Zaripova Ruzil. "Paper airplane - child's play and scientific research." "The dependence of the duration of the flight of a paper plane on its shape" What are the conditions for long-term planning of an aircraft

Scientific historical research work
Completed by: 11th grade student Ruzil Zaripova
Scientific adviser: Sarbaeva A.A.
MBOU secondary school with. Krasnaya Gorka

Introduction

Even the simplest aircraft model is a miniature aircraft with all its properties. Many well-known aircraft designers began with a passion for aircraft modeling. To build a good flying model, you need to work hard. Everyone has ever made paper airplanes and launched them into flight. Paper airplanes are gaining popularity all over the world. This led to the introduction of the new term aerogami. Aerogami - the modern name for the manufacture and launch of paper models of aircraft, one of the directions of origami (Japanese art of paper folding).
The relevance of this work is due to the ability to use the knowledge gained to conduct lessons in primary grades in order to arouse students' interest in the world of aviation and develop the necessary qualities and skills to use creative experience and knowledge in the study and development of aviation.
Practical significance is determined by the opportunity to hold a master class on folding paper airplanes of different models with primary school teachers, as well as the opportunity to hold competitions among students.
Object of study are paper models of airplanes.
Subject of study is the emergence and development of aerogi.
Research hypotheses:
1) paper models of airplanes are not only a fun toy, but something more important for the world community and the technical development of our civilization;
2) 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;
3) the best speed characteristics and flight stability are achieved by aircraft with a sharp nose and narrow long wings, and an increase in the wingspan can significantly increase the flight time of the glider.
Purpose of the study: to trace the history of the development of airfoils, to find out what impact this hobby has on society, what assistance paper aviation provides in the technical activities of engineers.
In accordance with the goal, we formulated the following tasks:

• Study information on this issue;
• Familiarize yourself with various models of paper planes and learn how to make them;
• To study the range and flight time of different models of paper planes.

Aerogami - paper aviation

Aerogami originates from the world famous origami. After all, the basic techniques, technique, philosophy come from him. The date of creation of paper airplanes should be recognized as 1909. However, the most common version of the time of invention and the name of the inventor is 1930, Jack Northrop, the founder of the Lockheed Corporation. Northrop used paper airplanes to test new ideas while building real airplanes. He concentrated on the development of "flying wings", which he considered the next stage in the development of aviation. Today, paper aviation, or aerogami, has gained worldwide fame. Everyone knows how to fold an elementary airplane and launch it. But today it is no longer just fun for one or two people, but a serious hobby, in which competitions are held all over the world. The Red Bull Paper Wings is probably the biggest paper aviator competition in the world. The championship debuted in Austria in May 2006 and was attended by athletes from 48 countries. The number of participants in the qualifying rounds, held around the world, exceeded 9,500 people. Participants traditionally compete in three categories: "Flight Range", "Flight Duration" and "Aerobatics".

Ken Blackburn is the world record holder for the launch of airplanes

The name of Ken Blackburn is known to all fans of paper aviation, and this is not surprising, because he created models that broke records in terms of range and flight time, said that a small airplane is an exact copy of a large one and that the same laws of aerodynamics apply to it as for real ones. World record holder Ken Blackburn was first introduced to the construction of square paper airplanes at the age of just 8 while attending his favorite aviation section. He noticed that long-span aircraft flew better and higher than conventional darts. To the displeasure of school teachers, young Ken experimented with the design of airplanes, devoting a lot of time to this. In 1977, he received the Guinness Book of Records as a gift and was determined to break the current 15-second record: his planes were sometimes in the air for more than a minute. The path to the record was not easy.
Blackburn studied aviation at the University of North Carolina, trying to achieve his goal. By that time, he realized that the result depended more on the strength of the throw than on the design of the aircraft. Several attempts brought his result to the level of 18.8 s. By that time, Ken had already turned 30. In January 1998, Blackburn opened the Book of Records and found that he had been thrown off the podium by a pair of Britons who showed a result of 20.9 s.
Ken couldn't let that happen. This time, a real sports coach took part in preparing the aviator for the record. In addition, Ken tested many aircraft designs and chose the best ones. The result of the last attempt was phenomenal: 27.6 s! On this Ken Blackburn decided to stop. Even if his record is broken, which must happen sooner or later, he has earned his place in history.

What forces act on a paper plane

Why do devices heavier than air fly - airplanes and their models? Remember how the wind drives leaves and pieces of paper along the street, lifts them up. A flying model can be compared to an object driven by a stream of air. Only the air is still here, and the model rushes, cutting through it. In this case, the air not only slows down the flight, but under certain conditions creates lift. Look at Figure 1(Appendix). Shown here is a cross section of an airplane wing. If the wing is located so that between its lower plane and the direction of motion of the aircraft there is a certain angle a (called the angle of attack), then, as practice shows, the speed of the air flow around the wing from above will be greater than its speed from below the wing. And according to the laws of physics, in that place of the flow, where the speed is greater, the pressure is less, and vice versa. That is why, when the aircraft is moving fast enough, the air pressure under the wing will be greater than above the wing. This pressure difference keeps the aircraft in the air and is called lift.
Figure 2 (Appendix) shows the forces acting on an aircraft or model in flight. The total effect of air on the aircraft is represented as an aerodynamic force R. This force is the resulting force acting on individual parts of the model: wing, fuselage, plumage, etc. It is always directed at an angle to the direction of motion. In aerodynamics, the action of this force is usually replaced by the action of its two components - lift and drag.
The lifting force Y is always directed perpendicular to the direction of movement, the drag force X is against the movement. The force of gravity G is always directed vertically downwards. The lift force depends on the wing area, flight speed, air density, angle of attack and aerodynamic perfection of the wing profile. The drag force depends on the geometrical dimensions of the fuselage cross section, flight speed, air density and the quality of surface treatment. Ceteris paribus, the model whose surface is finished more carefully flies further. The flight range is determined by the aerodynamic quality K, which is equal to the ratio of the lift force to the drag force, that is, the aerodynamic quality shows how many times the lift force of the wing is greater than the drag force of the model. In a gliding flight, the lift force of the model Y is usually equal to the weight of the model, and the drag force X is 10-15 times less, so the flight range L will be 10-15 times greater than the height H from which the gliding flight began. Consequently, the lighter the model, the more carefully it is made, the greater the flight range can be achieved.

Experimental study of paper airplane models in flight

Organization and research methods

The study was conducted in MBOU secondary school in the village of Krasnaya Gorka.

In the study, we set ourselves the following tasks:

• Familiarize yourself with the instructions for various models of paper planes. Find out what difficulties arise when assembling models.
• Conduct an experiment aimed at studying paper planes in flight. Are all models equally obedient when launched, how long do they spend in the air and what is the range of their flight.

A set of methods and techniques that we used to conduct the study:

• Simulation of many models of paper planes;
• Simulation of experiments to launch paper plane models.

During the experiment, we have identified the following sequencing:
1. Select the types of aircraft that are of interest to us. Make models of paper planes. Carry out in-flight tests of aircraft to determine their flight qualities (range and accuracy in flight, time in flight), launch method and ease of execution. Enter the data into a table. Select the models with the best results.
2. Three of the best models are made from different grades of paper. Carry out tests, enter the data in the table. Decide which paper is best suited for making paper airplane models.
Forms of records of the results of the study - record the data of the experiment in tables.
Primary processing and analysis of the results of the study was carried out as follows:

• Entering the results of the experiment into the appropriate forms of records;
• Schematic, graphic, illustrative presentation of the results (preparation of a presentation).
• Writing conclusions.

Description, analysis of the results of the study and conclusions about the dependence of the duration of the flight of a paper airplane on the model and method of launch

Experiment 1 Purpose: to collect information about models of paper planes; check how difficult it is to assemble models of different types; check the made models in flight.
Equipment: office paper, schemes for assembling paper models of aircraft, tape measure, stopwatch, forms for recording results.
Location: school corridor.
After studying a large number of instructions for paper plane models, we chose five models that I liked. Having studied in detail the instructions for them, we made these models from A4 office paper. After completing these models, we tested them in flight. We have entered the data of these tests in the table.

Table 1

	Paper airplane model name	Model drawing	Model assembly complexity (from 1 to 10 points)	Flight range, m (most)	Flight time, s (most)	Features at startup
1	Basic Dart		3	6	0,93	Twisted
2			4	8,6	1,55	Flying in a straight line
3	Fighter(Harrier Paper Airplane)		5	4	3	badly managed
4	Sokol F-16(F-16 Falcon Paper Airplane)		7	7,5	1,62	Poor planning
5	Space Shuttle Paper Airplane		8	2,40	0,41	Poor planning

Based on these test data, we have drawn the following conclusions:

• Collecting models is not as easy as one might think. When assembling models, it is very important to perform folds symmetrically, this requires some skill and skills.
• All models can be divided into two types: models suitable for launching for a flight distance, and models that perform well when launched for a flight duration.
• The model No. 2 Supersonic Fighter (Delta Fighter) behaved best when launched to a flight range.

Experiment 2

Purpose: to compare which paper models show the best results in terms of flight range and flight time.
Materials: office paper, notebook sheets, newsprint, tape measure, stopwatch, scorecards.
Location: school corridor.
We made the three best models from different grades of paper. The tests were carried out and the data were entered into a table. We concluded which paper is best used to make paper airplane models.

table 2

	Supersonic Fighter (Delta Fighter)	Flight range, m (most)	Flight time, s (most)	Additional Notes
1	Office paper	8,6	1,55	Long flight range
2	Newsprint	5,30	1,13
3	Notebook sheet of paper	2,6	2,64	It is easier and faster to make a model from paper in a box; a very long flight time

Table 3

	Sokol F-16(F-16 Falcon Paper Airplane)	Flight range, m (most)	Flight time, s (most)	Additional Notes
1	Office paper	7,5	1,62	Long flight range
2	Newsprint	6,3	2,00	Smooth flight, good planning
3	Notebook sheet of paper	7,1	1,43	Making a model from paper into a box is easier and faster

Table 4

	Basic Dart	Flight range, m (most)	Flight time, s (most)	Additional Notes
1	Office paper	6	0,93	Long flight range
2	Newsprint	5,15	1,61	Smooth flight, good planning
3	Notebook sheet of paper	6	1,65	It is easier and faster to make a model from paper in a box; a very long flight time

Based on the data obtained during the experiment, we made the following conclusions:

• It is easier to make models from notebook sheets in a box than from office or newsprint paper, but when tested, they do not show very good results;
• Models made of newsprint fly very beautifully;
• To obtain high results in terms of flight range, office paper models are more suitable.

findings
As a result of our research, we got acquainted with various models of paper planes: they differ in the complexity of folding, flight range and altitude, flight duration, which was confirmed during the experiment. Various conditions affect the flight of a paper plane: paper properties, the size of the plane, the model.

• Before you start assembling a paper airplane model, you need to decide what kind of model is needed: for the duration or flight range?
• In order for the model to fly well, the folds must be made evenly, exactly follow the dimensions indicated in the assembly diagram, make sure that all folds are performed symmetrically.
• It is very important how the wings are bent, the duration and range of the flight depend on it.
• Folding paper models develops abstract human thinking.
• As a result of the research, we learned that paper airplanes are used to test new ideas in the construction of real aircraft.

Conclusion
This work is devoted to the study of the prerequisites for the development of the popularity of paper aviation, the importance of origami for society, to identify whether a paper airplane is an exact copy of a large one, whether the same laws of aerodynamics apply to it as to real aircraft.
During the experiment, our hypothesis was confirmed: the best speed characteristics and flight stability are achieved by aircraft with a sharp nose and narrow long wings, and an increase in the wingspan can significantly increase the flight time of the glider.
Thus, our hypothesis that paper models of airplanes are not only a fun toy, but something more important for the world community and the technical development of our civilization, was confirmed.

List of information sources
http://www.krugosvet.ru/enc/nauka_i_tehnika/aviaciya_i_kosmonavtika/PLANER.html
http://igrushka.kz/vip95/bumavia.php http://igrushka.kz/vip91/paperavia.php
http://danieldefo.ru/forum/showthread.php?t=46575
Paper planes. – Moscow // Cosmonautics News. - 2008 -735. – 13 s
Paper #2: Aerogami, Print Fan
http://printfun.ru/bum2

Appendix

Aerodynamic forces

Rice. 1. Aircraft wing section
Lift force -Y
Resistance Force X
Gravity - G
Angle of attack - a

Rice. 2. Forces acting on an aircraft or model in flight

creative moments

Making a paper airplane out of office paper

I sign

Training



Making a paper airplane out of newspaper



I make a paper airplane from a notebook sheet

Study (left stopwatch)

I measure the length and record the results in a table

My planes

transcript

1 Research work Theme of the work Ideal paper airplane Completed by: Prokhorov Vitaly Andreevich, 8th grade student of the Smelovskaya secondary school Supervisor: Prokhorova Tatiana Vasilievna teacher of history and social studies of the Smelovskaya secondary school 2016

2 Contents Introduction The ideal airplane Components of success Newton's second law when launching an airplane Forces acting on an airplane in flight About the wing Launching an airplane Testing airplanes Models of airplanes Testing for flight range and glide time Model of an ideal airplane To summarize: a theoretical model Own model and its testing Conclusions List Appendix 1. Scheme of the impact of forces on an airplane in flight Appendix 2. Drag Appendix 3. Wing extension Appendix 4. Wing sweep Appendix 5. Mean aerodynamic chord of the wing (MAC) Appendix 6. Wing shape Appendix 7. Air circulation around the wing Appendix 8 Airplane Launch Angle Appendix 9. Airplane Models for the Experiment

3 Introduction Paper airplane (airplane) is a toy airplane made of paper. It is probably the most common form of aerogami, a branch of origami (the Japanese art of paper folding). In Japanese, such an aircraft is called 紙飛行機 (kami hikoki; kami=paper, hikoki=airplane). Despite the seeming frivolity of this activity, it turned out that launching airplanes is a whole science. It was born in 1930, when Jack Northrop, founder of the Lockheed Corporation, used paper airplanes to test new ideas on real airplanes. And the Red Bull Paper Wings paper plane launching competitions are held at the world level. They were invented by Briton Andy Chipling. For many years he and his friends were engaged in the creation of paper models, in 1989 he founded the Paper Aircraft Association. It was he who wrote the set of rules for launching paper planes, which are used by specialists from the Guinness Book of Records and which have become the official installations of the world championship. Origami, and then aerogami, has long been my passion. I've built various paper airplane models, but some of them flew great, while others fell right off the bat. Why does this happen, how to make a model of an ideal airplane (flying for a long time and far)? Combining my passion with knowledge of physics, I began my research. The purpose of the study: by applying the laws of physics, to create a model of an ideal airplane. Tasks: 1. To study the basic laws of physics that affect the flight of an airplane. 2. Derive the rules for creating the perfect airplane. 3

4 3. Examine the already created models of airplanes for proximity to the theoretical model of an ideal airplane. 4. Create your own model of an airplane that is close to the theoretical model of an ideal airplane. 1. Ideal airplane 1.1. Components of success First, let's deal with the question of how to make a good paper plane. You see, the main function of an airplane is the ability to fly. How to make an aircraft with the best performance. To do this, we first turn to observations: 1. An airplane flies faster and longer, the stronger the throw, except when something (most often a fluttering piece of paper in the nose or dangling lowered wings) creates resistance and slows down the forward progress of the airplane. . 2. No matter how hard we try to throw a sheet of paper, we will not be able to throw it as far as a small pebble having the same weight. 3. For a paper airplane, long wings are useless, short wings are more effective. Heavy airplanes don't fly far 4. Another key factor to take into account is the angle at which the airplane is moving forward. Turning to the laws of physics, we find the causes of the observed phenomena: 1. Flights of paper planes obey Newton's second law: the force (in this case, lift) is equal to the rate of change of momentum. 2. It's all about drag, a combination of air resistance and turbulence. The air resistance caused by its viscosity is proportional to the cross-sectional area of ​​the frontal part of the aircraft, 4

5 in other words, depends on how big the nose of the aircraft is when viewed from the front. Turbulence is the result of the action of eddying air currents that form around the aircraft. It is proportional to the surface area of ​​the aircraft, the streamlined shape significantly reduces it. 3. The large wings of the paper airplane sag and cannot resist the bending effect of the lifting force, making the airplane heavier and increasing drag. Excess weight prevents the aircraft from flying far, and this weight is usually created by the wings, with the greatest lift occurring in the region of the wing closest to the centerline of the aircraft. Therefore, the wings must be very short. 4. On launch, the air must strike the underside of the wings and be deflected downward to provide adequate lift to the aircraft. If the aircraft is not at an angle to the direction of travel and its nose is not up, lift will not occur. Below we will consider the basic physical laws that affect the airplane, in more detail Newton's second law when the airplane is launched. We know that the speed of a body changes under the influence of a force applied to it. If several forces act on the body, then the resultant of these forces is found, that is, a certain total total force that has a certain direction and numerical value. In fact, all cases of application of various forces at a particular moment in time can be reduced to the action of one resultant force. Therefore, in order to find how the speed of the body has changed, we need to know what force acts on the body. Depending on the magnitude and direction of the force, the body will receive one or another acceleration. This is clearly visible when the plane is launched. When we acted on the plane with a small force, it did not accelerate very much. When is power 5

6 impact increased, then the airplane acquired a much greater acceleration. That is, acceleration is directly proportional to the applied force. The greater the impact force, the greater the acceleration acquires the body. The mass of the body is also directly related to the acceleration acquired by the body as a result of the force. In this case, the mass of the body is inversely proportional to the resulting acceleration. The larger the mass, the smaller the acceleration will be. Based on the foregoing, we come to the conclusion that when the airplane is launched, it obeys Newton's second law, which is expressed by the formula: a \u003d F / m, where a is acceleration, F is the force of impact, m is the mass of the body. The definition of the second law is as follows: the acceleration acquired by a body as a result of an impact on it is directly proportional to the force or resultant of the forces of this impact and inversely proportional to the mass of the body. Thus, initially the airplane obeys Newton's second law and the flight range also depends on the given initial force and mass of the airplane. Therefore, the first rules for creating an ideal airplane follow from it: the airplane must be light, initially give the airplane a large force Forces acting on the airplane in flight. When an airplane flies, it is affected by many forces due to the presence of air, but all of them can be represented in the form of four main forces: gravity, lift, the force set at launch, and the force of air resistance (drag) (see Appendix 1). The force of gravity always remains constant. Lift counteracts the aircraft's weight and can be more or less than weight, depending on the amount of energy expended in propulsion. The force set at launch is counteracted by the force of air resistance (otherwise drag). 6

7 In straight and level flight, these forces are mutually balanced: the force set at launch is equal to the force of air resistance, the lift force is equal to the weight of the aircraft. With no other ratio of these four basic forces, straight and level flight is impossible. Any change in any of these forces will affect the way the aircraft flies. If the lift generated by the wings is greater than the force of gravity, then the airplane rises. Conversely, a decrease in lift against gravity causes the aircraft to descend, i.e., loss of altitude and its fall. If the balance of forces is not maintained, then the aircraft will curve the flight path in the direction of the prevailing force. Let us dwell in more detail on drag, as one of the important factors in aerodynamics. Frontal resistance is the force that prevents the movement of bodies in liquids and gases. Frontal resistance consists of two types of forces: forces of tangential (tangential) friction directed along the surface of the body, and pressure forces directed towards the surface (Appendix 2). The drag force is always directed against the velocity vector of the body in the medium and, together with the lifting force, is a component of the total aerodynamic force. The drag force is usually represented as the sum of two components: drag at zero lift (harmful drag) and inductive drag. Harmful resistance occurs as a result of the impact of the high-speed air pressure on the structural elements of the aircraft (all protruding parts of the aircraft create harmful resistance when moving through the air). In addition, at the junction of the wing and the “body” of the aircraft, as well as at the tail, airflow turbulences occur, which also give harmful resistance. Harmful 7

8 drag increases as the square of the aircraft's acceleration (if you double the speed, the harmful drag increases by a factor of four). In modern aviation, high-speed aircraft, despite the sharp edges of the wings and the super-streamlined shape, experience significant heating of the skin when they overcome the drag force with the power of their engines (for example, the world's fastest high-altitude reconnaissance aircraft SR-71 Black Bird is protected by a special heat-resistant coating). The second component of drag, inductive drag, is a by-product of lift. It occurs when air flows from an area of ​​high pressure in front of the wing into a rarefied medium behind the wing. The special effect of inductive resistance is noticeable at low flight speeds, which is observed in paper airplanes (A good example of this phenomenon can be seen in real aircraft during landing approach. The aircraft lifts its nose during landing approach, the engines begin to hum more increasing thrust). Inductive drag, similar to harmful drag, is in the ratio of one to two with the acceleration of the aircraft. And now a little about turbulence. The Explanatory Dictionary of the Encyclopedia "Aviation" gives a definition: "Turbulence is the random formation of non-linear fractal waves with increasing speed in a liquid or gaseous medium." In our own words, this is a physical property of the atmosphere, in which pressure, temperature, wind direction and speed are constantly changing. Because of this, air masses become heterogeneous in composition and density. And when flying, our airplane can get into descending (“nailed” to the ground) or ascending (better for us, because they lift the airplane from the ground) air currents, and these flows can also move randomly, twist (then the airplane flies unpredictably, twists and turns). eight

9 So, we deduce from what has been said the necessary qualities of creating an ideal airplane in flight: An ideal airplane should be long and narrow, tapering towards the nose and tail like an arrow, with a relatively small surface area for its weight. An airplane with these characteristics flies a greater distance. If the paper is folded so that the underside of the airplane is flat and level, lift will act on it as it descends and increase its range. As noted above, lift occurs when air hits the bottom surface of an aircraft that flies with its nose slightly raised on the wing. Wingspan is the distance between planes parallel to the plane of symmetry of the wing and touching its extreme points. The wing span is an important geometric characteristic of an aircraft that affects its aerodynamic and flight performance, and is also one of the main overall dimensions of an aircraft. Wing extension - the ratio of the wing span to its average aerodynamic chord (Appendix 3). For a non-rectangular wing, aspect ratio = (square of span)/area. This can be understood if we take a rectangular wing as a basis, the formula will be simpler: aspect ratio = span / chord. Those. if the wing has a span of 10 meters, and the chord = 1 meter, then the elongation will be = 10. The greater the elongation, the less the inductive drag of the wing associated with the flow of air from the lower surface of the wing to the upper one through the tip with the formation of end vortices. In the first approximation, we can assume that the characteristic size of such a vortex is equal to the chord - and with an increase in the span, the vortex becomes smaller and smaller compared to the wing span. nine

10 Naturally, the lower the inductive resistance, the lower the total resistance of the system, the higher the aerodynamic quality. Naturally, there is a temptation to make the elongation as large as possible. And here the problems begin: along with the use of high aspect ratios, we have to increase the strength and rigidity of the wing, which entails a disproportionate increase in the mass of the wing. From the point of view of aerodynamics, the most advantageous will be such a wing, which has the ability to create as much lift as possible with as little drag as possible. To assess the aerodynamic perfection of the wing, the concept of the aerodynamic quality of the wing is introduced. The aerodynamic quality of a wing is the ratio of the lift to the drag force of the wing. The best in terms of aerodynamics is an elliptical shape, but such a wing is difficult to manufacture, so it is rarely used. A rectangular wing is less aerodynamically advantageous, but much easier to manufacture. The trapezoidal wing is better in terms of aerodynamic characteristics than a rectangular one, but is somewhat more difficult to manufacture. Swept and triangular wings in terms of aerodynamics at low speeds are inferior to trapezoidal and rectangular (such wings are used on aircraft flying at transonic and supersonic speeds). The elliptical wing in plan has the highest aerodynamic quality - the minimum possible resistance with maximum lift. Unfortunately, a wing of this form is not often used due to the complexity of the design (an example of the use of a wing of this type is the English Spitfire fighter) (Appendix 6). Wing sweep angle of wing deviation from the normal to the axis of symmetry of the aircraft, projected onto the base plane of the aircraft. In this case, the direction to the tail is considered positive (Appendix 4). There are 10

11 sweep along the leading edge of the wing, along the trailing edge and along the quarter chord line. Reverse sweep wing (KOS) a wing with negative sweep (examples of aircraft models with reverse sweep: Su-47 "Berkut", Czechoslovak glider LET L-13) . Wing loading is the ratio of an aircraft's weight to its bearing surface area. It is expressed in kg/m² (for models - g/dm²). The lower the load, the lower the speed required to fly. The mean aerodynamic chord of the wing (MAC) is a straight line segment connecting the two most distant points of the profile from each other. For a wing rectangular in plan, the MAR is equal to the chord of the wing (Appendix 5). Knowing the value and position of the MAR on the aircraft and taking it as a baseline, the position of the center of gravity of the aircraft is determined relative to it, which is measured in% of the length of the MAR. The distance from the center of gravity to the beginning of the MAR, expressed as a percentage of its length, is called the center of gravity of the aircraft. It is easier to find out the center of gravity of a paper airplane: take a needle and thread; pierce the plane with a needle and let it hang on a thread. The point at which the aircraft will balance with perfectly flat wings is the center of gravity. And a little more about the wing profile is the shape of the wing in cross section. The wing profile has the strongest influence on all aerodynamic characteristics of the wing. There are quite a few types of profiles, because the curvature of the upper and lower surfaces is different for different types, as well as the thickness of the profile itself (Appendix 6). The classic is when the bottom is close to the plane, and the top is convex according to a certain law. This is the so-called asymmetrical profile, but there are also symmetrical ones, when the top and bottom have the same curvature. The development of airfoils has been carried out almost since the beginning of the history of aviation, and it is being carried out now (in Russia, TsAGI Central Aerohydrodynamic 11

12 Institute named after Professor N.E. Zhukovsky, in the USA such functions are performed by the Langley Research Center (a division of NASA)). Let's draw conclusions from the above said about the wing of an airplane: A traditional airplane has long narrow wings closer to the middle, the main part, balanced by small horizontal wings closer to the tail. The paper lacks the strength for such complex designs, bending and creasing easily, especially during the launch process. This means that paper wings lose aerodynamic characteristics and create drag. Traditionally designed airplanes are streamlined and fairly strong, their delta wings give a stable glide, but they are relatively large, create excessive drag and can lose rigidity. These difficulties can be overcome: Smaller and stronger lifting surfaces in the form of delta wings are made of two or more layers of folded paper, they better retain their shape during high-speed launch. The wings can be folded so that a slight bulge is formed on the upper surface, which increases the lift force, as on the wing of a real aircraft (Appendix 7). The solidly built design has a mass that increases starting torque, but without a significant increase in drag. If we move the deltoid wings forward and balance the lift with a long, flat V-shaped aircraft body closer to the tail, which prevents lateral movements (deviations) in flight, the most valuable characteristics of a paper airplane can be combined in one design. 1.5 Airplane launch 12

13 Let's start with the basics. Never hold your paper plane by the trailing edge of the wing (tail). Since the paper bends a lot, which is very bad for aerodynamics, any careful fit will be compromised. The aircraft is best held by the thickest set of paper layers near the nose. Usually this point is close to the center of gravity of the aircraft. To send the aircraft to the maximum distance, you need to throw it forward and upward as much as possible at an angle of 45 degrees (along a parabola), which was confirmed by our experiment with launching at different angles to the surface (Appendix 8). This is because during launch, the air must hit the underside of the wings and be deflected downward, providing adequate lift to the aircraft. If the aircraft is not at an angle to the direction of travel and its nose is not up, lift will not occur. The aircraft tends to have most of the weight rearward, which means the rear is down, the nose is up and lift is guaranteed. It balances the plane, allowing it to fly (unless the lift is too high, causing the plane to bounce up and down violently). In time-of-flight competitions, you should throw the plane to the maximum height so that it glides down longer. In general, the techniques for launching aerobatic aircraft are as diverse as their designs. And so is the technique for launching the perfect plane: A proper grip must be strong enough to hold the plane, but not so strong as to deform it. The folded paper ledge on the bottom surface under the airplane's nose can be used as a launch holder. When launching, keep the airplane at a 45 degree angle to its maximum height. 2.Testing airplanes 13

14 2.1. Airplane models In order to confirm (or refute, if they are wrong for paper airplanes), we selected 10 airplane models with different characteristics: sweep, wingspan, structure density, additional stabilizers. And of course we took the classic airplane model to also explore the choice of many generations (Appendix 9) 2.2. Flight range and gliding time test. fourteen

15 Model name Flight range (m) Duration of flight (metronome beats) Features at launch Pros Cons 1. Twisted Gliding Too flying Poor handling Flat bottom large wings Large Does not plan turbulence 2. Twisted Gliding Wings wide Tail Poor Unstable in flight Turbulence steerable 3. Dive Narrow nose Turbulence Hunter Twisting Flat bottom Weight of the bow Narrow body part 4. Gliding Flat bottom Big wings Guinness Glider Flying in an arc Bow shape Narrow body Long Arc flight gliding 5. Flying narrower wings Wide body straight, in Flight stabilizers No beetle end-of-flight arcing abruptly changes Abrupt change in flight path 6. Flying straight Flat bottom Wide body Traditional good Small wings No planing arcing 15

16 7. Dive Narrowed wings Heavy nose Flying in front Large wings, straight Narrow body shifted back Dive-bomber Arched (due to flaps on the wing) Structural density 8. Scout Flying along Small body Wide wings straight Gliding Small size in length Arched Dense construction 9. White swan Flying in a narrow body in a straight line Stable Narrow wings in a Flat bottom flight Dense construction Balanced 10. Stealth Flying in a curve straight Gliding Changes trajectory Axis of the wings is narrowed back No curve Wide wings Large body Not dense construction Flight duration (from largest to smallest): Glider Guinness and Traditional, Beetle, White Swan Flight length (from largest to smallest): White Swan, Beetle and traditional, Scout. The leaders in two categories came out: the White Swan and the Beetle. To study these models and, combining them with theoretical conclusions, take them as a basis for a model of an ideal airplane. 3. Model of an ideal airplane 3.1 To summarize: theoretical model 16

17 1. the airplane should be light, 2. initially give the airplane great strength, 3. long and narrow, tapering towards the nose and tail like an arrow, with a relatively small surface area for its weight, 4. the bottom surface of the airplane is flat and horizontal, 5 . small and stronger lifting surfaces in the form of delta wings, 6. fold the wings so that a slight bulge forms on the upper surface, 7. move the wings forward and balance the lift with the long flat body of the aircraft, having a V-shape towards the tail, 8. solidly built design, 9. the grip must be strong enough and by the ledge on the bottom surface, 10. launch at a 45 degree angle and to the maximum height. 11. Using the data, we made sketches of the ideal airplane: 1. Side view 2. Bottom view 3. Front view Having sketched the ideal airplane, I turned to the history of aviation to see if my conclusions coincided with aircraft designers. And I found a prototype aircraft with a delta wing developed after the Second World War: the Convair XF-92 - point interceptor (1945). And confirmation of the correctness of the conclusions is that it became the starting point for a new generation of aircraft. 17

18 Own model and its test. Model name Flight range (m) Flight duration (metronome beats) ID Features at launch Pros (proximity to the ideal airplane) Cons (deviations from the ideal airplane) Flies 80% 20% straight (perfection (for further Control Plans there is no limit) improvements) With a sharp headwind, it “rises” at 90 0 and turns around. My model is made on the basis of the models used in the practical part, the most similar to the “white swan”. But at the same time, I made a number of significant changes: a large delta shape of the wing, a bend in the wing (like in the “scout” and the like), the hull was reduced, and additional structural rigidity was given to the hull. It cannot be said that I am completely satisfied with my model. I would like to reduce the lower case, leaving the same density of construction. Wings can be given greater delta. Think about the tail. But it cannot be otherwise, there is time ahead for further study and creativity. This is exactly what professional aircraft designers do, you can learn a lot from them. What I will do in my hobby. 17

19 Conclusions As a result of the study, we got acquainted with the basic laws of aerodynamics that affect the airplane. Based on this, the rules were deduced, the optimal combination of which contribute to the creation of an ideal airplane. To test the theoretical conclusions in practice, we put together models of paper planes of various folding complexity, range and flight duration. During the experiment, a table was compiled, where the manifested shortcomings of the models were compared with theoretical conclusions. Comparing the data of theory and experiment, I created a model of my ideal airplane. It still needs to be improved, bringing it closer to perfection! eighteen

20 References 1. Encyclopedia "Aviation" / site Academician %D0%BB%D0%B5%D0%BD%D1%82%D0%BD%D0%BE%D1%81%D1% 82%D1%8C 2. Collins J. Paper planes / J. Collins: per. from English. P. Mironova. Moscow: Mani, Ivanov and Ferber, 2014. 160c Babintsev V. Aerodynamics for dummies and scientists / portal Proza.ru 4. Babintsev V. Einstein and lifting force, or Why does a snake need a tail / portal Proza.ru 5. Arzhanikov N.S., Sadekova G.S., Aerodynamics of aircraft 6. Models and methods of aerodynamics / 7. Ushakov V.A., Krasilshchikov P.P., Volkov A.K., Grzhegorzhevsky A.N., Atlas of aerodynamic characteristics of wing profiles / 8. Aircraft aerodynamics / 9. Movement of bodies in air / email zhur. Aerodynamics in nature and technology. Brief information on aerodynamics How do paper airplanes fly? / Interesting. Interesting and cool science Mr. Chernyshev S. Why does an airplane fly? S. Chernyshev, director of TsAGI. Journal "Science and Life", 11, 2008 / VVS SGV 4th VA VGK - forum of units and garrisons "Aviation and airfield equipment" - Aviation for "dummies" 19

21 12. Gorbunov Al. Aerodynamics for "dummies" / Gorbunov Al., Mr. Road in the clouds / jour. Planet July, 2013 Milestones in aviation: a prototype aircraft with a delta wing 20

22 Appendix 1. Scheme of the impact of forces on the airplane in flight. Lift force Acceleration given at launch Gravity Force Drag Appendix 2. Drag. Obstacle flow and shape Shape resistance Viscous friction resistance 0% 100% ~10% ~90% ~90% ~10% 100% 0% 21

23 Appendix 3. Wing extension. Appendix 4. Wing sweep. 22

24 Appendix 5. Mean aerodynamic wing chord (MAC). Annex 6. The shape of the wing. Cross section Plan 23

25 Appendix 7. Air circulation around the wing A vortex is formed at the sharp edge of the wing profile. When a vortex is formed, air circulation around the wing occurs. The vortex is carried away by the flow, and the streamlines smoothly flow around the profile; they are condensed over the wing Appendix 8. Plane launch angle 24

26 Appendix 9. Models of airplanes for the experiment Model from paper payment order 1 Name of payment order 6 Model from paper Name Fruit bat Traditional 2 7 Tail Dive Pilot 3 8 Hunter Scout 4 9 Guinness Glider White Swan 5 10 Stealth Beetle 26

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Incredible Facts

Many of us have seen, or maybe made, 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. It was they who invented the balloon and used paper for this. 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 make not just interesting models, but also flying ones.

* Also in the early 1930s, Jack Northrop of the Lockheed Corporation used several paper models of airplanes and wings for testing purposes. 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, an EVA-launched paper airplane 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. The National Aeronautics and Space Administration (NASA) sent a paper airplane into space on the Space Shuttle.

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

* NASA specialists together with astronauts held a master class for schoolchildrenin the hangar of his 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

Relevance: "Man is not a bird, but strives to fly" It so happened that a person has always been drawn to the sky. People tried to make wings for themselves, later flying machines. And their efforts were justified, they were still able to take off. The appearance of airplanes did not in the least diminish the relevance of the ancient desire ... In the modern world, aircraft have taken pride of place, they help people travel long distances, transport mail, medicines, humanitarian aid, put out fires and save people ... So who built the world's first airplane and made it to him a controlled flight? Who made this step, so important for mankind, which became the beginning of a new era, the era of aviation? I consider the study of this topic interesting and relevant.

Research objectives: 1. To study the history of the emergence of aviation, the history of the appearance of the first paper planes in the scientific literature. 2.Make aircraft models from different materials and organize an exhibition: "Our aircraft"

Object of study: paper models of airplanes Problematic question: Which model of a paper airplane will fly the longest distance and the longest glide in the air? Hypothesis: We assume that the Dart airplane will fly the longest distance, and the Glider airplane will have the longest gliding in the air Research methods: 1. Analysis of the literature read; 2.Modeling; 3. Study of paper airplane flights.

The first aircraft that was able to independently take off the ground and make a controlled horizontal flight was the Flyer-1, built by the brothers Orville and Wilbur Wright in the USA. The first aircraft flight in history took place on December 17, 1903. The Flyer stayed in the air for 12 seconds and flew 36.5 meters. The brainchild of the Wrights was officially recognized as the world's first heavier-than-air vehicle, which made a manned flight using an engine.

The flight took place on July 20, 1882 in Krasnoye Selo near St. Petersburg. The aircraft was tested by the assistant of Mozhaisky mechanic I.N. Golubev. The device ran up a specially built inclined wooden deck, took off, flew a certain distance and landed safely. The result, of course, is modest. But the possibility of flying on an apparatus heavier than air was clearly proven.

The history of the appearance of the first paper airplanes The most common version of the time of invention and the name of the inventor is 1930, Jack Northrop, co-founder of Lockheed Corporation. Northrop used paper airplanes to test new ideas in the construction of real aircraft. Despite the seeming frivolity of this activity, it turned out that launching airplanes is a whole science. She was born in 1930, when Jack Northrop, co-founder of Lockheed Corporation, used paper airplanes to test new ideas in the construction of real aircraft. 1930 Jack NorthropLockheed Corporation

Conclusion In conclusion, I want to say that while working on this project, we learned a lot of new interesting things, made a lot of models with our own hands, and became more friendly. As a result of the work done, we realized that if we are seriously interested in aeromodelling, then perhaps one of us will become a famous aircraft designer and design an airplane on which people will fly.

1. http://ru.wikipedia.org/wiki/Paper airplane...ru.wikipedia.org/wiki/Paper airplane annews.ru/news/detailannews.ru/news/detail opoccuu.com htmopoccuu.com htm 5. poznovatelno.ruavia/8259.htmlpoznovatelno.ruavia/8259.html 6. ru.wikipedia.orgwiki/Wright Brothersru.wikipedia.orgwiki/Wright Brothers 7. locals.md2012/stan-chempionom- mira…samolyotikov/locals.md2012/stan- chempionom- mira…samolyotikov/ 8 stranamasterov.ru from MK aircraft modulesstranamasterov.ru from MK aircraft modules

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 Yegorovich 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 flow creates lift and the aircraft 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 generated by the same pressure as profile wings, but of course this difference in pressure is not as 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 the drag of the 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.