Coursework on design. First approximation calculation of helicopter take-off weight Helicopter lift formula characteristics

INTRODUCTION

Helicopter design is a complex process that evolves over time, divided into interrelated design stages and phases. The aircraft being created must meet the technical requirements and meet the technical and economic characteristics specified in the design specifications. The terms of reference contain the initial description of the helicopter and its flight performance characteristics, ensuring high economic efficiency and competitiveness of the designed machine, namely: load capacity, flight speed, range, static and dynamic ceiling, service life, durability and cost.

The terms of reference are clarified at the stage of pre-design research, during which a patent search, analysis of existing technical solutions, research and development work are carried out. The main task of pre-design research is the search and experimental verification of new principles for the functioning of the designed object and its elements.

At the preliminary design stage, an aerodynamic design is selected, the appearance of the helicopter is formed, and the main parameters are calculated to ensure the achievement of the specified flight performance characteristics. These parameters include: the weight of the helicopter, the power of the propulsion system, the dimensions of the main and tail rotors, the weight of fuel, the weight of instrumentation and special equipment. The calculation results are used in developing the helicopter layout and drawing up a centering sheet to determine the position of the center of mass.

The design of individual helicopter units and components, taking into account the selected technical solutions, is carried out at the technical design development stage. In this case, the parameters of the designed units must satisfy the values ​​​​corresponding to the preliminary design. Some parameters can be refined in order to optimize the design. During technical design, aerodynamic strength and kinematic calculations of components, selection of structural materials and design schemes are performed.

At the detailed design stage, working and assembly drawings of the helicopter, specifications, picking lists and other technical documentation are prepared in accordance with accepted standards

This paper presents a methodology for calculating helicopter parameters at the preliminary design stage, which is used to complete a course project in the discipline "Helicopter Design".

1. First approximation calculation of helicopter take-off weight

where is the mass of the payload, kg;

Crew weight, kg.

Range of flight

2. Calculation of helicopter rotor parameters

2.1 Radius R, m, single-rotor helicopter main rotor calculated by the formula:

where is the take-off weight of the helicopter, kg;

g - free fall acceleration equal to 9.81 m/s 2;

p - specific load on the area swept by the main rotor,

=3,14.

Specific load value p the area swept by the screw is selected according to the recommendations presented in work /1/: where p= 280

We take the radius of the rotor equal to R= 7.9

Angular velocity , s -1, rotation of the main rotor is limited by the value of the peripheral speed R ends of the blades, which depends on the take-off weight of the helicopter and amounted to R= 232 m/s.

C -1.

RPM

2.2 Relative air densities on static and dynamic ceilings

2.3 Calculation of economic speed at the ground and on a dynamic ceiling

The relative area of ​​the equivalent harmful plate is determined:

Where S uh= 2.5

The value of economic speed near the ground is calculated V h, km/h:

Where I = 1,09…1,10 - induction coefficient.

Km/hour.

The value of the economic speed on the dynamic ceiling is calculated V ding, km/h:

Where I = 1,09…1,10 - induction coefficient.

Km/hour.

2.4 The relative values ​​of the maximum and economic on the dynamic ceiling are calculated horizontal flight speeds:

Where V max=250 km/h and V ding=182.298 km/h - flight speed;

R=232 m/s - peripheral speed of the blades.

2.5 Calculation of the permissible ratios of the thrust coefficient to the rotor filling for the maximum speed at the ground and for the economic speed at the dynamic ceiling:

at

2.6 Main rotor thrust coefficients at the ground and on the dynamic ceiling:

2.7 Calculation of rotor filling:

Main rotor filling calculated for cases of flight at maximum and economic speeds:

As a calculated fill value main rotor is taken to be the largest value of Vmax And V ding:

We accept

Chord length b and relative elongation rotor blades will be equal to:

Where zl is the number of main rotor blades (zl = 3)

2.8 Relative increase in rotor thrust to compensate for the aerodynamic drag of the fuselage and horizontal tail:

where Sф is the area of ​​the horizontal projection of the fuselage;

S th - area of ​​the horizontal tail.

S f =10 m 2;

S th =1.5 m2.

3. Calculation of the power of the helicopter propulsion system.

3.1 Calculation of power when hanging on a static ceiling:

The specific power required to drive the main rotor in hover mode on a statistical ceiling is calculated by the formula:

Where N H st- required power, W;

m 0 - take-off weight, kg;

g - free fall acceleration, m/s 2;

p - specific load on the area swept by the main rotor, N/m 2;

st - relative air density at the height of the static ceiling;

0 - relative efficiency main rotor in hover mode ( 0 =0.75);

Relative increase in main rotor thrust to balance the aerodynamic drag of the fuselage and horizontal tail:

3.2 Calculation of power density in level flight at maximum speed

The specific power required to drive the main rotor in horizontal flight at maximum speed is calculated by the formula:

where is the peripheral speed of the ends of the blades;

Relative equivalent harmful plate;

I uh- induction coefficient, determined depending on the flight speed according to the following formulas:

At km/h,

At km/h.

3.3 Calculation of power density in flight on a dynamic ceiling at economic speed

The specific power for driving a main rotor on a dynamic ceiling is:

Where ding- relative air density on the dynamic ceiling,

V ding- economic speed of the helicopter on a dynamic ceiling,

3.4 Calculation of specific power in flight near the ground at economic speed in the event of one engine failure during takeoff

The specific power required to continue takeoff at economic speed when one engine fails is calculated by the formula:

where is the economic speed at the ground,

3.5 Calculation of specific reduced powers for various flight cases

3.5.1 The specific reduced power when hanging on a static ceiling is equal to:

where is the specific throttling characteristic, which depends on the height of the static ceiling H st and is calculated by the formula:

0 - power utilization factor of the propulsion system in hovering mode, the value of which depends on the take-off weight of the helicopter m 0 :

At m 0 < 10 тонн

At 10 25 tons

At m 0 > 25 tons

3.5.2 Specific reduced power in horizontal flight at maximum speed is equal to:

where is the power utilization factor at maximum flight speed,

Throttle characteristics of engines depending on flight speed V max :

3.5.3 Specific reduced power in flight on a dynamic ceiling at economic speed V ding is equal to:

where is the power utilization factor at economic flight speed,

and - degrees of engine throttling, depending on the height of the dynamic ceiling H and flight speed V ding in accordance with the following throttle characteristics:

3.5.4 The specific reduced power in flight near the ground at economic speed with the failure of one engine on takeoff is equal to:

where is the power utilization factor at economic flight speed,

The degree of engine throttling in emergency mode,

n =2 - number of helicopter engines.

3.5.5 Calculation of the required power of the propulsion system

To calculate the required power of the propulsion system, the maximum value of the specific reduced power is selected:

Required power N helicopter propulsion system will be equal to:

Where m 0 1 - helicopter take-off weight,

g = 9.81 m 2/s - free fall acceleration.

W,

3.6 Selection of engines

We accept two turboshaft engines VK-2500 (TV3-117VMA-SB3) total power of each N=1.405 10 6 W

The VK-2500 engine (TV3-117VMA-SB3) is intended for installation on new generation helicopters, as well as for replacing engines on existing helicopters to improve their flight performance. It was created on the basis of the serial certified TV3-117VMA engine and is produced at the Federal State Unitary Enterprise “Plant named after V.Ya. Klimov."

4. Calculation of fuel mass

To calculate the mass of fuel that provides a given flight range, it is necessary to determine the cruising speed V cr. The cruising speed is calculated using the method of successive approximations in the following sequence:

a) the value of the first approach cruising speed is taken:

km/hour;

b) the induction coefficient is calculated I uh:

At km/h

At km/h

c) the specific power required to drive the main rotor in flight at cruising mode is determined:

where is the maximum value of the specific reduced power of the propulsion system,

Power change coefficient depending on flight speed V cr 1, calculated by the formula:

d) The second approach cruising speed is calculated:

e) The relative deviation of the speeds of the first and second approximations is determined:

When the cruising speed of the first approximation is clarified V cr 1, it is assumed to be equal to the calculated speed of the second approximation. Then the calculation is repeated from point b) and ends with the condition .

Specific fuel consumption is calculated using the formula:

where is the coefficient of change in specific fuel consumption depending on the operating mode of the engines,

Coefficient of change in specific fuel consumption depending on flight speed,

Specific fuel consumption at takeoff.

In case of flight in cruising mode the following is accepted:

At kW;

At kW.

Kg/W hour,

Mass of fuel consumed for flight m T will be equal to:

where is the specific power consumed at cruising speed,

Cruising speed,

L - range of flight.

5. Determination of the mass of helicopter components and assemblies.

5.1 The mass of the main rotor blades is determined by the formula:

Where R - rotor radius,

- filling the main rotor,

Kg,

5.2 The mass of the main rotor hub is calculated using the formula:

Where k Tue- weight coefficient of bushings of modern designs,

k l- coefficient of influence of the number of blades on the mass of the hub.

In the calculation you can take:

Kg/kN,

therefore, as a result of transformations we get:

To determine the mass of the main rotor hub, it is necessary to calculate the centrifugal force acting on the blades N Central Bank(in kN):

KN,

kg.

5.3 Booster control system weight, which includes the swashplate, hydraulic boosters, and the main rotor hydraulic control system is calculated using the formula:

Where b- chord of the blade,

k boo- the weight coefficient of the booster control system, which can be taken equal to 13.2 kg/m3.

Kg.

5.4 Weight of manual control system:

Where k RU- the weight coefficient of the manual control system, taken for single-rotor helicopters to be equal to 25 kg/m.

Kg.

5.5 The mass of the main gearbox depends on the torque on the main rotor shaft and is calculated by the formula:

Where k edit- weight coefficient, the average value of which is 0.0748 kg/(Nm) 0.8.

The maximum torque on the main rotor shaft is determined through the reduced power of the propulsion system N and propeller speed :

Where 0 - power utilization factor of the propulsion system, the value of which is taken depending on the take-off weight of the helicopter m 0 :

At m 0 < 10 тонн

At 10 25 tons

At m 0 > 25 tons

N m,

Main gearbox weight:

Kg.

5.6 To determine the mass of the tail rotor drive units, its thrust is calculated T ditch :

Where M nv- torque on the main rotor shaft,

L ditch- the distance between the axes of the main and tail rotors.

The distance between the axes of the main and tail rotors is equal to the sum of their radii and clearance between the ends of their blades:

Where - gap taken equal to 0.15...0.2 m,

The radius of the tail rotor, which, depending on the take-off weight of the helicopter, is:

When t,

When t,

At t.

Power N ditch, spent on rotating the tail rotor, is calculated by the formula:

Where 0 - relative efficiency of the tail rotor, which can be taken equal to 0.6...0.65.

W,

Torque M ditch transmitted by the steering shaft is equal to:

N m,

where is the speed of the steering shaft,

s -1,

Torque transmitted by the transmission shaft, N m, at rotation speed n V= 3000 rpm equal to:

N m,

Weight m V transmission shaft:

Wherek V- weight coefficient for the transmission shaft, which is equal to 0.0318 kg/(Nm) 0.67.

Weight m etc intermediate gearbox is equal to:

Where k etc- weight coefficient for the intermediate gearbox, equal to 0.137 kg/(Nm) 0.8.

Mass of the tail gearbox rotating the tail rotor:

Where k xp- weight coefficient for the tail gearbox, the value of which is 0.105 kg/(Nm) 0.8

kg.

5.7 The mass and main dimensions of the tail rotor are calculated depending on its thrust T ditch .

Thrust coefficient C ditch tail rotor is equal to:

Filling the tail rotor blades ditch is calculated in the same way as for the main rotor:

where is the permissible value of the ratio of the thrust coefficient to the tail rotor filling.

Chord length b ditch and relative elongation ditch tail rotor blades is calculated using the formulas:

Where z ditch- number of tail rotor blades.

Tail rotor blade weight m lr calculated using the empirical formula:

Centrifugal force value N cbd, acting on the tail rotor blades and perceived by the hub hinges,

Tail rotor hub weight m Tue is calculated using the same formula as for the main rotor:

Where N Central Bank- centrifugal force acting on the blade,

k Tue- weight coefficient for the bushing, taken equal to 0.0527 kg/kN 1.35

k z- weight coefficient depending on the number of blades and calculated by the formula:

5.8 Calculation of the mass of the helicopter propulsion system

Specific gravity of the helicopter propulsion system dv calculated using the empirical formula:

Where N- power of the propulsion system.

The mass of the propulsion system will be equal to:

kg.

5.9 Calculation of the weight of the fuselage and helicopter equipment

The mass of the helicopter fuselage is calculated by the formula:

Where S ohm- area of ​​the washed surface of the fuselage, which is determined by the formula:

M 2,

m 0 - first approach take-off weight,

k f- coefficient equal to 1.7.

kg,

Fuel system weight:

Where m T- mass of fuel spent on flight,

k ts- weight coefficient assumed for the fuel system to be 0.09.

Kg,

The weight of the helicopter landing gear is:

Where k w- weight coefficient depending on the chassis design:

For non-retractable landing gear,

For retractable landing gear.

kg,

The mass of the helicopter electrical equipment is calculated using the formula:

Where L ditch- the distance between the axes of the main and tail rotors,

z l- number of main rotor blades,

R - rotor radius,

l- relative elongation of the main rotor blades,

k etc And k el- weighting coefficients for electrical wires and other electrical equipment, the values ​​of which are equal to:

kg,

Weight of other helicopter equipment:

Where k etc- weighting coefficient, the value of which is 2.

kg.

5.10 Calculation of helicopter take-off weight of the second approximation

The mass of an empty helicopter is equal to the sum of the masses of the main units:

Second approach helicopter take-off weight m 02 will be equal to the sum:

Where m T - mass of fuel,

m gr- payload mass,

m ek- weight of the crew.

kg,

6. Description of the helicopter layout

The designed helicopter is made according to a single-rotor design with a tail rotor, two gas turbine engines and two-legged skis. The helicopter fuselage has a frame structure and consists of the nose and central parts, tail and end beams. In the bow there is a two-seat crew cabin consisting of two pilots. The cabin glazing provides good visibility; the right and left sliding blisters are equipped with emergency release mechanisms. In the central part there is a cabin with dimensions of 6.8 x 2.05 x 1.7 m, and a central sliding door with dimensions of 0.62 x 1.4 m with an emergency release mechanism. The cargo compartment is designed to transport cargo weighing up to 2 tons and is equipped with folding seats for 12 passengers, as well as attachment points for 5 stretchers. In the passenger version, the cabin contains 12 seats, installed with a pitch of 0.5 m and a passage of 0.25 m; and in the rear part there is an opening for the rear entrance door, consisting of two doors.

The tail boom is a riveted beam-stringer type structure with working skin, equipped with units for attaching a controlled stabilizer and a tail support.

Stabilizer with a size of 2.2 m and an area of ​​1.5 m 2 with a NACA 0012 profile of a single-spar design, with a set of ribs and duralumin and fabric covering.

Double-support skis, self-orienting front support, dimensions 500 x 185 mm, shaped main supports with liquid-gas double-chamber shock absorbers, dimensions 865 x 280 mm. The tail support consists of two struts, a shock absorber and a support heel; ski track 2m, ski base 3.5m.

Main rotor with hinged blades, hydraulic dampers and pendulum vibration dampers, installed with a forward inclination of 4° 30". All-metal blades consist of a pressed spar made of AVT-1 aluminum alloy, hardened by work hardening with steel hinges on the vibration stand, tail section, steel tip and tip The blades have a rectangular shape in plan with a chord of 0.67 m and NACA 230 profiles and a geometric twist of 5%, the peripheral speed of the blade tips is 200 m/s, the blades are equipped with a visual alarm system for spar damage and an electrothermal anti-icing device.

The tail rotor with a diameter of 1.44 m is three-blade, pushing, with a cardan-type hub and all-metal blades of rectangular shape in plan, with a chord of 0.51 m and a NACA 230M profile.

The power plant consists of two turboshaft gas turbine engines with a free turbine VK-2500 (TV3-117VMA-SB3) of the St. Petersburg NPO named after. V.Ya.Klimov total power of each N=1405 W, installed on top of the fuselage and closed by a common hood with opening flaps. The engine has a nine-stage axial compressor, an annular combustion chamber and a two-stage turbine. The engines are equipped with dust protection devices.

The transmission consists of main, intermediate and tail gearboxes, brake shafts, and a main rotor. The VR-8A three-stage main gearbox provides power transmission from the engines to the main rotor, tail rotor and fan for cooling, engine oil coolers and the main gearbox; The total capacity of the oil system is 60 kg.

The control is duplicated, with rigid and cable wiring and hydraulic boosters driven from the main and backup hydraulic systems. The AP-34B four-channel autopilot ensures stabilization of the helicopter in flight in roll, heading, pitch and altitude. The main hydraulic system provides power to all hydraulic units, and the backup system provides power only to the hydraulic boosters.

The heating and ventilation system supplies heated or cold air to the crew and passenger cabins; the anti-icing system protects the main and tail rotor blades, the front windows of the cockpit and engine air intakes from icing.

Equipment for instrument flights in difficult meteorological conditions day and night includes two attitude indicators, two NV speed indicators, a combined heading system GMK-1A, an automatic radio compass, and an RV-3 radio altimeter.

Communication equipment includes command VHF radio stations R-860 and R-828, communications HF radio stations R-842 and Karat, and an aircraft intercom SPU-7.

7. Helicopter alignment calculation

Table 1. Empty helicopter alignment sheet

Static moments are calculated M cx i And M su i relative to coordinate axes:

The coordinates of the center of mass of the entire helicopter are calculated using the formulas :

Table 2. Alignment sheet with maximum load

Table 3. Alignment sheet with 5% remaining fuel and full commercial load

Center of mass coordinates empty helicopter: x0 =-0.003; y0 =-1.4524;

Coordinates of the center of mass with maximum load: x0 =0.0293; y0 =-2.0135;

Coordinates of the center of mass with 5% fuel remaining and full commercial load viscous: x 0 = -0.0678; y 0 = -1,7709.

Conclusion

In this course project, calculations were made of the take-off weight of the helicopter, the mass of its components and assemblies, as well as the layout of the helicopter. During the assembly process, the alignment of the helicopter was clarified, the calculation of which is preceded by the preparation of a weight report based on weight calculations of the units and power plant, lists of equipment, equipment, cargo, etc. The purpose of the design is to determine the optimal combination of the main parameters of the helicopter and its systems that ensure the fulfillment of specified requirements.

Introduction

Helicopter design is a complex process that evolves over time, divided into interrelated design stages and phases. The aircraft being created must meet the technical requirements and meet the technical and economic characteristics specified in the design specifications. The terms of reference contain the initial description of the helicopter and its flight performance characteristics, ensuring high economic efficiency and competitiveness of the designed machine, namely: load capacity, flight speed, range, static and dynamic ceiling, service life, durability and cost.

The terms of reference are clarified at the stage of pre-design research, during which a patent search, analysis of existing technical solutions, research and development work are carried out. The main task of pre-design research is the search and experimental verification of new principles for the functioning of the designed object and its elements.

At the preliminary design stage, an aerodynamic design is selected, the appearance of the helicopter is formed, and the main parameters are calculated to ensure the achievement of the specified flight performance characteristics. These parameters include: the weight of the helicopter, the power of the propulsion system, the dimensions of the main and tail rotors, the weight of fuel, the weight of instrumentation and special equipment. The calculation results are used in developing the helicopter layout and drawing up a centering sheet to determine the position of the center of mass.

The design of individual helicopter units and components, taking into account the selected technical solutions, is carried out at the technical design development stage. In this case, the parameters of the designed units must satisfy the values ​​​​corresponding to the preliminary design. Some parameters can be refined in order to optimize the design. During technical design, aerodynamic strength and kinematic calculations of components, selection of structural materials and design schemes are performed.

At the detailed design stage, working and assembly drawings of the helicopter, specifications, picking lists and other technical documentation are prepared in accordance with accepted standards

This paper presents a methodology for calculating helicopter parameters at the preliminary design stage, which is used to complete a course project in the discipline "Helicopter Design".

1. First approximation calculation of helicopter take-off weight

where is the mass of the payload, kg;

Crew weight, kg.

Range of flight

kg.

2. Calculation of helicopter rotor parameters

2.1 Radius R, m, single-rotor helicopter main rotorcalculated by the formula:

,

where is the take-off weight of the helicopter, kg;

g- free fall acceleration equal to 9.81 m/s 2 ;

p - specific load on the area swept by the main rotor,

 =3,14.

Specific load valuepthe area swept by the screw is selected according to the recommendations presented in work /1/: wherep= 280

m.

We take the radius of the rotor equal toR= 7.9

Angular velocity , With -1 , rotation of the main rotor is limited by the value of the peripheral speed Rends of the blades, which depends on the take-off weight of the helicopter and amounted to R= 232 m/s.

With -1 .

rpm

2.2 Relative air densities on static and dynamic ceilings

2.3 Calculation of economic speed at the ground and on a dynamic ceiling

The relative area of ​​the equivalent harmful plate is determined:

WhereS uh = 2.5

The value of economic speed near the ground is calculated V h , km/h:

WhereI = 1,09…1,10 - induction coefficient.

km/hour

The value of the economic speed on the dynamic ceiling is calculated V ding , km/h:

,

WhereI = 1,09…1,10 - induction coefficient.

km/hour

2.4 The relative values ​​of the maximum and economic on the dynamic ceiling are calculated horizontal flight speeds:

,

,

WhereV max =250 km/h andV ding =182.298 km/h - flight speed;

 R=232 m/s - peripheral speed of the blades.

2.5 Calculation of the permissible ratios of the thrust coefficient to the rotor filling for the maximum speed at the ground and for the economic speed at the dynamic ceiling:

2.6 Main rotor thrust coefficients at the ground and on the dynamic ceiling:

,

,

,

.

2.7 Calculation of rotor filling:

Main rotor filling  calculated for cases of flight at maximum and economic speeds:

;

.

As a calculated fill value  main rotor is taken to be the largest value of  Vmax And  V ding :

We accept

Chord length b and relative elongation  rotor blades will be equal to:

, Where z l -number of main rotor blades( z l =3)

m,

.

2.8 Relative increase in rotor thrustto compensate for the aerodynamic drag of the fuselage and horizontal tail:

Where S f - horizontal projection area of ​​the fuselage;

S th - area of ​​the horizontal tail.

S f =10 m 2 ;

S th =1.5 m 2 .

3. Calculation of the power of the helicopter propulsion system.

3.1 Calculation of power when hanging on a static ceiling:

The specific power required to drive the main rotor in hover mode on a statistical ceiling is calculated by the formula:

,

Where N H st - required power, W;

m 0 - take-off weight, kg;

g - free fall acceleration, m/s 2 ;

p - specific load on the area swept by the main rotor, N/m 2 ;

 st - relative air density at the height of the static ceiling;

 0 - relative efficiency main rotor in hover mode (  0 =0.75);

Relative increase in main rotor thrust to balance the aerodynamic drag of the fuselage and horizontal tail:

.

3.2 Calculation of power density in level flight at maximum speed

The specific power required to drive the main rotor in horizontal flight at maximum speed is calculated by the formula:

,

where is the peripheral speed of the ends of the blades;

- relative equivalent harmful plate;

I uh - induction coefficient, determined depending on the flight speed according to the following formulas:

, at km/h,

, at km/h.

3.3 Calculation of power density in flight on a dynamic ceiling at economic speed

The specific power for driving a main rotor on a dynamic ceiling is:

,

Where  ding - relative air density on the dynamic ceiling,

V ding - economic speed of the helicopter on a dynamic ceiling,

3.4 Calculation of specific power in flight near the ground at economic speed in the event of one engine failure during takeoff

The specific power required to continue takeoff at economic speed when one engine fails is calculated by the formula:

,

where is the economic speed at the ground,

3.5 Calculation of specific reduced powers for various flight cases

3.5.1 The specific reduced power when hanging on a static ceiling is equal to:

,

where is the specific throttling characteristic, which depends on the height of the static ceiling H st and is calculated by the formula:

,

 0 - coefficient of power utilization of the propulsion system in hovering mode, the value of which depends on the take-off weight of the helicopterm 0 :

at m 0 < 10 тонн

at 10 25 tons

at m 0 > 25 tons

,

,

3.5.2 Specific reduced power in horizontal flight at maximum speed is equal to:

,

Where - power utilization factor at maximum flight speed,

- engine throttle characteristics depending on flight speed V max :

;

3.5.3 Specific reduced power in flight on a dynamic ceiling at economic speed V ding is equal to:

,

and - degrees of engine throttling, depending on the height of the dynamic ceiling H and flight speed V ding in accordance with the following throttle characteristics:

,

.

;

3.5.4 The specific reduced power in flight near the ground at economic speed with the failure of one engine on takeoff is equal to:

,

where is the power utilization factor at economic flight speed,

- degree of engine throttling in emergency mode,

n = 2 - number of helicopter engines.

,

,

3.5.5 Calculation of the required power of the propulsion system

To calculate the required power of the propulsion system, the maximum value of the specific reduced power is selected:

.

Required power N helicopter propulsion system will be equal to:

,

Where m 01 - take-off weight of the helicopter,

g = 9.81 m 2 /s is the acceleration of free fall.

W,

3.6 Selection of engines

We accept two turboshaft engineVK-2500(TV3-117VMA-SB3) total power of each N =1,405∙10 6 W

EngineVK-2500(TV3-117VMA-SB3) designed for installation on new generation helicopters, as well as for replacing engines on existing helicopters to improve their flight performance. It was created on the basis of the serial certified TV3-117VMA engine and is produced at the Federal State Unitary Enterprise “Plant named after V.Ya. Klimov."

4. Calculation of fuel mass

To calculate the mass of fuel that provides a given flight range, it is necessary to determine the cruising speedV cr . The cruising speed is calculated using the method of successive approximations in the following sequence:

a) the value of the first approach cruising speed is taken:

km/hour;

b) the induction coefficient is calculated I uh :

at km/h

at km/h

c) the specific power required to drive the main rotor in flight at cruising mode is determined:

,

where is the maximum value of the specific reduced power of the propulsion system,

- coefficient of power change depending on flight speed V cr 1 , calculated by the formula:

.

d) The second approach cruising speed is calculated:

.

e) The relative deviation of the speeds of the first and second approximations is determined:

.

When the cruising speed of the first approximation is clarified V cr 1 , it is assumed to be equal to the calculated speed of the second approximation. Then the calculation is repeated from point b) and ends with the condition .

Specific fuel consumption is calculated using the formula:

,

where is the coefficient of change in specific fuel consumption depending on the operating mode of the engines,

- coefficient of change in specific fuel consumption depending on flight speed,

- specific fuel consumption during takeoff.

In case of flight in cruising mode the following is accepted:

;

;

at kW;

at kW.

kg/W∙hour,

Mass of fuel consumed for flight m T will be equal to:

where is the specific power consumed at cruising speed,

- cruising speed,

L - range of flight.

kg.

5. Determination of the mass of helicopter components and assemblies.

5.1 The mass of the main rotor blades is determined by the formula:

,

Where R - rotor radius,

 - filling the main rotor,

kg,

5.2 The mass of the main rotor hub is calculated using the formula:

,

Where k Tue - weight coefficient of bushings of modern designs,

k l – coefficient of influence of the number of blades on the mass of the hub.

In the calculation you can take:

kg/kN,

,

therefore, as a result of transformations we get:

To determine the mass of the main rotor hub, it is necessary to calculate the centrifugal force acting on the bladesN Central Bank (in kN):

,

kN,

kg.

5.3 Booster control system weight, which includes the swash plate, hydraulic boosters, and the main rotor hydraulic control system is calculated using the formula:

,

Where b – chord of the blade,

k boo - weight coefficient of the booster control system, which can be taken equal to 13.2 kg/m 3 .

kg.

5.4 Weight of manual control system:

,

Where k RU - the weight coefficient of the manual control system, taken for single-rotor helicopters to be equal to 25 kg/m.

kg.

5.5 The mass of the main gearbox depends on the torque on the main rotor shaft and is calculated by the formula:

,

Where k edit – weight coefficient, the average value of which is 0.0748 kg/(Nm) 0,8 .

The maximum torque on the main rotor shaft is determined through the reduced power of the propulsion systemN and propeller speed  :

,

Where  0 - power utilization factor of the propulsion system, the value of which is taken depending on the take-off weight of the helicopterm 0 :

at m 0 < 10 тонн

at 10 25 tons

at m 0 > 25 tons

N∙m,

Main gearbox weight:

kg.

5.6 To determine the mass of the tail rotor drive units, its thrust is calculated T ditch :

,

Where M nv – torque on the main rotor shaft,

L ditch – the distance between the axes of the main and tail rotors.

The distance between the axes of the main and tail rotors is equal to the sum of their radii and clearance  between the ends of their blades:

,

Where  - gap taken equal to 0.15...0.2 m,

- radius of the tail rotor, which, depending on the take-off weight of the helicopter, is:

at t,

at t,

at t.

m,

m,

N,

Power N ditch , spent on rotating the tail rotor, is calculated by the formula:

,

Where  0 – relative efficiency of the tail rotor, which can be taken equal to 0.6...0.65.

W,

Torque M ditch transmitted by the steering shaft is equal to:

N∙m,

where is the speed of the steering shaft,

With -1 ,

Torque transmitted by the transmission shaft, N∙m, at rotational speed n V = 3000 rpm equal to:

N∙m,

N∙m,

Weight m V transmission shaft:

,

Where k V – weight coefficient for the transmission shaft, which is equal to 0.0318 kg/(Nm) 0,67 . kg

Centrifugal force value N cbd , acting on the tail rotor blades and perceived by the hub hinges,

Tail rotor hub weight m Tue is calculated using the same formula as for the main rotor:

,

Where N Central Bank - centrifugal force acting on the blade,

k Tue - weight coefficient for the bushing, taken equal to 0.0527 kg/kN 1,35

k z - weight coefficient depending on the number of blades and calculated by the formula: kg,

The mass of the helicopter electrical equipment is calculated using the formula:

,

Where L ditch – distance between the axes of the main and tail rotors,

z l – number of main rotor blades,

R – rotor radius,

 l – relative elongation of the main rotor blades,

k etc And k el - weighting coefficients for electrical wires and other electrical equipment, the values ​​of which are equal to:

,

Calculation and construction of landing polars 3.4 Calculation and construction... / S 0.15 10. General data 10.1 Takeoff weight aircraft kg m0 880 10 ...

I

Lifting force and thrust for forward movement of a helicopter are created using a main rotor. In this way, it differs from an airplane and a glider, in which the lift force when moving in the air is created by a load-bearing surface - a wing, rigidly connected to the fuselage, and thrust - by a propeller or jet engine (Fig. 6).

In principle, an analogy can be drawn between the flight of an airplane and a helicopter. In both cases, the lifting force is created due to the interaction of two bodies: air and an aircraft (airplane or helicopter).

According to the law of equality of action and reaction, it follows that with whatever force the aircraft acts on the air (weight or gravity), with the same force the air acts on the aircraft (lift).

When an airplane flies, the following phenomenon occurs: the oncoming oncoming air flow flows around the wing and is beveled down behind the wing. But air is an inextricable, rather viscous medium, and this bevelling involves not only the layer of air located in close proximity to the surface of the wing, but also its neighboring layers. Thus, when flowing around the wing, each second a fairly significant volume of air is beveled downwards, approximately equal to the volume of a cylinder, the cross-section of which is a circle with a diameter equal to the wing span, and the length is the flight speed per second. This is nothing more than the second flow of air involved in creating the lifting force of the wing (Fig. 7).

Rice. 7. The volume of air involved in creating the lift of the aircraft

From theoretical mechanics it is known that the change in momentum per unit time is equal to the acting force:

Where R - active force;

as a result of interaction with the aircraft wing. Consequently, the lifting force of the wing will be equal to the second increase in the amount of vertical motion in the outgoing jet.

And -velocity of flow slant behind the wing vertically in m/sec. In the same way, it is possible to express the total aerodynamic force of a helicopter's main rotor in terms of the second air flow rate and the flow shear velocity (the inductive speed of the outgoing air stream).

The rotating rotor sweeps away a surface that can be thought of as a load-bearing surface, similar to an airplane wing (Fig. 8). Air flowing through the surface swept by the rotor is, as a result of interaction with the rotating blades, thrown down at an inductive speed And. In the case of horizontal or inclined flight, air flows to the surface, swept by the main rotor at a certain angle (oblique blowing). Like an airplane, the volume of air involved in creating the total aerodynamic force of the main rotor can be represented as a cylinder, the base area of ​​which is equal to the surface area swept by the main rotor, and the length equals the flight speed, expressed in m/sec.

When the main rotor operates at a standstill or in vertical flight (direct blowing), the direction of the air flow coincides with the axis of the main rotor. In this case, the air cylinder will be located vertically (Fig. 8, b). The total aerodynamic force of the main rotor will be expressed as the product of the mass of air flowing through the surface swept by the main rotor in one second and the inductive speed of the outgoing jet:

inductive speed of the outgoing jet in m/sec. It is necessary to make a reservation that in the considered cases, both for the aircraft wing and for the helicopter rotor, the induced speed And the inductive velocity of the outgoing jet at some distance from the bearing surface is assumed. The inductive speed of the air stream that occurs on the load-bearing surface itself is half as large.

This interpretation of the origin of wing lift or the total aerodynamic force of the rotor is not entirely accurate and is only valid in an ideal case. It only fundamentally correct and clearly explains the physical meaning of the phenomenon. Here it is appropriate to note one very important circumstance arising from the analyzed example.

If the total aerodynamic force of the rotor is expressed as the product of the mass of air flowing through the surface swept by the rotor and the induced velocity, and the volume of this mass is a cylinder whose base is the surface area swept by the rotor and whose length is the flight speed, then absolutely it is clear that to create a thrust of a constant value (for example, equal to the weight of the helicopter) at a higher flight speed, and therefore with a larger volume of ejected air, a lower induced speed and, therefore, less engine power is required.

On the contrary, to maintain a helicopter in the air while “hovering” in place, more power is required than during flight at a certain forward speed, at which there is a counter flow of air due to the movement of the helicopter.

In other words, with the same power expended (for example, rated engine power), in the case of inclined flight at a sufficiently high speed, a higher ceiling can be achieved than with vertical ascent, when the overall speed of movement

there is less helicopter than in the first case. Therefore, the helicopter has two ceilings: static, when altitude is gained in vertical flight, and dynamic when the altitude is gained in inclined flight, and the dynamic ceiling is always higher than the static one.

The operation of a helicopter's main rotor and an airplane's propeller have much in common, but there are also fundamental differences, which will be discussed later.

Comparing their work, one can notice that the total aerodynamic force, and therefore the thrust of the helicopter rotor, which is a component of the force

Rin the direction of the hub axis, is always greater (5-8 times) with the same engine power and the same weight of the aircraft due to the fact that the diameter of the helicopter rotor is several times larger than the diameter of the aircraft propeller. In this case, the air ejection speed of the main rotor is less than the ejection speed of the propeller.

The amount of thrust of the main rotor depends to a very large extent on its diameter

Dand number of revolutions. When the screw diameter is doubled, its thrust will increase approximately 16 times; when the number of revolutions is doubled, the thrust will increase approximately 4 times. In addition, the thrust of the main rotor also depends on the air density ρ, the angle of installation of the blades φ (rotor pitch),geometric and aerodynamic characteristics of a given propeller, as well as the flight mode. The influence of the last four factors is usually expressed in the propeller thrust formulas through the thrust coefficient a t . .

Thus, the thrust of the helicopter rotor will be proportional to:

- thrust coefficient............. α r

It should be noted that the amount of thrust when flying near the ground is influenced by the so-called “air cushion”, due to which the helicopter can take off from the ground and rise several meters while expending less power than that required to “hover” at an altitude of 10- 15 m. The presence of an “air cushion” is explained by the fact that the air thrown by the propeller hits the ground and is somewhat compressed, i.e., it increases its density. The influence of the “air cushion” is especially pronounced when the propeller operates near the ground. Due to air compression, the thrust of the main rotor in this case, with the same power consumption, increases by 30-

40%. However, with distance from the ground this influence quickly decreases, and at a flight altitude equal to half the diameter of the propeller, the “air cushion” increases thrust by only 15- 20%. The height of the “air cushion” is approximately equal to the diameter of the main rotor. Further, the increase in traction disappears.

To roughly calculate the thrust value of the main rotor in hover mode, use the following formula:

coefficient characterizing the aerodynamic quality of the main rotor and the influence of the “air cushion”. Depending on the characteristics of the main rotor, the value of the coefficient A when hanging near the ground it can have values ​​of 15 - 25.

The main rotor of a helicopter has an extremely important property - the ability to create lift in the self-rotation (autorotation) mode in the event of an engine stop, which allows the helicopter to make a safe gliding or parachute descent and landing.

The rotating main rotor maintains the required number of revolutions during gliding or parachuting if its blades are set to a small installation angle

(l--5 0) 1 . At the same time, the lifting force is maintained, ensuring descent at a constant vertical speed (6-10 m/sec), s subsequent reduction of it when leveling before planting to l--1.5 m/sec.

There is a significant difference in the operation of the main rotor in the case of motor flight, when power from the engine is transmitted to the propeller, and in the case of self-rotating flight, when it receives the energy to rotate the propeller from the oncoming air stream.

In motorized flight, oncoming air flows into the rotor from above or from above at an angle. When the propeller operates in self-rotation mode, air flows onto the plane of rotation from below or at an angle from below (Fig. 9). The slant of the flow behind the main rotor in both cases will be directed downwards, since the induced speed, according to the momentum theorem, will be directed directly opposite to the thrust, i.e. approximately downward along the axis of the main rotor.

Here we are talking about the effective installation angle as opposed to the constructive angle.

Let's calculate the thrust of the main rotor. If we consider the surface (area F) swept by the screw during its rotation as an impenetrable plane, then we will see that pressure pi acts on this plane from above, and pressure p2 from below, and p-2 is greater than px.

From the second law of mechanics it is known that a mass receives acceleration only when some force acts on it. Moreover, this force is equal to the product of mass and acceleration and is directed in the direction of acceleration (in our case, downward).

What kind of power is this? On the one hand, it is obvious that this force is the result of the action of the propeller on the air. On the other hand, is this? force, according to the third law of mechanics, must correspond to an equal in magnitude and opposite in direction effect of air on the propeller. The latter is nothing more than the thrust force of the propeller.

However, if we look at a dynamometer that measures the actual thrust of the propeller, we find that our calculation is somewhat inaccurate. In reality, the thrust will be less, since we considered the operation of the propeller to be ideal and did not take into account the energy losses due to friction and the twisting of the air stream behind the propeller.

In fact, air particles approach the screw having not only an inductive speed in the axial direction, perpendicular to the plane of rotation, but also a twisting speed. Therefore, when calculating the inductive speeds of their suction and rejection u2, the swirling of air during rotation of the main rotor is also taken into account.

In the thrust formula, the lift coefficient su is similar to the thrust coefficient; the flight speed corresponds to the peripheral speed of the ends of the propeller blades, which has a radius r and angular velocity; the area of ​​the wing 5 corresponds to the area of ​​the disk swept by the propeller, r2. The coefficient is determined from the blowing curve of a given propeller at various angles of attack.

The value of the dimensionless thrust coefficient for a specific, already created propeller operating in a given mode can be calculated by dividing the thrust T of the propeller, expressed in kilograms, by the product of other parameters of the propeller, which also has a thrust force dimension of kg.

We have established that if the lift of an airplane is created by throwing air downward with the wing, then the lifting force of a helicopter is created by throwing air down with the main rotor.

When a helicopter has a forward speed, then, naturally, the volume of air thrown down increases.

Because of this, with the same power expended, the main rotor of a helicopter with forward speed develops more thrust than the rotor of a hanging helicopter.

And, conversely, to create the same thrust, less power must be transferred to the rotor of a helicopter having a forward speed than to the rotor of a hanging helicopter.

The decrease in required power with increasing speed occurs only up to a certain speed value, at which the increase in air resistance to the movement of the helicopter not only absorbs the gain in power, but even requires the latter to be increased.

PHYSICS OF THE ROTOR

A magnificent machine - a helicopter! Its remarkable qualities make it indispensable in thousands of cases. Only a helicopter can take off and land vertically, hang motionless in the air, move sideways and even tail first.

Where do such wonderful opportunities come from? What is the physics of its flight7 Let's try to briefly answer these questions.

A helicopter rotor creates lift. The propeller blades are the same propellers. Installed at a certain angle to the horizon, they behave like a wing in the flow of incoming air: pressure arises under the lower plane of the blades, and vacuum occurs above it. The greater this difference, the greater the lift. When the lifting force exceeds the weight of the helicopter, it takes off, but if the opposite happens, the helicopter descends.

If on an airplane wing the lift force appears only when the airplane is moving, then on the “wing” of a helicopter it appears even when the helicopter is standing still: the “wing” is moving. This is the main thing.

But the helicopter gained altitude. Now he needs to fly forward. How to do it? The screw only creates upward thrust! Let's look into the cockpit at this moment. He turned the control stick away from him. The helicopter tilted slightly on its nose and flew forward. Why?

The control knob is connected to an ingenious device - a transfer machine. This mechanism, extremely convenient for controlling a helicopter, was invented during his student years by academician B. N. Yuryev. Its design is quite complex, but its purpose is to enable the pilot to change the angle of the blades to the horizon at will.

It is not difficult to understand that during a horizontal flight of a helicopter, the pressure from its blades moves relative to the surrounding air at different speeds. The blade that goes forward moves towards the air flow, and the blade that turns back moves along the flow. Therefore, the speed of the blade, and with it the lifting force, will be higher when the blade moves forward. The propeller will tend to turn the helicopter on its side.

To prevent this from happening, the nonstrunters connected the blades to the axis movably, on hinges. Then the forward blade began to soar and flap with greater lifting force. But this movement was no longer transmitted to the helicopter; it flew calmly. Thanks to the flapping motion of the blade, its lifting force remained constant throughout the revolution.

However, this did not solve the problem of moving forward. After all, you need to change the direction of the propeller thrust and force the helicopter to move horizontally. This was made possible by the swashplate. It continuously changes the angle of each propeller blade so that the greatest lift occurs approximately in the rear sector of its rotation. The resulting thrust force of the main rotor tilts, and the helicopter, also tilting, begins to move forward.

It took a long time for such a reliable and convenient helicopter control device to be created. A device for controlling the direction of flight did not appear immediately.

You, of course, know that a helicopter does not have a rudder. Yes, it is not needed by a rotorcraft. It is replaced by a small propeller mounted on the tail. If the pilot tried to turn it off, the helicopter would turn itself. Yes, it turned so that it would begin to rotate faster and faster in the direction opposite to the rotation of the main rotor. This is a consequence of the reactive torque that occurs when the main rotor rotates. The tail rotor prevents the tail of the helicopter from turning under the influence of the reaction torque and balances it. And if necessary, the pilot will increase or decrease the tail rotor thrust. Then the helicopter will turn in the right direction.

Sometimes they do without a tail rotor altogether, installing two main rotors on helicopters, rotating towards each other. Reactive moments in this case, of course, are destroyed.

This is how the “aerial all-terrain vehicle” flies and the tireless worker - the helicopter.