how planes fly , one must first know the forces that cause the movement. The weight of the plane pushes it down, and lift pushes it up.
If these two are exactly equal, and the drag and thrust are also equal, the forces in both directions cancel each other, and a plane can stay motionless in the air. However, this is not a realistic situation. Air resistance has a leading role in how planes fly. The optimum air resistance is at 35, feet, which is the altitude commercial airplanes fly. The reason is that planes have minimal fuel expenditure at this height. When a plane gains enough velocity on the ground, the wing shape and angle will create enough lift with the air resistance, and the plane gets lifted.
Introduction to Flight Give students an enjoyable introduction to the world of flight with some fun activities, interesting facts and cool demonstrations. Introduction: People have always understood that flight was possible from observing birds, but it took thousands of years to actually achieve and there were many hurdles along the way. What are some examples of things that fly? Birds, planes, hot air balloons etc Can you group them into different types of flight? How do we control flight?
Demonstrations: There are a number of useful demonstrations you can do to help explain flight, they include: Using a hairdryer to float ping-pong or polystyrene balls. Releasing a blown up balloon so that it flies up a string connected from one side of a room to the other. Helium balloons. Giant air blowers to help show the Bernoulli principle in action.
Throwing paper airplanes of different designs, which work better and why? Activities: Your challenge is to hold a rectangular piece of paper close to your mouth, blow across the top of it and get the paper to move down. What's happening?
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