An example of calculating a catapult for an air launch of a space rocket. Aerodynamic heating of the rocket structure Drag coefficient at

Course project

Calculation of the aerodynamic coefficients of a cruise missile of the Tomahawk type

Introduction

pitch rocket flying aerodynamic

The design of an aircraft must necessarily include the calculation of its aerodynamic characteristics. The results obtained in the future allow us to assess the correctness of the choice of the aerodynamic scheme, to calculate the trajectory of the aircraft.

For calculations, a very important assumption is introduced: the aircraft should be considered stationary, and the oncoming air flow, on the contrary, is moving (the so-called "principle of motion reversal").

The second assumption used implies the dismemberment of the aircraft into separate components: body, empennage (wings and rudders), as well as their combinations. In this case, the characteristics are calculated separately for all components, and their sums, together with the interference corrections that determine the interaction effects, determine the aerodynamic coefficients and moments.

1. Cruise missiles

1.1 General

The process of creating modern CD is the most difficult scientific and technical task, which is being solved jointly by a number of research, design and engineering and production teams. The following main stages of the formation of the KR can be distinguished: tactical and technical assignment, technical proposals, preliminary design, working project, experimental development, bench and natural tests.

Work on the creation of modern CR samples is carried out in the following areas:

· Increasing the range and speed of flight to supersonic;

Use for guidance missiles combined multichannel systems detection and homing;

· Reduction of missile signature due to the use of stealth technology;

· Increasing the stealth of missiles by reducing the flight altitude to the limit and complicating the flight trajectory in its final section;

· Equipping the missile on-board equipment with a satellite navigation system, which determines the location of the missile with an accuracy of 10 ... .20 m;

· Integration of missiles for various purposes into a single missile system of sea, air and land-based.

The implementation of these areas is achieved mainly through the use of modern high technologies.

A technological breakthrough in aircraft and rocketry, microelectronics and computer technology, in the development of on-board automatic control systems and artificial intelligence, propulsion systems and fuels, electronic protection equipment, etc. created real developments of a new generation of CD and their complexes. It became possible to significantly increase the flight range of both subsonic and supersonic cruise missiles, increase the selectivity and noise immunity of on-board automatic control systems with a simultaneous decrease (more than twice) in weight and size characteristics.

Cruise missiles are classified into two groups:

· Ground-based;

· Sea-based.

This group includes strategic and operational-tactical missiles with a flight range from several hundred to several thousand kilometers, which, in contrast to ballistic missiles, fly to the target in dense layers of the atmosphere and have aerodynamic surfaces for this that create lift. Such missiles are designed to destroy important strategic ones.

Cruise missiles, capable of being launched from submarines, surface ships, ground complexes, and aircraft, provide the naval, ground and air forces with exceptional flexibility.

Their main advantages over BR are:

· Almost complete invulnerability in the event of a sudden nuclear missile attack by the enemy due to the mobility of the basing, while the location of silos with ballistic missiles is often known in advance to the enemy;

· Reduction in comparison with the BR of the cost of performing a combat operation to hit a target with a given probability;

· The fundamental possibility of creating an improved guidance system for the CD, operating autonomously or using a satellite navigation system. This system can provide a 100% chance of hitting a target, i.e. a miss close to zero, which will reduce the required number of missiles, and, consequently, operating costs;

· The possibility of creating a weapon system that can solve both strategic and tactical tasks;

· The prospect of creating a new generation of strategic cruise missiles with an even greater range, supersonic and hypersonic speeds, allowing retargeting in flight.

As a rule, nuclear warheads are used on strategic cruise missiles. On tactical versions of these missiles, conventional warheads are installed. For example, anti-ship missiles can be equipped with penetrating, high-explosive or high-explosive cumulative warheads.

The control system of cruise missiles depends significantly on the flight range, missile trajectory and radar target contrast. Long-range missiles usually have combined control systems, for example, autonomous (inertial, astro-inertial) plus homing at the end of the trajectory. Launching from a ground-based installation, a submarine, or a ship requires the use of a rocket booster, which is advisable to separate after fuel burnout, therefore, land-based and sea-based cruise missiles are made two-stage. When launching from a carrier aircraft, an accelerator is not required, since there is a sufficient initial speed. Solid propellant motors are usually used as an accelerator. The choice of the main engine is determined by the requirements of low specific fuel consumption and long flight time (tens of minutes or even several hours). For rockets whose flight speed is relatively low (M<2), целесообразно применять ТРД как наиболее экономичные. Для дозвуковых скоростей () используют ТРДД малых тяг (до 3000 Н). При М>2, the specific fuel consumption of turbojet and ramjet engines become comparable and other factors play the main role in choosing an engine: simplicity of design, low weight and cost. Hydrocarbon fuels are used as fuel for propulsion engines.

In this course project for further research, a cruise missile of the Tomahawk type will be considered as a prototype of an aircraft.

1.2 Tomahawk cruise missile

KR "Tomahawk" in nuclear warhead has a nuclear charge capacity of 200 kg. It is difficult to detect it by radar stations. The length of the KR is 6.25 m, and the weight is 1450 kg. In conventional combat, this missile is designed to strike at surface ships at ranges of up to 550 km from the launch site and at coastal targets at ranges of up to 1,500 km.

The sea-based cruise missile "Tomahawk" (BGM - 109A) is designed to strike important military and industrial targets. The firing range is 2500 km. The firing accuracy is no more than 200 m. The missile guidance system is combined, it includes an inertial system and a trajectory correction system along the contour of the terrain. Launch weight - 1225 kg, length 5.5 m, hull diameter - 530 mm, warhead weight - 110 kg. The missile is equipped with a 200 kg nuclear warhead. The missile entered service in 1984. Its combat use is envisaged both from submarines and from surface ships.

Figure: 1 Tomahawk cruise missile (BGM - 109A)

The flight path of the Tomahawk BGM-109С / D missile

Figure: 2 Flight trajectory of the BGM-109C / D Tomahawk missile:

2-area of \u200b\u200bthe first correction according to the TERCOM system;

3-march section TERCOM correction using the NAVSTAR system

4-correction of the trajectory according to the DSMAC system;

Tactical and technical characteristics

Firing range, km
BGM-109A when launched from a surface ship
BGM-109С / D when launched from a surface ship
BGM-109С / D when launched from a submarine
Maximum flight speed, km / h
Average flight speed, km / h
Rocket length, m
Rocket body diameter, m
Wingspan, m
Starting weight, kg


Warhead

	semi-armor-piercing - 120 kg
	cassette - 120 kg
Main engine F-107

Fuel weight, kg
Dry engine weight, kg

Length, mm
Diameter, mm

2. Calculation of aerodynamic characteristics by the analytical method of Lebedev-Chernobrovkin

Aerodynamic calculation is the most important element of aerodynamic research of an aircraft or its individual parts (hull, wings, empennage, control devices). The results of such a calculation are used in trajectory calculations, in solving problems related to the strength of moving objects, in determining the flight performance of an aircraft.

When considering aerodynamic performance, it is possible to use the principle of breaking down the characteristics into separate components for isolated hulls and bearing surfaces (wings and empennage), as well as their combinations. In the latter case, the aerodynamic forces and moments are determined as the sum of the corresponding characteristics (for an isolated body, wings, and tail) and interference corrections due to interaction effects.

Aerodynamic forces and moments can be determined using aerodynamic coefficients.

According to the representation of the total aerodynamic force and the total aerodynamic moment in the projections on the axis, respectively, of the velocity and associated coordinate systems, the following names of aerodynamic coefficients are adopted: - aerodynamic coefficients drag, lateral force rise;

To study the dynamics of an aircraft, it is necessary to take into account the acting forces and moments, including aerodynamic ones. The total aerodynamic force, which depends on a number of factors, can be represented by the components along the velocity axes of coordinates (x, y, z) or along the associated (), and the total aerodynamic moment M - expanded along the axes (). In the case of a symmetrical aircraft, the lift Y and the lateral force Z have the same dependences, respectively, on the angles of attack and slip, on the angles of deflection of the rudders and.

Geometric table

Name, dimension	The quantity	Value
		Console I	Console II

Case diameter, m
Amidships area, m 2
Bottom cut area, m 2
Bow length, m
Length of the cylindrical part, m
Body extension
The volume of the bow of the hull, m 3
Extension of the bow of the hull
Extension of the cylindrical part of the body
Narrowing aft hull
Full span of the bearing surface, m
The span of the bearing surface excluding the body diameter, m
Console side chord length, m
Console root chord length, m
Console end chord length, m
Area of \u200b\u200btwo consoles, m 2
Extension of consoles
Narrowing consoles
Console sweep angle along the leading edge
Tangent of the sweep angle of the consoles along the mid-chord line
The sweep angle of the consoles along the midline of the chords
Relative profile thickness
Average aerodynamic chord length, m
Coordinate z a.k. average aerodynamic chord, m
Coordinate x a.k. average aerodynamic chord with respect to
Distance from the front point of the body to the console, m

2.1 Lift force

The lifting force is determined by the formula

where is the velocity head, is the air density, is the characteristic area, (for example, the area cross section fuselage), - coefficient of lift.

The coefficient is usually determined in the velocity coordinate system 0xyz. Along with the coefficient, the coefficient of normal force is further considered, it is determined in the associated coordinate system.

These coefficients are related to each other by the ratio

We represent the aircraft in the form of a set of the following main parts: the body (fuselage), front (I) and rear (II) bearing surfaces. At small angles of attack and angles of deflection of the bearing surfaces, the dependences and are close to linear, i.e. can be represented as

here and are the angles of deflection of the front and rear bearing surfaces, respectively; and - values \u200b\u200band at; , are the partial derivatives of the coefficients with respect to the angles and, taken at.

The values \u200b\u200band for unmanned aircraft are in most cases close to zero, so they are not considered further. The rear bearing surfaces are taken as controls.

At small angles of attack and at can be set, then equality (2) takes the form. We represent the normal force of the aircraft as the sum of three terms

each of which is expressed through the corresponding coefficient of normal force:

Dividing equality (3) term by term and removing the derivative with respect to, we obtain at the point 0

where; - flow deceleration factors ;; ; - relative areas of aircraft parts. Let us consider in more detail the quantities included in the right-hand side of equality (4).

The first term takes into account the fuselage's own normal force, and at small angles of attack, it is equal to the normal force of the isolated fuselage (excluding the influence of the bearing surfaces).

The second term characterizes the normal force created by the front bearing surface and applied partly to the consoles and partly to the body in the zone of their influence.

The magnitude of this force is expressed in terms of the normal force of isolated wings (i.e. wings composed of two consoles) using the interference coefficient k:. The values \u200b\u200band kI are calculated at the Mach number.

The third term in expression (4) is similar to the second. The only difference is that when determining the angle of attack of the rear bearing surface, it is necessary to take into account the average angle of the slope of the flow caused by the front bearing surface:. At small angles of attack, the dependence is close to linear. In that case, the derivative can also be expressed as

All quantities included in (5) are calculated at the Mach number.

2.2 The derivative of the aircraft lift coefficient by the angle of deflection of the controls

let us differentiate expression (1) with respect to angle II:

At small angles this expression takes the following form:

Dividing equality (3) term by qS and taking the derivative with respect to, we obtain

characterizes the normal force of the rear surface, applied partly to the consoles, and partly to the body in the zone of their influence. The magnitude of this force is expressed through the interference coefficient and the relative efficiency of the controls n:

The calculation is presented in table. 3.3, where is the tail sweep angle; is the coefficient of lifting force reduction due to the gap between the rudder and the hull when the rudders are deflected.

Calculation table

The quantity

Calculation table

The quantity

2.3 Frontal resistance

The drag force is calculated by the formula

Let us represent the drag coefficient of the aircraft as the sum of two terms, where is the drag coefficient at; - coefficient of inductive resistance, which is understood as the resistance depending on the angles, and. The aircraft coefficient can be expressed as

where 1.05 is the correction for unaccounted for details; - the ratio of the total area of \u200b\u200ball consoles of the front bearing surface to the characteristic area; - the same for the rear bearing surface; , are the coefficients of the isolated parts of the aircraft.

2.4 Drag coefficient at

By its physical nature, the body drag at can be divided into frictional and pressure resistances. In accordance with this pressure, it is possible to express the drag coefficient of the hull at (referred to the midship area) as follows:

where the last three terms are pressure resistance.

2.5 Drag coefficient of bearing surfaces at

The methods for calculating the coefficient of the front and rear bearing surfaces are almost identical. The only difference is that the calculation should be carried out at the Mach number, and the calculation at.

The frontal resistance of the bearing surface with sharpened trailing edges at is made up of the profile and wave resistance. Accordingly, one can write

The profile resistance is due to the viscosity of the air. It is mainly determined by frictional forces and, to a small extent, by the pressure difference in the nose and tail of the airfoil.

Wave resistance - pressure resistance due to the compressibility of air. It occurs when the flow around the wings is accompanied by the appearance of shock waves.

For an aircraft with a cruciform arrangement of the wings (++), the drag force is created by two pairs of front and rear bearing surfaces; therefore, the coefficients and should be multiplied by the corresponding doubled dimensionless areas.

Calculation table and

The quantity

Calculation table

The quantity

2.6 Pitch moment

When studying the moments of forces acting on the aircraft, in particular, the moments of pitch, we will use the related coordinate system 0x1y1z1 The moment of pitch or longitudinal moment is caused by aerodynamic and reactive forces. Considering the moment of aerodynamic forces, it is convenient to introduce the concept of a dimensionless coefficient

The magnitude of the aerodynamic moment at a given speed and altitude depends on a number of factors, and primarily on the angle of attack and angles of deflection of the controls. In addition, the magnitude of the moment is influenced by the angular velocity of rotation of the aircraft, as well as the rate of change in the angle of attack and deflection of the rudders, characterized by the derivatives and. In this way,

For small values \u200b\u200bof the arguments, expression (6) can be represented as a linear function

where, etc. - partial derivatives of the pitching moment according to the corresponding parameters.

The dimensionless torque coefficient is a function of dimensionless parameters only. Since the quantities, and have the dimension I / s, then instead of them the dimensionless angular velocity and dimensionless derivatives, are introduced. General expression of the longitudinal moment coefficient at small values \u200b\u200bof parameters, etc. has the form

To simplify the writing of the quantities included in expressions (6) and (7), the index "I" will be omitted in what follows. In addition, we will omit the dashes in the notation of the partial derivatives

2.7 Moment of pitch at

Let us consider the magnitude of the aerodynamic longitudinal moment acting on the aircraft, provided that the angular velocity, the angle of attack and the angles of deflection of the controls remain unchanged in time.

Let us introduce the concept of the center of pressure of an aircraft. The center of pressure is a point on the longitudinal axis 0x1, through which the resultant - aerodynamic forces - passes.

The moment of aerodynamic forces relative to the center of pressure can be expressed as, and the moment coefficient

here is the coordinate of the aircraft's center of gravity, is the coordinate of the center of pressure (the report is made from the nose of the hull).

By analogy with the concept of the center of pressure of the entire aircraft, we also introduce the concept of the centers of pressure of its parts as points of application of the normal forces created by these parts.

From the equilibrium condition we have

From here we find the expression for:

At small angles of attack and angles of deflection of the rudders, it is convenient to use the concept of aerodynamic foci of an aircraft. The angle of attack of an aircraft is the point of application of that part of the normal force that is proportional to the angle of attack (i.e.). Then, with fixed controls, the moment of aerodynamic forces relative to the 0z1 axis passing through the focal point does not depend on the angle of attack. Similarly, it can be shown that the moment relative to the focus on does not depend on, and the moment relative to the focus on does not depend on.

Using the concept of aerodynamic foci, we can write the following expression for the coefficient of the aircraft pitching moment at small angles, and:

In these expressions, are the coordinates of the focuses along, and.

2.8 Pitch moment caused by aircraft rotation around the Z axis

Consider an aircraft flying with a speed v and simultaneously rotating around its axis (transverse) with an angular velocity.

When the aircraft rotates, each point of its surface acquires an additional speed equal to. As a result, the meeting angles of the flow with individual surface elements are different from the meeting angles for purely translational motion. Changing the meeting angles leads to the appearance of additional aerodynamic forces, which can be reduced to the resultant applied at the center of gravity and the moment relative to the transverse axis passing through the center of gravity.

The value is very small and is usually neglected in lift calculations.

The moment significantly affects the dynamic properties of the aircraft. It is called pitch damping moment or longitudinal damping moment.

The amount of damping moment is proportional to the angular velocity. Therefore.

Let us express the derivative in terms of the dimensionless moment coefficient and the dimensionless angular velocity. Since and, then, where is the rotational derivative of the torque coefficient.

Let's imagine the longitudinal damping moment as the sum of the moments created by the aircraft parts:. This expression can be rewritten in accordance with equality (9):

Reducing by, we get:

Calculation table and

The quantity

Calculation table

The quantity

2.9 Summary table of aerodynamic coefficients

3. Calculation of aerodynamic characteristics using the SolidWorks 2014 package

SolidWorks is a computer-aided design, engineering analysis and production preparation system for products of any complexity and purpose. CAD developer SolidWorks is SolidWorks Corp. (USA), an independent division of Dassault Systemes (France), a world leader in high-tech software. Developed by SolidWorks Corp. characterized by high indicators of quality, reliability and productivity, which, combined with qualified support, makes SolidWorks the best solution for industry and personal use. Software operates on the Windows platform, has support for the Russian language, and, accordingly, supports GOST and ESKD.

This package allows you to build an aircraft model and calculate aerodynamics using Flow Simulation, which is a fluid dynamic analysis module in the SolidWorks environment, minimizing errors that depend on the human factor.

In this course project, the Tomahawk RC model was built and aerodynamics were calculated using SolidWorks 2014 and SolidWorks Flow Simulation 2012.

The aircraft model built using CAD SolidWorks 2014 is shown in Figures 3 and 4.

Figure 3 - Side view of the model

Figure 4 - Front view of the model

3.2 Choice of angles of attack and flow velocity

The aerodynamic coefficients will be calculated for Mach: M \u003d 0.7, 1.2 and for the angle of attack b \u003d 0 degrees.

Aerodynamic forces and moments can be determined by knowing the aerodynamic coefficients.

According to the representation of the total aerodynamic force and the total aerodynamic moment in projections on the axes, respectively, of the velocity and associated coordinate systems, the following names of aerodynamic coefficients are adopted: - aerodynamic coefficients of drag, lift and lateral force; - aerodynamic coefficients of roll, yaw and pitch moments.

3.3 Calculation results

The calculation results are given for a flow rate of M \u003d 0.7 and M \u003d 1.2 at b \u003d 0 degrees. The results are shown in Figures 5-14 and Table 10.

For b \u003d 0 and M \u003d 1.2

Figure 5 - Results of speed change

Figure 6 - Results of pressure changes

Figure 7 - Results of density change

Figure 8 - Results of temperature change

For b \u003d 0 and M \u003d 0.7

Figure 9 - Results of speed change

Figure 10 - Results of pressure changes

Figure 11 - Results of density change

Figure 12 - Temperature change results

Figure 13-basic parameters for M \u003d 1.2

Figure 14 - basic parameters for M \u003d 0.7

Since we know the values \u200b\u200bof the lifting force and the frontal resistance force, we can express from the expressions Y \u003d c y qS and X \u003d c x qS with y and with x

Calculation table

Conclusion

In this course project, an aircraft of the type KR "Tomahawk" was considered and its aerodynamic coefficients were calculated.

As a result of the calculations, the values \u200b\u200bof the drag coefficients, the lift coefficients and the coefficients of aerodynamic moments were obtained. When considering aerodynamic performance, you can use the principle of breaking down the characteristics into separate components for insulated hulls and bearing surfaces (wings and empennage), as well as their combinations. In the latter case, aerodynamic forces and moments are determined as the sum of the corresponding characteristics (for an isolated body, wings, and empennage) and interference corrections due to interaction effects. Aerodynamic forces and moments can be determined using aerodynamic coefficients.

The results of calculating the aerodynamic coefficients and comparative analysis analytical method Lebedev-Chernobrovkin and numerical modeling are given in the table.

Comparative analysis of calculation results

A model of the investigated aircraft was created using CAD SolidWorks 2014 SP5.0 and its aerodynamics was investigated using SolidWorks Flow Simulation. As a result of the calculations performed, it should be considered that the numerical modeling technique allows avoiding calculation errors caused by the difference between the calculated and real shapes of the blown object. The technique also makes it possible to assess the degree of influence of inaccuracies in the manufacture of models on the results of their blowing in wind tunnels.

The analytical method of Lebedev-Chernobrovkin is based on semi-empirical laws obtained from the analysis of numerous experimental data. This method is not suitable for accurate scientific calculations, but can be used for educational purposes and for calculating aerodynamic coefficients in a first approximation.

Bibliographic list

1. Lebedev A.A., Chernobrovkin L.S. Flight dynamics. - M .: Mechanical Engineering, 1973 .-- 615 p .: ill.

2. Shalygin A.S. - Aerodynamic characteristics aircraft... - SPb: BSTU, 2003 .-- 119 p.

3. SolidWorks - the world standard for computer-aided design [Electronic resource] - http://www.solidworks.ru/products/ - date of treatment November 15, 2014

4. David Salomon. Curves and Surfaces for Computer Graphics. - Springer, 2006.

5.. B. Karpenko, S.M. Ganin "Domestic aviation tactical missiles" 2000

6. Synthesis of control in stabilization systems of unmanned aerial vehicles. Textbook edited by A.S. Shalygin. SPB 2005

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An air launch (launch from an aircraft) of an ILV with a mass of 103 tons is being considered. The catapult must accelerate it to a speed that ensures the missile leaves the aircraft without shock. The rocket moves on the yokes along the guides, and after one pair of yokes remains on the guides, under the influence of gravity it begins to acquire an angular velocity, as a result of which a collision with the aircraft ramp may occur.

This determines the lower limit on the ejection speed: uobc\u003e 12.5 m / s.

Compared to a mortar launch, launching ILV from an aircraft using a catapult has a number of advantages: there is no force (wave) and thermal effect of hot gases on the aircraft, the rocket can have aerodynamic surfaces, the dimensions of the launch system are reduced, which simplifies its layout in the cargo compartment, it can be removed the missile in the correct orientation (head towards the stream). The latter advantages allow the speed of the aircraft to be used to impart an initial velocity to the missile.

A catapult scheme with two pulling cylinders is used. The total mass of the moving parts of the catapult, based on preliminary calculations, was taken equal to 410 kg. Since the operating time of this catapult is much longer than that considered above, a scheme with two GGs operating in series is considered, which makes it possible to change the gas flow in a wider range than in a scheme with one GG. Taking into account the large distance between the power cylinders (2.5 m) and, therefore, the large length of the connecting pipelines, schemes are considered with two GGs feeding both power cylinders in series, and with two pairs of GGs, each pair feeding its own cylinder. To equalize the pressures between the cylinders, in this case, a connecting pipe with a diameter of 50 mm is used. Based on the strength of the rocket and the support nodes (elements against which the traverse of the catapult rests), the calculations were carried out for the values \u200b\u200bof the total force created by the catapult: Lcat \u003d 140 t and Lcat \u003d 160 t. Note that the total force acting on the aircraft at the start is less than these values \u200b\u200bby the magnitude of the friction force in the ILV yokes. This circuit uses a pneumatic braking device. When carrying out the calculations, it was taken into account that at the moment the catapult is triggered, the plane makes a "slide" maneuver. In this case, the pitch angle is 24 °, which additionally contributes to the acceleration of the ILV due to the projection of the force of gravity, and the apparent lateral acceleration of gravity in the cargo compartment is 3 m / s2. Low-temperature ballistic fuel is used with a combustion temperature at a constant pressure of 2200 K. The maximum pressure in the gas generator should not exceed 200-105 Pa.

In variant 1 with a maximum force of 140 tons (scheme with two pairs of gas generators), after a series of preliminary calculations, the operating time of the first chamber was chosen equal to 0.45 s, and the nozzle hole diameter was 27 mm. The diameter of the channels in the checkers is 4 mm, the initial combustion surface area of \u200b\u200bthe first chamber is 0.096 m2, and the charge mass is 1.37 kg (for each GG). The diameter of the nozzle opening of the second chamber is 53 mm, the diameter of the channels in the checkers is 7.7 mm, the initial combustion surface area is 0.365 m2, and the charge mass is 4.95 kg. The diameter of the working chamber of the power cylinder is 225 mm, the diameter of the rod is 50 mm, the piston path before the start of braking is 5.0 m.

The maximum ILV acceleration was 16.6 m / s2, the rocket speed at the moment of separation from the traverse was 12.7 m / s (since the length of the guides when using the catapult, as a rule, is greater than the course of the catapult, the rocket speed when leaving the guides differs from the speed that the catapult imparts to the rocket). The maximum temperature of the inner wall of the power cylinder is 837 K, the rod is 558 K.

Appendix 3 contains graphs corresponding to this option. The turn-on time of the second HG is selected in such a way that the pressure in the power cylinder remains unchanged. Taking into account the spread of the ignition time of the second GG in real conditions, it starts up a little later than the calculated time, therefore, the pressure curve in the power cylinders may have a small dip. If the second HS is started earlier, an unwanted pressure surge will appear on the curve. In fig. A3.1 shows the dependences of the pressures in the gas generator, working cylinders and in the braking chamber on the movement of the moving parts of the catapult. Representation of pressure as a function of the path makes it possible to more clearly evaluate the efficiency of the catapult's working cycle, since the work performed by it is proportional to the integral of the force (pressure) along the path. As can be seen from the curves, the area of \u200b\u200bthe integrand is close to the maximum possible (taking into account the limitation on the maximum force). The use of a two-stage HG allows for high speed.

For option 2 (a catapult developing a force of 160 tons), the diameter of the power cylinder was increased to 240 mm, the diameter of the rod to 55 mm. After a series of preliminary calculations, the operating time of the first chamber was chosen equal to 0.45 s, and the nozzle hole diameter was 28 mm. The diameter of the channels in the checkers is 4 mm, the initial combustion surface area is 0.112 m2, and the charge mass is 1.43 kg (for each GG). The diameter of the nozzle opening of the second chamber is 60 mm, the diameter of the channels in the checkers is 7.4 mm, the initial combustion surface area is 0.43 m2, and the charge mass is 5.8 kg. At the same time, the maximum ILV acceleration was 18.5 m / s2, the missile speed at the moment of separation from the traverse was 13.4 m / s. The maximum temperatures of the inner wall of the power cylinder (850 K) and the rod (572 K) practically did not change.

Next, consider a scheme in which both power cylinders are powered by the same two successively triggered GGs. To do this, you have to use a sufficiently large manifold (pipeline) connecting the gas generator to the gas cylinders. In this and subsequent versions, we consider that the pipeline is made of steel with increased heat resistance 12MX, yield point 280 MPa at a temperature of 293 K and 170 MPa at a temperature of 873 K, which has a high coefficient of thermal conductivity.

For variant 3 with a force of 140 tons, the diameter of the connecting pipeline is assumed to be 110 mm with a wall thickness of 13 mm. The diameter of the power cylinder, as in version 1, is 220 mm, the diameter of the rod is 50 mm. After a series of preliminary calculations, the operating time of the first chamber was chosen equal to 0.46 s, and the diameter of the nozzle hole was 40 mm. The diameter of the channels in the checkers is 16 mm, the initial combustion surface area is 0.43 m2, and the charge mass is 4.01 kg. The diameter of the nozzle opening of the second chamber is 84 mm, the diameter of the channels in the checkers is 8.0 mm, the initial combustion surface area is 0.82 m2, and the charge mass is 11.0 kg.

The maximum ILV acceleration was 16.5 m / s2, the rocket speed at the moment of separation from the traverse was 12.65 m / s (0.05 m / s less than in option 1). The maximum temperature of the inner wall of the power cylinder is 755 K, the rod is 518 K (decreased by 40-80 K due to heat loss in the pipeline). The maximum temperature of the inner wall of the pipeline is 966 K. This is a rather high, but quite acceptable temperature, given that the thickness of the zone in which the tensile strength of the material significantly decreases due to heating is only 3 mm.

For the variant of the catapult developing a force of 160 tons (variant 4), the diameter of the power cylinder is taken equal to 240 mm, the diameter of the rod is 55 mm, and the diameter of the pipeline is 120 mm. After a series of preliminary calculations, the operating time of the first chamber was chosen equal to 0.46 s, and the diameter of the nozzle hole was 43 mm. The diameter of the channels in the checkers is 16 mm, the initial combustion surface area is 0.515 m2, and the charge mass is 4.12 kg. The diameter of the nozzle opening of the second chamber is 90 mm, the diameter of the channels in the checkers is 7.8 mm, the initial combustion surface area is 0.95 m2, and the charge mass is 12.8 kg. At the same time, the maximum ILV acceleration is 18.4 m / s2, the missile speed at the moment of separation from the traverse is 13.39 m / s. The maximum temperatures of the inner wall of the power cylinder are 767 K, the rod is 530 K. The maximum temperature of the inner wall of the pipeline is 965 K. A decrease in the diameter of the pipeline to 95 mm leads to an increase in the temperature of its walls to 1075 K, which is still permissible.

In conclusion, let us consider the influence of the number of GGs on the reliability of the catapult. One single-stage GG will provide maximum reliability with minimum rocket ejection speed. In case of non-start of the main generator, the accident does not occur The emission rate can be increased by increasing the fuel burning rate, the indicator in the combustion law, the pressure at the end of the GG operation to 60-80 MPa (the pressure in the power cylinders and the pipeline remains unchanged), the pipeline diameter (initial volume).

The general two-stage GG has less reliability, but provides an increase in the rocket ejection speed. In the case of non-launch of the second stage, one of the following options occurs: the rocket is ejected at a low speed, excluding its further use, the rocket touches the aircraft with minor consequences (the inability to completely close the ramp,

the impossibility of subsequent pressurization of the cargo compartment), distortion or impact of the missile on the aircraft, leading to breakdowns or fire and, ultimately, to the death of the aircraft. To increase the reliability for this case, the following measures can be taken to prevent the worse development of events, duplication of the second stage main generator launch systems, and an increase in the first stage main generator operation time (due to which the rocket exit speed when only the first stage main generator is operating will increase so much that the consequences of non-launch will not be so dangerous) , change in the design of the aircraft, excluding its accident when the rocket exits at a lower speed. It should be noted that in the options under consideration, when only the first GG is triggered, the missile exit speed will decrease by 3-4 m / s.

AERODYNAMIC HEATING

Heating of bodies moving at high speed in air or other gas. A. n.- the result of the fact that air molecules attacking the body are inhibited near the body. If the flight is performed with supersonic sound. speed, deceleration occurs primarily in the shock wave arising in front of the body. Further deceleration of air molecules occurs directly at the very surface of the body, incl. boundary layer. When the flow of air molecules is decelerated, the energy of their chaotic (thermal) movement increases, that is, the gas temp-pa near the surface of a moving body increases. Max. temp-pa, to which the gas can heat up in the vicinity of a moving body, is close to the so-called. deceleration temp-re: T0 \u003d Tn + v2 / 2cp, where Tn is the incoming air temp-pa, v is the body's flight speed, cf. heat capacity of gas at constant. pressure. So, for example, when flying supersonic. aircraft with three times the speed of sound (approx. 1 km / s), the deceleration rate pa is approx. 400 ° C, and at the entrance to cosm. apparatus into the Earth's atmosphere from the 1st cosm. speed (about 8 km / s), the braking temperature reaches 8000 ° C. If in the first case it lasts long enough. flight, the temperature-pa of the aircraft skin can be close to the deceleration temperature, then in the second case the surface of the space. apparatus will inevitably begin to collapse due to the inability of materials to withstand such high temperatures.

From areas of gas with an increase. temperature-swarm heat is transferred to a moving body, A. n. There are two forms of A. n. - convective and radiation. Convective heating is a consequence of the transfer of heat from the outer, "hot" part of the boundary layer to the surface of the body by means of a pier. thermal conductivity and heat transfer when moving macroscopic. elements of the environment. Quantitatively, the convective heat flux qk is determined from the ratio: qk \u003d a (Te-Tw), where Te is the equilibrium temperature-pa (the limiting temperature-pa, to which the surface of the body could heat up if there was no energy removal), Tw - real temperature of the surface, and - coefficient. convective heat transfer, depending on the speed and altitude of flight, the shape and size of the body, as well as on other factors. The equilibrium temp-pa Te is close to the braking temp-re. Dependence coeff. a from the listed parameters is determined by the flow regime in the boundary layer (laminar or turbulent). In the case of a turbulent flow, convective heating becomes more intense. This is due to the fact that, in addition to the pier. thermal conductivity, turbulent velocity fluctuations in the boundary layer begin to play an essential role in energy transfer.

With an increase in the flight speed, the air temperature behind the shock wave and in the boundary layer increases, as a result of which the dissociation and ionization of molecules occurs. The resulting atoms, ions and electrons diffuse into a colder area - to the surface of the body. There, a reverse reaction (recombination) occurs, proceeding with the release of heat. This gives complement. contribution to convective A. n.

Upon reaching the flight speed \u003d 5000 m / s, the temp-pa behind the shock wave reaches values \u200b\u200bat which the gas begins to radiate energy. Due to the radiant transfer of energy from areas with increasing. temperature swarm to the surface of the body occurs radiation. heat. In this case, the greatest role is played by radiation in the visible and UV regions of the spectrum. When flying in the Earth's atmosphere at speeds below the 1st cosmic radiation. heating is small compared to convective heating. At the 2nd cosm. speed (11.2 km / s), their values \u200b\u200bbecome close, and at flight speeds of 13-15 km / s and higher, corresponding to the return of objects to the Earth after flying to other planets, main. the contribution is already made by the radiation. heat.

A. n. plays an important role in the return of space to the Earth's atmosphere. devices. To combat A. n. fly. devices are equipped with specials. thermal protection systems. There are active and passive thermal protection methods. In active methods, a gaseous or liquid coolant is forcibly supplied to the protected surface and takes over the main. part of the heat entering the surface. The gaseous coolant, as it were, blocks the surface from the effects of high-temperature ext. environment, and the liquid coolant, which forms a protective film on the surface, absorbs the heat approaching the surface due to heating and evaporation of the film, as well as the subsequent heating of vapors. In passive methods of thermal protection, the effect of the heat flux is assumed by the special. way constructed externally. shell or special coating applied to the base. design. Radiation thermal protection is based on the use as external. shell of material that maintains at high temperature pax sufficient mechanical. strength. In this case, almost all the heat flux approaching the surface of such a material is re-emitted to the surrounding production.

Most widespread in rocket-space. technology received thermal protection using destructible coatings, when the protected structure is covered with a layer of special. material, part of which under the influence of heat flow can be destroyed as a result of the processes of melting, evaporation, sublimation and chemical. reactions. In this case, DOS. part of the suitable heat is spent on the implementation of decomp. physical and chemical transformations. Additional barriers. the effect takes place due to blowing into the ext. environment of relatively cold gaseous products of destruction of heat-shielding material. An example of disintegrating heat-protective coatings is fiberglass and other organic plastics. and organosilicon. binders. As a means of protecting aircraft from A. n. also used carbon-carbon composites. materials.

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Word forms

"AERODYNAMIC HEATING" in books

High frequency heating

From the book Great Soviet Encyclopedia (YOU) of the author TSB

Aerodynamic moment

TSB

Aerodynamic heating

From the book Great Soviet Encyclopedia (AE) of the author TSB

Dielectric heating

From the book Great Soviet Encyclopedia (DI) of the author TSB

Induction heating

TSB

Infrared heating

From the book Great Soviet Encyclopedia (IN) of the author TSB

Metal heating

From the book Great Soviet Encyclopedia (NA) of the author TSB

Aerodynamic track

From the book Great Soviet Encyclopedia (SL) of the author TSB

7.1.1. RESISTIVE HEATING

author Team of authors

7.1.1. RESISTIVE HEAT Initial period. First experiments on heating conductors electric shock belong to the XVIII century. In 1749, B. Franklin (USA), while studying the discharge of a Leyden jar, discovered heating and melting of metal wires, and later on