Research work. Theme of work Ideal paper airplane

Many of us have seen, and maybe did paper airplanes and launched them, watching them soar in the air.

Have you ever wondered who was the first to create a paper plane and why?

Today, paper planes are made not only by children, but also by serious aircraft manufacturing companies - engineers and designers.

How, when and for what paper airplanes were used and are still used, you can find out here.

Some historical facts related to paper aircraft

* The first paper airplane was created about 2,000 years ago. It is believed that the first who came up with the idea of making paper airplanes were the Chinese, who were also fond of creating flying kites from papyrus.

* The Montgolfier brothers, Joseph-Michel and Jacques-Etienne, also decided to use paper for flying. They are the ones who invented Balloon and used paper for it. It happened in the 18th century.

* Leonardo da Vinci wrote about using paper to create ornithopter (aircraft) models.

* In the early 20th century, aircraft magazines used images of paper airplanes to explain the principles of aerodynamics.

See also: How to make a paper airplane

* In their quest to build the first human-carrying aircraft, the Wright brothers used paper planes and wings in wind tunnels.

* In the 1930s, the English artist and engineer Wallis Rigby designed his first paper airplane. This idea seemed interesting to several publishers, who began to cooperate with him and publish his paper models, which were quite easy to assemble. It is worth noting that Rigby tried to do not just interesting models but also flying.

* Also in the early 1930s, Jack Northrop of the Lockheed Corporation used several paper models aircraft and wings for testing. This was done before the creation of real large aircraft.

* During World War II, many governments restricted the use of materials such as plastic, metal and wood as they were considered strategically important. Paper has become commonplace and very popular in the toy industry. This is what made paper modeling popular.

* In the USSR, paper modeling was also very popular. In 1959, P. L. Anokhin's book "Paper Flying Models" was published. As a result, this book became very popular among modellers for many years. In it, one could learn about the history of aircraft construction, as well as paper modeling. All paper models were original, for example, one could find a flying paper model of the Yak aircraft.

Unusual facts about paper plane models

*According to the Paper Aircraft Association, a paper plane launched in outer space, will not fly, it will glide in a straight line. If a paper airplane does not collide with some object, it can soar forever in space.

* The most expensive paper plane was used in the space shuttle during the next flight into space. The cost of the fuel used to get the plane into space on the shuttle alone is enough to call this paper plane the most expensive.

* The largest wingspan of a paper airplane is 12.22 cm. An airplane with such wings could fly almost 35 meters before hitting the wall. Such an aircraft was made by a group of students from the Faculty of Aviation and Rocket Engineering at the Polytechnic Institute in Delft, the Netherlands.

The launch was carried out in 1995, when the aircraft was launched inside the building from a platform 3 meters high. According to the rules, the plane had to fly about 15 meters. If not for the limited space, he would have flown much farther.

* Scientists, engineers and students use paper airplanes to study aerodynamics. National Administration Aeronautics and Space Administration (NASA) sent a paper airplane into space on the Space Shuttle.

* Paper planes can be made various forms. According to record holder Ken Blackburn, airplanes made in the shape of an "X," hoop or futuristic spaceship, can fly just like simple paper planes if made right.

* NASA specialists together with astronauts held a master class for schoolchildrenin his hangar research center in 1992. Together they built large paper planes with a wingspan of up to 9 meters.

* The smallest paper origami airplane was created under a microscope by Mr. Naito from Japan. He folded an airplane from a sheet of paper measuring 2.9 square meters. millimeter. Once made, the airplane was placed on the tip of a sewing needle.

* The longest flight of a paper plane took place on December 19, 2010, and it was launched by the Japanese Takuo Toda, who is the head of the Japan Origami Airplane Association. The flight duration of his model, launched in the city of Fukuyama, Hiroshima Prefecture, was 29.2 seconds.

How to make a Takuo Toda airplane

Robot assembles a paper plane

Man will fly, relying not on the strength of his muscles, but on the strength of his mind.

(N. E. Zhukovsky)

Why and how an airplane flies Why can birds fly even though they are heavier than air? What forces lift a huge passenger plane that can fly faster, higher and farther than any bird, because its wings are motionless? Why can a glider that does not have a motor soar in the air? All these and many other questions are answered by aerodynamics - a science that studies the laws of interaction of air with bodies moving in it.

In the development of aerodynamics in our country, an outstanding role was played by Professor Nikolai Egorovich Zhukovsky (1847 -1921) - "the father of Russian aviation", as V. I. Lenin called him. Zhukovsky's merit lies in the fact that he was the first to explain the formation of the lift force of a wing and formulated a theorem for calculating this force. Zhukovsky not only discovered the laws underlying the theory of flight, but also paved the way for the rapid development of aviation in our country.

When flying on any aircraft there are four forces, the combination of which does not allow him to fall:

Gravity is the constant force that pulls the plane toward the ground.

Traction force, which comes from the engine and moves the aircraft forward.

Resistance force, opposite to the force of thrust and is caused by friction, slowing down the aircraft and reducing the lift of the wings.

lifting force, which is formed when the air moving over the wing creates a reduced pressure. Obeying the laws of aerodynamics, all aircraft rise into the air, starting with light sports aircraft

All aircraft at first glance are very similar, but if you look closely, you can find differences in them. They may differ in wings, tail, fuselage structure. Their speed, flight altitude, and other maneuvers depend on this. And each plane has only its own pair of wings.

To fly, you don't need to flap your wings, you need to make them move relative to the air. And for this, the wing just needs to report the horizontal speed. From the interaction of the wing with the air, lift will arise, and as soon as its value is greater than the weight of the wing itself and everything connected with it, the flight will begin. The matter remains small: to make a suitable wing and be able to accelerate it to the required speed.

Observant people noticed a long time ago that birds have wings that are not flat. Consider a wing whose bottom surface is flat and its top surface is convex.

The air flow on the leading edge of the wing is divided into two parts: one flows around the wing from below, the other - from above. From above, the air has to go a little longer than from below, therefore, from above, the air speed will also be slightly greater than from below. It is known that as the velocity increases, the pressure in the gas flow decreases. Here, too, the air pressure under the wing is higher than above it. The pressure difference is directed upwards, that's the lifting force. And if you add the angle of attack, then the lifting force will increase even more.

How does a real plane fly?

A real airplane wing is teardrop shaped, which means that the air passing over the top of the wing moves faster than the air passing through the bottom of the wing. This difference in air currents creates lift and the plane flies.

And the fundamental idea here is this: the air flow is cut in two by the leading edge of the wing, and part of it flows around the wing along the upper surface, and the second part along the lower. In order for the two streams to converge behind the trailing edge of the wing without creating a vacuum, the air flowing around the upper surface of the wing must move faster relative to the aircraft than the air flowing around the lower surface, since it has to travel a greater distance.

Low pressure from above pulls the wing in, while higher pressure from below pushes it up. The wing goes up. And if the lifting force exceeds the weight of the aircraft, then the aircraft itself hangs in the air.

Paper planes don't have shaped wings, so how do they fly? Lift is created by the angle of attack of their flat wings. Even with flat wings, you can see that the air moving over the wing travels a slightly longer distance (and moves faster). Lift is created by the same pressure as profile wings, but of course this difference in pressure is not so great.

The angle of attack of the aircraft is the angle between the direction of the speed of the air flow on the body and the characteristic longitudinal direction chosen on the body, for example, for an aircraft it will be the chord of the wing, it is the longitudinal construction axis, for a projectile or rocket it is their axis of symmetry.

straight wing

The advantage of a straight wing is its high lift coefficient, which allows you to significantly increase the specific load on the wing, and therefore reduce the size and weight without fear of a significant increase in takeoff and landing speed.

The disadvantage that predetermines the unsuitability of such a wing at supersonic flight speeds is a sharp increase in drag aircraft

delta wing

A delta wing is stiffer and lighter than a straight wing and is most often used at supersonic speeds. The use of a delta wing is determined mainly by strength and design considerations. The disadvantages of the delta wing are the emergence and development of a wave crisis.

CONCLUSION

If the shape of the wing and nose of a paper airplane is changed during modeling, then the range and duration of its flight may change.

The wings of a paper plane are flat. In order to provide a difference in air flow from above and below the wing (in order to form lift), it must be tilted to a certain angle (angle of attack).

Planes for the longest flights are not rigid, but they have a large wingspan and are well balanced.

Paper airplanes have a rich and long story. It is believed that they tried to fold an airplane out of paper with their own hands back in ancient China and in England during the time of Queen Victoria. Subsequent new generations of paper model enthusiasts developed new variants. Even a child can make a flying paper airplane, as soon as he learns the basic principles of folding a layout. simple circuit contains no more than 5-6 operations, instructions for creating advanced models are much more serious.

Different models will require different paper, differing in density and thickness. Certain models are able to move only in a straight line, some are able to write out a sharp turn. For the manufacture of different models, paper of a certain stiffness is required. Before you start modeling, try out different papers, select the required thickness and density. You should not collect crafts from crumpled paper, they will not fly. Playing with a paper airplane is a favorite pastime for most boys.

Before making a paper airplane, the child will need to turn on all his imagination, concentrate. When conducting children's holiday you can hold competitions between children, let them launch airplanes folded with their own hands.

Such an airplane can be folded by any boy. For its manufacture, any paper is suitable, even newsprint. After the child is able to make this type of airplane, more serious designs will be within his power.

Consider all the stages of creating an aircraft:

Prepare a piece of paper approximately A4 size. Place it with the short side towards you.
Bend the paper along the length, put a mark in the center. Expand the sheet, connect the top corner with the middle of the sheet.
Perform the same manipulations with the opposite angle.
Unfold the paper. Place the corners so that they do not reach the center of the sheet.
Bend a small corner, it should hold all other corners.
Bend the plane mockup along the centerline. The triangular parts are located on top, take the sides to the center line.

The second scheme of a classic aircraft

This common option is called a glider, you can leave it with a sharp nose, or you can make it blunt, bend it.

propeller plane

There is a whole direction of origami involved in the creation of models of paper airplanes. It is called aerogami. You can learn an easy way to make an origami paper airplane. This option is done very quickly, it flies well. This is exactly what will interest the baby. You can equip it with a propeller. Prepare a sheet of paper, scissors or a knife, pencils, a sewing pin that has a bead on the top.

Manufacturing scheme:

Place the sheet with the short side facing you, fold it in half lengthwise.
Fold the top corners towards the center.
The resulting side corners also bend to the center of the sheet.
Bend the sides again towards the middle. Iron all folds well.
To make a propeller, you will need a square sheet measuring 6 * 6cm, mark both of its diagonals. Make cuts along these lines, stepping back from the center a little less than a centimeter.
Fold the propeller, placing the corners to the center through one. Secure the middle with a beaded needle. It is advisable to glue the propeller, it will not spread.

Attach the propeller to the tail of the airplane mockup. The model is ready to run.

boomerang plane

The kid will be very interested in an unusual paper plane, which independently returns back to his hands.

Let's figure out how such layouts are made:

Place a sheet of A4 paper in front of you with the short side facing you. Bend in half along the long side, unfold.
Bend the top corners to the center, smooth down. Expand this part down. Straighten the resulting triangle, smooth out all the wrinkles inside.
Expand product reverse side, fold the other side of the triangle into the middle. Send the wide end of the paper in the opposite direction.
Perform the same manipulations with the second half of the product.
As a result of all this, a kind of pocket should form. Raise it to the top, bend it so that its edge lies exactly along the length of the paper sheet. Bend the corner into this pocket, and send the top one down.
Do the same with the other side of the plane.
Fold up the details on the side of the pocket.
Expand the layout, place the front edge in the middle. Protruding pieces of paper should appear, they must be folded. Details that resemble fins, also remove.
Expand layout. It remains to bend in half and carefully iron all the folds.
Decorate the front part of the fuselage, bend the pieces of the wings up. Run your hands along the front of the wings, you should get a slight bend.

The plane is ready for operation, it will fly further and further.

The flight range depends on the mass of the aircraft and the strength of the wind. The lighter the paper the mockup is made of, the easier it is to fly. But at strong wind he will not be able to fly far, he will simply be blown away. A heavy aircraft resists the wind flow more easily, but it has a shorter flight range. In order for our paper plane to fly along a smooth trajectory, it is necessary that both parts of it be exactly the same. If the wings turned out to be of different shapes or sizes, the plane will immediately go into a dive. It is advisable not to use adhesive tape, metal staples, glue in the manufacture. All this makes the product heavier, due to excess weight the plane won't fly.

Complex views

Origami airplane

PHYSICS OF A PAPER AIRPLANE.
REPRESENTATION OF THE FIELD OF KNOWLEDGE. EXPERIMENT PLANNING.

1. Introduction. Objective. General patterns of development of the field of knowledge. The choice of the object of study. mindmap.
2. Elementary physics of glider flight (BS). System of force equations.

9. Photographs of the aerodynamic overview of the characteristics of the tube, aerodynamic balance.
10. Results of experiments.
12. Some results on the visualization of vortices.
13. Relationship between parameters and design solutions. Comparison of options reduced to a rectangular wing. The position of the aerodynamic center and the center of gravity and the characteristics of the models.
14. Energy efficient planning. flight stabilization. World record tactic for flight duration.

18. Conclusion.
19. List of references.

1. Introduction. Objective. General patterns of development of the field of knowledge. The choice of the object of research. mindmap.

The development of modern physics, primarily in its experimental part, and especially in applied fields, proceeds according to a pronounced hierarchical pattern. This is due to the need for an additional concentration of resources necessary to achieve results, from the material support of experiments to the distribution of work between specialized scientific institutions. Regardless of whether it is carried out on behalf of the state, commercial structures or even enthusiasts, but the planning of the development of the field of knowledge, the management of scientific research is a modern reality.
The purpose of this work is not only to set up a local experiment, but also an attempt to illustrate modern technology scientific organization at its simplest level.
The first reflections preceding the actual work are usually fixed in free form, historically this happens on napkins. However, in modern science, this form of presentation is called mind mapping - literally “thinking scheme”. It is a diagram in which geometric shapes everything fits in. which may be relevant to the issue at hand. These concepts are connected by arrows indicating logical connections. At first, such a scheme may contain completely different and unequal concepts that are difficult to combine into a classical plan. However, this diversity allows you to find a place for random guesses and unsystematized information.
A paper airplane was chosen as the object of research - a thing familiar to everyone since childhood. It was assumed that setting up a series of experiments and applying the concepts elementary physics will help to explain the features of flight, and also, perhaps, will allow us to formulate general design principles.
The preliminary collection of information showed that the area is not as simple as it seemed at first. Of great help was the research of Ken Blackburn, an aerospace engineer, holder of four world records (including the current one) for planning time, which he set with airplanes of his own design.

With regard to the task, the mind map looks like this:

This is a basic outline that represents the intended structure of the study.

2. Elementary physics of glider flight. System of equations for weights.

Gliding is a special case of aircraft descent without the participation of thrust generated by the engine. For non-motorized aircraft- gliders, as a special case - paper planes, gliding is the main mode of flight.
Gliding is carried out due to weights balancing each other and aerodynamic force, which in turn consists of lift and drag forces.
The vector diagram of the forces acting on the aircraft (glider) during flight is as follows:

The condition for straightforward planning is the equality

The condition for planning uniformity is equality

Thus, to maintain rectilinear uniform planning, both equalities are required, the system

Y=GcosA
Q=GsinA

3. Delving into the basic theory of aerodynamics. laminar and turbulent. Reynolds number.

A more detailed understanding of flight is given by modern aerodynamic theory, based on the description of the behavior different types air flows, depending on the nature of the interaction of molecules. There are two main types of flows - laminar, when the particles move along smooth and parallel curves, and turbulent, when they are mixed. As a rule, there are no situations with ideally laminar or purely turbulent flow, the interaction of both of them creates a real picture of the operation of the wing.
If we consider a specific object with finite characteristics - mass, geometric dimensions, then the flow properties at the level of molecular interaction are characterized by the Reynolds number, which gives a relative value and denotes the ratio of force impulses to fluid viscosity. How more number, the less the influence of viscosity.

Re=VLρ/η=VL/ν

V (speed)
L (size characteristic)
ν (coefficient (density/viscosity)) = 0.000014 m^2/s for air at normal temperature.

For a paper airplane, the Reynolds number is about 37,000.

Since the Reynolds number is much lower than in real aircraft, this means that the viscosity of the air plays a much larger role, resulting in increased drag and reduced lift.

4. How conventional and flat wings work.

A flat wing from the point of view of elementary physics is a plate located at an angle to a moving air stream. The air is "thrown" at an angle downwards, creating an oppositely directed force. This is the total aerodynamic force, which can be represented as two forces - lift and drag. Such an interaction is easily explained on the basis of Newton's third law. A classic example of a flat reflector wing is a kite.

The behavior of a conventional (plano-convex) aerodynamic surface is explained by classical aerodynamics as the appearance of a lifting force due to the difference in the speeds of the flow fragments and, accordingly, the difference in pressures from below and above the wing.

A flat paper wing in the flow creates a vortex zone on top, which is like a curved profile. It is less stable and efficient than a hard shell, but the mechanism is the same.

The figure is taken from the source (See references). It shows the formation of an airfoil due to turbulence on the upper surface of the wing. There is also the concept of a transition layer, in which the turbulent flow becomes laminar due to the interaction of air layers. Above the wing of a paper airplane, it is up to 1 centimeter.

5. Overview of three aircraft designs

Three different designs of paper planes with different characteristics were chosen for the experiment.

Model No. 1. The most common and well-known design. As a rule, the majority imagines it when they hear the expression “paper plane”.

Model number 2. "Arrow", or "Spear". characteristic model with a sharp wing angle and an expected high speed.

Model number 3. Model with high aspect ratio wing. Special design, assembled on the wide side of the sheet. It is assumed that she has good aerodynamic data due to the high aspect ratio wing.

All planes were assembled from the same sheets of paper with a specific gravity of 80 grams / m ^ 2 A4 format. The mass of each aircraft is 5 grams.

6. Feature sets, why they are.

To obtain characteristic parameters for each design, it is necessary to determine these parameters themselves. The mass of all aircraft is the same - 5 grams. It is quite easy to measure the planning speed for each structure and angle. The ratio of the height difference and the corresponding range will give us the lift-to-drag ratio, essentially the same glide angle.
Of interest is the measurement of the lift and drag forces at different angles of attack of the wing, the nature of their changes in the boundary regimes. This will allow to characterize the structures on the basis of numerical parameters.
Separately, it is possible to analyze the geometric parameters of paper planes - the position of the aerodynamic center and the center of gravity for different forms wing.
By visualizing the flows, one can achieve a visual image of the processes occurring in the boundary layers of air near the aerodynamic surfaces.

7. Preliminary experiments (chamber). Obtained values for speed and lift-to-drag ratio.

To determine the basic parameters, a simple experiment was carried out - the flight of a paper airplane was recorded by a video camera against the background of a wall with metric markings. Since the frame interval for video shooting (1/30 second) is known, the gliding speed can be easily calculated. According to the drop in altitude, the glide angle and the aerodynamic quality of the aircraft are found on the corresponding frames.

On average, the speed of the airplane is 5-6 m / s, which is not so little.
Aerodynamic quality - about 8.

8. Requirements for the experiment, Engineering task.

To recreate flight conditions, we need laminar flow up to 8 m/s and the ability to measure lift and drag. The classic method of aerodynamic research is the wind tunnel. In our case, the situation is simplified by the fact that the airplane itself is small in size and speed and can be directly placed in a tube of limited dimensions.
Therefore, we are not hindered by the situation when the blown model differs significantly in dimensions from the original, which, due to the difference in Reynolds numbers, requires compensation during measurements.
With a pipe section of 300x200 mm and a flow rate of up to 8 m / s, we need a fan with a capacity of at least 1000 cubic meters / hour. To change the flow rate, an engine speed controller is needed, and for measurement, an anemometer with appropriate accuracy. The velocity meter does not have to be digital, it is quite possible to get by with a deflected plate with angle graduations or a liquid anemometer, which has greater accuracy.

The wind tunnel has been known for a long time, Mozhaisky used it in research, and Tsiolkovsky and Zhukovsky have already developed it in detail modern technology experiment, which has not fundamentally changed.
To measure the drag force and lift force, aerodynamic balances are used, which make it possible to determine the forces in several directions (in our case, in two).

9. Photographs of the wind tunnel. Overview of pipe characteristics, aerodynamic balance.

The desktop wind tunnel was implemented on the basis of a sufficiently powerful industrial fan. Mutually perpendicular plates are located behind the fan, which straighten the flow before entering the measuring chamber. The windows in the measuring chamber are equipped with glass. A rectangular hole for holders is cut in the bottom wall. Directly in the measuring chamber, a digital anemometer impeller is installed to measure the flow velocity. The pipe has a slight constriction at the exit to “boost” the flow, which reduces turbulence at the expense of speed reduction. The fan speed is controlled by a simple household electronic controller.

The characteristics of the pipe turned out to be worse than the calculated ones, mainly due to the discrepancy between the fan performance and the passport characteristics. The flow boost also reduced the velocity in the measurement zone by 0.5 m/s. As a result maximum speed- slightly above 5 m / s, which, nevertheless, turned out to be sufficient.

Reynolds number for pipe:

Re = VLρ/η = VL/ν

V (speed) = 5m/s
L (characteristic) = 250mm = 0.25m
ν (factor (density/viscosity)) = 0.000014 m2/s

Re = 1.25/ 0.000014 = 89285.7143

Measurements have shown that the accuracy is quite sufficient for basic modes. However, it was difficult to fix the angle, so it is better to develop an appropriate mounting scheme with markings.

10. Results of experiments.

When purging the models, two main parameters were measured - the drag force and the lifting force, depending on the flow velocity at a given angle. A family of characteristics was constructed with sufficiently realistic values to describe the behavior of each aircraft. The results are summarized in graphs with further normalization of the scale relative to the speed.

11. Relationships of curves for three models.

Model number 2.
Model with the worst flight characteristics. Large sweep and short wings are designed to work better on high speeds, which happens, but the lift does not grow enough and the plane really flies like a spear. In addition, it does not stabilize in flight properly.

Model number 3.
The representative of the "engineering" school - the model was conceived with special characteristics. High aspect ratio wings do work better, but the drag increases very quickly - the plane flies slowly and does not tolerate acceleration. To compensate for the lack of rigidity of the paper, numerous folds in the toe of the wing are used, which also increases the resistance. Nevertheless, the model is very revealing and flies well.

12. Some results on the visualization of vortices

If you introduce a source of smoke into the stream, you can see and photograph the streams that go around the wing. We did not have special smoke generators at our disposal, we used incense sticks. To increase the contrast, a special filter for photo processing was used. The flow rate also decreased because the density of the smoke was low.

Flow formation at the leading edge of the wing.

Turbulent tail.

Also, the flows can be examined using short threads glued to the wing, or with a thin probe with a thread at the end.

13. Relationship between parameters and design solutions. Comparison of options reduced to a rectangular wing. The position of the aerodynamic center and the center of gravity and the characteristics of the models.

It has already been noted that paper as a material has many limitations. For low flight speeds, long narrow wings have best quality. It is no coincidence that real gliders, especially record holders, also have such wings. However, paper planes have technological limitations and their wings are not optimal.
To analyze the relationship between the geometry of models and their flight characteristics, it is necessary to bring a complex shape to a rectangular analogue by the area transfer method. The best way to do this is with computer programs that allow you to imagine different models in a universal form. After the transformations, the description will be reduced to the basic parameters - span, chord length, aerodynamic center.

The interconnection of these quantities and the center of mass will make it possible to fix the characteristic values for various types behavior. These calculations are beyond the scope of this work, but can be easily done. However, it can be assumed that the center of gravity for a paper plane with rectangular wings is at a distance of one to four from nose to tail, for an aircraft with delta wings - at one second (the so-called neutral point).

14. Energy efficient planning. flight stabilization.
World record tactic for flight duration time.

Based on the curves for lift and drag, one can find an energetically favorable flight mode with the least losses. This is certainly important for long-range liners, but it can also come in handy in paper aviation. By slightly modernizing the airplane (edge bending, weight redistribution), you can achieve the best performance flight or vice versa, transfer the flight to critical mode.
Generally speaking, paper planes do not change characteristics during flight, so they can do without special stabilizers. The tail, which creates resistance, allows you to shift the center of gravity forward. Straightness of flight is maintained due to the vertical plane of the fold and due to the transverse V of the wings.
Stability means that the aircraft, when deflected, tends to return to a neutral position. The point of glide angle stability is that the aircraft will maintain the same speed. The more stable the plane, the more speed, like the model #2. But, this trend needs to be curtailed - lift must be used, so the best paper planes, for the most part, have neutral stability, this is the best combination of qualities.
However, the established regimes are not always the best. The world record for the longest flight was set with a very specific tactic. Firstly, the start of the airplane is carried out in a vertical straight line, it is simply thrown onto maximum height. Secondly, after stabilization at the top point due to the relative position of the center of gravity and the effective wing area, the airplane must itself go into normal flight. Thirdly, the weight distribution of the airplane is not normal - it has an underloaded front part, therefore, due to the large resistance that does not compensate for the weight, it slows down very quickly. At the same time, the lifting force of the wing drops sharply, it nods down and, falling, accelerates with a jerk, but again slows down and freezes. Such oscillations (cabration) are smoothed out due to inertia at the fading points and, as a result, the total time spent in the air is longer than normal uniform glide.

15. A little about the synthesis of a structure with given characteristics.

It is assumed that having determined the main parameters of a paper airplane, their relationship, and thus completing the analysis stage, it is possible to proceed to the task of synthesis - based on the necessary requirements, create a new design. Empirically, amateurs all over the world do this, the number of designs has exceeded 1000. But there is no final numerical expression for such work, just as there are no special obstacles to doing such research.

16. Practical analogies. Flying squirrel. Wing suite.

It is clear that a paper airplane is, first of all, just a source of joy and a wonderful illustration for the first step into the sky. A similar principle of soaring is used in practice only by flying squirrels, which are not of great economic importance, at least in our lane.

A more practical equivalent of a paper plane is the "Wing suite" - a wingsuit for skydivers that allows horizontal flight. By the way, the aerodynamic quality of such a suit is less than that of a paper plane - no more than 3.

17. Return to the mind map. The level of development. Questions raised and options further development research.

Taking into account the work done, we can apply a coloring on the mind map indicating the completion of the tasks. Green color here indicates points that are at a satisfactory level, light green - issues that have some limitations, yellow - areas affected, but not developed to the extent necessary, red - promising, in need of additional research.

18. Conclusion.

As a result of the work, the theoretical basis for the flight of paper planes was studied, experiments were planned and carried out, which made it possible to determine the numerical parameters for various designs and general relationships between them. The complex mechanisms of flight are also affected, from the point of view of modern aerodynamics.
The main parameters affecting the flight are described, comprehensive recommendations are given.
In the general part, an attempt was made to systematize the field of knowledge based on the mind map, and the main directions for further research were outlined.

19. List of references.

1. Paper plane aerodynamics [Electronic resource] / Ken Blackburn - access mode: http://www.paperplane.org/paero.htm, free. - Zagl. from the screen. - Yaz. English

2. To Schütt. Introduction to the physics of flight. Translation by G.A. Wolpert from the fifth German edition. - M.: United Scientific and Technical Publishing House of the USSR NKTP. Edition of technical and theoretical literature, 1938. - 208 p.

3. Stakhursky A. For skillful hands: Desktop wind tunnel. Central Station young technicians named after N.M. Shvernik - M .: Ministry of Culture of the USSR. Main Directorate of the Printing Industry, 13th Printing House, 1956. - 8 p.

4. Merzlikin V. Radio-controlled models of gliders. - M: Publishing house DOSAAF USSR, 1982. - 160 p.

5. A.L. Stasenko. Flight physics. - M: Science. Main edition of physical and mathematical literature, 1988, - 144 p.

Being the father of practically a graduate high school, was embroiled in a funny story with an unexpected ending. It has an educational part and a touching life-political part.
Post on the eve of Cosmonautics Day. Physics of a paper plane.

Shortly before the new year, the daughter decided to check her own progress and found out that the physical student, when filling out the journal backdated, instructed some extra fours and the semi-annual grade hangs between "5" and "4". Here you need to understand that physics in grade 11 is, to put it mildly, a non-core subject, everyone is busy with training for admission and a terrible exam, but it affects the overall score. With a groaning heart, for pedagogical reasons, I was denied intervention - like sort it out yourself. She braced herself, came to find out, rewrote some independent one right there and got a six-month five. Everything would be fine, but the teacher asked, as part of resolving the issue, to register for the Volga scientific conference(Kazan University) to the section "Physics" and write some report. Participation of a student in this shnyaga counts for annual attestation teachers, well, and like "then we'll close the year for sure." The teacher can be understood, normal, in general, an agreement.

The child loaded up, went to the organizing committee, took the rules of participation. Since the girl is quite responsible, she began to think and come up with some topic. Naturally, she turned to me, the closest technical intellectual of the post-Soviet era, for advice. There was a list of winners of past conferences on the Internet (they give diplomas of three degrees), this guided us, but did not help. The reports consisted of two varieties, one - "nanofilters in oil innovations", the second - "photographs of crystals and an electronic metronome". For me, the second kind is normal - children should cut a toad, and not rub glasses for government grants, but we didn’t have much ideas. I had to follow the rules, something like "preference is given independent work and experiments."

We decided that we would make some kind of funny report, visual and cool, without zaum and nanotechnologies - we will amuse the audience, participation is enough for us. Time was a month and a half. Copy-paste was fundamentally unacceptable. After some thought, we decided on the topic - "Physics of a paper airplane". I once spent my childhood in aircraft modeling, and my daughter loves airplanes, so the topic is more or less close. It was necessary to make a completed practical study of physical orientation and, in fact, write a paper. Next, I will post the abstract of this work, some comments and illustrations / photos. At the end there will be the end of the story, which is logical. If you are interested, I will answer questions with already detailed fragments.

It turned out that the paper plane has a tricky stall at the top of the wing, which forms a curved zone similar to a full-fledged airfoil.

Three different models were taken for experiments.

Model No. 1. The most common and well-known design. As a rule, the majority imagines it when they hear the expression “paper plane”.
Model number 2. "Arrow", or "Spear". A characteristic model with a sharp wing angle and an assumed high speed.
Model number 3. Model with high aspect ratio wing. Special design, assembled on the wide side of the sheet. It is assumed that it has good aerodynamic data due to the high aspect ratio wing.
All planes were assembled from identical sheets of A4 paper. The mass of each aircraft is 5 grams.

To recreate flight conditions, we need laminar flow up to 8 m/s and the ability to measure lift and drag. The classical method of such research is the wind tunnel. In our case, the situation is simplified by the fact that the airplane itself has small dimensions and speed and can be directly placed in a tube of limited dimensions. Therefore, we are not hindered by the situation when the blown model differs significantly in size from the original, which, due to the difference in Reynolds numbers, requires compensation during measurements.
With a pipe section of 300x200 mm and a flow rate of up to 8 m / s, we need a fan with a capacity of at least 1000 cubic meters / hour. To change the flow rate, an engine speed controller is needed, and for measurement, an anemometer with appropriate accuracy. The velocity meter does not have to be digital, it is quite possible to get by with a deflected plate with angle graduations or a liquid anemometer, which has greater accuracy.

The wind tunnel has been known for a long time, it was used in research by Mozhaisky, and Tsiolkovsky and Zhukovsky have already developed in detail the modern experimental technique, which has not fundamentally changed.

The characteristics of the pipe turned out to be worse than the calculated ones, mainly due to the discrepancy between the fan performance and the passport characteristics. The flow boost also reduced the velocity in the measurement zone by 0.5 m/s. As a result, the maximum speed is slightly above 5 m/s, which, nevertheless, turned out to be sufficient.

Reynolds number for pipe:
Re = VLρ/η = VL/ν
V (speed) = 5m/s
L (characteristic) = 250mm = 0.25m
ν (coefficient (density/viscosity)) = 0.000014 m^2/s
Re = 1.25/ 0.000014 = 89285.7143

To measure the forces acting on the aircraft, elementary aerodynamic balances with two degrees of freedom based on a pair of electronic jewelry scales with an accuracy of 0.01 gram were used. The aircraft was fixed on two racks at the right angle and mounted on the platform of the first scales. Those, in turn, were placed on a movable platform with a lever transmission of horizontal force to the second scales.
Measurements have shown that the accuracy is quite sufficient for basic modes. However, it was difficult to fix the angle, so it is better to develop an appropriate mounting scheme with markings.

Model No. 1.
Golden mean. The design corresponds to the material - paper. The strength of the wings corresponds to the length, the weight distribution is optimal, so a properly folded aircraft is well aligned and flies smoothly. It is the combination of such qualities and ease of assembly that made this design so popular. The speed is less than the second model, but more than the third. At high speeds, the wide tail is already beginning to interfere, which previously perfectly stabilized the model.
Model number 2.
Model with the worst flight characteristics. The large sweep and short wings are designed to work better at high speeds, which is what happens, but the lift does not grow enough and the plane really flies like a spear. In addition, it does not stabilize in flight properly.
Model number 3.
The representative of the "engineering" school - the model was specially conceived with special characteristics. High aspect ratio wings do work better, but the drag increases very quickly - the plane flies slowly and does not tolerate acceleration. To compensate for the lack of rigidity of the paper, numerous folds in the toe of the wing are used, which also increases the resistance. Nevertheless, the model is very revealing and flies well.

Some results on the visualization of vortices
If you introduce a source of smoke into the stream, you can see and photograph the streams that go around the wing. We did not have special smoke generators at our disposal, we used incense sticks. To increase the contrast, a photo processing filter was used. The flow rate also decreased because the density of the smoke was low.
Flow formation at the leading edge of the wing.

Turbulent tail.

Also, the flows can be examined using short threads glued to the wing, or with a thin probe with a thread at the end.

It is clear that a paper airplane is, first of all, just a source of joy and a wonderful illustration for the first step into the sky. A similar principle of soaring in practice is used only by flying squirrels, which are not of great national economic importance, at least in our lane.

I came up with the theme, the plan - 70 percent, theory editing, pieces of iron, general editing, speech plan.
She collected the whole theory, up to the translation of articles, measurements (very laborious, by the way), drawings / graphs, text, literature, presentation, report (there were many questions).

I'm skipping the section where general view the problems of analysis and synthesis are considered, which make it possible to construct the reverse sequence - the design of an airplane according to given characteristics.

Taking into account the work done, we can apply a coloring on the mind map indicating the completion of the tasks. Green indicates points that are at a satisfactory level, light green - issues that have some limitations, yellow - areas affected, but not adequately developed, red - promising, in need of additional research (funding is welcome).

The month flew by unnoticed - the daughter was digging the Internet, driving a pipe on the table. Scales squinted, airplanes were blown past theory. The output turned out to be 30 pages of decent text with photographs and graphs. The work was sent to the correspondence tour (only a few thousand works in all sections). A month later, oh horror, they posted a list of face-to-face reports, where ours was side by side with the rest of the nanocrocodiles. The child sighed sadly and began to sculpt a presentation for 10 minutes. They immediately ruled out reading - to speak, so vividly and meaningfully. Before the event, they staged a run-through with timing and protests. In the morning, a sleepy speaker with the right feeling “I don’t remember and don’t know anything” drank at KSU.

By the end of the day, I began to worry, no answer - no hello. There was such a shaky state when you don’t understand whether a risky joke was a success or not. I didn’t want the teenager to somehow get sideways this story. It turned out that everything was delayed and her report fell as much as 4 pm. The child sent an SMS - "she told everything, the jury laughs." Well, I think, okay, thanks at least do not scold. And about an hour later - "diploma of the first degree." This was completely unexpected.

We thought about anything, but against the backdrop of a completely wild pressure of lobbied topics and participants, getting the first prize for a good, but informal work is something from a completely forgotten time. After that, she already said that the jury (quite authoritative, by the way, no less than CFM) nailed zombie nanotechnologists with lightning speed. Apparently, everyone is so fed up in scientific circles that they unconditionally put up an unspoken barrier to obscurantism. It got to the ridiculous - the poor child read out some wild scientisms, but could not answer what the angle was measured in during his experiments. Influential scientific leaders turned a little pale (but quickly recovered), it is a mystery to me why they had to arrange such a disgrace, and even at the expense of children. As a result, all the prizes were given to nice guys with normal lively eyes and good topics. The second diploma, for example, was given to a girl with a model of the Stirling engine, who briskly launched it at the department, quickly changed modes and meaningfully commented on all sorts of situations. Another diploma was given to a guy who was sitting on a university telescope and looking out for something there under the guidance of a professor who clearly did not allow any outside "help". This story gave me some hope. In what is the will of ordinary, normal people to the normal order of things. Not a habit of a predetermined injustice, but a readiness for efforts to restore it.

The next day, at the award ceremony, the chairman of the selection committee approached the winners and said that they were all enrolled ahead of schedule in the Faculty of Physics of KSU. If they want to enter, they simply have to bring documents out of competition. This benefit, by the way, really existed at one time, but now it has been officially canceled, as well as additional preferences for medalists and Olympiads (except, it seems, winners Russian Olympiads). That is, it was a pure initiative of the Academic Council. It is clear that now there is a crisis of applicants and they are not eager for physics, on the other hand, this is one of the most normal faculties with a good level. So, correcting the four, the child was in the first line of enrolled. I can’t imagine how she will manage this, I’ll find out - I’ll unsubscribe.

Would a daughter pull such a job alone?

She also asked - like dads, I didn’t do everything myself.
My version is this. You did everything yourself, you understand what is written on each page and you will answer any question - yes. You know more about the region than those present here and your acquaintances - yes. I understood the general technology of a scientific experiment from the inception of an idea to the result + side studies - yes. Did a great job, no doubt. She put forward this work on a general basis without patronage - yes. Protected - ok. The jury is qualified - without a doubt. Then this is your student conference award.

I am an acoustic engineer, a small engineering company, I graduated from systems engineering in aviation, I still studied later.