Calculation of the wing section for bending. Calculation of wing strength. Selection of cross-section parameters of elements
1. Choosing a prototype aircraft
The MiG-3 was chosen as the prototype aircraft.
Fig. 1 General view of the Mig-3 aircraft
1.1 Description of the KSS wing of the MiG-3
The wing consisted of three parts: an all-metal center section and two wooden consoles.
The wing had a Clark YH profile with a thickness of 14-8%. The sweep of the wing is +1 degrees, and the transverse V is 5 ° for the MiG-1 and 6 ° for the MiG-3. Wing aspect ratio 5.97.
The all-metal (duralumin) center section had a structure consisting of a main spar, two auxiliary spars and ten ribs. The main spar had 2 mm thick duralumin walls with reinforcing profiles and shelves made of steel 30HGSA. In cross-section, the spar was an I-beam. The auxiliary spars were of a similar design. The plating of the upper part of the center section was reinforced with five stringers. The entire structure was riveted. There were wheel arches between the front and main spars. Ribs in the area of \u200b\u200bthe wheel arches were reinforced. Between the main and rear spars there were compartments with two fuel tanks, each with a capacity of 150 liters (on the I-200 prototype, the tanks were 75-liter). The tanks were made of AMN alloy and, with the exception of the first series, had self-sealing walls. The center section lining under the tanks was removable and reinforced with riveted profiles. The panel was fastened with six-millimeter screws. The connection of the center section with the fuselage frame was detachable, which simplified the repair of the vehicle.
The wing consoles were wooden. Their design consisted of a main spar, two auxiliary spars and 15 ribs. The main spar had a box shape, at the center section it had seven layers, and at the endings there were five layers of pine plywood 4 mm thick. Shelves with a width of 14-15 mm were made of delta wood. The width of the spar at the center section is 115 mm, at the ends - 75 mm.
Box-shaped auxiliary spars had birch plywood walls with a thickness of 2.5 to 4 mm. Casein glue, screws and nails were used to connect the frame to the wing skin. The leading edge of the wing was partially covered with thick plywood, and between the first and sixth ribs it had a sheathing of duralumin sheet, which was attached to the inner frame with screws. Outside, the entire wing was covered with marquise and covered with colorless varnish. In later series aircraft, metal slats were attached to the leading edge.
On the underside of the wooden consoles were the attachment points for the outboard weapons, service holes and numerous drains.
The consoles were connected to the center section at three points, one on each spar. The connection was closed with a strip of aluminum sheet.
Shrenk-type flaps consisted of four parts: two under the center section and two under the consoles. All-metal flaps had transverse reinforcements at the junction with the ribs and one stringer. All flap elements were riveted. The flaps were hinged to the rear spar. The flaps were set in motion by a pneumatic actuator providing two fixed positions: 18 g and 50 g. The flap area was 2.09 m².
Ailerons of the "Fries" type with aerodynamic compensation. Metal frame with fabric covering (ACT-100 fabric). Each aileron consisted of two parts on a common axis, fixed at three points. This separation facilitated the work of the ailerons in the event that, due to excessive overloads, wing deformation began. On the left aileron was a steel rocker. Ailerons deviated upward by 23 degrees and down by 18 degrees. The total area of \u200b\u200bthe ailerons was 1.145 m².
wing aircraft power circuit
2. Determination of the geometric and mass characteristics of the aircraft
Since the calculation of the wing loads will be performed using the NAGRUZ.exe program, we need some data concerning the geometry and mass of the aircraft.
Length: 8.25 m
Wingspan: 10.2 m
Height: 3.325 m
Wing area: 17.44 m2
Wing profile: Clark YH
Wing elongation ratio: 5.97
Empty weight: 2699 kg
Normal takeoff weight: 3355 kg
With machine guns under the wing: 3510 kg
Mass of fuel in internal tanks: 463 kg
Volume of fuel tanks: 640 l
Power plant: 1 × liquid cooling AM-35A
Engine power: 1 × 1350 hp. from. (1 × 993 kW (takeoff))
Propeller: three-bladed VISH-22E
Propeller diameter: 3 m
Chord root [2.380m]
Chord end
Wingspan
Safety factor
Takeoff weight
Operational overload
Sweep angle along the wing chord quarter line
Relative thickness of the profile in the root section
Relative thickness of the profile at the end section
Wing weight
Number of fuel tanks in the wing
Specific gravity of fuel
The relative coordinates of the origin of the chords of the tanks
The relative coordinates of the end chords of the tanks
Initial chords of tanks
Tank end chords
Distance from the conventional axis to the central point line. fuel in the root and end sections of the wing [1.13m; 0.898 m]
Number of units
Aggregate relative coordinates
Distance from the conventional axis to the central point. aggregates
Distance from the conventional axis to the central line. at the root and end of the wing [0.714m; 0.731m]
The distance from the conditional axis to the c.zh line. at the root and end of the wing
Distance from the conventional axis to the central point line. at the root and end of the wing
Unit weight
Relative wing circulation 11 values:
The wing mass is about 15% of the dry weight of the aircraft, i.e. 0.404 tons.
Designation of operational overload and safety factor
All aircraft are divided into three classes depending on the degree of required maneuverability:
Class B - limitedly maneuverable aircraft that maneuver mainly in the horizontal plane ( 
).
Class B - non-maneuverable aircraft that do not perform any abrupt maneuver ( 
).
Fighters belong to class A, therefore we choose operational overload
The maximum operational overload during the maneuver of the aircraft with the take-off and landing mechanization retracted is determined by the formula:
The safety factor f is assigned from 1.5 to 2.0 depending on the duration of the load and its repeatability during operation. We take it equal to 1.5.
4. Determination of loads acting on the wing
The wing structure is calculated according to breaking loads
G is the takeoff weight of the aircraft.
Safety factor.
1 Determination of aerodynamic loads
The aerodynamic load is distributed over the wingspan in accordance with the change in the relative circulation (when calculating the coefficient, the influence of the fuselage and engine nacelles can be neglected). The values \u200b\u200bshould be taken from the table (4.1.1) depending on the characteristics (elongation, tapering, center section length, etc.).
Table 4.1 Circulation
Cross-sectional distribution of circulation for trapezoidal wings
For swept wings 
According to the diagram of distributed loads q aer, calculated for 12 sections, the diagrams of Q aer are constructed sequentially. and M aer. ... Using the known differential dependences, we find
where is the shearing force in the wing section from the aerodynamic load;
where is the moment of the aerodynamic load in the wing section.
Integration is carried out numerically using the trapezoidal method (Fig. 3). Based on the results of calculations, diagrams of bending moments and shearing forces are plotted.
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
where b is a chord.
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.
2.2 Determination of distributed mass forces from the weight of fuel tanks
Distributed linear mass load from fuel tanks
where γ is the specific gravity of the fuel;
B is the distance between the side members, which are the tank walls.
Relative profile thickness in section:
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 as 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 about the conditional axis
3.1 Determination 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. 3).
and build a plot.
3.2 Determination from the distributed mass forces of the wing (s)
The mass forces distributed over the wing span act along the line of the centers of gravity of its structure (see Fig. 3).
where is the calculated concentrated force from the weight of the wing part between two adjacent sections;
The shoulder from the point of application of the force to the axis.
Values \u200b\u200bare calculated similarly. Diagrams and are plotted according to the calculations.
3.3 Determination from concentrated forces
where is the estimated weight of each unit or load;
Distance from the center of gravity of each unit or load to the axle.
After the calculation, the total moment from all the forces acting on the wing is determined and a diagram is constructed.
4.4 Determination of design values \u200b\u200band for a given wing section
To determine and follows:
find the approximate position of the center of rigidity (Fig. 4)
where is 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. 5) according to the formulas:
5. The choice of the structural-power scheme of the wing, the selection of the design section parameters
1 The choice of structural and power wing scheme
For the calculation, a two-spar wing of a coffered structure is taken.
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 profile is selected that corresponds in thickness to the type of aircraft under consideration and table 3 is drawn up. 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:
where y is the calculated value of the ordinate;
Tabular ordinate value;
Tabular value of the relative wing profile thickness.
For a swept wing, a sweep correction should be made using the formulas
Table 5.1 Coordinates of the profile are normal and taking into account the correction for sweep Data recalculation results:
|
Uv tabl,% |
Un tabl,% |
||||
5.3 Selection of section parameters
3.1 Determination of normal forces acting on the wing panel
Side member belts and stringers with attached sheathing absorb the bending moment. The forces loading the panels can be determined from the expression:
F is the wing cross-sectional area, limited by the extreme spars;
B is the distance between the outer side members (fig. 7).
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 shelves - 
, ,
.
The values \u200b\u200bof the coefficients a, b, g are given in Table 4 and depend on the wing type.
Table 5.2
For the calculation we will use a coffered wing.
3.2 Determination of sheathing thickness
The thickness of the skin d for the stretched zone is determined according to the 4th theory of strength
where is the tensile strength of the sheathing material;
g - coefficient, the value of which is given in table 5.2
For a compressed zone, the sheathing thickness should be taken equal to 
.
3.3 Determining the pitch of stringers and ribs
The pitch of the stringers and ribs is chosen in such a way 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 deflection value is achieved in the center of the plate under consideration:
Cylindrical sheathing rigidity.
The values \u200b\u200bof the coefficients d are taken depending on. Typically this ratio is 3. d \u003d 0.01223.
The distance between stringers and ribs should be chosen so that
Number of stringers in a compressed panel
where is the arc length 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.
But, in order not to overshadow the structure, we will take the rib spacing equal to 450 mm.
3.4 Determination of the cross-sectional area of \u200b\u200bstringers
Sectional area of \u200b\u200bthe stringer in the compressed zone in the first approximation
where is the critical stress of the stringers in the compressed zone (in the first approximation).
Sectional area of \u200b\u200bstringers in the tension zone
where is the tensile strength of the stringer material.
From the available list of standard rolled corner profiles with a bulb, the closest profile with a cross-sectional area of \u200b\u200b3.533 cm 2 suitable in area.
3.5 Determination of the cross-sectional area of \u200b\u200bthe side members
The area of \u200b\u200bthe flanges of the side members in the compressed zone
F l szh. \u003d 17.82 cm 2
where σ cr.l-on is the critical stress at the loss of stability of the spar flange. σ cr. l-on 0.8 σ B
The area of \u200b\u200beach shelf of two spar wings is found from the conditions
F l.c. 2 \u003d 12.57 cm 2 F l.s. 2 \u003d 5.25 cm 2
The area of \u200b\u200bthe side members in the extended area
F l. \u003d 15.01 cm 2
F l bed 1 \u003d 10.58 cm 2 F l bed 2 \u003d 4.42 cm 2
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.
where is the critical shear stress of the wing spar wall buckling (Fig. 9). For calculations, all four sides of the wall should be taken freely supported:
where 
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 placed (Fig. 10). 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.
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 is the actual cross-sectional area of \u200b\u200bthe 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 is the modulus of the material 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, is substituted in the formula (6.1) instead.
We determine the coordinates and centers of gravity of the sections of the longitudinal elements of the profile relative to arbitrarily chosen axes x and y 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:
Through the found center of gravity, draw the axes and (it is convenient to choose the axis 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.
To calculate the local form of buckling, consider the buckling of the free stringer flange as a plate hinged on three sides (Fig. 12). In fig. 12 indicates: a - the step of the ribs; b 1 is the height of the free stringer shelf (Fig. 11). For the plate under consideration, it is calculated using the asymptotic formula (6.8), in which
where k σ is a coefficient depending on the loading and bearing conditions of the plate,
d c - thickness of the free stringer shelf.
For the case under consideration
For comparison with the actual stresses obtained as a result of the reduction, the lower stress is selected, 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.
List of references
1. G.I. Zhytomyr "Aircraft Design". Moscow mechanical engineering 2005
Over the course of many decades, a gradual increase in the speed of ships was achieved mainly by increasing the power of the installed engines, as well as improving the hull lines and improving the propellers. Nowadays, shipbuilders - including amateur designers - have the opportunity to use a qualitatively new way.
As you know, the resistance of water to the movement of the vessel can be divided into two main components:
1) resistance depending on the shape of the housing and the energy consumption for wave formation, and
2) frictional resistance of the body against water.
With an increase in the speed of a displacement vessel, the resistance to its movement increases sharply, mainly due to an increase in wave resistance. With an increase in the speed of the planing vessel, due to the presence of a dynamic force that lifts the hull of the glider out of the water, the first component of the resistance is significantly reduced. Even broader prospects for increasing travel speed without increasing engine power are opened by the use of a new principle of movement on water - movement on hydrofoils. The wing, having (at the same lifting force) significantly higher hydrodynamic characteristics than the planing plate, can significantly reduce the drag of the vessel in the mode of movement on the wings.
The boundaries of the profitability of applying various principles of movement on water are determined by the relative speed of the vessel, for which the Froude number is used:
υ is the speed of movement;
g - acceleration of gravity; g \u003d 9.81 m / s 2;
L - characteristic linear dimension of the vessel - its length.
Considering that L is proportional to the cubic root of D (where D is the ship's displacement), the displacement number is often used:
Usually, housings with displacement contours have less resistance at speeds corresponding to the frud number P rD< 1; при больших значениях относительной скорости (F rD > 2, 3) planing contours are used for ships and it is advisable to install wings.
At low speeds, the resistance of the boat with wings is slightly higher than the resistance of the glider (Fig. 1) due to the resistance of the wings themselves and the struts connecting the hull to the wings. But with an increase in speed, due to the gradual exit of the hull from the water, its resistance to movement begins to decrease and at the speed at which the hull is completely detached from the water, it reaches its lowest value. At the same time, the resistance of the boat on the wings is significantly less than the resistance of the glider, which makes it possible to obtain higher travel speeds with the same engine power and displacement.
During the operation of hydrofoils, their other advantages over speedboats were revealed, and above all, higher seaworthiness, due to the fact that when moving on the wings, the hull is above the water and does not experience shock waves. When sailing at low speeds, the wings also have a beneficial effect, reducing the pitching of the boat. Negative qualities (for example, large draft at anchorage, bulkiness of the wings) do not at all reduce the importance of vessels on the wings, which provide high comfort of navigation in combination with high speed of movement. The advantages of winged ships have won them wide popularity in many countries of the world.
This article presents the basic concepts and dependencies from the theory of wing motion in water and methods for calculating and designing wing systems as applied to small displacement vessels.
Hydrodynamics of the hydrofoil
The simplest example of a hydrofoil is a thin rectangular plate set at an angle to the direction of its movement. However, to get more lift with less resistance, wings of more complex shapes are currently used. Despite the fact that the issues of theory and experimental research of the hydrofoil have not yet been largely developed, the main dependencies have already been obtained and extensive experimental material has been collected, allowing to correctly assess the influence of various factors on the hydrodynamics of the wing and design its structure.The shape of the wing (Fig. 2) is determined by its span l, chord b, sweep angle χ and deadrise angle β. Additional parameters are the wing area in plan S \u003d lb and the relative aspect ratio λ \u003d l 2 / S. For a rectangular wing with a chord constant along the span λ \u003d l / b.
The position of the wing in relation to the flow is determined by the geometric angle of attack of the airfoil α, that is, the angle between the chord of the wing and the direction of its movement.
The main importance for the characteristics of the wing is its profile - the section of the wing by a plane perpendicular to the span. The wing profile is determined by the thickness e, the concavity of the midline of the profile f, as well as the angle of zero lift α 0. Profile thickness is variable along the chord. Usually, the maximum thickness is in the middle of the profile chord or slightly offset towards the nose. The line passing through the middle of the profile thickness in each section is called the midline of curvature or the midline of the profile. The ratio of the maximum thickness and the arrow of the maximum concavity of the midline to the chord determines the relative thickness and concavity of the profile and is designated accordingly e and f. The values e and f and their geometrical position along the length of the chord are expressed in its shares.
Consider the flow around a flat wing of infinite aspect ratio as it moves in an infinite fluid.
The flow incident on the wing with a velocity υ at a certain positive angle of attack α accelerates on the upper side of the airfoil and slows down on the lower side. In this case, according to Bernoulli's law, the pressure on the upper side decreases, and on the lower side it increases (compared to the pressure in the undisturbed liquid). In fig. 3 is a graph illustrating the change in the dimensionless pressure coefficient:
along the chord of the hydrofoil profile.
Here Δр \u003d р - р o, where р is the pressure at the corresponding point of the profile, and р о is the pressure in the unperturbed liquid.
Negative values \u200b\u200bof the pressure coefficient indicate rarefaction (p<Р о), положительные - на наличие давления (р>R about).
The resulting pressure difference creates an upward force on the wing, that is, the lift of the wing.
As you can see from the figure, the area of \u200b\u200bthe rarefaction plot is much larger than the area of \u200b\u200bthe increased pressure plot. Numerous experiments show that about 2/3 of the lift is generated on the upper ("suction") side of the profile due to vacuum, and about 1/3 on the lower ("injection") side due to the pressure increase.
The resultant of the pressure forces acting on the wing represents the total hydrodynamic force, which can be decomposed into two components:
Y is the lift of the wing, perpendicular to the direction of movement;
X - resistance force, the direction of which coincides with the direction of movement.
The point of application of the resultant of these forces on the profile is characterized by the moment M relative to the front point of the profile.
Experimental studies have shown that the lifting force Y, the resistance force X and their moment M are expressed by the dependences:
ρ is the density of water (for sea water ρ \u003d 104, and for fresh water ρ \u003d 102 kg sec 2 / m 4);
υ is the speed of the flow on the wing (the speed of the wing in the flow);
b - wing chord;
S is the wing area;
С y, С x, С m - dimensionless hydrodynamic coefficients, respectively, of lift force, resistance force and moment.
The coefficients C y, C x, C m are the main characteristics of the wing, independent of the environment in which the wing moves (air or water). Currently, there is no sufficiently accurate method for the theoretical calculation of the hydrodynamic coefficients of the wing (in particular C x and C m) for various types of airfoils. Therefore, to obtain accurate wing characteristics, these coefficients are determined experimentally by blowing in wind tunnels or towing in pilot pools. The test results are given in the form of diagrams of dependences of the coefficients C y, C x, C m on the angle of attack α.
For the general characteristics of the wing, the concept of the hydrodynamic quality of the wing K is additionally introduced, which represents the ratio of the lift force to the drag force:
Often the characteristics of the wing are given in the form of the "Lilienthal polar", which expresses the dependence of C y on C x. The experimental points and the corresponding angles of attack are marked on the polar. In fig. 4 and 5 show the hydrodynamic characteristics of the segment profile "Göttingen No. 608". As you can see, the values \u200b\u200bof the hydrodynamic coefficients are determined by the angle of attack of the wing. In fig. 6 shows the pressure distribution for three angles of attack. With an increase in the angle on the upper surface of the wing, the degree of rarefaction increases, and on the lower surface, excess pressure increases; the total area of \u200b\u200bthe pressure diagram at α \u003d 3 ° is much larger than at α \u003d 0 °, which ensures an increase in the coefficient C y.
On the other hand, with a decrease in the angle of attack, the Cy coefficient falls almost linearly down to zero. The value of the angle of attack at which the lift coefficient is equal to zero determines the angle of zero lift α о. The angle of zero lift depends on the shape and relative thickness of the profile. With a further decrease in the angle of attack of the wing, the lift becomes negative.
Until now, we have been talking about the characteristics of a deeply submerged wing of infinite span. Real wings have a definite aspect ratio and work near the free surface of the liquid. These differences leave a significant imprint on the hydrodynamic characteristics of the wing.
For a wing with λ \u003d ∞, the pressure distribution pattern in each wing span is the same. At a wing with a finite span, the liquid flows through the ends of the wing from the overpressure area to the vacuum area, equalizing the pressure and thereby reducing the lift. In fig. 7 shows the pressure variation along the wing span of the final aspect ratio. Since liquid overflow occurs mainly in the extreme sections of the wing, its effect decreases with increasing aspect ratio and practically at λ \u003d 7 ÷ 9 the wing characteristics correspond to infinite span (Fig. 8).
Another factor affecting the operation of the wing is the presence of a free liquid surface near it - the boundary of two media with a large difference in mass densities (ρ of water ≈ 800 ρ of air). The influence of the free surface on the lift is explained by the fact that the wing, having a certain thickness, raises the liquid layer, restricting it the less the closer the wing is to the free surface. This allows the liquid to flow around the wing at a lower speed than during a large submersion; the values \u200b\u200bof rarefaction on the upper surface of the wing are reduced.
In fig. 9 shows the change in the pressure diagram depending on the change in the relative depth of immersion under the free surface for the wing of the segmented profile (the relative immersion of the wing is understood as the ratio of the distance from the wing to the liquid surface to the chord value). As you can see, the influence of the free surface is not the same for the suction and delivery sides of the wing. Numerous experiments have established that the effect of immersion affects mainly the pressure diagram above the wing, while the area of \u200b\u200bincreased pressure remains almost unchanged. The degree of influence of dive on the lift of the wing decreases rapidly with increasing dive.
Below, in Fig. 12 is a graph illustrating the decrease in vacuum on the upper surface of the wing as it approaches the free surface. It follows from this graph that the influence of the free surface is small even at a dive equal to the wing chord, and at h \u003d 2 the wing can be considered deeply submerged. In fig. 10, a, b, c shows the hydrodynamic characteristics of a flat wing of a segmented profile with an elongation λ \u003d 5 and a thickness of e \u003d 0.06 for various relative immersions.
For a real wing, it is necessary to take into account the total effect of all the factors listed above: the shape of the wing, its aspect ratio, relative immersion, etc.
The next parameter on which the magnitude of the forces developing on the wing depends is the speed of movement. From the point of view of wing hydrodynamics, there is a certain velocity value, exceeding which leads to significant changes in wing characteristics. The reason for this is the development on the wing of the phenomenon of cavitation and related violations of the smooth flow around the airfoil by the fluid flow.
With an increase in the speed of movement, the rarefaction on the wing reaches values \u200b\u200bat which small bubbles filled with steam and gases begin to emerge from the water. With a further increase in the flow velocity, the cavitation region expands and occupies a significant part of the suction side of the wing, forming a large vapor-gas bubble on the wing. At this stage of cavitation, the lift and drag coefficients begin to change sharply; in this case, the hydrodynamic quality of the wing decreases.
Due to the negative effect of cavitation on the characteristics of the wing, it was necessary to create profiles of special geometry. At present, all airfoils are subdivided into airfoils operating in the pre-cavitation flow regime and airfoils with highly developed cavitation. Note that all the dependences given by us refer to non-cavitating wings (the characteristics of cavitating profiles are not considered in this article).
In order to prevent the harmful effect of cavitation on the operation of the wing, it is necessary, when calculating it, to check for the possibility of cavitation. The occurrence of cavitation is possible at those points of the profile where the pressure drops slightly below the pressure of saturated water vapors, as a result of which vapors and gases are able to evolve from the liquid, concentrating around the smallest bubbles of air and gases dissolved in water. This condition can be written as:
Coefficient P min for segment profiles can be determined depending on the coefficient of lift and relative thickness according to the Gutsche plot shown in Fig. 11. The Gutsche plot and the calculation according to the above formula are valid for the case of wing motion in an infinite liquid. But, as already noted, the approach of the wing to the free surface reduces the amount of rarefaction on the wing, thereby increasing the value of the maximum velocity of the cavitation-free flow around the wing.
In this case:
where the value of q is taken according to the graph (Fig. 12).
It should be noted that the correct choice of the geometric characteristics of the profiles, as well as their operating modes, allows the onset of cavitation to be postponed to 120-130 km / h, i.e., to high values \u200b\u200bof the speed of movement, which are quite sufficient for small boats and motorboats.
The sweep of the wing has a positive effect on the distance from the beginning of cavitation. In this case, the following relationship takes place:
In addition to cavitation, it is necessary to consider the phenomenon of air breakthrough to the wing, which also strongly depends on the speed of the wing and causes a significant change in the hydrodynamic characteristics. When air breaks through to the wing, there is a sharp decrease in the lift coefficient due to a drop in rarefaction on the upper side of the wing to atmospheric pressure, which is accompanied by a loss of lift and the failure of the wing under the action of the load on it.
The occurrence of air breakthrough largely depends on the maximum value of vacuum on the airfoil and the depth of the wing. Slightly submerged wings, which are very close to the surface of the water when moving, are especially susceptible to this phenomenon. Therefore, the profiles of low-submerged wings are made with a sharp leading edge in order to reduce the magnitude of the vacuum peak on the suction side (Fig. 13). For deeply submerged elements, the likelihood of air breakthrough to the wing is reduced, and therefore it is possible to use profiles with a rounded nose.
In practice, air breakthrough to the wing can sometimes be caused by any objects hitting the wing (floating grass, pieces of wood, etc.), damage to the smooth surface of the wing or its edges, as well as the proximity of cavitating struts, stabilizers, etc.
Design of wing devices
The design of the boat's wing devices consists of a consistent solution of a number of technical problems, sometimes contradicting each other. For example, an increase in the relative elongation of the wings, which has a beneficial effect on the hydrodynamic characteristics, deteriorates the strength of the structure and increases its dimensions.The main quality of the wing system should be to ensure sufficient vertical, longitudinal and lateral stability of the kattsra movement, i.e., maintaining constant equality between the load on the wing and the hydrodynamic forces arising on it during movement. All three types of sustainability are closely related and are achieved in the same ways.
During the acceleration of the boat, as already indicated, the lift of the wings increases; since in this case the weight of the boat remains constant, maintaining the equality:
possibly by changing either the submerged wing area S or the lift coefficient C y.
A typical example of the regulation of the lift force by changing the wetted area of \u200b\u200bthe wings is the well-known "stacked" type of wing device. In this case, the device consists of a series of wings located one above the other and in turn emerging from the water as the speed of the boat increases. An abrupt change in the submerged area of \u200b\u200bthe wings when the next plane leaves the water can be eliminated by applying dead-lift. It should be noted that the "stacked" wing devices, which provide the boat with good stability of movement and easy access to the wings, have low values \u200b\u200bof hydrodynamic quality due to the mutual influence of closely spaced planes and a large number of elements and their interfaces. Therefore, more often used wings are of a higher quality and are highly keeled wing planes of a large span, crossing the surface of the water (Fig. 14). When a boat with such a wing device tilts, additional wing areas from the side of the tilted side enter the water, creating a restoring moment.
Another way to ensure the stability of the boat movement - by changing the coefficient of lift of the wings - can be carried out by changing the angle of attack or approaching the wing to the free surface of the water.
The change in the angle of attack of the wing is made automatically depending on the speed of movement and the position of the boat relative to the water surface. Most of the existing automatic systems carry out a change in the angle of attack depending on the change in the depth of the wing. In this case, the angle of attack can be changed by turning either the entire wing or only part of it. Automatic control angles of attack of the wings allows to obtain high stability of movement, however, a serious obstacle to the widespread use of automation is the complexity of the design of the wings and control systems. An example of a much simpler and more accessible system for manufacturing is a design that provides a change in the angle of attack of the nose wing using a lever with a float planing over the water surface. With an increase in the immersion of any of the nasal wings, the system provides a corresponding increase in the angles of attack, however, achieving stability of movement of such a system is difficult.
The second way to change the lift coefficient is based on the fact that with an increase in stroke speed, the wings sink decreases and the lift coefficient decreases. The application of this method is possible if the design mode of operation of the wings is their movement near the free surface. Vertical, longitudinal and lateral stability of motion on lightly loaded wings is usually easily ensured with the correct choice of lift coefficients and the appropriate selection of the angles of attack of the wings and is quite sufficient in the mode when the wing moves near the water surface.
When the boat rolls in the wing sections located closer to the free surface, the lifting force decreases, and in the submerged sections (from the side of the banked side), it increases. This creates a recovery moment directed in the opposite direction to the roll. The central parts of the wing do not change the dive as much and affect the recovery moment to a lesser extent. In fig. 15 is a graph showing the ratio of the restoring moment created by the wing tips to the moment of the entire wing.
It can be seen from the graph that a special role is played by the extreme sections of the wing with a length of about 1/4 of the span.
Analytically, the restoring moment of a flat inclined wing is expressed by the formula:
From the formula, we can conclude that the restoring moment depends on the geometric characteristics of the wing - span l and relative aspect ratio λ; their increase leads to improved stabilization of the wing in the fluid flow, which must be taken into account when designing wing devices.
Lateral stability of motion in transient modes (before entering the wing) in boats with low-submerged wings is often insufficient. In order to increase stability, additional wing elements are used that emerge from the water at a high speed. Such elements can serve as additional wings located above the main plane, or planing plates.
The stability of movement can also be increased by using so-called stabilizers, which are an extension of the main plane. Stabilizers can be either the same chord as the main plane, or widening towards the ends. The upper part of the stabilizers, located close to the free surface, even during large dives of the main plane, ensures the stability of the boat. The deadrise angle of the stabilizers should be within 25-35 °. For (β<25° по засасывающей стороне стабилизаторов на основную плоскость может попасть атмосферный воздух; стабилизаторы с β>35 ° are ineffective. The angle of attack of the stabilizers (in vertical sections) is usually the same as that of the main plane, or more by ~ 0.5 °. Sometimes, to increase the efficiency of stabilizers, the angle of attack is made variable, starting from 0 ° at the bottom (with respect to the main plane) and up to 1.5-2 ° at the upper end.
Of particular importance for wings operating near the free surface is the configuration of the nose of their profile. In fig. 16 shows the profiles of the hydrofoils that received the greatest res-space, and in table. 1 shows the ordinates for their construction.
The Walchner velocity profile with a rounded nose has good hydrodynamic characteristics and a high value of the velocity of the onset of cavitation, however, the use of this profile is limited to the elements of wing devices located at significant (more than half of the wing chord) dives from the water surface.
For low-submerged elements, sharp-edged profiles are used, which have somewhat worse characteristics, but provide a more stable flow regime.
For deeply submerged elements, as well as for wing stabilizers, a convex-concave “hole” segment can be used along with the plano-convex segment. The "hole" profile has a higher hydrodynamic quality than a flat segment, but it is more difficult to manufacture.
In some cases, to improve the hydrodynamic quality, the segmental profiles are modified by shifting the position of the maximum thickness from the middle of the profile to the nose (positioning it at 35-40% of the chord) or simply slightly filling the nose of the profile.
The value of the maximum profile thickness is selected based on the conditions for ensuring good hydrodynamic characteristics, structural strength and the absence of cavitation. Usually e \u003d 0.04 ÷ 0.07; the concavity of the lower surface of the "lune" profile f n - 0.02.
For supporting racks, biconvex segment profiles are used with low resistance coefficients; usually their e \u003d 0.05.
The main disadvantage of low-submerged wing devices is their low seaworthiness: the wings are often bare, losing lift. The resulting vibrations of the boat can be so significant that movement on the wings becomes impossible due to very strong impacts on the water; the speed of movement is sharply reduced.
The seaworthiness of a boat on low-submerged wings can be improved by using additional elements located below or above the main plane.
In the first case (Fig. 17, a), an additional deeply submerged element, which is little affected by waves and creates a constant lifting force, has a stabilizing effect on the boat, reducing the possibility of the roof falling through. The load on such elements can be up to 50% of the load on the entire device. For boats of small displacement, the dimensions of the deeply submerged plane are so small that when sailing on clogged fairways, such a plane can be easily damaged, therefore it is advisable to use seaworthy elements in the form of a "gull" (Fig. 17.6). The device of the "gull" in the middle part of the low-submerged wing, without reducing the stability characteristics, improves the seaworthiness of the boat. The deadrise angle of the "gull" is selected within the range of 25-35 °; for reasons of stability, the span is taken to be no more than 0.4-0.5 of the full span of the plane. The somewhat lower efficiency of the "gull" (in comparison with a flat deeply submerged element) is justified by the simplicity and reliability of the design.
Installation of additional planes above the main one (Fig. 17, c) does not eliminate wing failures, however, their entry into the water reduces the amplitude of pitching and softens the impact of the hull on the water. This scheme has slightly higher resistance at full speed than schemes with a deeply submerged element (due to the possibility of washing out additional planes), however, with the correct placement and selection of the area of \u200b\u200bthese additional planes, it is possible to reduce the boat resistance in the transient mode, when they simultaneously work as starting , accelerating the exit of the boat to the wings.
Some improvement in the seaworthiness of the boat can be obtained due to the sweep of the wings. In this case, the wing area is spread across the wave front, which reduces the possibility of simultaneous exposure of the entire wing plane. In addition, seaworthiness in waves improves with an increase in the angle of attack of the wing by 1-1.5 ° compared to the angle of attack in calm water. Therefore, it is desirable to have such a system for attaching the wing device to the hull, which would make it easy to change the angle of attack of the wing depending on the state of waves; This system, moreover, greatly facilitates the process of selecting the optimal angles of attack of the wings during the test period of the boat.
The seaworthiness of the boat also largely depends on the distribution of the boat's weight between the wing devices. For the currently most common boats with two wings (bow and stern), three options for the distribution of the boat's weight can be conditionally distinguished:
1)
the bulk of the weight (more than 70-75%) falls on the nose device;
2)
the weight of the boat is distributed approximately equally between the bow and stern;
3)
the bulk of the weight comes from the feed unit
In foreign boat designs, all three methods of weight distribution are equally often used; in the practice of domestic boat building, the second option is most often used. As practice has shown, this load distribution provides the boat with the best seaworthiness.
The first step in the design of a hydrofoil boat is to determine the achievable speed from a given engine power (or to solve the inverse problem).
The speed of the boat can be determined from the formula:
N e - power consumption of the existing engine, l. from.;
η is the general propulsive efficiency of the mechanical installation, taking into account the losses during the operation of the shaft line and the propeller;
R is the total resistance of the boat (kg) when moving at a speed υ (m / s).
The total resistance can be expressed through the value of the hydrodynamic quality K:
Then formulas (1), (2) take the form:
It is extremely difficult to accurately determine the water resistance to the movement of a hydrofoil boat by calculation. Currently, this is done using the results of tests of towed models in experimental basins or in open water. The model is made in exact accordance with nature, but on a reduced scale. When recalculating the resistance according to the results of model tests on nature, it is usually assumed that the values \u200b\u200bof the hydrodynamic quality of the model and the designed boat at the same relative speed (with the equality of the Froude numbers of the model and nature) are equal in all modes of motion.
A similar recalculation of the hydrodynamic quality can be made from any accepted prototype to the designed boat.
The value of the total propulsive efficiency is defined as:
For boats with a direct drive, the engine is a propeller, η m \u003d 0.9 ÷ 0.95. When the gearbox is included in the shafting η m \u003d (0.9 ÷ 0.95); ηηreduct \u003d 0.8 ÷ 0.9. For motor boats with an angular column (Z-shaped transmission to the propeller) η m is in the range of 0.8 ÷ 0.95, depending on the quality of the transmission.
An accurate determination of η p is possible only when calculating the propeller action curves. This value depends on many factors: travel speed; number of revolutions; the accepted dimensions of the propeller; the relative position of the wings, protruding parts and the propeller, etc. Note that the choice and manufacture of a propeller is a difficult and very important matter.
For well-chosen and carefully manufactured propellers η p \u003d 0.6 ÷ 0.75 at speeds of 30-50 km / h (at high speeds η p drops somewhat).
Making a model and determining its towing resistance is difficult and expensive, so this method is unacceptable for individual construction. Usually, in such cases, an approximate method is used, based on the use of statistical data from tests of existing boats.
Since there may not be data on the values \u200b\u200bof K and η p even for built boats, it is necessary to use the propulsive quality coefficient K η when determining the required power or the achievable speed according to (3) and (4), the value of which can be calculated if the power, the speed and displacement:
When using the coefficient of propulsion quality obtained in this way, it must be corrected taking into account the differences between the designed boat and the prototype boat.
With an increase in the speed of movement to a speed corresponding to the onset of cavitation on the wings, a decrease in the hydrodynamic quality occurs mainly due to an increase in the resistance of the protruding parts, splash and aerodynamic resistance (i.e., air resistance). The magnitude of these components of resistance depends on the square of the speed of movement and the surface area of \u200b\u200bboth the protruding parts and the body itself, moistened with water or in the air.
For existing hydrofoil boats, the resistance of protruding parts, splash and aerodynamic drag at a speed of 60-70 km / h is 20-25%, and for small boats - up to 40% of total resistance.
The main issue in the design of a hydrofoil boat with high hydrodynamic quality, good propulsion and seaworthiness is the choice of hydrofoil elements.
The initial value for choosing the size of the wing is the area of \u200b\u200bits submerged part, which is determined from the ratio:
The lift coefficient is selected in the range of 0.1-0.3; in general, C y depends on the design speed. The value of the lift coefficient of the aft wing to increase the stability of movement is taken 20-50% more than that of the bow.
The dimensions of the wing (span l and chord b) are assigned after the wing area has been determined, taking into account the need to ensure a sufficiently high hydrodynamic quality, the lateral stability of the vessel and the strength of the wing.
As already noted, the elongation determines the magnitude of the hydrodynamic quality. Usually, λ \u003d l / b\u003e 5. It should be borne in mind that an increase in the wingspan significantly increases the lateral stability of the ship while underway.
For small boats, roll stability while underway is especially important. Operational experience shows that the total wingspan should not be less than the width of the boat's hull and less than 1.3 - 1.5 m.
For boats with low relative speeds, the fulfillment of these requirements does not cause complications while ensuring the strength of the wings. It is possible to use fenders with two or three struts made of steel, aluminum-magnesium alloys, or even wood. The use of a wing with inclined stabilizers (trapezoidal) allows reducing the number of struts to one or two. However, as the relative speed increases, the strength of the wings becomes a decisive factor. To ensure the strength of the wings, it is necessary to install a large number of struts, which is highly undesirable due to the increase in resistance and the additional possibility of air breakthrough to the upper surface of the wing; you have to make planes of variable width or use schemes with free-standing wings.
In fig. 18 shows curves showing the change in the effective stresses in the wing depending on the design speed of the boat. These curves are plotted for the bow wing of a boat with a displacement of 500 kg, which has two low-submerged flat wings, the load between which is equally distributed.
The graph shows the dependencies for two cases:
- the wing, based on the conditions for ensuring lateral stability, has one plane (dashed curves);
- a wing consists of two free-standing wings with a given aspect ratio (curves shown by solid lines).
As can be seen from the graph, at a speed of more than 10-12 m / s, to ensure the strength of the wing of the first variant, it is necessary either to install a third strut, which will somewhat reduce the hydrodynamic quality, or to use a material with increased mechanical properties... At the same time, for freestanding wings, when installed one by one, the same stresses appear at a much higher speed (20-25 m / s).
The above graph can be used to select the material of the wings when designing boats with similar displacement. In each specific case, more detailed and accurate calculations of the strength of the wings have to be carried out, considering the wing as a frame consisting of plane rods and struts.
As the experience of operating ships and testing hydrofoils has shown, when moving in waves, the wing is subjected to loads that much exceed the static load Y. The resulting overloads are caused by sinkholes when the wing passes through the waves, a change in the wing angle of attack due to the appearance of longitudinal and vertical roll and the presence of orbital speeds water particles during waves, as well as changes in the immersion of the wings. In this regard, when calculating the strength of the wings, it is necessary to introduce increased safety margins:
Usually, for low-submerged elements, n \u003d 3. Considering that with an increase in the submergence of the wing, the change in lift on it, caused by the influence of the free surface, decreases, for deep-submerged planes the safety factor can be slightly reduced.
When calculating the strength of the elements of the wings emerging from the water during movement, it is necessary to set a certain conditional load that may arise on them when moving on waves, with a roll, etc. It is considered that this load is random and the safety margin decreases to n \u003d 1.25 ÷ 1.5.
In addition to determining the basic dimensions of the bearing planes, when designing, it is necessary to determine the height of the racks. At the same time, the designer meets with conflicting requirements. On the one hand, an increase in the height of the wing struts improves the seaworthiness of the vessel, reduces the amount of drag during the course both in rough and calm water. On the other hand, an increase in the height of the struts can lead to a deterioration in the longitudinal and lateral stability of the boat, and most importantly, it causes an increase in the resistance of the boat in the modes preceding the movement on the wings (due to an increase in the wetted surface of the struts, additional propeller shaft brackets, etc.) ...
Usually, the following considerations are taken into account when determining the height of the posts. The most important factor is the maximum distance from the axis of the propeller to the hull, determined by the general conditions of the mechanical installation on the boat (engine, outboard motor) and the operating conditions of the propeller. For example, with the Moskva outboard motor, this distance does not exceed 230-250 mm (which corresponds to a transom height of 290-300 mm); further deepening (lowering) of the motor is impractical, as it can cause deterioration in starting, water ingress into cylinders and candles, etc.
When using stationary engines, one should proceed from the conditions for placing the engine along the length of the boat and ensuring a normal shaft inclination angle (no more than 10-12 °). The use of a Z-shaped gear (angular column) allows to increase the distance from the screw to the housing, even when installing a stationary motor.
The height of the aft wing struts h k should be such that when moving on the wings, the propeller does not become exposed and does not suck in atmospheric air. It is advisable to place the propeller under the wing plane, leaving a gap between the wing and the blade equal to 10-15% of the propeller diameter.
When installing outboard motors, the wing is usually installed at the level of the so-called anti-cavitation plate.
The height of the front wing struts h p is determined based on the value of the trim of the boat when moving on the wings and can be calculated by the formula:
This formula is approximate, since it does not take into account the deformation of the water surface behind the nose wing, which affects the angle of the running trim.
For existing motor boats and cutters ψ \u003d 1 ÷ 3 °. For boats with relatively high speeds, the trim angle is chosen a little less, since in this case the mode of going to the wings shifts to lower speeds and the resistance on the “hump” decreases.
One of the main issues solved when designing a hydrofoil boat is access to the wings. For boats with high relative speeds, this issue can become the main one.
During acceleration, when the lift of the wings is still small, the boat moves on the hull. With an increase in speed, the lift of the wings increases, and the boat begins to move first on the bow wing and hull, and with a further increase in speed, on both wings. At the moment the boat enters the bow wing, the resistance of the water to movement reaches the highest value; on the resistance curve, this moment corresponds to a characteristic "hump" (see Fig. 1). As the hull leaves the water, its wetted surface decreases and the resistance falls. At a certain speed - the so-called speed of entering the wings - the body is completely lifted off the water. When choosing the wing areas, the design is not only the maximum speed, but also the speed of separation from the water.
The lift of the wings at all speeds of the boat balances its weight. Therefore, if at the maximum speed v the submerged wing area S and the lift coefficient С у, and at the separation speed υ о the wing area S о and the lift coefficient С y0, then the following condition must be fulfilled:
Due to the fact that at maximum speed the flat wing is submerged a little, and at the lift-off speed its submersion is much greater, the value of C y0 is usually 1.5-2 times greater than C y. In addition, at the beginning of the course on the wings, the trim of the boat is usually greater than at the maximum speed, which also leads to an increase in C y0 (approximately 1.2-1.5 times) due to an increase in the angle of attack of the wing α.
Taking into account that the submerged area of \u200b\u200bthe flat wing remains constant, from the above equality (7) it can be obtained that for a boat with a flat, low-submerged wing, the take-off speed is:
Experience shows that overcoming the hump of resistance with such a ratio of speeds is possible only at low relative speeds. In fig. 19 shows the change in the resistance of boats of the same displacement, but having different maximum design speeds. As can be seen from the above graph, while at maximum speed the drag remains almost constant, at the exit mode on the wings it increases significantly with an increase in the take-off speed.
To overcome the hump of resistance at high relative speeds, boats with flat wings must have auxiliary planing surfaces or additional wings, or be able to change the angle of attack of the main wing planes on the move. To reduce the rate of separation of the body from the water, it is necessary to significantly increase the total area of \u200b\u200bthe bearing surfaces. Additional bearing surfaces should be located so that as the speed increases and the main planes rise, they gradually come out of the water and do not create additional resistance; for this it is recommended to make them keeled (deadlift angle 20-30 °) and not to bring them closer to the hull and main planes at a distance less than the wing chord.
To increase the effectiveness of the starting elements, it is advisable to install the upper elements with a greater angle of attack than the lower ones. The installation of auxiliary planes located (during the course at maximum speed) above the water surface, as already noted, increases the seaworthiness and stability of the vessel.
As seen from Fig. 19, at the speeds of the ship entering the wings, the main part of the resistance is the resistance of the hull. Accordingly, to facilitate acceleration, the hull of the vessel should have a well-streamlined line similar to that of conventional vessels, designed to travel at speeds corresponding to the wing entry mode.
Table 2 shows the main elements and comparatives! characteristics of five domestic motor boats with hydrofoils and a six-seater winged boat "Volga" (Fig. 20), well illustrating the above provisions.
Calculation of the wing device for the plastic motor boat "L-3"
As an example, the calculation of the wings made for the plastic motor boat "L-3" ("MK-31") is given, the main elements of which are indicated in table. 2. Its body is made of fiberglass based on polyester resins, reinforced with fiberglass. Case weight 120 kg. A boat without wings, having four people on board, develops (with the Moskva motor) a speed of only about 18 km / h, so it was decided to install hydrofoils to increase the speed (Fig. 21, 22).When designing the wings, in addition to the basic requirements for ensuring the stability of the boat movement, the following tasks were set:
- ensure high speed performance of a motor boat with a full displacement of 480 kg (four people on board) when installing the same outboard engine "Moscow";
- ensure satisfactory seakeeping performance with ria wings fully loaded at 300 mm wave height.
The wing areas were calculated in the following order.
Determining the design speed of the boat... Since the chosen wing scheme of the boat is similar to the scheme used on P. Korotkov's boat, and their speeds are close, the value of the propulsive quality for the boat "L-3" was taken the same as on the boat of P. Korotkov, that is, K η \u003d 5 , 45.
With this value of K η, the speed of the motor boat:
Determination of wing sizes... Based on the position of the center of gravity of the boat and the placement of the stern wing, the position of the bow wing along the length was determined. Since it is assumed that the load on the wings is equally distributed:
To exclude the negative effect of the bow wing on the stern distance between them, there should be at least 12-15 chords of the bow wing and for this boat is L k \u003d 2.75 m.
To obtain high speed and seaworthiness and reduce drag in the mode of reaching the wings, the average value of the lift coefficient on the nose wing was taken equal to C yn \u003d 0.21. In this case, the value of the coefficient of lift of the low-loaded parts of the wing is slightly less than this value, which ensures increased stability of the wing during movement; the average value Su of a deeply submerged element is somewhat higher due to its significant submersion. The lift coefficient of the aft wing, taking into account the low speed of the boat, was taken equal to C yk \u003d 0.3.
For the chosen values \u200b\u200bof C y, the wing area (i.e., the projection area of \u200b\u200bthe wing on the horizontal plane) is equal to:
To ensure sufficient lateral stability, the span of the nose wing is taken l n \u003d 1.5 m; hence the wing chord:
It was decided to make the stern wing within the dimensions of the boat; under this condition, its span turned out to be l n \u003d 1350 mm, and the chord:
With the selected wing sizes, large plane elongations λ n \u003d 7.5 and λ k \u003d 8.5 provide a high hydrodynamic quality of the boat.
For the case under consideration, the span of the "gull" was initially assumed to be 500 mm. However, in order to increase the absolute and relative depth of the deeply submerged element and thereby increase the seaworthiness of the wing, it was decided, while maintaining the area of \u200b\u200bthe deeply submerged element and its deadrise angle, to increase its span to 600 mm by reducing the average chord value to 170 mm. In order not to change the area of \u200b\u200blow-submerged planes, the total wing span was increased to 1550 mm.
As the calculation of the strength of the wings showed, when moving in calm water, the stresses in the wings reach values \u200b\u200bof ο \u003d 340 kg / cm 2. With a safety factor n \u003d 3, the strength of the wings can be ensured by using a material ο T \u003d 1200 kg / cm 2.
To reduce the weight of the wing device, a well-weldable anticorrosive aluminum-magnesium alloy of the AMg-5V brand, having ο T \u003d 1200 kg / cm 2, was chosen as a material.
The design of the boat's wing device is shown in Fig. 23.
Determination of wing strut heights... According to the conditions for placing the engine on the transom of the boat, the height of the aft wing strut h k \u003d 140 mm was chosen (while the height of the cutout for the motor clamp on the transom was 300 mm).
Having given the value of the running trim ψ \u003d 1 ° 20 ", we obtained the height of the nose wing strut:
The accepted values \u200b\u200bof the lift coefficients are slightly higher than those on P. Korotkov's boat, however, there is no need to fear an increase in resistance in the “hump” mode, since the relative speed of the “L-3” boat is much lower than that of the prototype boat. In addition, the large width of the bottom of the boat and longitudinal corrugations-redans somewhat reduce the resistance of the boat's hull in the mode of entering the wings.
To improve the running and operational qualities of the boat, the wing device was given the following design features:
- the free ends of the nose wing are smoothly rounded, which reduces the end losses due to vortex formation and thereby increases the hydrodynamic quality and stability of motion;
- the leading edge of the low-submerged parts of the wings is bent down by 1 mm, which, by decreasing the angle of entry of the wing into the water, reduces splashing during the course on waves, when the wing periodically jumps out of the water, cutting through the wave;
- the struts of the nose wing are made of variable cross-section: the parts of the struts that are during movement in the water are thinner, and at the junctions with the hull, they are thicker. This reduces the resistance of the strut during movement without reducing the strength of the wing;
- wing struts are tilted forward above the waterline at the design speed, which reduces splashing when the struts cross the water surface;
- the bow and stern fenders have attachments that allow you to easily change the angles of the wings to select the optimal angles of attack for different boat loads and depending on the sea;
- the design of the nose wing attachment provides for the possibility of installing a mechanism that allows you to select the angles of attack of the wing on the fly.
The given scheme for calculating the wing device for the motor boat "L-3" can mainly be used to calculate the wings of any motor boats and boats. However, in each specific case, its own peculiarities may arise, which will cause a change in the sequence or the need for more detailed calculations and clarifications.
Manufacturing, installation and testing of the wing device
For the manufacture of wings, a variety of materials are practically used, however, most often the wings are made of steel or aluminum-magnesium alloys, welded (and for simplicity - solid).Most laborious process is the processing of the wings along the profile. There are several ways to obtain a given wing profile, but the most common two of them (Fig. 24):
1) wing planes are made from blanks cut from a pipe. The diameter of the billet pipe for a profile in the form of a circular segment can be determined from the nomogram (Fig. 25). The inner surface of the pipe is milled onto a plane, and the outer surface is sawed to the desired profile;
2) the wing planes are made of sheet material. To obtain the desired profile, the upper surface is punctured or milled along the given ordinates, and the resulting "steps" are sawed off manually.
If it is necessary to obtain a convex-concave profile, the wing plane is bent or the material is selected mechanically.
Small wings can be made by hand filing if machining is impossible.
In the process of processing and to check the profiles of finished wings and struts, templates are usually used that are made according to the specified ordinates with an accuracy of ± 0.1 mm. Deviations of the profile from the template should not exceed ± 1 ° / o of the maximum wing thickness.
After processing the planes and racks, the wings are assembled. To ensure the accuracy of assembly and prevent deformations during welding, it is recommended that the wings be assembled and welded in a jig, which can be made of metal or even wood. Weld seams must be filed.
To reduce the possibility of air breakthrough along the struts to the upper surface of the wing, the places where the struts meet the planes should have smooth transitions along the radii, and the transition radius in the largest section of the wing should not exceed 5% of its chord, and the largest transition radius at the nozzles should be 2-3 mm.
The assembled wing should not have deviations exceeding the following values:
- wingspan and chord ± 1% of the wing chord;
- stance chord ± 1% stance chord;
- divergence of installation angles on the right and left sides ("twist") ± 10 ";
- skew of planes along the length of the boat and the heights of the racks ± 2-3 mm.
If painting is provided to protect the wings from corrosion, then after finishing filing, the surface is painted and then polished. Various enamels and varnishes, polyester and epoxy resins and other waterproof coatings are usually used to paint the wings. During operation, varnish-and-paint coatings often have to be renewed, since water flowing around the wing at high speeds causes their rapid destruction.
The finished wing is installed on the boat. The position of the wings relative to the body must be maintained in accordance with the calculation. The horizontalness of the planes is checked by the level, and the installation angles are checked by goniometers with an accuracy of ± 5 ".
The attachments of the wings to the hull must be sufficiently rigid and strong to ensure that the angles of attack are fixed during movement when the wing is subjected to significant overloads. In addition, the mounts should allow easy change (within ± 2 ÷ 3 °) of the angles of the main wing planes. For boats that differ significantly from the prototype in the chosen wing configuration, relative speed or other characteristics.
It is advisable to provide for the possibility of permutation of the wings in height (to select the optimal position).
As practice has shown, the fulfillment of these requirements for the accuracy of manufacturing and installation of hydrofoils is necessary condition; often, even small deviations from the specified dimensions can lead to complete failure or unnecessary spending of time and money on correcting errors and fine-tuning the wing device. Usually a boat with properly made wings easily gets out of the water from the very beginning and moves on the wings; only a little fine-tuning is required - the selection of the optimal angles of attack to obtain stable movement in the entire speed range and to ensure the best running and seaworthiness.
The initial angles of installation of the Wings are usually taken to be those at which the angles of attack of the wings relative to the line connecting the outgoing edges of the wings are equal: on the bow wing 2-2.5 °, and on the aft wing 1.5-2 °. During the final testing of the boat, in addition to clarifying the angles of the installation of the wings, it is necessary to comprehensively test the boat: to establish its high-speed, seaworthy and maneuverable qualities: to make sure that it is completely safe to sail on it.
Before carrying out fine-tuning tests, the displacement of the boat must be brought to the calculated one. It is recommended to weigh the boat and determine the position of its center of gravity along the length. In addition, the engine must be checked in advance.
During the tests of the boat, the following rules must be observed:
1) tests should be carried out in calm weather and no waves;
2) there should be no extra people on the boat; all test participants must be able to swim and have personal life-saving appliances;
3) the boat should not have an initial heel of more than 1 °;
4) acceleration should be done gradually: before each new increase in speed, it is necessary to make sure that the steering device is working properly and that the boat has sufficient lateral stability both on a straight course and when maneuvering. In case of dangerous phenomena - significant increasing rolls, burying the hull in water, loss of lateral stability and controllability - the speed of the course must be reduced and the reasons causing these phenomena must be found;
5) before starting the boat acceleration, make sure that the path is clear and there is no danger of sudden appearance on the course of ships, boats, floating people and objects. Testing should not be carried out in places where other ships and buoys are congregated or in the immediate vicinity of beaches;
6) all rules for driving boats and motor boats must be strictly observed.
The following cases may occur during testing:
1. The boat does not go out onto the bow wing. The reasons for this may be a small angle of attack of the bow wing or too bow centering of the boat. In order for the boat to come out onto the bow wing, it is necessary to change the centering of the boat or, if this does not give results, gradually increase the angle of installation of the bow wing (by 20 "); in this case, you can slightly reduce the angle of installation of the stern wing (by 10-20"). The angle of attack of the bow wing should be chosen so that the boat easily exits and moves steadily on the bow wing. When entering the nose wing, the speed of movement should increase.
2. The boat does not go to the aft wing. The reasons may be a small angle of attack of the aft wing or too aft centering. This can be eliminated in the same two ways: by changing the centering of the boat or by gradually increasing the angle of installation of the aft wing (by 20 /); if at the same time the boat stops coming out onto the bow wing, its angle of attack should also be increased (by 10 ").
3. After entering the stern wing, the boat smoothly falls onto the bow wing; there are no disruptions from the plane of the nasal wing. This phenomenon is caused by a decrease in the angle of attack of the nose wing due to a decrease in the trim angle when flying on the wings. It is necessary to increase the nose wing mounting angle by 10-20 ".
4. After reaching the stern wing, the boat falls sharply onto the bow wing; at the same time, flow breaks and wing exposure can be observed on the nose wing. The angle of attack of the nose wing is large and should be reduced by 5-10 ".
5. During the course of the boat, the stern wing collapses on the wings; while the stern wing goes at a shallow depth, breakdowns are observed. The aft wing angle of attack is large and should be reduced by 10-20 ".
6. The boat goes out onto the wings with a lot of roll; the roll increases with increasing speed. Check the alignment of the installation angles of the wings on the right and left sides and eliminate the "twisting" of the planes. If the roll decreases while gaining speed, this indicates that the lateral stability is low in the mode of the boat entering the wings. To increase the stability of the boat during acceleration, the following measures can be recommended: increase the angles of attack of the bow wing in order to reduce its sinking at the exit; reduce coal! attacks of the stern wing in order to "tighten" (transfer to high speeds) the exit to the stern wing; install additional stabilizing elements on the nose wing.
7. The boat has insufficient lateral stability when maneuvering on the wings. This phenomenon can be eliminated by the same measures as in clause 6.
8. The boat has poor controllability on the wings. The reasons for this may be insufficient rudder efficiency, an undesirable ratio of the areas of the fore and aft wing struts, etc. The controllability can be somewhat improved by installing additional sprat on the bow wing.
In case of the opposite phenomenon - poor stability of movement on the course - the sprat should be installed on the stern wing. The area of \u200b\u200bsprat is selected experimentally.
Of course, in some cases, these activities may not lead to the desired result. The reasons for failure can be very different: the wrong ratio of loads, areas, lift coefficients, heights of wing struts, etc. To find out the reason in each specific case, it is necessary to compare several phenomena, analyze the measurements of the speed of movement, running trim and other values.
After obtaining a stable movement on the wings in the entire speed range, you can proceed to the selection of the optimal angles of the wings. During the final adjustment, the angles of attack of the wings should be changed by a very small amount (about 5 ") and all the time the adjustment should be monitored by measuring the speed at various modes of movement, acceleration time and other characteristics.
When the angles of installation of the wings are finally selected, it is possible to conduct seaworthy tests, the purpose of which is to determine the maximum wave height at which the boat can move on the wings, and measure the speed at the same time. The tests should be carried out at different heading angles in relation to the running of the waves.
If the design of the attachment of the bow wing allows you to easily change the angles of attack of the wing, you can conduct seaworthy tests of the boat at increased angles of installation of the bow wing.
The sea test is also a test of the strength of the wings. After sea trials, the boat and the wings must be carefully inspected. If breakages, cracks and deformations are found, it is necessary to find out the reasons for their appearance and strengthen these structures.
Only after comprehensive testing can the boat be considered fit for daily use. However, it should not be forgotten that any hydrofoil vessel is still in many ways experimental, in connection with which increased attention is needed to ensure the safety of navigation.
Before considering what is the lift of an airplane wing and how to calculate it, we will imagine that an airliner is a material point that moves along a certain trajectory. To change this direction or force of movement, acceleration is required. It is of two types: normal and tangential. The first seeks to change the direction of movement, and the second affects the speed of the point. If we talk about an airplane, then its acceleration is created by the lifting force of the crane. Let's take a closer look at this concept.
Lift is part of the aerodynamic force. It rises sharply when the angle of attack changes. Thus, the maneuverability of the aircraft is directly related to the lift.
The aircraft wing lift is calculated using a special formula: Y \u003d 0.5 ∙ Cy ∙ p ∙ V ∙ 2 ∙ S.
- Cy is the lift coefficient of an airplane wing.
- S is the wing area.
- Р - air density.
- V is the flow rate.
The aerodynamics of an airplane wing, which affects it during flight, is calculated as follows:
F \u003d c ∙ q ∙ S, where:
- C is the shape factor;
- S - area;
- q is the velocity head.
It should be noted that in addition to the wing, the lift is created using other components, namely the horizontal tail.
Those who are interested in aviation, in particular its history, know that the first plane took off in 1903. Many are interested in the question: why did it happen so late? For what reasons did this not happen before? The thing is that scientists for a long time wondered how to calculate lift and determine the size and shape of an aircraft wing.
If we take Newton's law, then the lift is proportional to the angle of attack in the second degree. Because of this, many scientists believed that it was impossible to invent an airplane wing of a small span, but with good characteristics. It was only at the end of the 9th century that the Wright brothers decided to create a structure with a small span with a normal lifting force.
Airplane alignment
What affects 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. Because of this, as the aircraft's speed 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 vessels 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. The configuration of its wings also has an important influence. For example, the famous TU-154 flies at 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 liners 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? I must say 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 aircraft 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 has a negative effect on 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 can 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
The basic version is the An-148-100 regional aircraft, which provides transportation in a single-class layout 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. Conducted marketing research showed that the basic aircraft in terms of its technical and economic characteristics meets the requirements of a large number of airlines.
The An-148-100 aircraft is made according to the high-wing design with D-436-148 engines placed on pylons under the wing. This allows to increase the level of protection of engines and 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 make it possible to use the An-148-100 on a network of technically poorly equipped airfields.
Modern flight and 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 a high intensity of flights at high level comfort for the crew.
Passenger comfort is provided at the level of comfort on mainline aircraft and is achieved by a rational layout and composition of service rooms, deep ergonomic optimization of the general and individual passenger compartment space, 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 the maintenance of the aircraft's airworthiness within life cycle 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 family of aircraft also includes the following modifications:
a passenger plane 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 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 \u200b\u200bthe 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 angle along the leading edge is more than 15 ° (Fig. 1), we introduce an equivalent straight wing of equal area, and all calculations are carried out for this equivalent wing. 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
.
Flat 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's find the relative coordinate of the line of pressure centers. 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 \u003d 0 km;
- aircraft cruising speed (\u003d kg),
Dive speed,
.
Then: C x \u003d 0.013; C d \u003d 0.339; α 0 \u003d 2 о
We place the spars in the wing:
Front spar 15% of the chord from the wing nose;
The rear spar at a distance of 75% of the chord from the wing nose (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 units located on the wing.
We find the masses of the units through their relative masses from the takeoff mass of the aircraft
Wing weight;
Power plant weight;
Since there are 2 engines on the plane, we will take the mass of one engine equal
.
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 fuel weight (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 forces 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 trapezoid method.
, 
,
The calculation is made according to the following formulas:
;
; ,
, .
Similarly, we calculate the values \u200b\u200bof bending moments:
,
The results obtained are entered 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:
.
The results obtained are entered 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 |
| 5840,2499 | ||||||||
| 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 |
| 3144,1876 | ||||||||
| 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 reference axis.
We build a summary diagram (Fig. 9)
Checking the correctness of plotting the wing loads.
From the diagram \u003d 20592kg.
Determination of the point of position of the shear force in the design section
Knowing the shear force and reduced moment in the design section (\u003d 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 - 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 \u200b\u200band 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 \u003d 5 (mm), δ p \u003d 4 (mm),
Determine the number of stringers on the upper and lower parts of the cross-section:. (fig. 10)
The loads received 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 extended 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 \u200b\u200bone 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,
Is the coefficient taking into account the delay in switching on power circuit plating compared to stringers,.
Then we find the required area of \u200b\u200bstringers in the stretched panel: Fig. eleven
Knowing the required area of \u200b\u200bthe stringer, we will choose a stringer with a close 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 a longitudinal strength set in a 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 \u200b\u200bone stringer in the compressed zone,
The attached planking area is determined by the formula:
.
Then the required stringer area is:
Knowing the required area of \u200b\u200bthe stringer, from the assortment of profiles, we will choose a stringer with a similar cross-sectional area (Fig. 12). This is a bulbogon PR102-23, 
,,. Figure: 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 riveted to the skin.
for stringer shelf:
.
Since\u003e, 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 \u200b\u200bthe 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 shearing 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 rigidity)
Find the wall thickness:
, ,
. .
Determining the distance between ribs
The distance between the ribs is determined from the condition of equal strength in case of local loss of stability of the stringer and in case of 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 stringer section with the attached skin relative to the axis passing through the center of gravity of this section and parallel to the skin plane;
- 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 factor 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 will 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 projection of bending moments on the main central axes (Fig. 17):
Determine the reduced stresses in the section elements:
We determine the real 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 for subsequent approximations for each structural element will be carried out using a computer. (Appendix 1)
After reaching the convergence of the reduction factors, it is necessary to determine the excess strength factors 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 \u200b\u200bof 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 from 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 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 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 angle of twisting 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 independently work for normal stresses, the diagram changes abruptly at each longitudinal element, remaining constant between the elements, then from the integral we pass to the sum
Determine the relative angle of twisting of the wing section when the moment M \u003d 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 circuit
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).
m.
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 \u003d 0.7 and φ e \u003d 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 \u200b\u200bof the parameters:
MPa - initial gas pressure in the shock absorber;
- coefficient of preliminary tightening of the shock absorber;
- gear ratio at the beginning of the 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:
m.
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
m.
We find the parameters using the following algorithm.
To find the unknowns and use the equations
1
2
3
After some transformations
4
Here is the gear ratio corresponding to the shock absorber travel
Coefficient of completeness of the shock absorber compression diagram when absorbing work. For telescopic racks 
.
The first of equalities (3) has the form of a quadratic equation
, 5
where 
, 6
7
from equality (5)
8
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 \u003d 0 axis gives the value S max \u003d 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
m.
Wherein:
0.589 + 0.1045 \u003d 0.6935\u003e 0.55 - the condition is met.
By setting the parameter values:
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 the 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 down the equilibrium equation for the rack relative to the hinge
The diagram of the bending moments acting in the plane of the aircraft movement is shown in Figure 23.
The maximum moment, equal to 489.57 kNm, 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 
kNm.
The torque is equal to
and only loads the cylinder.
Selection of cross-section parameters 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, 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
kN.
At the upper end of the rod, the gas presses against the rod with force
Therefore, between the sections passing through the upper and lower axle boxes, the rod is compressed by force
below the section of the lower axle box - by force
Gas acts on the cylinder through the seal with an axial force
stretching the cylinder. When constructing a diagram of N c, the forces F Tr and S z should also be taken into account. The final form of the diagrams of axial forces N c and N w is shown in Fig. 25
where is the wing elongation,
L - wingspan, m, L \u003d 8 m,
S - wing area, m 2, S \u003d 12 m 2.
where η is the narrowing of the wing
b o - root chord, m, b o \u003d 5.43 m,
b k - end chord, m, b k \u003d 2.5 m.
Wing extension
Sweep angle: 0 0
Determination of loads acting on the wing
Loads acting on the wing: for a given loading case, we determine the safety factors and the maximum operational overload. The values \u200b\u200bof operational overloads, depending on the maximum velocity head and flight mass, are determined from the table of aircraft types.
For this type of aircraft, we take n e \u003d 8.
Based on the loading case, we choose the safety factor f \u003d 2.
The design overload is determined by the formula.
Hence n p \u003d 8 × 2 \u003d 16.
The case corresponds to a curvilinear flight with (deflected ailerons or diving) and with the maximum possible speed corresponding to the high-speed flow q max. max. The given values \u200b\u200bare,;.
This case is typical for loading the tail section of the wing. Due to the rearward movement of the center of pressure, a significant torque is exerted on the wing.
The calculated aerodynamic load of a straight wing is determined by the formula:
where G is the weight of the aircraft, kg, G \u003d 17000 kg,
relative circulation over the span of a straight wing, taking into account the change in the coefficient of lift of the wing over the span and narrowing of the wing.
For a swept wing, the value should be adjusted by an amendment to take into account the sweep of the wing. The values \u200b\u200bare taken from the graphs. Then we calculate by the formula:
The mass forces of the wing structure are determined by the formula:
where is the weight of the wing, \u003d 0.11.
The mass forces from the weight of the fuel are determined by the formula:
where is the fuel weight, kg.
All calculations are summarized in table 1.
Table 1
|
The quantity | ||||||||||||||||
Based on the calculated data, we plot the calculated aerodynamic linear load, the calculated mass linear load, and the calculated total linear load (Fig. 1).
Fig. 1 Diagrams, and
Construction of design diagrams
The initial data for calculating the strength of the wing are the diagrams of shear forces, bending and torques plotted along the wing span.
When plotting the diagrams, the wing is represented as a two-support beam with consoles, loaded with distributed and concentrated forces. Supports are the attachment points of the wing to the fuselage.
We determine the reactions of the supports:
Diagrams, you need to build from the total load
Using differential dependencies:
we obtain expressions for any wing section:
For each section, we find the increment of the shearing force:
.
Summing up the values \u200b\u200bfrom the free end and taking into account the values \u200b\u200bof concentrated loads and fuselage reactions, we obtain the value of the shear force in an arbitrary wing section
.
Similarly, we determine the value of the bending moment in any section of the wing:
,
.
Taking the number of sections i \u003d 10, ∆z \u003d 0.5 m.
Taking into account the sweep of the wing, the shearing force and bending moment are determined by the formulas:
where is the sweep angle.
The results are summarized in Table 2.
table 2
Based on the data obtained, we plot the bending moments (Fig. 2).
To plot torques, the true torque must be defined relative to the center of the bend (stiffness). Let us take the coordinate of the position of the line of bending centers (stiffness):
x w \u003d 0.38 in SECH.
Then a \u003d 0.2b SES, and 1 \u003d 0.4b SES.
Linear torque in any section relative to the line of bending centers, axis is determined as follows:
The total torque will be equal to:
With sweep:.
The diagram is built only up to the fuselage side. When determining, it is also convenient to use the trapezoidal method using Table 3:
Where ; .
Table 3
Figure: 2 Diagrams of linear torque m and torque.
Wing design calculation
At this stage, we will select the values \u200b\u200bof the cross-sectional area of \u200b\u200bthe wing load-bearing elements. The power circuit of the wing is two-spar, the aerodynamic profile is NASA2411.
Determine the taper angle of the wing:
where is the relative thickness of the profile.
From here 
.
The shearing force in the design section is equal to:
where u is the height of the first and second spars,
Modulus of elasticity of belt materials.
From shear forces in the walls of the side members, linear tangential forces act:
Linear tangential forces in the walls of the side members from the torque:
where is the area of \u200b\u200bthe contour of the inter-spar part of the section.
Total tangential flows in the walls of the side members from shearing forces and torques:
The wall thicknesses of the side members and skin are determined by the following formulas:
where 
- breaking shear stress.
We take the pitch of the stringers 118 mm, we get the number of stringers
Determine the forces acting on the upper and lower wing panels:
Where is the section height,
Number of stringers
The width of the inter-spar wing.
The coefficient 0.9 in the value takes into account the weakening of the sheathing with rivet holes.
The total area of \u200b\u200bthe stretched and compressed side member belts:
For tight belts,
- for stretched belts,
where we take equal.