How to calculate the wing. Calculation of the wing sugar of an aircraft model with a curved contour. Calculation of a wing of high aspect ratio

The wingspan of an aircraft at the design stage is determined by the load on the wingspan. The fact is that the flight performance of an aircraft is far from the least dependent on the wing span, and with the available takeoff weight, on the load on the span:

Where
G - weight;
- wingspan.

N.E. Zhukovsky's theorem on the lift of a wing, derived in 1906, looks like a formula as follows:

Where
Y is the lift of the wing;
- air density;
V - flight speed;
Г - speed circulation.

When analyzing the development of aircraft, the dependence is used:

,(3)

Where
N - engine power;
- efficiency screw.

In the case of steady horizontal flight, the lift of the wing is balanced by the weight of the aircraft:

Taking into account (1) and (4), formulas (2) and (3) will appear in the following form:

,(5)
.(6)

Formula (5) shows the existence of a relationship between the swing load and the air density and flight speed, but due to the complexity of determining the circulation, it is not very suitable for practical calculations at the design stage. Formula (6), with its simplicity in practice, gives very large errors, since the initial dependence (3) assumes a rigid connection between the lift of the wing and the inductive resistance, and it is also assumed that the flight occurs at ground level.

If we proceed, as mentioned above, from the fact that in steady horizontal flight the lift is equal to the weight (4), and the drag force is balanced by the propeller thrust:

Where
X - resistance force;
P is the thrust of the power plant,

then, having carried out simple transformations (the full calculation of which will be omitted due to the small volume of the journal article), we obtain a formula that allows us to determine the load on the effective wing span of an aircraft, taking into account the flight mode, the degree of engine throttling, and efficiency. propeller, speed and altitude in the form of the following relationship:

,(8)

Where
- load on the effective wingspan of the aircraft (kg / m);
- flight mode coefficient;
- coefficient of throttling of the engine;
- estimated engine power (hp); - air density at the design flight altitude;
- engine altitude coefficient;
V - flight speed (km / h).

In turn, the odds look like this:

,(9) ,(10)

Where
- coefficient of the shape of the wing in the plan;
- drag coefficient at zero lift;
- coefficient of inductive resistance;
- actual engine power (hp);
- rated engine power (hp).

With takeoff weight and effective wingspan, the effective span load is:

The loss of engine power in the assessment is taken into account as follows:

,(12)

Where
- efficiency screw (see above);
- efficiency reducer.

At the aircraft design stage, the coefficients Cx and Cxi are, as a rule, unknown, but due to the properties of the inductive resistance, the polar of the aircraft is close to a quadratic parabola (and the calculated polar, i.e., obtained not as a result of blowing, is a parabola). For a quadratic parabola, the following relations are true (see Fig. 1):

Economic cruise flight, point 1;
- mode of maximum aerodynamic quality (Kmax), point 2;
- economic flight mode, point 3.

In the maximum quality mode, as is known, the greatest flight range is ensured. Economy mode allows you to reach the maximum flight duration. The economic cruise mode is most suitable for commercial transport operations. The coefficient values are shown below:

0 - for an elliptical wing in plan;
= 0.002 ... 0.005 - for a wing with a center section;
= 0.02 ... 0.08 - for a trapezoidal wing;
= 0.05 ... 0.12 - for a rectangular wing.
The efficiency of the screw can be taken as follows:
= 0.65 ... 0.75 - for a fixed pitch propeller (FPP);
= 0.7 ... 0.85 - for a variable pitch propeller (VSP).
Reducer efficiency lies within:
= 0.94 ..., 0.96 - for V-belt transmission;
= 0.97 ... 0.98 - for gear transmission.
In the absence of a gearbox in the power plant of the ALS:
= 1;
= 0,55...0,65.

Engine power decreases with increasing altitude. The power drop factor of low-rise engines, as well as the air density values depending on the flight altitude, are given in Table 1

Table 1

Power drop ratio of low-rise reciprocating engine
depending on the flight altitude

The engine throttling factor can be varied in a wide range and a specific value is chosen by the designer.

After using formula (8), due to which, in fact, this article is being written, the load on the effective swing is determined, with a known take-off weight from (11), you can easily obtain the value of the effective swing:

It remains for us to determine the geometric wingspan from the available effective span. Below are formulas that allow us to do this for the case of a classical monoplane. If you have the task of designing an aircraft (or ultralight aircraft) of another layout scheme, then you, dear reader, should take into account the peculiarities of the scheme you have chosen. Although for an initial, rough estimate, you can use this technique.

,(14)

Where
S - wing area in plan (sq. M);
Si is the total area in the plan occupied by the ventral and engine nacelles of the aircraft (sq. M).
In turn:

,(15)

Where
- the area of the ventral part of the wing (m2);
Si is the wing area occupied by the engine nacelle (m2), see Fig. 2.

As the statistics of the ULV meetings shows, "home-made designers", due to their technological simplicity, often use a rectangular wing.

For such a wing, formula (14) will appear in the form:

,(16)

Where
- the wingspan occupied by the ventral and engine nacelles.
The final solution to equation (16) will be the expression:

,(17)

which can be solved using Bradis tables if you do not have a calculator at hand. Quite good results are given by an approximate dependence:

,(18)

but it must be remembered that this formula can be used only at the very initial stage, the so-called "stage of zero approximation".

If the wing shape differs from rectangular, the solution of dependence (14) presents certain difficulties, which in practice can be avoided only by using computer technology. If it is impossible to involve a computer in work (there is no computer itself or the corresponding software), you can use formula (17) or (18), and then, by the method of successive approximations, determine the geometric wing span using formula (14), specifying Si at each step. Regarding the issue of approximations, by right of the most "venerable" specialist in the field of formula (8), I recommend using it as a design one, with subsequent refinement of the range based on the results of blowdowns or verification calculations for an aircraft with a takeoff weight of more than 500 ... 600 kg. For an aircraft with a takeoff weight of less than 500 kg, this formula may turn out to be the only way to determine the wing span, since the wing design techniques described in the books "Aircraft Design" by N.A.Fomin or S.M. Eger are commensurate in their labor intensity with the labor costs of manufacturing an ultralight. (and, as a rule, "too tough" for a self-made individual).

At this point, dear reader, we finish the description of the formula (8) itself, as well as the additions necessary for its use, and now, according to the already established tradition, we will consider an example. For calculation data, see table. 2.

table 2

Parameter	Dimension	Airplane number 1	Airplane number 2

The calculation itself with explanations is given in table. 3.

Table 3

Parameter	Dimension	Airplane number 1	Airplane number 2	Note
				Cruising mode
				according to the formula (9)
				according to the formula (12)
				according to the formula (8)
				according to the formula (13)
				according to the formula (14)

The obtained calculation results are comparable with the actually existing machines in table. four.

Table 4

The initial data for the calculation (Table 2) were taken from and for ANT-37 and TsKB-26, respectively. It should be reported that these aircraft participated in the competition of the Red Army Air Force in 1936 for a long-range bomber, both were equipped with fixed pitch propellers and had two low-rise M-85 engines, and for their time were quite advanced technology.

From personal experience of communicating with "self-made" I know that many of them like to read magazines and other publications, often with the aim of finding some ready-to-use technical solution, therefore, should be given in Table. 5 is a final example, which also takes into account the specifics of the "ANON" magazine.

Basic data F16

Table 1

1. Determination of the lateral force and bending moment in the design wing section

1.1 Determination of wing lift

The amount of lift of the wing is determined by the formula:

where is the flight weight of the aircraft;

Operational overload;

Safety factor;

1.2 Diagram of the air load on the wing

We divide the wing into 10 conditional sections, and measure the lengths of the obtained chords bi in the drawing (see Appendix), then we substitute them into formulas (3), (4), (5). The calculations themselves were made in the Microsoft Excel software application (table 2.).

The distribution of the air load on the wing in the first approximation is taken proportional to the chords and is calculated by the formula:

where is the value of the linear air load on the wing;

The size of the chord of the section;

1.3 Wing mass load diagram

The linear load on the wing from its own weight is determined by the formula:

where is the weight of the wing.

1.4 Diagram of the load from the mass of fuel

The value of the linear load on the wing from the weight of the fuel is determined by the formula:

where is the fuel weight.

1.5 The summary diagram of the linear load on the wing

The total linear load diagram was obtained by adding the linear load diagrams on the wing from the air load, the loads from the wing mass and the fuel mass.

1.6 Shear force diagram

The transverse force diagram was obtained by graphically integrating the diagram of the total linear load on the wing, then local loads from the units located on the wing are added to it - in this case, there are no aggregates on the wing.

1.7 Bending moment diagram

The diagram of bending moments was obtained by the method of graphical integration of the shear force diagram.

Table 1.2

1.8 The values of the shear force and bending moment in the design section of the wing

The values of the shear force and bending moment in the design wing section - in the zone - were taken from the obtained diagrams of the shear force and bending moment and are:

2. Design calculation of the wing in the zone

2.1 Initial data

lifting wing cross-section planking

Chord length in a given section:.

The amount of effort in a given section:; ...

The fraction of the bending moment perceived by the side members: w = 50%.

Power element material: D16T,.

Spar positions: 1st; 2nd.

Reduction coefficients of belts of side members, stringers and skins:

when working in tension:; ; ;

when working in compression:; ; ...

Number of stringers:, step h = 0.098m.

2.2 Calculation of the basic dimensions of the section

2.3 Replacement of the caisson part of the wing with a rectangular section of two chords and two walls

2.4 Replacing the action with the action of a pair of forces and

2.5 Sizing of the strength members of the lower chord

2.5.1 Determination of the dimensions of the lower chords of the side members

2.5.2 Shape and dimensions of the lower chords of the side members

2.5.3 Selection of stringers

Profile 410018, is suitable.

2.5.4 Determination of sheathing thickness

Sheathing with a thickness of 0.8 mm is suitable.

2.6 Sizing of the strength elements of the upper chord

2.6.1 Determination of the dimensions of the upper chords of the side members

2.6.2 Shape and dimensions of the upper chords of the side members

2.6.3 Selection of stringers

Profile 710022 is suitable,.

2.6.4 Determination of sheathing thickness

Sheathing with a thickness of 1 mm is suitable.

2.7 Wall thicknesses of side members

3. Calculation of the dimensions of the connecting bolts OCHK wing with center section

3.1 Calculation of bolts for side members

Longitudinal force in the cross section of the OCHK connection with the center section:

Since the side members (upper) perceive half of the load coming to the upper chord, and the number of bolts is 4 (see appendix), the bolt diameter is determined from the condition of strength with respect to normal stresses.

Suppose bolts made of steel 30HGSA - allowable stress (safety factor is taken into account in clause 1.1), where.

3.2 Calculation of Sheathing Fitting Bolts

Since the sheathing takes half of the load coming to the upper chord, and the number of bolts is 7 (see Appendix), pitch 90mm, then the bolt diameter is determined from the condition of strength with respect to normal stresses.

What influences the rise of an airplane into the air?

Many people are afraid to fly in airplanes, because they do not know how it flies, what determines its speed, how high it rises, and much more. After studying this, some change their minds. How does the plane go up? Let's figure it out.

Looking closely at the wing of the aircraft, you can see that it is not flat. The lower part is smooth and the upper part is convex. Due to this, when the speed of the aircraft increases, the air pressure on its wing changes. Since the flow rate is low at the bottom, the pressure increases. And as the speed increases at the top, the pressure decreases. Due to such changes, the plane is pulled up. This difference is called the lift of an aircraft wing. This principle was formulated by Nikolai Zhukovsky at the beginning of the 20th century. In the initial attempts to send the ship into the air, this Zhukovsky principle was applied. Current ships fly at a speed of 180-250 km / h.

Takeoff speed

When the liner picks up speed, it rises directly upward. The take-off speed is different, it depends on the size of the aircraft. Another important influence is the configuration of its wings. For example, the famous Tu-154 flies at a speed of 215 km / h, and Boeing 747 - 270 km / h. Slightly lower flight speed of Airbus A 380-267 km / h.

If we take average data, then today's airliners fly at a speed of 230-240 km / h. However, speed can vary due to wind acceleration, liner weight, weather, runway, and other factors.

Landing speed

It should be noted that the landing speed is also variable, as well as the takeoff speed. It can vary depending on what model of the airliner, what area it is, wind direction, etc. But if we take average data, then the plane lands at an average speed 220-240 km / h... It is noteworthy that the speed in the air is calculated relative to the air, not the ground.

Airplane flight altitude

Many are interested in the question: what is the flight altitude of airliners? It must be said that in this case there are no specific data either. The height may vary. If we take average figures, then passenger airliners fly at an altitude of 5-10 thousand meters. Large passenger planes fly at a higher altitude - 9-13 thousand meters. If the plane climbs above 12 thousand meters, then it starts to fail. Due to the thin air, there is no normal lifting force and there is a lack of oxygen. That is why you should not fly so high, as there is a threat of a plane crash. Often, planes do not rise above 9 thousand meters. It is noteworthy that too low an altitude negatively affects the flight. For example, you cannot fly below 5 thousand meters, as there is a threat of a lack of oxygen, as a result of which the power of the engines decreases.

What can cause the plane flight to be canceled?

low visibility when there is no guarantee that the pilot will be able to land the aircraft in the desired location. In this case, the liner may simply not see the runway, which may lead to an accident;
technical condition of the airport. It happens that some equipment at the airport has stopped working or there are malfunctions in the operation of one or another system, due to which the flight may be postponed to another time;
the state of the pilot himself. It happened more than once that the pilot could not control the flight at the right time and there was a need for a replacement. It's no secret that there are always two pilots on the liner. That is why it takes a certain amount of time to find a co-pilot. Thus, the flight may be slightly delayed.

Only with full preparation and under favorable meteorological conditions can the aircraft be sent to flight. The decision to send is taken by the aircraft commander. He is solely responsible for ensuring that the aircraft operates safely.

In contact with

Ministry of General Education of the Russian Federation

Novosibirsk State Technical University

DESIGN AND CALCULATION

ELEMENTS OF AIRCRAFT AIRCRAFT FOR STRENGTH.

WING.

Methodical instructions for the implementation of coursework

and graduation projects for students

III-V courses (specialty 1301)

Faculty of Aircraft

Novosibirsk

Compiled by V.A. Burns Candidate of Engineering Sciences,

E.G. Podruzhin Candidate of Engineering Sciences,

B.K. Smirnov, technical sciences.

Reviewer: V.L. Prisekin, Doctor of Technical Sciences, prof.

The work was done at the department

aircraft and helicopter construction

Novosibirsk State

Technical University, 2000

TASKS, CONTENT AND ORDER OF PERFORMANCE

COURSE PROJECT

The purpose of the course project is a deeper and more detailed acquaintance of students with the design features of the aircraft and mastering the practical methods of calculating the strength of the elements of the airframe of the aircraft.

The assignment for the course project provides for the solution of the following tasks:

Selection of an aircraft prototype according to its characteristics, which are the initial data for the project.

Determination of the mass and geometric characteristics of the aircraft required for calculating the loads, according to the selected prototype, wing layout.

Assignment of operational overload and safety factor for a given design case.

Determination of loads acting on the wing when the aircraft performs a given maneuver, plotting diagrams.

the choice of the type of structural-power scheme of the wing (spar, caisson, monoblock) and the selection of section parameters (the distance from the wing root to the design section is set by the teacher).

Calculation of the wing section for bending.

Calculation of the wing shear section.

torsional wing section calculation.

Checking the wing skin and side member walls for strength and stability.

Strength calculation of wing elements (as instructed by the teacher).

Notes.

All calculations are carried out on a PC, a printout of the calculation results is inserted into the explanatory note.

The required amount of calculations from the listed sections of the project is assigned by the teacher individually.

The settlement and explanatory note is drawn up in accordance with GOST 2.105-79.

The course project is defended publicly, by all students of the group at the same time.

Legend:

L - wingspan;

S is the wing area;

 - wing lengthening;

 - narrowing of the wing;

The relative thickness of the wing section profile;

The relative thickness of the profile, respectively, at the root and

wing end sections;

 0.25 - sweep of the wing along the line of chord quarters;

G is the takeoff weight of the aircraft;

G cr. - wing weight;

b - the current chord of the wing;

b root - root chord of the wing;

b conc. - terminal chord of the wing;

f is the safety factor;

- maximum operational overload in the direction of the Y axis;

- relative circulation of a straight flat wing;

- relative wing circulation taking into account sweep;

q aer - linear aerodynamic load on the wing;

Q aer - shearing force in the wing section from aerodynamic load;

M aer - moment of aerodynamic load in the wing section;

Q cr - shearing force from the weight of the wing;

M cr - moment of force of weight in the wing section;

G fuel is the weight of the fuel in the wing tanks;

Q fuel - cutting force from the weight of the fuel tanks;

G agr - weight of aggregates and concentrated loads;

M fuel - moment of forces of weight of fuel tanks;

Q sosr - shearing force from concentrated masses;

M sosr - moment of concentrated inertial forces;

N - tensile force acting in the wing panel;

 - sheathing thickness;

H - spar height;

e is the pitch of the stringers;

a is the distance between the ribs;

n is the number of stringers;

F page - cross-sectional area of the stringer;

F ln - cross-sectional area of the side member flange;

 st - spar wall thickness;

 in - stress of the ultimate strength of the material;

 cr, cr - buckling stresses, respectively, in compression and shear;

E - modulus of longitudinal elasticity;

G - shear modulus;

 - Poisson's ratio.

PROCEDURE FOR STRENGTH CALCULATION ON A PC

The aircraft wing is calculated on a PC. The calculation is divided into several stages. At the first stage, the loads acting on the wing are determined. The information required for this is entered into the PC in a dialogue mode in response to requests that appear on the computer screen after the NAGR.EXE program is launched. In the future, a data file NAGR.DAT is created, where the entered information is entered, and in subsequent calculations, you can change the initial data in the data file.

Before using the NAGR.EXE program, it is necessary to prepare the initial data for the calculation of loads, which includes the choice of the aircraft prototype, the establishment of the mass and geometric characteristics of the aircraft, the wing layout, the assignment of the operational overload values and the safety factor

When calculating the loads, the following parameters are entered into the PC (formatless input):

root and end chord [m];

wingspan [m];

safety factor [b / r];

takeoff weight of the aircraft [t];

operational overload [b / r];

relative circulation (11 values from Table 1) [b / r];

sweep angle along the wing chord quarter line [deg];

relative thickness of the profile in the root and end sections [b / r];

wing weight [t];

the number of fuel tanks in the wing [b / r];

specific weight of fuel [t / m 3];

relative coordinates of the initial and end chords of the tanks [b / r];

initial chords of tanks [m];

end chords of tanks [m];

distance from the conventional axis (Fig. 1) to the central point line. fuel in the root and end sections of the wing [m];

number of units [b / r];

aggregate weight [t];

relative coordinates of aggregates [b / r];

distance from the conventional axis to the central point. aggregates [m];

distance from the conventional axis to the line c. etc. in the root and end sections of the wing [m];

distance from the conventional axis to the line c. f. in the root and end sections of the wing [m];

distance from the conventional axis to the line c. m. in the root and end sections of the wing [m];

The results of calculations using the NAGR.EXE program are entered into the NAGR.DAT file, which contains the data entered at the first stage with appropriate comments, and also displays the wing area, its narrowing, elongation, operational and breaking loads acting in the wing, and tables calculated by the program. loads acting in the wing from various force factors:

aerodynamic load table (Table 1);

table of loads from the weight of the wing structure (Table 2);

table of loads from the weight of fuel tanks (table 3);

table of loads from concentrated forces (table 4)

table of total shearing forces and bending moments from all force factors (Table 5);

table of moments of all forces acting on the wing, relative to the z-axis conv. (Table 6);

a table of bending and torque moments acting in the sections of the normal axis of the wing stiffness (Table 7);

At the second stage, using the REDUC.EXE program, the wing bending is calculated by the method of reduction coefficients. The preparation of the initial data for the REDUC.EXE program consists in the choice of the type of the wing power scheme, the selection of the design section parameters (see paragraphs 5.1-5.3). The method for calculating the wing section for bending by the method of reduction coefficients is described in clause 6.1.

The initial data for the REDUC.EXE program (for the program, the input of the initial data is implemented in two modes - dialog and file) are:

number of stringers on the upper wing panel [b / r];

number of stringers on the lower wing panel [b / r];

the height and thickness of the free flanges of the stringers in the compressed (top) wing panel [cm];

cross-sectional area of stringers [cm 2];

moments of inertia of the stringers of the top panel [see 4];

x, y coordinates of the stringers' centers of gravity [cm];

moduli of elasticity of materials of stringers and spars [kg / cm 2];

skin thickness on the upper and lower wing panels [cm];

number of side members [b / r];

cross-sectional area of the side members [cm 2];

coordinates x, y of the centers of gravity of the flanges of the side members [cm];

spar heights [cm];

tensile strength stresses for materials of spars and stringers [kg / cm 2];

bending moment [kgcm];

rib step [cm];

pitch of stringers in compressed and stretched wing panels [cm];

The calculation results of the REDUC.EXE program are tables placed in the REZ.DAT file, in which the following values are given for each iteration:

stringer and spar numbers;

cross-sectional areas of stringers and spars;

total cross-sectional area of reinforcing elements with attached skin;

the values of the reduction factors;

critical stresses in stringers with general buckling;

critical stresses in stringers with local buckling;

allowable stresses in stringers and side members;

actual stresses in stringers and spars.

In addition to the above information, two data files CORD.DAT and DAN.DAT are generated. In the first of these files, the x, y coordinates of the centers of gravity of the stringers are entered, and in the second the rest of the information entered in the dialog mode when the program is first accessed, which makes it possible to correct the entered information more efficiently during further work with the program.

At the third stage, the wing cross-section is calculated for shear and torsion. The method for calculating the wing cross-section for shear and torsion is described in clauses 7.1, 8.1, 8.2. Programs for these calculations are compiled independently.

At the fourth stage, a conclusion on the strength of the wing is prepared. The preparation of this opinion is carried out in accordance with clause 9.

At the fifth stage, the design and strength calculation of the wing element is carried out. The element specified by the teacher is subject to design.

Strength calculation of a wing element implies the development of a design scheme; determination of loads acting on a given element; calculation of stresses; selection of the characteristics of an element based on the condition of its strength.

METHODOLOGY OF SOLVING THE PROBLEMS OF THE COURSE PROJECT

I... Selecting a prototype aircraft based on its characteristics

The initial data for the project are the following characteristics: wing span L, wing area S, wing taper η, relative airfoil thickness in the root and end sections of the wing, wing sweep along the chord quarter line χ 0.25, aircraft take-off weight G, design case (A , A ′, B, etc.). According to the geometric and mass characteristics of the aircraft, its prototype is determined, for example, by work.

2. Establishment of mass and geometric characteristics of the aircraft, wing layout

For the found prototype, the features of the wing layout (the number and location of engines, chassis, fuel tanks, controls, mechanization, concentrated loads on the external suspension nodes), the weight of the fuel and units located on the wing are determined. If the mass characteristics of the units cannot be found in the literature, then their values are determined (in agreement with the teacher) using statistical data for the type of aircraft under consideration.

Using the found geometric characteristics, the wing is sketched on a scale of 1: 5, 1: 6, 1:10, 1:25, and its layout is performed (placement of spars, fuel tanks, chassis, propulsion systems, various cargoes, etc.). The geometric characteristics of the wing required for its construction are determined by the formulas:

, ,

The sweep angle of the wing χ is given along the line passing through the quarter-chords (Fig. 1). On a wing drawn to scale, it is necessary to draw a line of centers of gravity, a line passing through quarter chords, a line of centers of pressure, conventional coordinate axes and divide the wing into sections;. Here .

3. Assignment of operational overload and safety factor

The value of the operational overload and the safety factor for a given aircraft and design case are assigned using works and lecture material. In the text of the explanatory note, it is necessary to justify the choice of the numerical values of these parameters. Depending on the degree of required maneuverability, all aircraft are divided into three classes

Class A - maneuverable airplanes, which include airplanes performing abrupt maneuvers, such as fighters (). Short-term overload for such aircraft can reach 10-11 units.

Class B - airplanes with limited maneuverability, which maneuver mainly in the horizontal plane ().

Class B - non-maneuverable aircraft that do not perform any abrupt maneuvers ().

Transport and passenger aircraft are classified as class B, bombers are classified as class B or C. Fighters are classified as class A.

All variety of loads acting on an aircraft is reduced to design modes or design cases, which are summarized in a special document. Designated cases are designated by letters of the Latin alphabet with indices. Table 1 shows some design cases of aircraft loading in flight.

The safety factor f is assigned from 1.5 to 2.0 depending on the duration of the load and its repeatability during operation.

The maximum operational overload during the maneuver of the aircraft with the take-off and landing mechanization retracted is determined as follows

at m 8000 kg

at m  27500 kg

For intermediate values of the flight mass, the overload is determined by the formula

4

... Determination of loads acting on the wing

The wing structure is calculated based on breaking loads

4.1 Determination of aerodynamic loads

The aerodynamic load is distributed over the wingspan according to the change in relative circulation
(when calculating
the influence of the fuselage and engine nacelles can be neglected). The values should be taken from the work, where they are set in the form of graphs or tables for various wing sections depending on its characteristics (aspect ratio, tapering, center section length, etc.). You can use the data given in table 2.

table 2

Cross-sectional distribution of circulation for trapezoidal wings

The calculated linear aerodynamic load (the direction q of the aerial. Can be approximately considered perpendicular to the plane of the chords of the wing) for a flat wing at

(1)

For fenders with arrow visibility

, (2)

(3)

When sweep is taken into account, wing twist is not taken into account. For wings with a sweep χ ›35 о, formula (3) gives an error in the values of circulation up to 20%.

The calculation method for non-planar wings of any shape is described in the work.

According to the diagram of distributed loads q ae, calculated for 12 sections by formulas (1) or (2), diagrams of Q ae are plotted sequentially. and M aer. ... Using the known differential dependences, we find

Integration is carried out numerically using the trapezoidal method (Fig. 2). Based on the results of calculations, diagrams of bending moments and shearing forces are plotted.

4.2 Determination of mass and inertial forces

4.2.1 Determination of the distributed forces from the dead weight of the wing structure. The distribution of mass forces over the wingspan with a slight error can be considered proportional to the aerodynamic load.

or proportionally to chords

The linear mass load is applied along the line of the centers of gravity of the sections, usually located at 40-50% of the chord from the nose. By analogy with aerodynamic forces, Q cr are determined. and M cr. ... Diagrams are plotted based on the results of the calculations.

4.2.2 Determination of the distributed mass forces from the weight of the fuel tanks. Distributed linear mass load from fuel tanks

where γ is the specific gravity of the fuel; B - the distance between the side members, which are the walls of the tank (Fig. 3).

The relative thickness of the profile in the section

4.2.3 Construction of diagrams from concentrated forces. Concentrated inertial forces from units and weights located in the wing and attached to the wing are applied at their centers of gravity and are taken parallel to the aerodynamic forces. Calculated concentrated load

The results are presented in the form of plots Q sop. and M sat. ... The total diagrams Q Σ and M xΣ of all forces applied to the wing are plotted, taking into account their signs:

4.3 Calculation of the moments acting with respect to the conditional axis

4.3.1 Definition
from aerodynamic forces. Aerodynamic forces act along the line of centers of pressure, the position of which is assumed to be known. Having drawn the wing in plan, we mark the position of ΔQ air i on the line of pressure centers and, according to the drawing, determine h air i (Fig. 5).

Next, we calculate
and
by formulas

and build a plot.

4.3.2. Determination from the distributed mass forces of the wing (and
). The mass forces distributed over the wing span act along the line of the centers of gravity of its structure (see Fig. 5).

Where
- the calculated concentrated force from the weight of the wing part between two adjacent sections;
- shoulder from the point of application of force to the axis
... The values are calculated similarly
... According to the calculations, diagrams and are plotted.

4.3.3 Definition
from concentrated forces.

where, the estimated weight of each unit or load;
- the distance from the center of gravity of each unit or load to the axle.

After calculating
the total moment is determined
from all the forces acting on the wing, and the diagram is constructed (meaning the algebraic sum).

4.4 Determination of design values
and
for a given wing section

To determine and follows:

Find the approximate position of the center of stiffness (Fig. 6)

Where
- the height of the i-th spar; - distance from the selected pole A to the wall of the i-th spar; m is the number of side members;

Calculate the moment about the Z-axis passing through the approximate position of the center of rigidity and parallel to the Z-axis conv.

;

For a swept wing, make a sweep correction (Fig. 7) according to the formulas

5. The choice of the structural-power scheme of the wing, selection of parameters

design section

5.1 Choice of structural and structural wing scheme

The type of structural-power wing scheme is selected using the recommendations set out in the lectures and works.

5.2 Selection of the profile of the design section of the wing

The relative thickness of the profile of the design section is determined by the formula (4). A symmetrical (for simplicity) profile is selected from the work, corresponding in thickness the considered type of aircraft and compiled table 3. The selected profile is drawn on graph paper on a scale (1:10, 1:25). If the profile of the required thickness is absent in the reference book, you can take the profile closest in thickness from the reference book and recalculate all the data using the formula

Table 3.

where y is the calculated value of the ordinate;
- tabular value of the ordinate;
- tabular value of the relative thickness of the wing profile.

For a swept wing, a sweep correction should be made according to the formulas

5.3 Selection of section parameters (approximate calculation)

5.3.1 Determination of normal forces acting on the wing panel

For subsequent calculations, we will assume that the directions
, and
in the design section (Fig. 8). The side member belts and stringers with attached sheathing absorb the bending moment. The forces loading the panels can be determined from the expression

Where
; F - cross-sectional area of the wing, limited by the extreme spars; B is the distance between the outer side members; (fig. 9).

For a stretched panel, take the force N with a plus sign, for a compressed panel - with a minus sign.

Based on statistical data, the calculation should take the forces perceived by the side member flanges -
,
.

The values of the coefficients , ,  are given in Table 4 and depend on the wing type.

Table 4.

5.3.2. Determination of the thickness of the skin. The thickness of the skin раст for the stretched zone is determined according to the 4th theory of strength:

Where - tensile strength of the skin material;  - coefficient, the value of which is given in Table 4. For a compressed zone, the thickness of the skin should be taken equal to
.

5.3.3 Determination of the pitch of stringers and ribs. Stringer step and ribs a are chosen so that the wing surface does not have unacceptable waviness.

To calculate the deflections of the skin, we consider it freely supported on stringers and ribs (Fig. 10). The greatest value of the deflection is achieved in the center of the plate under consideration:

Where
-specific wing loading; -cylindrical sheathing rigidity. The values of the coefficients d depending on
are given in the work. Usually this ratio is 3.

The distance between stringers and ribs should be chosen so that
.

Number of stringers in a compressed panel

Where - the length of the arch of the sheathing of the compressed panel.

The number of stringers in the stretched panel should be reduced by 20%. As noted above, the distance between the ribs
.

5.3.4 Determination of the cross-sectional area of stringers. Sectional area of the stringer in the compressed zone in the first approximation

Where
is the critical stress of stringers in the compressed zone (in the first approximation
).

Sectional area of stringers in the stretched zone

where is the tensile strength of the stringer material.

5.3.5 Determination of the cross-sectional area of the side members. The area of the flanges of the side members in the compressed zone

Where
- critical stress at loss of stability of the side member flange.
(the tensile strength of the spar material is taken).

The area of each flange of a two-spar wing is found from the conditions

, (5)

and for a three-spar wing

The area of the side members in the tension zone

where k is a coefficient that takes into account the weakening of the spar belts by fixing holes; with riveted connection k = 0.9 ÷ 0.95.

The area of each shelf is found similarly to the area in the compressed zone from conditions (5) or (6).

5.3.6 Determination of the wall thickness of the side members. We assume that the entire shearing force is perceived by the walls of the side members

Where is the force perceived by the wall of the i-th spar. For a three-spar wing (n = 3)

Where
- the height of the walls of the spars in the design section of the wing.

Wall thickness

. (7)

Here is the critical stress for the loss of stability of the wing spar wall from shear (Fig. 11). For calculations, all four sides of the wall should be taken freely supported:

Where
for a> , for a should be replaced in (8) by a, and in the formula for - on the
... Formula (8) is valid for

Substituting the values
from (8) to (7), we find the wall thickness of the i-th spar

6. Calculation of the wing section for bending

To calculate the wing section for bending, the profile of the calculated wing section is drawn, on which numbered stringers and spars are located (Fig. 12). Stringers should be placed in the nose and tail of the profile with a larger pitch than between the side members. The calculation of the wing section for bending is carried out by the method of reduction factors and successive approximations.

6.1 Procedure for calculating the first approximation

The reduced cross-sectional areas of longitudinal ribs (stringers, spar belts) with attached skin are determined in the first approximation

Where - the actual cross-sectional area of the i-th rib;
- attached sheathing area (- for a stretched panel,
- for a compressed panel); - reduction factor of the first approximation.

If the material of the flanges of the side members and stringers is different, then the reduction should be made to the same material through the reduction factor in the modulus of elasticity

Where - material module of the i-th element; - the modulus of the material to which the structure is reduced (as a rule, this is the material of the belt of the most loaded spar). Then

In the case of different materials of the belts of the side members and stringers, the formula (9) is replaced by
.

Determine the coordinates and centers of gravity of sections of longitudinal profile elements relative to arbitrarily selected axes and (fig. 12) and calculate the static moments of the elements
and
.

Determine the coordinates of the center of gravity of the section of the first approximation by the formulas

,
.

Draw axes through the found center of gravity and (axis it is convenient to choose parallel to the chord of the section) and determine the coordinates of the centers of gravity of all elements of the section relative to the new axes.

We calculate the moments of inertia (axial and centrifugal) of the reduced section relative to the axes and:

, ,
.

Determine the angle of rotation of the main central axes of the section:

If the angle α is more than 5 о, then the axes and should be rotated by this angle (the positive value of the angle corresponds to the clockwise rotation of the axes) and then calculate with respect to the main central axes. In order to simplify the calculation, it is recommended to calculate the angle α only when calculating the last approximation. Usually, if the axis is chosen parallel to the chord of the section, the angle α turns out to be insignificant and can be neglected.

Determine the stresses in the elements of the section in the first approximation

Received voltages compare with
and
for the compressed panel and with
and - for a stretched panel.

6.2 Determination of critical stringer stresses

The critical stringer stress is calculated from the condition of the general and local forms of buckling. To calculate
the general form of buckling we use the expression

, (10)

Where
... Here
- critical stress calculated by Euler's formula:

(11)

Where - coefficient depending on the conditions of support of the ends of the stringer; - step of ribs; - flexibility of the stringer with attached sheathing; - radius of gyration relative to the central axis of the section.

In formula (11) under should be understood
, but for the sake of simplicity, the position of the main inertial axis is assumed to be the same as the x-axis.

In turn

where is the moment of inertia of the stringer with the attached skin relative to the x-axis (Fig. 13);
- cross-sectional area of the stringer with attached sheathing. The width of the attached sheathing is taken equal to 30 δ (Fig. 13).

Where
- moment of inertia of the attached skin relative to its own central axis x 1 (usually the values are small);
- the moment of inertia of the stringer relative to its own central axis x 2.

To calculate the local form of buckling, consider the buckling of a free stringer shelf as a plate hinged on three sides (Fig. 14). In fig. 14 denoted: a - the step of the ribs; b 1 - the height of the free stringer shelf (Fig. 13). For the considered plate
is calculated by asymptotic formula (10), in which

where k σ is a coefficient depending on the conditions of loading and support of the plate,  с is the thickness of the free flange of the stringer.

For the case under consideration

For comparison with the actual stresses obtained as a result of the reduction, the lower stress is chosen, found from the calculations of the general and local buckling.

In the process of reduction, it is necessary to pay attention to the following: if the stresses in the compressed flange of the spar turn out to be greater or equal to the destructive in any of the approximations, then the wing structure is not able to withstand the design load and must be strengthened. In this case, no further approximations should be made. If in any compressed stringer numbered "k" (with attached casing) the stress turns out to be less, then the reduction coefficient for it and in the subsequent approximation should be left the same; if in any compressed stringer (with attached casing) with the number "m" the voltage is greater
then, in the subsequent approximation, the reduction factor should be calculated by the formula

;

if there is tension in any stringer does not exceed, then the structure is clearly overweight and requires relief.

In the stretched zone, the reduction coefficients are refined in the process of successive approximations in the same way, but the calculated stresses are compared not with, but with .

As a result, we obtain new refined reduction coefficients of the subsequent approximation
... Next, we calculate the next approximation in the same order and again refine the reduction coefficients. The calculation continues until the reduction coefficients of the two subsequent approximations practically coincide (within 5%).

7. Calculation of the wing shear section

The calculation of the wing section for shear is carried out without taking into account the effect of torsion (the transverse force is considered to be applied at the center of the section stiffness, assuming that the walls of the spars and the skin work for the shear).

7.1 Calculation procedure

To calculate a multi-contour shear section, longitudinal cuts are made in the panels so that the contour becomes open. For the section of the wing, it is convenient to make cuts in the plane of the chords at the toe of the wing and in the walls of the spars (Fig. 15). In the places of the cuts, unknown closing linear tangential forces are applied.

Linear tangential forces in the skin of the panels, the wing sections are determined as the sum of the linear tangential forces
in an open loop and closing efforts. Efforts are determined by the formula

, (12)

Where
- design cutting force;
- the static moment of the area of a part of the section bounded by the 1st and (i-1) - m ribs (the accepted order of numbering of the ribs is obvious from Fig. 14);
- the main moment of inertia of the entire section, and the position of the center of gravity is taken from the last approximation of the calculation for bending.

In formula (12), the direction of the lateral force is considered positive if it coincides with the positive direction of the y-axis, i.e. up. The positive directions of shear force flows coincide with the clockwise direction of the origin of coordinates.

To determine the closing flows of linear tangential forces, we compose the canonical equations

Coefficients of canonical equations (elements of the matrix
and vectors
) are defined by the expressions:

,
,
,

(here the summation is carried out over the panels, where
are not equal to zero, respectively),

,
, - reduced shear modulus (for duralumin sheathing
) ;
- reduced sheathing thickness
;
- reduction factor of plating.

The shear modulus of the wing panel skin is not equal to the shear modulus of the skin material, but also depends on its curvature, thickness, spacing of ribs and stringers (dimensions of the reinforcing cage), reinforcing profiles, and the nature of the plate loading. The values of the shear modulus are more or less accurately determined empirically for a given design. In the calculation, it is necessary for the most part to use the average values of G obtained from tests of similar structures. As

then when calculating we will use the values of the reduction coefficients shown in Fig. 15. The values of the coefficient for skin made of other material should be multiplied by - the fluxes of linear tangential forces in the open contour of the wing section from shear;

Based on the results of the calculation, we construct a total diagram of the flows of linear shear forces from shear and torsion along the contour of the design section of the wing. When constructing a summary diagram, we put the positive values of the flows inside the section contour.

9. Checking the skin and side member walls for strength and stability

As a result of the verification calculation, a conclusion should be given on the strength of the selected wing section. For this, the sheathing and side member walls are tested for strength and stability.

Maximum normal stresses acting on the corresponding skin panel (or side member walls), taking into account

and the values of the skin reduction factor are found by the expression

When checking the sheathing for strength, the values of the coefficient are calculated

Kravets A.S. Characteristics of aviation profiles. - M .: Oborongiz, 1939.

Makarevsky A.I., Korchemkin N.N., Frenchman T.A., Chizhov V.M. The strength of the aircraft. - M .: Mechanical engineering, 1975.280s.

Uniform airworthiness standards for civilian transport aircraft of the CMEA member countries. - Moscow: TsAGI Publishing House, 1985.470s.

Odinokov Yu.G. Aircraft strength calculation. - M .: Mechanical Engineering, 1973.392s.

Strength, stability, fluctuations: Handbook in 3 volumes / Ed. Birgera I.A., Panovko Ya.G. - M: Mechanical Engineering, 1971.

Aviation. Encyclopedia. Ed. Svishcheva G.P. - M: Publishing house of the big Russian encyclopedia, 1994.736s.

Heinz A.F. Schmidt. Flieger - Jahrbuch. - Berlin: Transpress VEB Verlag für Verkehrswesen, 1968-1972.168S.

Heinz A.F. Schmidt. Flieger - Jahrbuch. - Berlin: Transpress VEB Verlag für Verkehrswesen, 1973.168S.

Heinz A.F. Schmidt. Flieger - Jahrbuch. - Berlin: Transpress VEB Verlag für Verkehrswesen, 1980.168S.

Heinz A.F. Schmidt. Flügzeuge aus aller Welt. V. 1 - 4. - Berlin: Transpress VEB Verlag für Verkehrswesen, 1972 - 1973.

Calculation of the necessary ... or suspended for maintenance of elements constructions aircraft at different levels. For increase...

Feasibility study of the project aircraft

Abstract >> Economics

2.2. Methodology calculation cost indicators aircraft, its systems ……………………………………………………………………… ... 29 2.3. Payment cost indicators ... material in bulk constructions glider... Tm = 30 * V pl T w = 0.2 * G about where G about - takeoff weight aircraft T pl = 1.5 * ...

Calculation of the hydraulic system MIG-

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At supersonic speeds. Glider aircraft is a body in ... restrictions imposed on construction aircraft by the maximum velocity head q. ... when extending the stem:; ; ; ; ; ; ; ; ; ... Payment hydraulic cylinder body (thin-walled pipe made of ...

Design of assembly fixtures

Abstract >> Industry, production

Ensuring high manufacturability constructions is that design developed with by calculation for use with ... errors in the manufacture of parts. Assembling parts glider aircraft in assembly fixtures ensure the accuracy of the finished ...

The basic version is the An-148-100 regional aircraft, which provides transportation in a single-class configuration from 70 passengers with a seat pitch of 864 mm (34 ‘’) to 80 passengers with a seat pitch of 762 mm (30 ‘’). In order to provide flexibility to meet the requirements of various airlines, as well as to reduce operating costs and increase the profitability of transportation, certification of the base aircraft is envisaged in options with a maximum flight range of 2200 to 5100 km. Cruising speed is 820-870 km / h. Marketing research has shown that the base aircraft meets the requirements of a large number of airlines in terms of its technical and economic characteristics.

The An-148-100 is a high-wing aircraft with D-436-148 engines placed on pylons under the wing. This makes it possible to increase the level of protection of the engines and the wing structure from damage by foreign objects. The presence of an auxiliary power unit, an on-board system for registering the state of the aircraft, as well as a high level of serviceability and reliability of the systems allow using the An-148-100 on a network of technically poorly equipped airfields.

Modern flight-navigation and radio communication equipment, the use of multifunctional indicators, fly-by-wire flight control systems allow the AN-148-100 to be used on any air routes, in simple and difficult weather conditions, day and night, including on routes with high flight intensity at high the level of comfort for the crew.

Passenger comfort is provided at the level of comfort on long-haul aircraft and is achieved by a rational layout and composition of service rooms, deep ergonomic optimization of the general and individual space of the passenger compartment, the use of modern seats, interior design and materials, as well as the creation of comfortable climatic conditions and low noise levels. The rationally chosen length of the passenger compartment and the placement of passengers in a row according to the 2 + 3 scheme allow the operator to obtain various single-class and mixed layouts in the range of 55-80 passengers with salons of economic, business and first class. A high degree of continuity of design and technological solutions and operational unification of the An-148-100 with successfully operated An aircraft, the use of Hi-Tech components of equipment and systems of domestic and foreign production provide the An-148-100 with a high competitive level of economic efficiency, technical and operational excellence.

Maintenance of the An-148-100 aircraft is based on meeting the requirements of international standards (ICAO, MSG-3) and ensures that the airworthiness of the aircraft is maintained within the life cycle of operation, with an intensity of up to 300 hours per month with an availability factor of more than 99.4%, while minimizing maintenance costs (1.3 man-hours per hour of flight).

The An-148 aircraft family also includes the following modifications:

a passenger aircraft providing transportation of 40-55 passengers at a distance of up to 7000 km; administrative for 10 - 30 passengers with a range of up to 8700 km;

cargo version with side cargo door for transportation of general cargo on pallets and in containers;

cargo-passenger option for mixed transport "passengers + cargo".

A fundamental feature of the creation of the An-148 family is the use of maximum unification and continuity of units and components of the base aircraft - wing, empennage, fuselage, power plant, passenger and aircraft equipment.

Calculation of a wing of high aspect ratio

Wing geometry

–The area of the swept wing;

Swept wing lengthening;

Swept wing span;

Narrowing of the swept wing;

Root chord of the wing;

Terminal chord of the wing;

Wing sweep angle along the leading edge.

Since the wing of this aircraft is swept and the leading edge angle is more than 15 ° (Fig. 1), we introduce an equivalent straight wing of the same area, and all calculations are performed for this equivalent wing. We introduce the straight wing by rotating the swept wing so that the straight line passing along the half of the chord of the straight wing is perpendicular to the fuselage axis (Fig. 2). In this case, the span of a straightened wing

Straightened wing area:

moreover, as a parameter, we take a value equal to the distance from the end of the straightened wing console to the aircraft axis, since the scheme of this aircraft is a high-winged plane (Fig. 3)

... Then.

Let us find the relative coordinate of the line of the centers of pressure. To do this, we determine the lift coefficient for the design case A.

Takeoff weight of the given aircraft;

- air density at an altitude of H = 0 km;

- aircraft cruising speed (= kg),

Dive speed,

Then: C x = 0.013; C d = 0.339; α 0 = 2 о

We place the spars in the wing:

Front spar 15% of the chord from the wing tip;

The rear spar at a distance of 75% of the chord from the wing tip (Fig. 5).

In the design section () the height of the front spar , rear- .

Determination of wing loads

The wing is affected by air forces distributed over the surface and mass forces from the wing structure and from the fuel placed in the wing, concentrated forces from the mass of the units located on the wing.

We find the masses of the units through their relative masses from the take-off mass of the aircraft:

Wing weight;

Power plant weight;

Since there are 2 engines on an airplane, the mass of one engine will be taken equal to

Distribution of air load along the wing length.

The load is distributed along the wing length according to the law of relative circulation:

where is the relative circulation,

In the case of a swept wing, the relative circulation is determined by the formula:

where - the influence of the sweep of the wing, (- the sweep angle of the quarter of the chord).

Table - Distribution of air load along the wing console

zrel	0	0,1	0,2	0,3	0,4	0,5	0,6	0,7	0,8	0,9	1
 G45	-0,235	-0,175	-0,123	-0,072	-0,025	0,025	0,073	0,111	0,135	0,14	0
G pl	1,3859	1,3701	1,3245	1,2524	1,1601	1,0543	0,9419	0,8271	0,7051	0,5434	0
D	1,27404	1,2868	1,265952	1,218128	1,1482	1,0662	0,976648	0,879936	0,76936	0,61004	0
qw, H / m	36430,7	36795,5	36199,4	34831,9	32832,3	30487,6	27926,9	25161,4	21999,5	17443,9	0,0

Wing span distribution of mass load.

, where is the wing chord.

We distribute the mass load from the weight of the fuel in proportion to the cross-sectional areas of the fuel tanks

, where is the specific gravity of the fuel.

where is the weight of the fuel (for the AN 148 aircraft).

The total linear load on the wing is found by the formula:

We place the origin of coordinates at the root of the wing; we number the sections from the root towards the end of the wing, starting from.

We enter the calculation results in the table.

	z, m	b (z), m				, kg / m	, kg / m	, kg / m	, kg / m
0	0	4,93	1,3435	-0,060421	1,283079	4048,02	505,33	2187,441	1355,25
0,1	1,462	4,559	1,3298	-0,044994	1,284806	4053,46	467,30	1870,603	1715,56
0,2	2,924	4,188	1,2908	-0,031625	1,259175	3972,60	429,27	1578,541	1964,79
0,2	2,924	4,188	1,2908	-0,031625	1,259175	3972,60	429,27	0	3543,33
0,3	4,386	3,817	1,2228	-0,018512	1,204288	3799,44	391,24	0	3408,20
0,4	5,848	3,446	1,1484	1,141972	3602,84	353,22	0	3249,62
0,4	5,848	3,446	1,1484	1,141972	3602,84	353,22	1068,742	2180,88
0,5	7,31	3,075	1,057	0,006428	1,063428	3355,03	315,19	851,0063	2188,84
0,6	8,772	2,704	0,9571	0,018769	0,975869	3078,79	277,16	658,0454	2143,59
0,7	10,234	2,333	0,8538	0,028539	0,882339	2783,71	239,13	489,86	2054,72
0,8	11,696	1,962	0,743	0,03471	0,77771	2453,62	201,11	346,45	1906,06
0,9	13,158	1,591	0,6091	0,035996	0,645096	2035,23	163,08	227,8153	1644,34
0,95	13,889	1,4055	0,4593	0,032139	0,491439	1550,45	144,06	177,7887	1228,60
1	14,62	1,22	0	0	0	0,00	0,00	0	0

We build diagrams of functions, and (Fig. 7)

Plotting shear forces, bending and reduced moments.

When determining the law of distribution of transverse forces and bending moments along the length of the wing, we first find the functions and from the effect of the distributed load. To do this, in a tabular way, we calculate the integrals using the trapezoidal method.

, ,

The calculation is made according to the following formulas:

;

; ,

, .

Similarly, we calculate the values of bending moments:

We enter the results obtained in table 2.

table 2

	z, m	ΔQ, kg	Q, kg	ΔM, kgm	M, kgm
0	0	2244,77	20592,41	196758,3	1016728
0,1	1,462	2690,34	18347,64	172115,8	819969,8
0,2	2,924	2969,13	15657,30	152033,9	647854
0,3	4,386	3127,09	12688,17	130883,4	495820,1
0,4	5,848	3194,27	53414,20	121865,8	364936,7
0,5	7,31	3167,01	43712,46	87477,02	243070,9
0,6	8,772	3068,96	34081,88	66035,43	155593,9
0,7	10,234	2895,33	24644,21	57833,87	89558,46
0,8	11,696	2595,34	15538,14	24598,34	31724,59
0,9	13,158	1602,68	6337,4565	7126,248	7126,248
1	14,62	0	0	0	0

It is necessary to take into account the impact of concentrated mass forces:

, ;

Let's build diagrams, (fig. 8)

When constructing a diagram of the reduced moments, we first set the position of the reference axis. It passes through the leading edge of the wing parallel to the “z” axis. We plot the linear moments from the action of distributed loads, and.

For running moments:

Distances from the points of application of loads to the datum axis.

The moment is considered positive if it acts counterclockwise.

By integrating the plot, we obtain the reduced moments from the action of distributed loads. The calculation scheme is as follows:

We enter the results obtained in table 3:

Table 3

qv	qkr	qt	av	akr	at	mz	dM	M
4027,11	502,72	2187,44	1,67127	2,2185	2,3664	438,75654	42399,48
4032,53	464,88	1870,60	1,69219	2,1982393	2,335009	1434,007	1368,9901	41030,49
3952,09	427,05	1578,54	1,713111	2,1779786	2,303619	2203,8936	2659,3053	38371,18
3952,09	427,05	1578,54	1,713111	2,1779786	2,303619	5840,2499	2659,3053	38371,18
3779,82	389,22	1311,25	1,734031	2,1577179	2,272228	6371,3749	3610,3448	34760,84
3584,23	351,39	1068,74	1,754951	2,1374572	2,240837	6780,5438	4297,6997	30463,14
3584,23	351,39	1068,74	1,754951	2,1374572	2,240837	3144,1876	4297,6997	30463,14
3337,71	313,56	851,01	1,775871	2,1171965	2,209446	3383,2196	4771,5346	25691,6
3062,89	275,73	658,05	1,796792	2,0969357	2,178056	3491,9366	5025,7392	20665,86
2769,34	237,90	489,86	1,817712	2,076675	2,146665	3488,2576	5102,522	15563,34
2440,94	200,07	346,45	1,838632	2,0564143	2,115274	3343,7442	4994,1933	10569,15
2024,72	162,24	227,82	1,859553	2,0361536	2,083884	2959,9915	4608,0307	5961,119
1542,45	143,32	177,79	1,870013	2,0260233	2,068188	2226,3231	3791,1959	2169,923
0,00	0,00	0,00	1,880473	2,0158929	2,052493	0	2169,9229	0

The reduced moment from the action of concentrated masses is found by the formula:

where is the distance from the center of gravity of the th tank to the axis of reference.

We build a summary diagram (Fig. 9)

Checking the correctness of plotting the wing loads.

From the diagram = 20592kg.

Determination of the point of position of the shear force in the design section

Knowing the shear force and the reduced moment in the design section (= 0.2), it is possible to find the point of application of the transverse force along the chord of the wing of the design section:

The coordinate is plotted from the reference axis.

Design calculation of the wing section

In the design calculation, it is necessary to select the load-bearing elements of the wing cross-section: spars, stringers and skin. We will select materials for the longitudinal elements of the wing section and enter their mechanical characteristics in Table 4.

Table 4

The pitch of the stringers is found from the condition that the waviness of the wing surface does not exceed a certain value. The quantity must satisfy the inequality

Here and is the pressure in horizontal flight on the lower and upper surfaces of the wing;

- Punch ratio, for duralumin;

- modulus of elasticity of the first kind of skin material.

The values and are assumed to be approximately equal

The parameter is a relative deflection, the recommended value of which is not more than.

Setting the pitch of the stringers, we find the thickness of the skin, satisfying the inequality (Table 5).

Table 5.

For strength reasons, we will increase the thickness of the skin by taking

δ comp = 5 (mm), δ p = 4 (mm),

Determine the number of stringers on the upper and lower parts of the cross-section:. (fig. 10)

The loads perceived by the panels will be equal

The load perceived by the panel can be represented by

Selection of a longitudinal strength set in a stretched zone

The force in the stretched zone is determined by the equality

where is the number of stringers in the stretched zone taken into account in the design calculation,

- cross-sectional area of one stringer,

- the thickness of the sheathing in the tensioned zone.

Since the panel is solid milled:

- coefficient taking into account the concentration of stresses and weakening of the section by holes for rivets or bolts,

- coefficient that takes into account the delay in the inclusion of the skin in the power circuit in comparison with stringers,.

Then we find the required area of stringers in the stretched panel: Fig. eleven

Knowing the required area of the stringer, we will choose a stringer with a similar cross-sectional area from the assortment of profiles. We choose an equal-walled square PR100-22, ,, (Figure 11).

Determine the areas of the spar belts

The area should be distributed between the extended flanges of the front and rear side members.

Selection of the longitudinal strength set in the compressed zone

The force in the compressed zone is found by the formula:

where is the number of stringers in the compressed zone taken into account in the design calculation,

- design breaking stress of the stringer in the compressed zone,

- cross-sectional area of one stringer in the compressed zone,

The attached planking area is determined by the formula:

Then the required stringer area:

Knowing the required area of the stringer, from the assortment of profiles, select a stringer with a similar cross-sectional area (Fig. 12). This is a bulbogon PR102-23, ,,. Fig. 12

The critical stresses of local buckling of the selected stringer are determined by the formula:

Coefficient that takes into account the conditions for fixing the edges of the wall.

We will check stringers for local stability for all stringer walls, except for those riveted to the skin.

for stringer shelf:

Since>, they need to be adjusted according to the formulas:

, , ,

The width of the attached skin, working with stringer stresses, is determined by:

Attached planking area:

The total area of the side member flanges:

We distribute the area between the compressed shelves of the front and rear side members in proportion to the squares of their heights:

We take the ratio of the width of the flange of the spar to its thickness, then

1 spar:

, ; , ;

2 spar:

, ; , .

Selection of side member wall thicknesses

Determine the moments of inertia of the side members.

Transferring a shear force with static zero to the center of stiffness, we notice that this force is equivalent to two forces:

and torque

These forces cause shear force flows in the side member walls (Fig. 13).

If we assume that the torque is perceived only by the outer contour of the wing section, then this moment is balanced by the flow of tangential forces

Then, depending on the location of the transverse force (before or after the center of stiffness)

Find the wall thickness:

, ,

. .

Determining the distance between ribs

The distance between the ribs is determined from the condition of equal strength with local loss of stability of the stringer and with a general loss of stability of the stringer with attached skin.

The critical buckling stresses of the stringer are determined by the formula:

where is the moment of inertia of the section of the stringer with the attached skin relative to the axis passing through the center of gravity of this section and parallel to the plane of the skin;

- the distance between the ribs.

Wing check calculation

The purpose of the verification calculation is to check the strength of the structure with the actual geometry and physical and mechanical characteristics of the materials of the structure by the method of reduction factors.

To determine the reduction coefficient of the zero approximation, let us construct a deformation diagram of the materials of the skin, stringers and spars. Deformation parameters are given in Table 4.

Having a deformation diagram, we choose a fictitious physical law. At design loads, the stresses in the most durable structural element - the spar - are close to the ultimate resistance. Therefore, it is advisable to draw a fictitious physical law through a point (Fig. 14).

compressed zone :

Spar : ,

Stringer: .

We determine the reduction factor of the zero approximation in stretched zone :

Spar: ,

Stringer: .

Let us determine the reduced areas of the elements. Actual areas of section elements:

Reduced areas:

Further calculations are presented in Table 6.

Next, you need to find the coordinates of the center of gravity of the reduced section. Determine the position of the central axes of the reduced section. The initial axes are chosen as passing through the nose of the profile in accordance with its geometry (Fig. 15).

The coordinates of the center of gravity of the reduced section are determined as follows:

where is the number of concentrated areas in the section.

We find the coordinates of the lumped elements in the central axes as follows:

Determine the axial and centrifugal moments of inertia of the reduced section in the central axes:

Calculate the coordinates of the elements in the main central axes

... (Table 6)

Determine the moments of inertia in the main central axes

Determine the projections of bending moments on the main central axes (Fig. 17):

Determine the reduced stresses in the section elements:

We determine the actual stresses in the longitudinal elements from the condition of equality of the deformation of the real and reduced sections according to the deformation diagram (Fig. 18).

After finding the actual stresses, we determine the reduction factor of the subsequent approximation for each structural element:

The determination of the reduction factors of subsequent approximations for each structural element will be carried out using a computer. (Attachment 1)

After reaching the convergence of the reduction coefficients, it is necessary to determine the excess strength coefficients in the elements:

In the stretched zone - in the compressed zone.

Table 5

Table 5 (continued)

Checking calculation for shear stresses

Let us estimate the strength of the cladding of the modified section. The casing is in a flat stress state. Shear stresses act in it, the values of which are obtained on the basis of a computer calculation:

and normal stresses, which are equal. (Table 7)

Let us determine the critical buckling stress of the skin:

The distance between the ribs is the pitch of the stringers.

If the skin loses its stability against shear () and works as a diagonally stretched field (Fig. 19), then additional tensile normal stresses appear in it, determined by the formula:

where is the angle of inclination of the diagonal waves.

Thus, the stress state at the points of the sheathing located near the stringers is determined by the formulas:

. .

The strength condition corresponding to the criterion of the energy of shaping has the form:

The coefficient characterizing the excess of the sheathing strength is determined by the formula:

We enter the results obtained in table 7.

We build a diagram of shear stresses (Fig. 20)

Table 7

Calculation of the center of rigidity of the wing section

The center of stiffness is the point about which the contour of the cross-section is twisted, or it is the point where the contour does not twist when a shear force is applied. According to these two definitions, there are 2 methods for calculating the position of the center of stiffness: fictitious force method fictitious moment method. Since the verification calculation for the shear stresses was carried out, and the diagram of the total PKU was built, then to calculate the center of stiffness of the section, we use the fictitious moment method.

Determine the relative twist angle of the 1st contour. Diagram q S - known.

In accordance with Mohr's formula, we apply a unit moment to the first contour:

Since the sheathing does not work independently for normal stresses, the diagram changes abruptly at each longitudinal element, remaining constant between the elements, then we pass from the integral to the sum

We determine the relative angle of twisting of the wing section when the moment M = 1 is applied to it to the entire contour. Unknowns are q 01 q 02, to determine them, we write two equations: the equilibrium equation relative to point A (lower belt of the front spar) and the equation of equality of the relative angles of twisting of the first and second contours (analogue of ur-th compatibility of deformation).

where are the doubled areas of the contours.

To calculate the relative angles, we will use Mohr's formula. Applying a unit moment to each contour

Thus, the equations for calculating the unknowns and take the form

Solving which, we find

After finding `М 1 and` М 2, we determine the relative angle of twisting of the first circuit, from the application to the section of the unit moment:

Determine the amount of torque in the wing section from the acting loads. Since the deformation is linear, the twist angle is directly proportional to the value of M cr, then:

Determine the distance from the transverse force to the center of rigidity (Fig. 21).

Operational work absorbed by the shock absorption system during landing:

where is the operational vertical landing speed equal to

But since , then we take m / s.

kJ.

One rack perceives operational work

kJ.

Calculating the operational work absorbed by the tires during landing

find a job perceived by a shock absorber

The shock absorber travel is calculated by the formula

Coefficient of completeness of the shock absorber compression diagram when perceiving work.

φ e - gear ratio during the piston stroke S e.

Since a telescopic rack is considered and it is assumed that at the moment the wheels touch the ground, the axis of the rack is perpendicular to the earth's surface, then η e = 0.7 and φ e = 1.

To determine the transverse dimensions of the shock absorber, we find from the equality

the area over which the gas acts on the shock absorber rod.

Let's set the values of the parameters:

MPa - initial gas pressure in the shock absorber;

- coefficient of preliminary tightening of the shock absorber;

- gear ratio at the beginning of shock absorber compression;

m 2.

For a shock absorber with a seal attached to the cylinder, the outer diameter of the rod is equal to:

We assume the thickness of the O-rings. Then for the inner diameter of the cylinder

The initial volume V 0 of the gas chamber is found by the formula

Height of the gas chamber with uncompressed shock absorber

We find the parameters using the following algorithm.

To find the unknowns and use the equations

After some transformations

Here is the gear ratio corresponding to the shock absorber travel

Coefficient of completeness of the diagram of compression of the shock absorber when absorbing work. For telescopic racks .

The first of equalities (3) has the form of a quadratic equation

, 5

Where , 6

from equality (5)

Substituting from (8) into the second equation of (3) we obtain the transcendental equation

whose root is the required value.

The calculations are summarized in table. eight

Table 8.

We build a graph in the coordinate system (S max, f) (Fig. 22).

The point of intersection of the curve with the f = 0 axis gives the value S max = 0.55.

From dependence (8) we find

Gas pressure in the shock absorber at its maximum compression

MPa.

Liquid level height above the upper axle box

Wherein:

0.589 + 0.1045 = 0.6935> 0.55 - the condition is met.

By setting the values of the parameters:

m - constructive stroke of the shock absorber;

m is the total height of the axle boxes;

m - rod support base;

m - the total size of the shock absorber attachment points;

we get the length of the shock absorber in an uncompressed state

Shock absorber length at operational compression

Determination of rack loads

Design overload factor:

The calculated vertical and horizontal loads on the rack are equal:

The force is distributed between the wheels in a ratio of 316.87: 210.36, and the force is 79.22: 52.81.

Plotting bending moments

The rack is a combined system. First, using the sectional method, we find the force in the brace. We write for the rack the equation of equilibrium relative to the hinge

The diagram of bending moments acting in the plane of the aircraft movement is shown in Figure 23.

The maximum moment, equal to 489.57kNm, acts at the hitch point of the chassis.

The diagram of bending moments acting in the plane perpendicular to the plane of the aircraft movement is shown in Figure 24.

The jump on the diagram at the point of attachment of the rod to the cylinder, created by an eccentric force applied (vertical projection of the force in the rod), is equal to kNm.

The torque is equal to

and only loads the cylinder.

Selection of the parameters of the cross-section of elements

In the design calculation for the telescopic rack, the wall thicknesses of the cylinder and the rod are selected. First, for each of the indicated elements, we select a section in which the bending moment has a maximum value. Axial forces and torque are not taken into account in the design calculation. From the condition of strength

where k is the coefficient of plasticity, we take;

W - moment of resistance

, ;

MPa.

From this equation we find

Knowing the outer diameter of the rod, we get the inner

Then the wall thickness .

Similarly, we find the value for the cylinder, but since the outer diameter of the cylinder is unknown, then in the zero approximation we take it equal to m.Then we get

Plotting Axial Force

Estimated gas pressure in the shock absorber

Gas presses against the stem with force

The discrepancy between the force P sh and the external load of 528.127 kN is explained by the presence of friction forces in the axle boxes. Thus, the friction force in one axle box is equal to the value

kN.

At the upper end of the stem, the gas presses against the stem with a force

Consequently, between the sections passing through the upper and lower axle boxes, the rod is compressed by the force

below the section of the lower axle box - by force

The gas acts on the cylinder through the seal with an axial force

stretching the cylinder. When constructing a diagram of N c, one should also take into account the forces F tr and S z. The final form of the diagrams of axial forces N c and N w is shown in Fig. 25