A new theory of aviation .. an Egyptian solves a dilemma that has remained unanswered for more than a century

The scene was chaotic in the British House of Commons; After the Frenchman Louis Bleriot managed to cross the English Channel with a plane heavier than air, the British opposition took the opportunity to launch a fierce attack on the Secretary of State for War Richard Haldane (1905-1912 AD) and led it by force. . formulated question intended to answer the question: Why did you not arrive in Britain to invent an airplane to help it defend its territory?

Halden did not answer these questions and said he had previously explained “the mechanisms the military must follow if it wants to fly … and there are no other explanations for this.” Then, in turn, he began planning. for Britain to reach the United States, which the Wright brothers managed to build an airplane, and France, whose chief engineer, Playrio, designed an airplane capable of crossing the English Channel.

Haldane’s vision was that aircraft production required “science” and that the “trial and error” method followed by brothers Wright and Playrio could not be supported, so the man decided – even before the Playrio could cross the English Channel – that set up a committee An aeronautics consultant whose mission is to develop a unified aviation theory that answers the most important question: How do airplanes fly?

With the establishment of that committee we can say that a new era of aviation has been born … an era led by science.

With the accumulation of experience and after performing thousands of calculations, scientists – English and German – came up with a unified theory that could be relied upon to build different types of aircraft, a theory that was later called the “flight theory”.

This theory says that birds do not just fly by flapping their wings, but use gliding in the air to travel long distances, but the case is different for airplanes.

In order for an airplane to take off into the air, a force equal to or greater than the force of gravity, called the lift, must be created.

In airplanes heavier than air, the lift is created by air flowing over the wing, the shape of the wing causes air to flow to the top faster than to the bottom, and rapidly flowing air reduces the pressure of the surrounding air, and because pressure of air is greater under the wing than above, the lifting force is created that lifts the aircraft.

To understand how an arm generates elevation, it is necessary to use two equations important to the physical sciences, namely, the Bernoulli equation, which explains the change in pressure that can be generated by the flowing currents of liquids (liquid or air), and continuity. equation, which states that the product of density, area and velocity A moving object must always have a constant value.

After much research, scientists decided to use the theory of the air vortex to explain the flight process. proportion to the force of the air vortex.Scientists used that theory to start immediately In the design of the wing, the shape of the wing will have a severe effect on the generation of the air vortex.

To estimate the force of the vortex, the scientists used equations formulated by one of the greatest mathematicians of the eighteenth century, Leonhard Euler.

These equations can arrive at solutions for calculating the forces flowing from the fluid flow, but the crisis of using them is that they lead to an infinite number of solutions rather than to a specific solution. The rear end is pointed and captures a value of the air vortex at that point.

This was the real beginning of the aviation era, says Haitham Ezzat Taha, a professor of aeronautical engineering at the University of California-Irvine – in an exclusive statement to Al-Alam, which recently re. capable of calculating air vortex values ​​in any shape of aircraft wings, not just sharp wings.

airplane wing design

Fortunately, the shape of the aircraft wing follows a design that makes it – in popular parlance – drawn in shape, ending with a sharp point at the back. Euler’s equation says that when there is such a sharp point, the resulting air velocity at this point is infinite, which does not happen in reality of course.

By applying the Cotta equations, it is possible to calculate a value for the vortex that gives a specific velocity at the sharp point, and thus the exact force of the vortex can be solved through this equation, and accordingly, the correct arm can be designed for aircraft size.

But there is a major requirement for wing design, which is for the wing to be narrowed at the top in order to generate sufficient lifting force to support the weight of the aircraft.

As a result, flight theory became very specific and limited and relied entirely on Cotta’s theory, says Mohamed Zakaria, a doctorate in aeronautics from Virginia Tech, who was not involved in the study: that theory imposed limitations on heavy on the arm. design process. “The wing must be smooth and sharp, otherwise the vortex can not be calculated in any way, and therefore you can not conclude the lifting force that is essential for flight.”

Here arises the need for a new theory, “which the Egyptian scholar Haitham Taha Zaki was able to make,” according to Zakaria’s statements to Al-Ilm.

According to what was published in the Journal of Fluid Mechanics, the Egyptian researcher – with the help of another researcher working at the same university – was able to use a revolutionary mathematical formula that could calculate the lifting force of any wing shape. “This means that the equation can be used to calculate the forces of elevation in a square, triangle, circle or any other shape that is not necessarily stressed at the end, which is revolutionary and adds a lot to flight theory. “, Says Zakaria.

But why do we need a new theory in the first place? What is its significance? How can it contribute to the advancement of the aircraft industry?

In his statements to Al-Alam, Taha says: The classical theory of ascension, which is based on the Cotta equation, is very limited. “The theory can not be applied to smooth effective shapes that do not contain a sharp tip, as the traditional flight theory collapses, and we are in 2022 there is no mathematical model that can calculate the rise in a shape like this that does not contains a sharp point. “

Not only that, but what if a shape has more than one sharp point?

In that case, no single vortex leads to a speed limited to all sharp points, so Cotta’s theorem becomes useless, “Yes a shape that has only one sharp point, but flies that way “which makes it forward as it does inside the feathers of a helicopter in flight? Forward,” says Taha, who points out that this scenario cannot be applied through the Cotta equation.

Also, “Kota” set a precondition for the application of his theory, that the flight be stable, “but, if we are talking about rapid changes, as occurs in maneuvers or in the flight of birds and insects from the wing collision, then the equation of Kuta is fundamentally inaccurate, “says” Taha “.

Formulation of a new theory

This dilemma – represented by the inability of scientists to calculate the force of the vortex that generates the lifting force in open-ended shapes – lasted exactly 112 years (Kota theorized in 1910), and in recent years, Taha has tried to solve it. this problem. .

Using the sciences of theoretical and analytical mechanics, “Taha” managed to formulate his new theory.

Taha suggested the application of a physical principle known as the “least effort”. This principle assumes the existence of a certain variable that nature always works to provide the body with the price paid for each path, and simply the path with the lowest price. this is the exact path that nature chooses. ” This principle also states that the sum of kinetic energy minus the potential energy in motion is the “price” that nature always works to offer.

When we return to the theory of flight; To apply this principle, the solution to the dilemma seems very simple, “Euler gives us an infinite number of solutions. We do not know which nature to choose. Nature simply chooses the solution at the lowest price.” Taha says that was his idea for six years, “I work in it day and night.”

When “Taha” tested this principle, he found that the resulting lift force is zero, “and this was a shocking thing that requires wonder, as it seems that nature does not care about providing kinetic energy when air flows around the arm. So which is the variable that nature is trying to provide in all the air flow around which wing?

Taha insisted on completing his research, using another principle, which was almost unknown, called the “smallest curvature” of scientist Hertz. Taha says: The principle is very simple and profound, “We all know that if the body is free and not exposed to any external force, it moves in a straight line according to Newton’s first law, and now, if this body is constrained, that is, it must follow a certain motion (such as motion on a certain surface for example), its motion will deviate from the straight line due to this constraint. ” Hertz’s principle states that this finite Body will deviate from its nature (motion in a straight line) only to the extent that it corresponds to the constraint, viz. , the deviation from the straight line will be smaller than it is, provided the movement is in line with the constraint.

But how can these principles be applied to flight theory?

Because each of Euler’s infinite solutions corresponds to a certain value of the vortex force and the lift force, it is now possible to calculate the curvature at each flow point and add all these curves to obtain a odd number that represents the total curvature for each solution, “Now we can draw the total curvature on the vertical axis and the force of the vortex is on the horizontal axis”, and so there exists a value of the vortex that gives less curvature than all other values, and this seems to be the force of the whirlpool imposed by nature according to the Hertz principle.

To illustrate, let’s take an ordinary arm with a sharp tip. What is the force of the vortex or the force created? It is the same force given by the Cotta equation, and if we take any other form and follow the same theory, we will get the force of the vortex and the lifting force without any problem thanks to the combination of Euler equations and the principle of no more of the little one. the curvature of the Hertz world.

The strength of this theory comes from the fact that it is based on the basics of mechanics, and not like the Cotta equation that puts us in specific conditions, and can also be applied to any shape, whether in fixed or variable flight. forward or backward, according to “Zechariah.”

There is a particular achievement regarding the new theory.

But why is this work particularly important for the wing production process? Can we witness a plane with a square or circular wing or without a sharp tip at the end of the wing?

“Taha” says: The optimal design for the wings at the present time is the design with a sharp end, but all things are to be expected. “Taha” speaks of the principle of “generalization,” which is the essence of science; Theories – for the most part – do not contradict each other, but rather complement each other and build the wall of knowledge, “In this work I and the great scientist” Kotta “were not at odds, but his theory was simply “But my theory has become more general, as Kouta’s theory sets limits, I focus on creativity in design, and my new theory opens the door to thinking and innovation.”

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