How paper airplanes fly. "Dependence of the flight duration of a paper airplane on its shape." Origami airplane

Relevance: “Man is not a bird, but strives to fly.” It just so happens that man has always been drawn to the sky. People tried to make wings for themselves, and later aircraft. And their efforts paid off; they were able to take off after all. The advent of airplanes did not in the least diminish the relevance of the ancient desire... modern world aircraft have taken pride of place, they help people travel long distances, transport mail, medicine, humanitarian aid, put out fires and save people... So who built the world's first airplane and made a controlled flight on it? Who took this step, so important for humanity, which became the beginning of a new era, the era of aviation? I find the study of this topic interesting and relevant.

Research objectives: 1.Study by scientific literature the history of aviation, the history of the appearance of the first paper airplanes. 2.Make airplane models from different materials and organize an exhibition: “Our Airplanes” 3.Carry out flight tests for the right choice aircraft model and paper type for the longest distance and longest glide in the air

Object of study: paper airplane models Problem question: Which paper airplane model will fly the longest distance and glide for the longest time in the air? Hypothesis: We assume that the Dartik 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.Research on paper airplane flights.

The first aircraft that was able to take off the ground independently and perform controlled horizontal flight was Flyer 1, built by the brothers Orville and Wilbur Wright in the USA. The first flight of an airplane in history was carried out on December 17, 1903. The Flyer stayed in the air for 12 seconds and flew 36.5 meters. The Wrights' brainchild was officially recognized as the world's first heavier-than-air vehicle to make 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 Mozhaisky’s assistant mechanic I.N. Golubev. The device ran along a specially constructed inclined wooden flooring, took off, flew a certain distance and landed safely. The result, of course, is modest. But the possibility of flight on a device 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 design of real airplanes. Despite the seeming frivolity of this activity, it turned out that flying airplanes was a whole science. She was born in 1930, when Jack Northrop, co-founder of the Lockheed Corporation, used paper airplanes to test new ideas in the design 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 we did, we realized: if we get seriously involved in aircraft modeling, then perhaps one of us will become a famous aircraft designer and design an airplane that people will fly on.

1. http 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 airplane modulesstranamasterov.ru from MK airplane modules

Being the father of almost a graduate high school, was drawn into a funny story with an unexpected ending. It has an educational part and a touching life-political part.
Fasting on the eve of Cosmonautics Day. Physics of a paper airplane.

Shortly before the New Year, my daughter decided to check her own academic performance and found out that the physics teacher, when filling out the journal after the fact, had given some extra B's and the six-month grade was hanging between "5" and "4". Here you need to understand that physics in the 11th grade is, to put it mildly, a non-core subject, everyone is busy with training for admission and the terrible Unified State Exam, but it affects the overall score. With a creaking heart, for pedagogical reasons, I refused to intervene - like figure it out yourself. She pulled herself together, came to find out, rewrote some independent work right there and received 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) in the “physics” section and write some kind of report. The student’s participation in this shit counts towards the annual certification of teachers, and it’s like, “Then we’ll definitely close the year.” The teacher can be understood; in general, this is a normal agreement.

The child loaded up, went to the organizing committee, and 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. On the Internet we found a list of winners of past conferences (they give diplomas of three degrees), this gave us some guidance, but did not help. The reports were of two types, one - “nanofilters in oil innovations”, the second - “photos of crystals and an electronic metronome”. For me, the second variety is normal - children should cut a toad, and not earn points for government grants, but we haven’t really gotten any more 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 gibberish or nanotechnology - we would amuse the audience, participation was enough for us. It was a month and a half long. Copy-paste was fundamentally unacceptable. After some thought, we decided on the topic - “Physics of a paper airplane.” I spent my childhood in aircraft modeling, and my daughter loves airplanes, so the topic is more or less close. It was necessary to complete a practical physical research 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 an end to the story, which is logical. If you are interested, I will answer the questions in already expanded fragments.

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

For the experiments we took three different models.

Model No. 1. The most common and well-known design. As a rule, most people imagine exactly this when they hear the expression “paper plane.”
Model No. 2. “Arrow” or “Spear”. Characteristic model with acute angle wing and expected high speed.
Model No. 3. Model with a high aspect ratio wing. Special design, assembled along the wide side of the sheet. It is assumed that it has good aerodynamic properties 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 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 applied. Since the frame interval for video shooting is known (1/30 of a second), the gliding speed can be easily calculated. Based on the drop in altitude, the glide angle and aerodynamic quality of the aircraft are found in the corresponding frames.
On average, the speed of an airplane is 5–6 m/s, which is not so little.
Aerodynamic quality - about 8.

To recreate flight conditions, we need laminar flow of up to 8 m/s and the ability to measure lift and drag. The classic method for 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 pipe of limited dimensions. Therefore, we are not bothered 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 cross-section of 300x200 mm and a flow speed of up to 8 m/s, we will need a fan with a capacity of at least 1000 cubic meters/hour. To change the flow speed, you need an engine speed controller, and to measure it, an anemometer with appropriate accuracy. The speed meter does not have to be digital; it is quite possible to get by with a deflectable plate with an angle graduation or a liquid anemometer, which has greater accuracy.

The wind tunnel has been known for quite a long time; Mozhaisky used it in research, and Tsiolkovsky and Zhukovsky have already developed it in detail modern technology experiment, which has not changed fundamentally.

The desktop wind tunnel was implemented on the basis of a fairly powerful industrial fan. Behind the fan there are mutually perpendicular plates that 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. A digital anemometer impeller is installed directly in the measuring chamber to measure the flow velocity. The pipe has a slight narrowing at the outlet to “back up” the flow, which reduces turbulence at the cost of reducing speed. The fan speed is controlled by a simple household electronic controller.

The characteristics of the pipe turned out to be worse than calculated, mainly due to the discrepancy between the fan performance and the specifications. The flow back-up also reduced the speed in the measurement area by 0.5 m/s. As a result, the maximum speed is slightly higher than 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 scales with two degrees of freedom were used based on a pair of electronic jewelry scales with an accuracy of 0.01 grams. The plane was fixed on two stands at the desired angle and installed on the platform of the first scales. Those, in turn, were placed on a movable platform with a lever transmitting 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 was better to develop an appropriate fastening scheme with markings.

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

Model No. 1.
Golden mean. The design corresponds as closely as possible to the material - paper. The strength of the wings corresponds to their length, the weight distribution is optimal, so a properly folded aircraft aligns well and flies smoothly. It was the combination of such qualities and ease of assembly that made this design so popular. The speed is less than that of the second model, but greater than that of the third. At high speeds, the wide tail, which previously perfectly stabilized the model, begins to interfere.
Model No. 2.
The 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 increase enough and the plane really flies like a spear. Additionally, it does not stabilize properly in flight.
Model No. 3.
A representative of the “engineering” school, the model was specially conceived with special characteristics. High aspect ratio wings actually work better, but the drag increases very quickly - the plane flies slowly and does not tolerate acceleration. To compensate for the insufficient rigidity of the paper, numerous folds are used in the toe of the wing, which also increases resistance. However, the model is very impressive and flies well.

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

Turbulent “tail”.

Flows can also be examined using short threads glued to the wing, or 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 is used in practice only by flying squirrels, which do not have great national economic importance, at least in our region.

A more practical similarity to a paper airplane is the “Wing suite” - a wing suit for paratroopers that allows horizontal flight. By the way, the aerodynamic quality of such a suit is less than that of a paper airplane - no more than 3.

I came up with a topic, a plan - 70 percent, theory editing, hardware, general editing, a speech plan.
She collected all the theory, right down to translating articles, measurements (very labor-intensive, by the way), drawings/graphs, text, literature, presentation, report (there were many questions).

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

Taking into account the work done, we can add coloring to the mind map indicating the completion of the assigned tasks. Green indicates areas that are at a satisfactory level, light green indicates issues that have some limitations, yellow indicates areas that have been touched upon but not adequately developed, and red indicates promising areas that require additional research (funding is welcome).

A month flew by unnoticed - my daughter was surfing the Internet, running a pipe on the table. The scales were tilting, the airplanes were blowing past the theory. The output was 30 pages of decent text with photographs and graphs. The work was sent to the correspondence round (only several thousand works in all sections). Another month later, horror of horrors, they posted a list of in-person reports, where ours was adjacent to the rest of the nanocrocodiles. The child sighed sadly and began to make a presentation for 10 minutes. They immediately excluded reading - speaking, so vividly and meaningfully. Before the event, there was a run-through with timing and protests. In the morning, the sleep-deprived speaker, with the correct feeling of “I don’t remember or know anything,” went to KSU for a saw.

By the end of the day I began to worry, no answer - no hello. There is such a precarious state when you don’t understand whether the risky joke was a success or not. I didn’t want the teenager to somehow end up with this story. It turned out that everything was delayed and her report came at 4 pm. The child sent an SMS: “I told you everything, the jury is laughing.” Well, I think, okay, thank you, at least they don’t scold me. And after about another hour - a “first degree diploma”. This was completely unexpected.

We thought about anything, but against the backdrop of absolutely wild pressure from lobbied topics and participants, to receive the first prize for good, but informal work is something from a completely forgotten time. Later she said that the jury (quite authoritative, by the way, no less than the Faculty of Mathematical Sciences) killed the zombified nanotechnologists with lightning speed. Apparently, everyone has been so fed up in scientific circles that they have unconditionally put up an unspoken barrier to obscurantism. It got to the point of ridiculousness - the poor child read out some wild science, but could not answer what the angle was measured in his experiments. Influential scientific supervisors turned slightly pale (but quickly recovered), it’s a mystery to me why they would organize 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 received by a girl with a model of a Stirling engine, who quickly started it up in the department, quickly changed modes and intelligently commented on all sorts of situations. Another diploma was given to a guy who was sitting on a university telescope and looking for something under the guidance of a professor who definitely did not allow any outside “help.” This story gave me some hope. The fact that there is a will of ordinary, normal people to the normal order of things. Not a habit of predetermined injustice, but a readiness to make efforts to restore it.

The next day, at the award ceremony, the chairman of the admissions committee approached the winners and said that all of them had been early enrolled in the physics department of KSU. If they want to enroll, they simply have to bring documents outside the competition. This benefit, by the way, actually existed once, but now it has been officially cancelled, just as additional preferences for medalists and Olympiads have been canceled (except, it seems, for the winners of 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 to study physics; on the other hand, this is one of the most normal faculties with a good level. So, correcting the four, the child ended up in the first line of those enrolled. I can’t imagine how she will manage this, but if I find out, I’ll write it down.

Would your daughter be able to do this kind of work alone?

She also asked - like dad, I didn’t do everything myself.
My version is like this. You did everything yourself, you understand what is written on every page and you can answer any question - yes. Do 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 research - yes. She did a significant job - no doubt. She put forward this work on a general basis without patronage - yes. Defended - ok. The jury is qualified - without a doubt. Then this is your reward for the school conference.

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

Palkin Mikhail Lvovich

Paper airplanes are a well-known paper craft that almost everyone can make. Or I knew how to do it before, but forgot a little. No problem! After all, you can fold an airplane within a few seconds by tearing out a sheet of paper from an ordinary school notebook.
One of the main problems paper airplane- short flight time. Therefore, I would like to know whether the duration of the flight depends on its shape. Then you can advise your classmates to make a plane that will break all records.

Object of study

Paper airplanes different forms.

Subject of study

Flight duration of paper airplanes of different shapes.

Hypothesis

If you change the shape of a paper airplane, you can increase the duration of its flight.

Target

Determine the paper airplane model with the longest flight duration.

Tasks

Find out what forms of paper airplane exist.
Fold paper airplanes in different patterns.
Determine whether the duration of the flight depends on its shape.

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Research member of the scientific society "Umka" of the Municipal Educational Institution "Lyceum No. 8 of Novoaltaisk" Mikhail Lvovich Palkin Scientific supervisor Goar Matevosovna Ovsepyan

Topic: “My paper plane is taking flight!” (dependence of the flight duration of a paper airplane on its shape)

Relevance of the chosen topic Paper airplanes are a well-known paper craft that almost everyone can make. Or I knew how to do it before, but forgot a little. No problem! After all, you can fold an airplane within a few seconds by tearing out a sheet of paper from an ordinary school notebook. One of the main problems of a paper airplane is its short flight time. Therefore, I would like to know whether the duration of the flight depends on its shape. Then you can advise your classmates to make a plane that will break all records.

The object of research is paper airplanes of various shapes. The subject of the study is the flight duration of paper airplanes of various shapes.

Hypothesis: If you change the shape of a paper airplane, you can increase the duration of its flight. Goal: Determine the paper airplane model with the longest flight duration. Objectives Find out what forms of paper airplane exist. Fold paper airplanes in different patterns. Determine whether the duration of the flight depends on its shape.

Methods: Observation. Experiment. Generalization. Research plan: Selection of topic - May 2011 Formulation of hypothesis, goals and objectives - May 2011 Study of material - June - August 2011 Conducting experiments - June-August 2011. Analysis of the results obtained - September-November 2011.

There are many ways to fold paper to make an airplane. Some options are quite complex, while others are simple. For some, it is better to use soft, thin paper, and for others, on the contrary, thicker paper. The paper is pliable and at the same time has sufficient rigidity, retains its given shape, making it easy to make airplanes out of it. Let's consider a simple version of a paper airplane that everyone knows.

An airplane that many people call a “fly”. It folds up easily and flies quickly and far. Of course, to learn how to launch it correctly, you will have to practice a little. Below a series of sequential drawings will show you how to make an airplane out of paper. Watch and try it!

First, fold a sheet of paper exactly in half, then bend one of its corners. Now it’s not difficult to bend the other side in the same way. Bend as shown in the picture.

Bend the corners to the center, leaving between them short distance. We bend the corner, thereby securing the corners of the figure.

Let's bend the figure in half. Bend back the “wings”, leveling the bottom of the figure on both sides. Well, now you know how to make an origami airplane out of paper.

There are other options for assembling a flying model aircraft.

Having folded a paper airplane, you can color it with colored pencils and glue identification marks.

This is what happened to me.

To find out whether the duration of an airplane's flight depends on its shape, let's try to run different models in turn and compare their flight. Tested, flies great! Sometimes when starting, it may fly “nose down”, but this is fixable! Just bend the tips of the wings up slightly. Typically, the flight of such an airplane consists of quickly soaring up and diving down.

Some airplanes fly straight, while others follow a winding path. Airplanes for the longest flights have a large wingspan. Planes shaped like a dart - they are just as narrow and long - fly at higher speeds. Such models fly faster and more stable, and are easier to launch.

My discoveries: 1. My first discovery was that he really flies. Not randomly and crookedly, like an ordinary school toy, but straight, fast and far. 2. The second discovery is that folding a paper airplane is not as easy as it seems. Actions must be confident and precise, bends must be perfectly straight. 3. Open air launch is different from indoor flight (the wind either hinders or helps it in flight). 4 . The main discovery is that the flight duration significantly depends on the design of the aircraft.

Material used: www.stranaorigami.ru www.iz-bumagi.com www.mykler.ru www.origami-paper.ru Thank you for your attention!

Scientific historical research work
Completed by: 11th grade student Ruzilya Zaripova
Scientific supervisor: Sarbaeva A.A.
MBOU secondary school in Krasnaya Gorka village

Introduction

Even the simplest airplane model is a miniature airplane with all its properties. Many famous aircraft designers began with a hobby of aircraft modeling. It takes a lot of work to build a good flying model. All people have ever done paper airplanes and sent them flying. Paper airplanes are gaining popularity all over the world. This led to the introduction of the new term aerogami. Aerogami is the modern name for the production and launch of paper airplane models, one of the directions of origami (the Japanese art of folding paper).
The relevance of this work is due to the opportunity to use the acquired knowledge to conduct lessons in primary school in order to arouse students’ interest in the world of aviation and develop the necessary qualities and abilities to use creative experience and knowledge in the study and development of aviation.
Practical significance determined by the opportunity to conduct a master class on folding paper airplanes of different models with teachers primary classes, as well as the opportunity to hold competitions among students.
Object of study are paper airplane models.
Subject of research is the emergence and development of aerogi.
Research hypotheses:
1) paper airplane models 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, 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: trace the history of the development of aerogami, find out what impact this hobby has on society, what assistance paper aviation provides in the technical activities of engineers.
In accordance with this goal, we formulated the following tasks:

Study information on this issue;
Get acquainted with various models of paper airplanes and learn how to make them;
Study the range and flight time of different models of paper airplanes.

Aerogami - paper aviation

Aerogami originates from the world famous origami. After all, the basic techniques, technology, 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, founder of the Lockheed Corporation.

Northrop used paper airplanes to test new ideas in the design of real airplanes. He concentrated on developing "flying wings", which he considered the next stage in the development of aviation. Nowadays, paper aviation, or aerogami, has gained worldwide fame. Every person knows how to fold a basic airplane and launch it. But today it is no longer just fun for one or two people, but a serious hobby for which competitions are held all over the world.

Red Bull Paper Wings is perhaps the biggest paper aviator competition in the world. The championship debuted in Austria in May 2006, with athletes from 48 countries taking part. The number of participants in qualifying rounds held around the world exceeded 9,500 people. Participants traditionally compete in three categories: “Flight range”, “Flight duration” and “Aerobatics”.

Ken Blackburn - world record holder for launching 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 for range and flight time, talked about how a small airplane is an exact copy of a large one and that it is subject to the same laws of aerodynamics as to real ones. World record holder Ken Blackburn was first introduced to the design of square paper airplanes at the age of just 8 while visiting his favorite aviation section. He noticed that planes with a larger wingspan flew better and higher than conventional dart planes. To the displeasure of his 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 sometimes stayed in the air for more than a minute. The path to the record was not easy.
Blackburn, studying aviation at the University of North Carolina, tried to achieve his goal. By then he realized that the result depended more on the force of the throw than on the design of the aircraft. Several attempts brought his result to the level of 18.8 seconds. By that time, Ken had already turned 30. In January 1998, Blackburn opened the Book of Records and discovered that he had been knocked off the pedestal by a pair of Britons who showed a result of 20.9 seconds.
Ken couldn't allow this to happen. This time, a real sports coach took part in preparing the aviator for the record. In addition, Ken tested many aircraft designs and selected the best ones. The result of the last attempt was phenomenal: 27.6 s! Ken Blackburn decided to stop there. Even if his record is broken, which is bound to happen sooner or later, he has earned his place in history.

What forces act on a paper airplane?

Why do heavier-than-air vehicles fly - airplanes and their models? Remember how the wind blows leaves and pieces of paper along the street and lifts them up. A flying model can be compared to an object driven by a stream of air. Only the air here is still, 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 positioned so that there is a certain angle a (called the angle of attack) between its lower plane and the direction of movement of the aircraft, then, as practice shows, the speed of the air flow flowing around the wing from above will be greater than its speed from below the wing. And according to the laws of physics, in the place of the flow where the speed is greater, the pressure is less, and vice versa. This is why, when the plane moves fast enough, the air pressure under the wing will be greater than above the wing. This pressure difference keeps the plane in the air and is called lift.
Figure 2 (Appendix) shows the forces acting on an airplane or model in flight. The total effect of air on an aircraft is represented as an aerodynamic force R. This force is the resulting force acting on individual parts of the model: wing, fuselage, tail, etc. It is always directed at an angle to the direction of movement. In aerodynamics, the action of this force is usually replaced by the action of its two components - the lift force and the drag force.
The lifting force Y is always directed perpendicular to the direction of movement, the drag force X is directed against the movement. The force of gravity G is always directed vertically downwards. Lift 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 geometric dimensions of the fuselage cross-section, flight speed, air density and the quality of surface treatment. All other things being equal, the model whose surface is finished more carefully flies farther. The flight range is determined by the aerodynamic quality K, 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 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 more height N, 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 carried out in the municipal budgetary educational institution secondary school in the village of Krasnaya Gorka.

In the study we set ourselves the following tasks:

Review the instructions for various paper airplane models. Find out what difficulties arise when assembling models.
Conduct an experiment to study paper airplanes in flight. Are all models equally obedient when launched, how long do they spend in the air and what is their flight range?

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

Simulation of many paper airplane models;
Simulation of paper airplane model launch experiments.

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

Entering the experimental results into the appropriate record forms;
Schematic, graphical, illustrative presentation of results (preparing a presentation).
Writing conclusions.

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

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

Table 1

	Paper airplane model name	Model drawing	Difficulty of assembling the model (from 1 to 10 points)	Flight range, m (maximum)	Flight time, s (maximum)	Features at launch
1	Basic Dart		3	6	0,93	Twisting
2			4	8,6	1,55	Flying in a straight line
3	Fighter (Harrier Paper Airplane)		5	4	3	Poorly managed
4	Falcon 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 the data from these tests, we made the following conclusions:

Assembling models is not as easy as you might think. When assembling models, it is very important to make symmetrical folds; this requires certain dexterity and skills.
All models can be divided into two types: models suitable for long-range launching, and models that perform well when launching long-range.
Model No. 2 Supersonic Fighter (Delta Fighter) behaved best when launching at range.

Experiment 2

Goal: 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, forms for recording results.
Location: school corridor.
We made the three best models from different types of paper. Tests were carried out and the data was entered into a table. We concluded which paper is best to use for making paper airplane models.

table 2

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

Table 3

	Falcon F-16(F-16 Falcon Paper Airplane)	Flight range, m (maximum)	Flight time, s (maximum)	Additional Notes
1	Office paper	7,5	1,62	Long range
2	Newsprint	6,3	2,00	Smooth flight, plans well
3	Notebook sheet of paper	7,1	1,43	It’s easier and faster to make a model using checkered paper

Table 4

	Basic Dart	Flight range, m (maximum)	Flight time, s (maximum)	Additional Notes
1	Office paper	6	0,93	Long range
2	Newsprint	5,15	1,61	Smooth flight, plans well
3	Notebook sheet of paper	6	1,65	Making a model from checkered paper is easier and faster; very long flight time

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

It is easier to make models from checkered notebook sheets 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, models made from office paper are more suitable.

conclusions
As a result of our research, we became familiar with various models of paper airplanes: they differ in the complexity of folding, flight range and altitude, and flight duration, which was confirmed during the experiment. The flight of a paper airplane is influenced by various conditions: the properties of the paper, the size of the airplane, the model. The experiments carried out made it possible to develop the following recommendations for assembling paper airplane models:

Before you start assembling a paper airplane model, you need to decide what type of model is needed: for duration or flight range?
In order for the model to fly well, the folds must be made evenly, the dimensions specified in the assembly diagram must be followed exactly, and all bends must be made symmetrically.
It is very important how the wings are curved; the duration and range of the flight depends on this.
Folding paper models develops a person's abstract thinking.
As a result of our research, we learned that paper airplanes are used to test new ideas in the design of real airplanes.

Conclusion
This work is devoted to studying the prerequisites for the development of the popularity of paper aviation, the importance of origami for society, identifying whether a paper airplane is an exact copy of a large one, and whether the same laws of aerodynamics apply to it as to real airplanes.
During the experiment, the hypothesis we put forward 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 airplane models 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 airplanes. – Moscow // Cosmonautics news. – 2008 –735. – 13 s
Article "Paper #2: Aerogami", Print Fan
http://printfun.ru/bum2

Application

Aerodynamic forces

Rice. 1. Section of an airplane wing
Lift -Y
Resistance force X
Gravity - G
Angle of attack - a

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

Creative moments

Making a paper airplane from office paper

I sign

Preparation

Making a paper airplane from newspaper

Making a paper airplane from a piece of notebook paper

Research (Stopwatch on the left)

I measure the length and write the results in a table

My planes

PHYSICS OF PAPER PLANE.
REPRESENTATION OF THE AREA OF KNOWLEDGE. PLANNING THE EXPERIMENT.

1. Introduction. Goal of the work. General patterns of development of the field of knowledge. Selecting a research object. Mind map.
2. Elementary physics of glider flight (BS). System of force equations.

9. Photos of the aerodynamic tube. Review of the characteristics of the pipe, aerodynamic scales.
10. Experimental results.
12. Some results on 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 center of gravity and the characteristics of the models.
14. Energy efficient planning. Flight stabilization. World record tactics for flight duration.

18. Conclusion.
19. List of references.

1. Introduction. Goal of the work. General patterns of development of the field of knowledge. Selection of research object. Mind map.

The development of modern physics, primarily in its experimental part, and especially in applied areas, occurs according to a clearly expressed hierarchical scheme. This is caused by the need for additional concentration of resources necessary to achieve results, ranging from material support for experiments to the distribution of work between specialized scientific institutes. Regardless of whether this is carried out on behalf of the state, commercial structures or even enthusiasts, but planning the development of a field of knowledge, management scientific research- this is a modern reality.
The purpose of this work is not only to set up a local experiment, but also to attempt to illustrate modern technology scientific organization at the simplest level.
The first thoughts that precede the actual work are usually recorded in free form; historically, this happens on napkins. However, in modern science This form of presentation is called mind mapping - literally “scheme of thinking.” It is a diagram into which everything fits in the form of geometric shapes. 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, such diversity allows room 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 concepts elementary physics will help explain the features of flight, and may also allow us to formulate general design principles.
Preliminary collection of information showed that the area is not as simple as it seemed at first. Much help came from the research of Ken Blackburn, an aerospace engineer who holds four world records (including a current one) during gliding, which he set with airplanes of his own design.

In relation to the task at hand, the mind map looks like this:

This is a basic diagram representing the intended structure of the study.

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

Gliding is a special case of an aircraft descending without the participation of thrust generated by the engine. For non-motorized aircraft- gliders, as a special case - paper airplanes, planning is the main flight mode.
Planning is carried out due to weight and aerodynamic force balancing each other, 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 basic aerodynamic theory. Laminarity and turbulence. Reynolds number.

A more detailed understanding of flight is given by modern aerodynamic theory, which is based on a description of the behavior of different types of air flows, depending on the nature of the interaction of molecules. There are two main types of flows - laminar, when particles move along smooth and parallel curves, and turbulent, when they mix. As a rule, there are no situations with ideally laminar or purely turbulent flow; the interaction of both creates a real picture of the operation of the wing.
If we consider a specific object with finite characteristics - mass, geometric dimensions, then the properties of the flow 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 the viscosity of the liquid. How larger number, the less influence of viscosity.

Re= VLρ/η=VL/ν

V (speed)
L (size specification)
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 airplanes, this means that air viscosity plays a much more significant role, resulting in increased drag and decreased lift.

4. How a regular and flat wing work.

From the point of view of elementary physics, a flat wing is a plate located at an angle to the moving air flow. The air is “thrown back” at a downward angle, creating an opposing force. This is the total aerodynamic force, which can be represented in the form of two forces - lift and drag. This interaction is easily explained on the basis of Newton's third law. Classic example flat wing-reflector - kite.

The behavior of a conventional (plane-convex) aerodynamic surface is explained by classical aerodynamics as the appearance of lift due to the difference in the velocities of flow fragments and, accordingly, the difference in pressure from below and above the wing.

A flat paper wing in the flow creates a vortex zone at the 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 the list of 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 a turbulent flow becomes laminar due to the interaction of layers of air. Above the wing of a paper airplane it is up to 1 centimeter.

5. Review of three aircraft designs

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

Model No. 1. The most common and well-known design. As a rule, most people imagine exactly this when they hear the expression “paper plane.”

Model No. 2. “Arrow” or “Spear”. A distinctive model with a sharp wing angle and expected high speed.

Model No. 3. Model with a high aspect ratio wing. Special design, assembled along the wide side of the sheet. It is assumed that it has good aerodynamic properties due to the high aspect ratio wing.

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

6. Sets of characteristics, why they are.

To obtain characteristic parameters for each design, you need to actually determine these parameters. The mass of all aircraft is the same - 5 grams. It is quite simple to measure the gliding speed and angle for each structure. The ratio of the height difference and the corresponding range will give us the aerodynamic quality, essentially the same glide angle.
It is of interest to measure the lift and drag forces at different angles of attack of the wing, and the nature of their changes at boundary conditions. This will allow the structures to be characterized based on numerical parameters.
Separately, you can analyze the geometric parameters of paper airplanes - the position of the aerodynamic center and center of gravity for different wing shapes.
By visualizing flows, one can achieve a visual representation of the processes occurring in the boundary layers of air near aerodynamic surfaces.

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

On average, the speed of an 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 of 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 pipe of limited dimensions.
Consequently, we are not bothered 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 cross-section of 300x200 mm and a flow speed of up to 8 m/s, we will need a fan with a capacity of at least 1000 cubic meters/hour. To change the flow speed, you need an engine speed controller, and to measure it, an anemometer with appropriate accuracy. The speed meter does not have to be digital; it is quite possible to get by with a deflectable plate with an angle graduation or a liquid anemometer, which has greater accuracy.

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

9. Photos of the wind tunnel. Review of pipe characteristics, aerodynamic balances.

Reynolds number for pipe:

Re = VLρ/η = VL/ν

V (speed) = 5m/s
L (characteristic)= 250mm = 0.25m
ν (coefficient (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 was better to develop an appropriate fastening scheme with markings.

10. Experimental results.

11. Relationships between curves for three models.

Model No. 2.
The 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 increase enough and the plane really flies like a spear. Additionally, it does not stabilize properly in flight.

Model No. 3.
A representative of the “engineering” school, the model was conceived with special characteristics. High aspect ratio wings actually work better, but the drag increases very quickly - the plane flies slowly and does not tolerate acceleration. To compensate for the insufficient rigidity of the paper, numerous folds are used in the toe of the wing, which also increases resistance. However, the model is very impressive and flies well.

12. Some results on vortex visualization

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

Formation of flow at the leading edge of the wing.

Turbulent “tail”.

Flows can also be examined using short threads glued to the wing, or 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-breaking ones, also have such wings. However, paper airplanes have technological limitations and their wings are less than optimal.
To analyze the relationship between the geometry of models and their flight characteristics, it is necessary to reduce a complex shape to a rectangular analogue using the area transfer method. Computer programs that allow you to present different models in a universal form cope best with this. After the transformations, the description will be reduced to basic parameters - span, chord length, aerodynamic center.

The mutual relationship between 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 airplane with rectangular wings is at a distance of one in four from nose to tail, for an airplane with delta wings it is at one half (the so-called neutral point).

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

Based on the curves for lift and drag forces, it is possible to find an energetically favorable flight mode with the least losses. This is certainly important for long-haul airliners, but it can also be useful in paper aviation. By slightly modernizing the airplane (bending the edges, redistributing the weight) you can achieve best characteristics flight or vice versa, transfer the flight to critical mode.
Generally speaking, paper airplanes do not change their 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 bend 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 plane will maintain the same speed. The more stable the plane, the higher the speed, like model #2. But, this tendency must be limited - lift must be used, so the best paper airplanes, for the most part, have neutral stability, this best combination qualities
However, established regimes are not always the best. The world record for longest flight duration was set using very specific tactics. Firstly, the airplane is launched in a vertical straight line; it is simply thrown to its maximum height. Secondly, after stabilization at the top point due to relative position center of gravity and effective wing area, the airplane itself must go into normal flight. Thirdly, the weight distribution of the airplane is not normal - its front part is underloaded, so 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 nose-downs and, falling, accelerates with a jerk, but again slows down and freezes. Such oscillations (pitching) are smoothed out due to inertia at the fading points and ultimately total time being in the air more than normal uniform gliding.

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

It is assumed that having determined the main parameters of a paper airplane, their relationship and thereby completing the analysis stage, one can move on to the task of synthesis - creating a new design based on the necessary requirements. Empirically, amateurs all over the world do just that; 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 carrying out 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 region.

17. Return to mind map. Level of development. Questions raised and options for further development of research.

Taking into account the work done, we can add coloring to the mind map indicating the completion of the assigned tasks. Green indicates items that are at a satisfactory level, light green indicates issues that have some limitations, yellow indicates areas that have been touched upon but not adequately developed, and red indicates promising areas that require additional research.

18. Conclusion.

As a result of the work, the theoretical basis for the flight of paper airplanes was studied, experiments were planned and carried out, which made it possible to determine the numerical parameters for different designs and the general relationships between them. Complex flight mechanisms are also touched upon, from the point of view of modern aerodynamics.
The main parameters affecting the flight are described and comprehensive recommendations are given.
In the general part, an attempt was made to systematize the field of knowledge based on a 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. - Cap. from the screen. - Yaz. English

2. To Schuette. 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. Editorial office of technical and theoretical literature, 1938. - 208 p.

3. Stakhursky A. For skilled hands: Tabletop 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,: DOSAAF USSR Publishing House, 1982. - 160 p.

5. A.L. Stasenko. Physics of flight. - M: Science. Main editorial office of physical and mathematical literature, 1988, - 144 p.