Calculation of helicopter lift. Coursework on design. Calculation of the mass of a helicopter propulsion system

Introduction

Helicopter design is a complex process that develops over time, divided into interrelated project stages and stages. Created aircraft must satisfy technical requirements and comply with the technical and economic characteristics specified in the design specifications. Technical task contains the initial description of the helicopter and its flight performance characteristics, ensuring high economic efficiency and competitiveness of the designed vehicle, 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 and analysis of existing technical solutions, research and development work. 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 development stage technical project. In this case, the parameters of the designed units must satisfy the values corresponding preliminary design. Some parameters can be refined in order to optimize the design. At 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 materials are prepared. technical documentation 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 parameters main rotor helicopter

2.1Radius R, m, of the main rotor of a single-rotor helicopter is 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,

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

s -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

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

Where I= 1.09...1.10 - induction coefficient.

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

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

w 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 maximum speed near the ground and for economic speed on a 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 s calculated for cases of flight at maximum and economic speeds:

;

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

We accept

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

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

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

where S f is the area of the horizontal projection of the fuselage;

S th - area of the horizontal tail.

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 ;

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

h 0 - relative efficiency main rotor in hover mode ( h 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 D 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 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:

x 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 level flight at maximum speed is equal to:

Where - power utilization factor at maximum flight speed,

Throttle characteristics of engines depending on flight speed Vmax :

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 Specific reduced power in flight near the ground at economic speed when one engine fails 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 01 - helicopter take-off weight,

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

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:

b) the induction coefficient is calculated I uh :

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,

s- filling the main rotor,

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,

5.3 The mass of the booster control system, which includes the swashplate, hydraulic boosters, and main rotor control hydraulic system, is calculated by 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/m 3 .

5.4 Manual control system weight:

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

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 w :

Where x 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:

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 d between the ends of their blades:

Where d- 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:

at t,

at t.

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

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

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 rotational speed n V = 3000 rpm is equal to:

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.

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

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 s 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 l ditch tail rotor blades is calculated using the formulas:

Where z ditch- number of tail rotor blades.

Tail rotor blade weight m lr

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 g dv calculated using the empirical formula:

Where N- power of the propulsion system.

The mass of the propulsion system will be equal to:

5.9 Calculation of the mass of the fuselage and equipment of the helicopter

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 0 – first approach take-off weight,

k f- coefficient equal to 1.7.

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.

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.

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 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:

Weight of other helicopter equipment:

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

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.

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. Cabin glazing provides good review, 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. Main hydraulic system provides power to all hydraulic units, and the backup one - 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 rotation 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

Unit name	Unit weight, m i, kg	Coordinate x i center of mass of the unit, m	Unit static moment M xi	Coordinate y i center of mass of the unit, m	Unit static moment M yi
1 main rotor
1.1 Blades	127	0	0	0	0
1.2 Bushing	122	0	0	0	0
2 Control system
2.1 Booster control system	43	-0,5	-146	-0,9	-262,8
2.2 Manual control system	195	2,7	648	-3,6	-864
3 Transmission
3.1 Main gearbox	361	0	0	-1	-1005
3.2 Intermediate gearbox	58	-1,3	-75,4	-9,9	-574,2
3.3 Tail gearbox	21	-11,3	-745,8	0	0
3.4 Transmission shaft	17	-5,3	-291,5	-1,3	-71,5
4 Tail rotor
4.1 Blades	10	-11,3	-768,4	0	0
4.2 Bushing	59	-11,3	-553,7	0	0
5 Propulsion system	276	1,1	652,3	-1,3	-770,9
6 Fuel system	64	0,5	92,5	-3,2	-592
7 Fuselage
7.1 Bow (15%)	30.6	3,8	604,2	-2,6	-413,4
7.2 Middle part (50%)	102	0	0	-2,6	-1383
7.3 Tail section (20%)	40.8	-6,6	-1406	-1,5	-319,5
7.4 Fastening the gearbox (4%)	14.4	0,2	8.4	-1	-42
7.5 Hoods (11%)	22.4	0,3	35,1	-1,1	-128,7
8 Skis
8.1 Main (82%)	90.2	-1,1	-212,3	-3,8	-733,4
8.2 Front (16%)	17.6	2,8	103,6	-3,9	-144,3
8.3 Tail support (2%)	22	-9,6	-432	-2,4	-108
9 Electrical equipment	286	3,1	1457	-3	-1410
10 Equipment
10.1 Instruments in the cockpit (25%)	71.5	4,2	579,6	-2,6	-358,8
10.2 Radio equipment (27%)	77.2	4,1	610,9	-3	-447
10.3 Hydraulic equipment (20%)	57.2	-1,4	-155,4	-0,7	-77,7
10.4 Pneumatic equipment (6%)	17.1	-0,7	-23,1	-1,5	-49,5
Sum	2202	-0,003	-20,15	-1,4524	-9755,7

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

Coordinates of the center of mass of an empty helicopter: x 0 = -0.003; y 0 = -1.4524;

Coordinates of the center of mass with maximum load: x 0 =0.0293; y 0 = -2.0135;

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

Conclusion

In this course project, calculations of the take-off weight of the helicopter, the mass of its components and assemblies, as well as the layout of the helicopter were carried out. 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, statements 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.

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

2.1Radius R, m, of the main rotor of a single-rotor helicopter is 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,

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

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 Suh= 2.5

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

Where I

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

Where I= 1.09...1.10 - induction coefficient.

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

Where Vmax=250 km/h and Vding=182.298 km/h - flight speed;

wR=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 s calculated for cases of flight at maximum and economic speeds:

As a calculated fill value s main rotor is taken to be the largest value of sVmax And sVding:

We accept

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

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

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

where S f is the area of the horizontal projection of the fuselage;

S th - area of the horizontal tail.

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 while hovering on a statistical ceiling is calculated using the formula:

Where N Hst- required power, W;

m 0 - take-off weight, kg;

g-gravitational acceleration, m/s 2 ;

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

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

h 0 - relative efficiency main rotor in hover mode ( h 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;

Iuh- 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:

whereD ding- relative air density on the dynamic ceiling,

Vding- 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 if 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 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 Hst and is calculated by the formula:

x 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

at 10 25 tons

at m 0 > 25 tons

3.5.2 Specific reduced power in level 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 Vmax :

3.5.3 Specific reduced power in flight on a dynamic ceiling at economic speed Vding 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 Vding in accordance with the following throttle characteristics:

3.5.4 Specific reduced power in flight near the ground at economic speed when one engine fails 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 01 - helicopter take-off weight,

g=9.81 m 2 /s-gravitational acceleration.

3.6 Selection of engines

We accept two turboshaft engines VK-2500 (TV3-117VMA-SB3) with a 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 is 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 Vcr.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:

b) the induction coefficient is calculated Iuh:

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 Vcr 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:

The first approximation cruising speed is being clarified Vcr 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:

kg/W∙hour,

Mass of fuel consumed for flight mT 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,

s- filling the main rotor,

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

Where kTue- weight coefficient of bushings of modern designs,

kl- coefficient of influence of the number of blades on the mass of the hub.

In the calculation you can take:

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 NCentral Bank(in kN):

5.3 The mass of the booster control system, which includes the swashplate, hydraulic boosters, and main rotor control hydraulic system, is calculated by the formula:

Where b- chord of the blade,

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

5.4 Manual control system weight:

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

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

Where kedit- 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 w:

Where x 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

at 10 25 tons

at m 0 > 25 tons

Main gearbox weight:

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

Where Mnv- torque on the main rotor shaft,

Lditch- 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 d between the ends of their blades:

Where d- 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:

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

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

Torque Mditch transmitted by the steering shaft is equal to:

where is the speed of the steering shaft,

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

Weight mV transmission shaft:

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

Weight metc intermediate gearbox is equal to:

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

Mass of the tail gearbox rotating the tail rotor:

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

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

Thrust coefficient Cditch tail rotor is equal to:

Filling the tail rotor blades sditch 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 bditch and relative elongation lditch tail rotor blades is calculated using the formulas:

Where zditch- number of tail rotor blades.

Tail rotor blade weight mlr

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

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

Where NCentral Bank-centrifugal force acting on the blade,

kTue- 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 gdv calculated using the empirical formula:

Where N- power of the propulsion system.

The mass of the propulsion system will be equal to:

5.9 Calculation of the mass of the fuselage and equipment of the helicopter

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

Where Sohm- area of the washed surface of the fuselage, which is determined by the formula:

m 0 - first approach take-off weight,

kf-coefficient equal to 1.7.

Fuel system weight:

Where mT- the mass of fuel spent on flight,

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

The weight of the helicopter landing gear is:

Where kw-weight coefficient depending on the chassis design:

For fixed landing gear,

For retractable landing gear.

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

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

zl- number of main rotor blades,

R- rotor radius,

ll- relative elongation of the main rotor blades,

ketc And kel- weighting coefficients for electrical wires and other electrical equipment, the values of which are equal to:

Weight of other helicopter equipment:

Where ketc-weight coefficient, the value of which is 2.

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 mT- mass of fuel,

mgr- payload mass,

mek- weight of the crew.

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-leg 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.

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 with a 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 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.

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

Unit name	Unit weight, m i, kg	Coordinate x i center of mass of the unit, m	Unit static moment M xi	Coordinate y i center of mass of the unit, m	Unit static moment M yi
1Main rotor
1.1 Blades
1.2 Bushing
2 Control system
2.1 Booster control system
2.2 Manual control system
3 Transmission
3.1 Main gearbox
3.2 Intermediate gearbox
3.3 Tail gearbox
3.4 Transmission shaft
4 Tail rotor
4.1 Blades
4.2 Bushing
5 Propulsion system
6 Fuel system
7 Fuselage
7.1 Bow (15%)
7.2 Middle part (50%)
7.3 Tail section (20%)
7.4 Fastening the gearbox (4%)
7.5 Hoods (11%)

8.1 Main (82%)
8.2 Front (16%)
8.3 Tail support (2%)
9 Electrical equipment
10 Equipment
10.1 Instruments in the cockpit (25%)
10.2 Radio equipment (27%)
10.3 Hydraulic equipment (20%)
10.4 Pneumatic equipment (6%)

Static moments are calculated M cxi And M sui 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

Unit name	Unit weight, m i, kg	Coordinate x i center of mass of the unit, m	Unit static moment M xi	Coordinate y i center of mass of the unit, m	Unit static moment M yi
Helicopter
Fuel tanks 1 and 2

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

Unit name	Unit weight, m i, kg	Coordinate x i center of mass of the unit, m	Unit static moment M xi	Coordinate y i center of mass of the unit, m	Unit static moment M yi
Helicopter

Coordinates of the center of mass of an empty helicopter: x 0 = -0.003; y 0 = -1.4524;

Coordinates of the center of mass with maximum load: x 0 =0.0293;y 0 =-2.0135;

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

Conclusion

In this course project, calculations of the take-off weight of the helicopter, the mass of its components and assemblies, as well as the layout of the helicopter were carried out. 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, equipment lists, 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 the specified requirements.

To the calculation of helicopter flight characteristics at the design stage

In his publications in 1999-2000. "AON" magazine has repeatedly raised the question of the feasibility of developing and producing helicopters in Ukraine various classes. After the scientific and practical conference “Advanced multi-purpose Ukrainian helicopter of the XXI century”, organized on the basis of Aviaimpex LLC in October 1999, there has been some progress in resolving this problem. Currently, a number of projects for the development and production of light helicopters are being implemented in Ukraine. Some samples and mock-ups of the designed helicopters were presented at the Aviamir-XXI air shows in 1999 and 2000.

We were especially impressed by the letter from V.N. Alekseev from Dnepropetrovsk ("AON" No. 12, 1999), in which he called for the creation of the necessary theoretical and scientific base, necessary for the development of helicopter manufacturing in our state. This must be done because there are specialized helicopter companies, research institutes and universities that would be deeply involved in issues of theoretical and experimental research in the areas of aerodynamic and strength calculations, motion dynamics, control systems, etc. in relation to a helicopter, there is currently no such thing in Ukraine. At the same time, foreign companies pay great attention to the creation of modeling centers and the development of effective mathematical models, investing considerable funds in this.

At the stage of the preliminary design (advanced design), when the basic design solutions are laid down, the aerodynamic and weight parameters of the helicopter, its units and systems are determined, it is necessary to find the area of geometric and kinematic parameters of the main and tail rotors, at which the flight performance requirements specified in the tactical and technical requirements are met. technical characteristics of the future helicopter. In this case, it is necessary to make maximum use of statistical data on domestic (Soviet) and foreign analogues, as well as modern mathematical methods and calculation models.

In the helicopter design process, there are always several intermediate stages that must be achieved within a strictly defined time frame at a certain cost. Violation of schedule or budget constraints can lead to very serious consequences for both the project and the organization leading the design. Figure 1 shows the increase in the cost of making changes to the design of an aircraft at various stages of its creation, which indicates the importance and responsibility of the decisions made at the preliminary design stage.

In this article, the authors propose a numerical method for calculating the main flight characteristics of a helicopter, based on the well-known approach to the aerodynamic calculation of a helicopter using the Mil-Yaroshenko method. In contrast to the graphic-analytical Mil-Yaroshenko method, the proposed approach allows us to numerically solve the problem of aerodynamic calculation of a simplified layout consisting of a main and tail rotors, based on the equations of the Glauert-Lock impulse theory.

1. Statement of the problem. Basic relationships

We consider the steady straight flight of a helicopter with small angles of inclination of the trajectory. At a given rotor speed (RO), we assume that its thrust balances the weight of the helicopter. It is possible to change the projection of the resultant force of the NV on the direction of movement of the helicopter only by changing the angle of attack of the main rotor (Fig. 2). To maintain the balance of forces vertically, it is necessary to change the angle of the collective pitch of the propeller and the power transmitted to the propeller.

We write the equation of motion of a helicopter in steady horizontal flight as:

To equations (1) we add an equation expressing the equality of the power on the NV shaft Nн and the power plant of the helicopter Nsu

where x is the power loss factor.

The angle between the direction of the resultant and the normal to the velocity vector can be determined from the relation

(N/T<< 1), и в горизонтальном полете выполняется условие R » T. Тогда уравнения движения вертолета (1) - (2) принимают вид

The coefficient of harmful drag of a helicopter, related to the swept area of the air force;

Coefficient

filling NV;

Peripheral speed of the tip of the HB blade.

The angle of inclination of the resultant force NV required for horizontal flight is found from the first equation of the system (4)

The maximum angle of inclination of the trajectory during a steady climb is found from the relationship:

where is the value of the angle of inclination of the resultant when using the entire available power of the power plant at a given flight mode.

The calculation task is to determine the required angle of inclination of the resultant for each steady helicopter flight mode. The flight mode of a helicopter is determined by the flight altitude H, the propeller operating mode coefficient m or the relative flight speed. The vertical speeds of a steady climb are found using the formula

The values of the coefficients of longitudinal force and torque NV included in formulas (3), (4) were determined using the formulas of works. These formulas look like this:

Flow coefficient

(8)

Angle of attack NV

Torque coefficient NV

Longitudinal force coefficient

The coefficients of the first harmonics of the flapping movements of the blades included in equations (10) and (11) were found using simplified formulas (12) - (14).

The value of the tip loss coefficient B NV included in formulas (8) - (14) was determined according to the recommendations, and the inertial-mass characteristics of the blade can be calculated using approximate formulas.

When calculating the characteristics of the tail rotor (RT), it was assumed that the condition for the helicopter's path balancing was met in all flight modes:

From this condition the required value of the RV thrust coefficient was found:

where are the fill factor and the peripheral speed of the tip of the PB blade, respectively.

Then, using formulas (8) - (14), the aerodynamic characteristics of the RV were calculated.

Of great practical interest are the characteristics of helicopter descent in self-rotating mode. In this case, it is important to know the required values of the collective pitch angles j 0.7 NV depending on the descent speed in order to maintain a constant specified rotation speed of the NV.

The calculation of the helicopter's descent characteristics in the self-rotating NV mode is carried out on the basis of the aerodynamic quality of the helicopter, (17).

t is the NV thrust coefficient at a given flight mode;

NV propulsive force coefficient in self-rotation mode.

The helicopter's descent angle in self-rotation mode NV is equal to the inverse quality of the helicopter

We find the horizontal and vertical components of the helicopter’s descent speed from the relations

The proposed method makes it possible to calculate the main flight characteristics of a helicopter at the stages of preliminary design, when the profile of the blades is selected, the geometric, kinematic, inertial-mass parameters of the main and tail rotors, the characteristics of the power plant and the flight weight of the helicopter are known.

The calculation is performed for various altitudes in the range of flight values of the operating mode coefficient when changing the collective pitch angles of the blades from j 0.7 = 2° to 20° in steps of 2°.

2. Justification of the reliability of the results obtained

Justification of the reliability of the results obtained using the proposed method was carried out on the basis of solving test problems to determine the flight characteristics of known helicopters.

In Fig. Figure 3 shows the dependence of the characteristic flight speeds of the Mi-4 and Mi-34 helicopters on altitude. The calculation results are compared with the work data. For the Mi-4 helicopter, the calculation was performed for flight weight m=7200 kg and the peripheral speed of the blade tip wR=196 m/s; the Mi-34 helicopter was calculated in the sports aerobatic version with m=1020 kg and wR=206 m/s.

A comparison of the calculated data on the required collective pitch angles of the Mi-34 helicopter for horizontal flight at the nominal engine operating mode (wR=180 m/s) for various altitudes is illustrated in Fig. 4.

On the graphs in Fig. Figure 5 shows the dependences of the vertical speed and descent angle of the Mi-4 helicopter in the NV self-rotation mode for an altitude of H = 0 km.

The limited scope of the article does not allow us to provide all the calculated material for these helicopters.

Methodological studies have shown that the proposed method makes it possible to analyze the influence of numerous parameters that determine the flight mode of a helicopter on its flight characteristics with a sufficient degree of accuracy. Within the range of changes in the operating mode coefficient m from 0.08 to 0.3, when the angles of attack of the blade sections along the HB disk do not exceed the maximum permissible, the assumptions made in theory about the linearity of the dependence Cy(a) and Схрр=const are valid, this method ensures an error calculations not exceeding 8-10%. For light helicopters, this corresponds to a load on the swept area G/F of up to 25 kgf/m2 and maximum flight speeds of up to 220-230 km/h.

3. Examples of calculations

The article presents some results of calculations of the flight characteristics of the Robinson R22 (m=620 kg, wR=217 m/s) and Hughes 269B/300 (m=930 kg, wR=202 m/s) helicopters. The geometric and kinematic parameters of the main and tail rotors, as well as helicopters in general, are taken from the work.

The R22 helicopter has a two-blade NV with a diameter of 7.67 m (sн=0.03) and a NACA-63015 blade profile, the load on the swept area is 13.45 kgf/m2. The power plant uses one Lycoming U-320-B2C piston engine with takeoff power N=160 hp.

The model 269/300 helicopter uses a three-bladed propeller with a diameter of D = 8.18 m (sн = 0.04) and a blade profile of NACA-0015, the load on the swept area is 17.7 kgf/m2. The Lycoming HIO-360D piston engine provides takeoff power of 190 hp.

Figure 6 shows the operating altitude and speed ranges for steady level flight of the R22 and Hughes 269/300 helicopters. Maximum ground speeds are 190 km/h for the Robinson R22 helicopter and 175 km/h for the Hughes 269/300. The values of the economic speed Vec, which ensures the maximum steady climb mode, are also shown here.

The required values of the helicopter's collective pitch angle when descending in the self-rotating mode near the ground are presented in Fig. 7. At these values of jc, the constant rotation speed of the NV is ensured.

5. Johnson W. Helicopter theory. Book 1. M.: Mir, 1983.

6. Braverman A.S. Quality and propulsive efficiency of the helicopter. Linearization of aerodynamic calculation // To the calculation of helicopter flight characteristics. Proceedings of TsAGI im. prof. N.E. Zhukovsky, issue 2448, 1989.

7. Statistical data of foreign helicopters / Reviews No. 678. TsAGI im. prof. N.E. Zhukovsky, M.: ONTI TsAGI, 1988.

8. Araslanov S. A. What helicopters does Ukraine need? // General Aviation, No. 10, 1999.

Introduction

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

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)

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.

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

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.

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.

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,

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:

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Introduction

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 The radius R, m, of the main rotor of a single-rotor helicopter is 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,

The value of the specific load p on the area swept by the propeller is selected according to the recommendations presented in work /1/: where p=280

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

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

s -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 e =2.5

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

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

where I = 1.09…1.10 is the induction coefficient.

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

where V max =250 km/h and V din =182.298 km/h - flight speed;

wR=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 s is calculated for flight cases at maximum and economic speeds:

;

The largest value of s Vmax and s V dyn is taken as the calculated filling value s of the main rotor:

We accept

The chord length b and the relative elongation l of the main rotor blades will be equal to:

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

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

where S f is the area of the horizontal projection of the fuselage;

S th - area of the horizontal tail.

S th =1.5 m 2.

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