A method for calculating a takeoff path for a helicopter category a flight

Abstract

This invention discloses a method for calculating the takeoff trajectory of a helicopter in Category A flight. The key technical points include the following calculation steps: S1: Statistically analyze the parameters of a twin-engine helicopter and the parameters of the engines it uses; S2: Based on the statistically analyzed parameters, calculate the power required for forward flight of the twin-engine helicopter and plot N. xu -V0 curve; S3: Calculate the safe takeoff speed of the twin-engine helicopter based on the power required for forward flight and the statistical power of a single helicopter engine; S4: Calculate the lift and forward thrust provided by the helicopter rotor based on the statistical parameters; S5: Calculate the critical takeoff decision point of the twin-engine helicopter and plot the critical takeoff decision point curve; S6: Based on the calculated critical takeoff decision point of the twin-engine helicopter, calculate the takeoff trajectory of the twin-engine helicopter in Category A flight according to the location of the failure point, and plot the Category A takeoff trajectory curve of the helicopter.

Description

Technical Field

[0001] This invention relates to the field of aviation takeoff trajectory calculation technology, and more specifically to a method for calculating the takeoff trajectory of a helicopter in Category A flight. Background Technology

[0002] Helicopters possess high maneuverability at low altitudes and speeds, making them widely applicable in aerial surveillance and detection, security patrols, relay communications, reconnaissance and strike operations, short- and medium-haul transportation, and sightseeing tourism. They are a staple product in the civil aviation market and for emergency rescue departments. Therefore, helicopters are widely used worldwide, but this also brings stringent safety requirements for them.

[0003] For helicopters, engine failure is one of the leading causes of helicopter flight accidents, and ensuring flight safety after engine failure has always been a key focus of helicopter flight safety research. Currently, to improve safety, helicopters are generally configured with twin or multiple engines to ensure that even in the event of a single engine failure (OEI), the helicopter still has the power to climb. In this case, multi-engine helicopters (including twin-engine helicopters, with twin-engine configurations being the most common) are subject to Category A flight requirements, especially during takeoff and climb. How to fly after a single engine failure requires making the correct decision between landing and go-around. Summary of the Invention

[0004] In view of the shortcomings of the existing technology, the purpose of this invention is to provide a method for calculating the takeoff trajectory of helicopters in Category A flight, so as to solve the problem that there is no method for calculating the takeoff trajectory of helicopters in Category A flight in the existing technology.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A method for calculating the takeoff trajectory of a helicopter in Category A flight includes the following calculation steps:

[0007] S1: Statistics on the parameters of twin-engine helicopters and the parameters of the engines they use;

[0008] S2: Based on the statistical parameters, calculate the power required for forward flight of the twin-engine helicopter. and draw curve;

[0009] S3: Based on the power required for forward flight of the twin-engine helicopter And statistics on single-engine emergency power Calculate the safe takeoff speed for a twin-engine helicopter. ;

[0010] S4: Based on the statistical parameters, calculate the upward rotation force and forward thrust provided by the helicopter rotor;

[0011] S5: Based on the safe takeoff speed and the upspin force and forward thrust provided by the helicopter rotor, calculate the critical takeoff decision point for the twin-engine helicopter and plot the critical takeoff decision point curve for the helicopter.

[0012] S6: Based on the calculated critical decision point for takeoff of the twin-engine helicopter, and according to the location of the failure point, calculate the takeoff trajectory of the twin-engine helicopter in Category A flight, and plot the Category A takeoff trajectory curve of the helicopter.

[0013] The definition of safe takeoff speed in step S3 includes:

[0014] Within the threshold altitude range, the power required by the helicopter to maintain a stable flight at different speeds and a climb rate of 0.5 m / s is calculated to obtain the speed-power curve. Then, based on the single-engine emergency power... Find the left intersection point of the single-engine emergency power versus speed-power curve; the corresponding speed is the safe takeoff speed. ;

[0015] Calculate the climb power factor of a twin-engine helicopter using the following formula. :

[0016]

[0017] In the formula This refers to the weight coefficient of a twin-engine helicopter. The relative climb rate of a twin-engine helicopter;

[0018]

[0019] In the formula, For the climb rate of a twin-engine helicopter, The rotor radius; The rotor's angular velocity;

[0020] Calculate the climb power of a twin-engine helicopter using the following formula. :

[0021]

[0022] In the formula: Characterizes atmospheric density;

[0023] When the twin-engine helicopter flies at a certain forward speed and maintains a stable climb rate, the algebraic sum of the required power for level flight and climb is... for:

[0024]

[0025] What is the safe takeoff speed for a twin-engine helicopter? :

[0026]

[0027] In the formula, This refers to the emergency power output of a single engine.

[0028] Furthermore, the parameters for the twin-engine helicopter in step S1 include: total helicopter weight G, rotor rotation angular velocity... Number of blades k, rotor airfoil, rotor radius R, rotor solidity ;

[0029] The engine parameters used in the twin-engine helicopter include: single-engine emergency power. 30-second single-engine emergency power Engine 2-minute single-engine emergency power Engine emergency power per 30 minutes ;

[0030] The power required for forward flight of the twin-engine helicopter in step S2 Specifically, this includes: the power required by the rotor. Power required for the tail rotor Power loss in reducer and transmission system Engine installation losses .

[0031] Furthermore, the required power of the rotor The calculation is as follows:

[0032] S21: Calculate the atmospheric density;

[0033] The solution for atmospheric density under non-standard atmospheric conditions is as follows:

[0034]

[0035]

[0036] In the formula, For flight altitude, Atmospheric temperature, The atmospheric density at sea level;

[0037] S22: Calculate the tensile coefficient and lift coefficient :

[0038]

[0039]

[0040]

[0041] In the formula, For rotor lift; The rotor radius; The rotor's rotational angular velocity; This refers to the forward flight speed of the helicopter; The forward ratio; This is the tip loss coefficient. ≈0.92; For rotor realism;

[0042] S23: Calculate the rotor-type drag power. Specifically, it includes:

[0043] Calculate the power coefficient of the type resistance using the following formula :

[0044]

[0045]

[0046] In the formula, This is the resistance power correction factor for hovering mode; This takes into account the non-uniformity of the distribution of the resistivity along the span direction; The drag coefficient at the characteristic profile of the blade;

[0047] Rotor-type power resistance for:

[0048]

[0049] S24: Calculate the rotor induced power Specifically, it includes:

[0050] Calculate the induced power coefficient using the following formula :

[0051]

[0052]

[0053] In the formula, This is the correction factor for induced power during hovering. , , change; This represents the relative value of the induced velocity at the propeller disk plane during hovering.

[0054]

[0055] In the formula: It is the tensile coefficient; This is the tip loss coefficient;

[0056] Rotor induced power for:

[0057]

[0058] S25: Calculate waste resistance power Specifically, it includes:

[0059] Calculate helicopter exhaust drag using the following formula :

[0060]

[0061] In the formula, , These are the drag coefficients and frontal areas of each windward component on the helicopter;

[0062] Calculate waste resistance power for:

[0063]

[0064] Rotor power required for: .

[0065] Furthermore, the tail rotor requires power The calculation specifically includes: for a single-rotor helicopter with a tail rotor, when flying forward, the power required by the tail rotor consists of shape drag power and induced power;

[0066] S26: Calculate the tail rotor type resistance power. Specifically, it includes:

[0067] Calculate the power coefficient of the type resistance using the following formula :

[0068]

[0069]

[0070] In the formula, This is the resistance power correction factor for hovering mode; This takes into account the non-uniformity of the distribution of the resistivity along the span direction; The drag coefficient at the characteristic profile of the tail rotor blade;

[0071] Tail rotor type resistance power for:

[0072]

[0073] S27: Calculate the tail rotor induced power Specifically, it includes:

[0074] Calculate the induced power coefficient using the following formula :

[0075]

[0076]

[0077] In the formula, This is the correction factor for induced power during hovering. ; The relative value of the induced velocity at the tail rotor plane;

[0078]

[0079] In the formula: This is the tail rotor thrust coefficient; The tail rotor tip loss coefficient;

[0080] Tail rotor induced power for:

[0081]

[0082] Tail rotor required power for: .

[0083] Furthermore, the power loss of the reducer and transmission system refers to the loss caused by friction between gears and within bearings, as well as aerodynamic resistance or wind resistance, accounting for 2%-4% of the engine power.

[0084] The engine installation loss This means that when the engine is installed on a helicopter, its output power is less than that of the bench test, accounting for 3%-6% of the engine power.

[0085] The power required for the helicopter to fly forward is calculated as follows:

[0086]

[0087] Calculate different forward flight speeds The power required for the next flight ,draw curve.

[0088] Furthermore, the calculation of the upward rotation force and forward thrust provided by the rotor in step S4 includes:

[0089] S41: Let the rotor's spinning force be... The forward pulling force is Clearly define the forces acting on the helicopter during the go-around process and record the aerodynamic resultant force of the rotor. It equals the rotor lift T, and constructs the slipstream theory rotor disk force diagram, and also constructs the helicopter power curve;

[0090] S42: Calculate the rotor lift provided by the rotor during effective forward flight of the dual engines. and forward tension :

[0091] Calculate the hovering curve:

[0092] Selecting the tensile coefficient A series of calculation points, take ;

[0093] Calculate the lift coefficient at the characteristic profile of the blade using the following formula. ;

[0094]

[0095] Based on calculations The shape drag coefficient can be obtained by referring to the blade polar curve. ;

[0096] Calculate the power factor using the following formula:

[0097]

[0098] Calculate the relative value of the induced velocity at the propeller disk plane during hovering using the following formula:

[0099]

[0100] The induced power coefficient during hovering was obtained as follows:

[0101]

[0102] The required power factor for wave impedance is calculated as follows:

[0103]

[0104] In the formula: The critical Mach number M for the sudden increase in blade airfoil drag and the lift coefficient The relationship is obtained;

[0105] Calculate the total power demand factor using the following formula:

[0106]

[0107] According to the corresponding , , make curve;

[0108] When a single engine fails, the following formula shall be used for calculation:

[0109] The corresponding power is the emergency power of a single engine. Calculate the corresponding tensile coefficient Calculate the relative value of the induced velocity at the propeller disk plane during single-engine hovering using the following formula. ;

[0110]

[0111] The induced velocity at the propeller disk during forward flight is :

[0112]

[0113]

[0114] In the formula, represents the relative value of the induced velocity at the propeller disk;

[0115] Given the forward velocity is The aerodynamic resultant force of the helicopter rotor after a single engine failure is calculated using the following formula. :

[0116]

[0117]

[0118] In the formula This represents the velocity value of the deflected airflow after passing through the propeller disk;

[0119] Calculate the rotor's spinning force using the following formula. and the forward thrust of the rotor :

[0120]

[0121]

[0122] In the formula This is the maximum rotor disk angle of attack.

[0123] Furthermore, the takeoff critical decision point in step S5 is a combination of flight altitude and speed. The takeoff critical decision point forms a critical decision curve during flight. The intersection of the critical decision curve and the helicopter takeoff trajectory is the takeoff critical decision point for the corresponding takeoff mode.

[0124] The beneficial effects of this invention are as follows: Starting with the takeoff trajectory of a helicopter in Category A flight, this invention proposes a method for calculating the required power, safe takeoff speed, and critical takeoff decision point for helicopters. It also calculates the takeoff trajectory for twin-engine helicopters in Category A flight, resulting in a simpler calculation process and more accurate results. Before flight testing, it can provide corresponding trajectory references for different single-engine failure points of helicopters. Especially during flight, it helps pilots make timely judgments after engine failure, providing theoretical support for subsequent flights and offering preliminary guidance for subsequent flight tests. This method facilitates convenient and reliable type certification, saving time, manpower, and resources. Attached Figure Description

[0125] Figure 1 This is a schematic diagram of the process of the present invention;

[0126] Figure 2 A comparison chart of power requirements for helicopter forward flight;

[0127] Figure 3 A diagram illustrating the safe takeoff speed for helicopters;

[0128] Figure 4 Power required for forward flight of the UH-60A helicopter;

[0129] Figure 5 This is a diagram illustrating the safe takeoff speed for the UH-60A helicopter.

[0130] Figure 6 This is a schematic diagram of the critical decision point curve for takeoff of the UH-60A helicopter.

[0131] Figure 7 This is a schematic diagram of the Category A takeoff trajectory of a UH-60A helicopter after a single engine failure.

[0132] Figure 8 This is a force diagram of the propeller disk in slipstream theory. Detailed Implementation

[0133] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Identical components are denoted by the same reference numerals. It should be noted that the terms "front," "rear," "left," "right," "upper," and "lower" used in the following description refer to directions in the accompanying drawings, and the terms "bottom surface," "top surface," "inner," and "outer" refer to directions toward or away from the geometric center of a specific component, respectively.

[0134] refer to Figures 1 to 8 The diagram illustrates a specific implementation of the helicopter takeoff trajectory calculation method for Category A flight according to the present invention, which includes the following calculation steps:

[0135] S1: Statistics on the parameters of twin-engine helicopters and the parameters of the engines they use;

[0136] S2: Based on the statistical parameters, calculate the power N required for forward flight of the twin-engine helicopter. xu And plot N xu -V0 curve;

[0137] S3: Based on the power N required for forward flight of the twin-engine helicopter. xu And the statistical data on the single-engine emergency power P OEI Calculate the safe takeoff speed V for a twin-engine helicopter. toss ;

[0138] S4: Based on the statistical parameters, calculate the lift and forward thrust provided by the helicopter rotor;

[0139] S5: Based on the safe takeoff speed and the lift and forward thrust provided by the helicopter rotor, calculate the critical takeoff decision point for the twin-engine helicopter and plot the critical takeoff decision point curve for the helicopter.

[0140] S6: Based on the calculated critical decision point for takeoff of the twin-engine helicopter, and according to the location of the failure point, calculate the takeoff trajectory of the twin-engine helicopter in Category A flight, and plot the Category A takeoff trajectory curve of the helicopter.

[0141] As a further improvement of the present invention, the parameters of the twin-engine helicopter in step S1 include: total helicopter weight G, rotor rotational angular velocity Ω, number of rotor blades k, rotor airfoil, rotor radius R, and rotor solidity. ;

[0142] The engine parameters used in the twin-engine helicopter include: single-engine emergency power P. OEI 30s single-engine emergency power P OEI-30s Engine 2-minute single-engine emergency power P OEI-2min Engine 30-minute single-engine emergency power P OEI-30min ;

[0143] In step S2, the power N required for the twin-engine helicopter to fly forward is... xu Specifically, this includes: the required power P of the rotor. r The tail rotor requires power P TR Power loss P in reducer and transmission system RE.T Engine installation loss P SET .

[0144] As a further improvement of the present invention, the required power P of the rotor is... r The calculation is as follows:

[0145] S21: Calculate the atmospheric density;

[0146] The solution for atmospheric density under non-standard atmospheric conditions is as follows:

[0147]

[0148] In the formula, H is the flight altitude, and t is the atmospheric temperature. The atmospheric density at sea level;

[0149] S22: Calculate the tensile coefficient C T And lift coefficient Cy:

[0150]

[0151]

[0152]

[0153] In the formula, T is the rotor lift; R is the rotor radius; Ω is the rotor rotation angular velocity; V0 is the forward speed of the helicopter; is the forward ratio; B is the tip loss coefficient, B≈0.92; For rotor realism;

[0154] S23: Calculate the rotor-type drag power N x Specifically, it includes:

[0155] The type resistance power factor m is calculated using the following formula. kx :

[0156]

[0157] In the formula, For hovering state type impedance power correction coefficient; ≈1.0-1.1, which takes into account the non-uniformity of the distribution of the resistivity along the span (usually taken as 1.05). The drag coefficient at the characteristic profile of the blade;

[0158] Rotor-type resistance power N x for:

[0159]

[0160] S24: Calculate the rotor induced power N i Specifically, it includes:

[0161] The induced power coefficient m is calculated using the following formula. ki :

[0162]

[0163] In the formula, This is the correction factor for induced power during hovering. ≈1.05-1.10, depending on C T , change; This represents the relative value of the induced velocity at the propeller disk plane during hovering.

[0164]

[0165] In the formula: C T B is the tension coefficient; B is the tip loss coefficient.

[0166] Rotor induced power N i for:

[0167]

[0168] S25: Calculate the waste resistance power N f Specifically, it includes:

[0169] Calculate helicopter exhaust drag using the following formula :

[0170]

[0171] In the formula, C x S and S represent the drag coefficient and frontal area of ​​each windward component on the helicopter, respectively.

[0172] Find the waste resistance power N f for:

[0173]

[0174] The required power P of the rotor r For: P r =N x +N i +N f .

[0175] As a further improvement of the present invention, the tail rotor requires power P TR The calculation specifically includes: for a single-rotor helicopter with a tail rotor, when flying forward, the power required by the tail rotor consists of shape drag power and induced power;

[0176] S26: Calculate the tail rotor type resistance power N tx Specifically, it includes:

[0177] The type resistance power factor m is calculated using the following formula. tkx :

[0178]

[0179] In the formula, For hovering state type impedance power correction coefficient; ≈1.0-1.1, which takes into account the non-uniformity of the distribution of the resistivity along the span (usually taken as 1.05). The drag coefficient at the characteristic profile of the tail rotor blade;

[0180] Tail rotor type resistance power N tx for:

[0181]

[0182] S27: Calculate the tail rotor induced power N ti Specifically, it includes:

[0183] The induced power coefficient m is calculated using the following formula. tki :

[0184]

[0185] In the formula, J is the correction coefficient for induced power in hovering state; J0≈1.05-1.10; The relative value of the induced velocity at the tail rotor plane;

[0186]

[0187] In the formula: C Tt B is the tail rotor thrust coefficient; t The tail rotor tip loss coefficient;

[0188] Tail rotor induced power N ti for:

[0189]

[0190] Tail rotor required power P TR For: P TR =N tx +N ti .

[0191] As a further improvement of the present invention, the power loss of the reducer and transmission system refers to the loss caused by friction between gears and within bearings, as well as aerodynamic resistance or wind resistance, accounting for 2%-4% of the engine power.

[0192] The engine installation loss P SET This means that when the engine is installed on a helicopter, its output power is less than that of the bench test, accounting for 3%-6% of the engine power.

[0193] The power required for the helicopter to fly forward is calculated as follows:

[0194]

[0195] Calculate the power N required for forward flight at different forward flight speeds V0. xuPlot the Nxu-V0 curve.

[0196] As a further improvement of the present invention, the definition of the safe takeoff speed in step S3 includes:

[0197] Within the threshold altitude range, calculate the power required by the helicopter when it is flying stably at different speeds and a climb rate of 0.5 m / s, obtain the speed-power curve, and then calculate the single-engine emergency power P. OEI Find the left intersection point of the single-engine emergency power versus speed-power curve; the corresponding speed is the safe takeoff speed V. toss ;

[0198] Calculate the climb power factor m of a twin-engine helicopter using the following formula. kp :

[0199]

[0200] In the formula C G This refers to the weight coefficient of a twin-engine helicopter. The relative climb rate of a twin-engine helicopter;

[0201]

[0202] In the formula, For the climb rate of a twin-engine helicopter;

[0203] Calculate the climb power of a twin-engine helicopter using the following formula. :

[0204]

[0205] In the formula: Characterizes atmospheric density.

[0206] As a further improvement of the present invention, the power N required by the twin-engine helicopter when flying at a certain forward speed and maintaining a stable climb rate is... sum

[0207]

[0208] Find the safe takeoff speed V for a twin-engine helicopter. toss :

[0209]

[0210] In the formula, P OEI This refers to the emergency power output of a single engine.

[0211] As a further improvement of the present invention, the calculation of the lift and forward thrust provided by the rotor in step S4 includes:

[0212] S41: Let the rotor lift be Y and the forward thrust be X. Clarify the forces acting on the helicopter during the go-around process. Let the aerodynamic resultant force R of the rotor be equal to the rotor thrust T. Construct the rotor disk force diagram based on slipstream theory. Also, construct the helicopter power curve.

[0213] S42: Calculate the rotor lift Y and forward thrust X provided by the rotor during forward flight:

[0214] Calculate the hovering curve:

[0215] Select C T The series of calculation points, take C T =0.006~0.020;

[0216] Calculate the lift coefficient C of the blade characteristic profile using the following formula. y7 ;

[0217]

[0218] Based on the calculated C y7 The shape drag coefficient C is obtained by referring to the blade polar profile. x7 ;

[0219] Calculate the power factor using the following formula:

[0220]

[0221] Calculate the relative value of the induced velocity at the propeller disk plane during hovering using the following formula:

[0222]

[0223] The induced power coefficient during hovering was obtained as follows:

[0224]

[0225] The required power factor for wave impedance is calculated as follows:

[0226]

[0227] In the formula: The critical Mach number M for sudden increase in blade airfoil drag and lift coefficient C y The relationship is obtained;

[0228] Calculate the total power demand factor using the following formula:

[0229]

[0230] According to the corresponding C T m K , make curve;

[0231] The corresponding power is the single-engine emergency power P. OEI Calculate the corresponding tensile coefficient Calculate the relative value of the induced velocity at the propeller disk plane during hovering using the following formula. ;

[0232]

[0233] The induced velocity at the propeller disk during forward flight is :

[0234]

[0235]

[0236] In the formula, represents the relative value of the induced velocity at the propeller disk;

[0237] Given the forward velocity is The rotor thrust T after a single engine failure of the helicopter is calculated using the following formula:

[0238]

[0239]

[0240] In the formula This represents the velocity value of the deflected airflow after passing through the propeller disk;

[0241] Calculate the rotor lift Y and the rotor forward thrust X using the following formulas:

[0242]

[0243]

[0244] In the formula This is the maximum rotor disk angle of attack.

[0245] The calculation of the takeoff critical decision point in step S5 is as follows:

[0246] Considering the helicopter's horizontal and vertical motion separately, let's first analyze the forces acting on the helicopter in the horizontal direction to obtain its acceleration variation. The helicopter experiences drag during forward flight and a horizontal thrust generated by the rotor. The drag force at a certain moment during forward flight is... :

[0247]

[0248] In the formula: For forward flight speed at different times, It is the product of the drag coefficients and the frontal area of ​​each windward component on the helicopter in the horizontal direction.

[0249] It can be seen that the forward drag of a helicopter is related to its forward speed. This can be observed from the helicopter's power requirement curve; as the forward speed increases, the required power first decreases and then increases, reaching a minimum at the economical speed. Therefore, in the event of engine failure, to ensure a safe go-around, the forward speed should be increased as quickly as possible to reduce the required power. After engine failure, the pilot should apply maximum longitudinal control to the rotor disc to provide the maximum forward force, enabling the helicopter to reach the safe takeoff speed in the shortest possible time.

[0250] The horizontal acceleration at this moment can be obtained by the following formula:

[0251]

[0252] In the formula, This represents the horizontal thrust of the rotor when the rotor disk angle of attack is at its maximum at the current moment.

[0253] The change in horizontal velocity is calculated by superimposing the changes in velocity over infinitesimal time intervals, and the forward velocity after the infinitesimal time interval is obtained by calculating the velocity at the previous moment:

[0254]

[0255] In the formula: The time interval is 0.1s.

[0256] Similarly, the horizontal displacement within a infinitesimal time interval and the displacement after the infinitesimal time interval are calculated using the forward velocity at the current moment:

[0257]

[0258]

[0259] The helicopter's speed and displacement are continuously iterated at every moment until the forward speed is greater than or equal to the safe takeoff speed. The time it takes for the helicopter to accelerate from its horizontal speed to its safe takeoff speed after a single engine failure is obtained:

[0260]

[0261] In the formula: n1 is the number of iterations of the horizontal velocity.

[0262] To establish a vertical motion model for the helicopter within time t1, we first need to consider the following: When the engine fails, the reduced rotor collective pitch leads to lift loss, and considering drag, the helicopter will descend at a variable speed. As the helicopter's forward speed increases, its power requirement gradually decreases, leaving surplus power to provide lift, causing the helicopter to gradually decelerate until it begins to climb. However, due to the different speeds at the time of engine failure, the time it takes for the helicopter to accelerate to its safe takeoff speed varies. This means that when the helicopter reaches its safe takeoff speed, its vertical velocity could be negative (i.e., the helicopter is descending), positive (i.e., the helicopter is ascending), or even zero. Therefore, calculations and analyses are needed for different scenarios.

[0263] The helicopter was in stable flight just moments before failure, with its vertical velocity at zero. Therefore, the vertical velocity was zero at the moment of failure. As the helicopter's descent speed changes, its vertical drag will also change.

[0264]

[0265] In the formula: For forward flight speed at different times, It is the product of the drag coefficient and the frontal area of ​​each windward component on the helicopter in the vertical direction.

[0266] The vertical acceleration at this moment can be obtained by the following formula. :

[0267]

[0268] By using the initial velocity and acceleration of each infinitesimal time interval, we can calculate the velocity after each infinitesimal time interval, the height of descent during each infinitesimal time interval, and the vertical displacement after each infinitesimal time interval.

[0269]

[0270]

[0271]

[0272] In the formula: Δt is the infinitesimal time of 0.1s.

[0273]

[0274] In the formula: n2 is the number of velocity iterations in the first stage in the vertical direction.

[0275] If the calculated vertical velocity after time t1 is greater than zero, it indicates that the helicopter has stopped descending and is now ascending, meaning it has passed the lowest altitude point during the go-around process. The cumulative descent altitude when the descent velocity is zero is the maximum descent altitude of the helicopter after a single engine failure.

[0276] If the calculated vertical velocity after time t1 is zero, it indicates that the helicopter has stopped descending and has begun to ascend, meaning it has reached its lowest altitude during the go-around process. The altitude calculated at this point is the landing altitude after a single engine failure. Afterwards, adjust the rotor disc angle of attack to maintain the helicopter's forward velocity at V. toss The flight remains unchanged, gradually climbs, and then performs subsequent operations to complete the go-around and departure.

[0277] If the calculated vertical velocity after time t1 is less than zero, it means that the helicopter is still descending, but its forward speed has reached the safe takeoff speed. At this point, the helicopter can be manipulated to maintain zero horizontal acceleration and maximize vertical acceleration. Calculate the thrust F, horizontal component Q, and vertical component C provided by the rotor disc at this time:

[0278]

[0279]

[0280]

[0281] Since the helicopter is still descending, the drag force is:

[0282]

[0283] The vertical acceleration at this moment can be obtained by the following formula:

[0284]

[0285] By using the initial velocity and acceleration of each infinitesimal time interval, we can calculate the velocity after each infinitesimal time interval, the height of descent during each infinitesimal time interval, and the total vertical displacement during each infinitesimal time interval.

[0286]

[0287]

[0288]

[0289] If the calculated vertical velocity is zero, it means the helicopter has stopped descending and started to ascend, indicating it is at its lowest altitude during the go-around process. The descent altitude at this point, combined with the descent altitudes mentioned earlier, gives the maximum descent altitude the helicopter can reach after a single engine failure.

[0290] The descent time for the entire phase is:

[0291]

[0292] In the formula: n3 is the number of the second iteration of the vertical velocity.

[0293] By changing the forward speed of the helicopter when a single engine fails, the corresponding landing altitude can be calculated. The airworthiness regulations stipulate that the lowest point of the helicopter during the go-around process after a single engine failure must not be lower than 4.5m above the ground. Therefore, the safe takeoff decision point altitude of the helicopter at different failure speeds can be calculated.

[0294] According to airworthiness regulations, another condition for a helicopter to safely go around is to maintain a forward speed of V. toss At this point, the helicopter's climb rate needs to reach at least 0.5 m / s². Therefore, during the helicopter's upward climb, its downward resistance is:

[0295]

[0296] The vertical acceleration at this moment can be obtained by the following formula:

[0297]

[0298] By using the initial velocity and acceleration of each infinitesimal time interval, the velocity and vertical displacement after each infinitesimal time interval can be calculated:

[0299]

[0300]

[0301]

[0302] The horizontal displacement during this process is:

[0303]

[0304] When the helicopter's climb speed reaches 0.5 m / s, the corresponding time is:

[0305]

[0306] In the formula: n4 is the number of iterations of the vertical climbing speed.

[0307] When the helicopter was If the descent stops within a certain time period, the total time from the point of failure to when the helicopter reaches a climb rate of 0.5 m / s is:

[0308]

[0309] In contrast, helicopters are If the helicopter continues to descend during the time period, the total time from the point of failure to when it has a climb rate of 0.5 m / s is:

[0310]

[0311] The total time for the helicopter to complete the above process after failure should be less than or equal to the rated time corresponding to the emergency power of a single engine. If it exceeds this time, it means that the helicopter cannot complete the go-around using the emergency power and can only land. If the total time is less than the rated time, it means that the helicopter has the ability to successfully go-around after failing at the takeoff safety decision point.

[0312] The critical decision point for helicopter takeoff is a combination of altitude and speed, therefore there is more than one possible combination. For any specific takeoff method, there is a different critical decision point on the takeoff trajectory. The calculated result of the helicopter's critical decision point should be a curve; the intersection of this curve and the helicopter's takeoff trajectory is the critical decision point for the corresponding takeoff method. The helicopter's critical decision point is obtained based on the calculation results of the above calculation model.

[0313] The calculation of the Class A takeoff trajectory in step S6 is as follows:

[0314] After establishing a climb rate of 0.5 m / s, switch the engine power state to 2 min OEI power, and the helicopter will operate at V... toss Flying forward at a rate of 0.5 m / s, the helicopter climbs to 10.5 m above the ground. During this time, the helicopter moves at a constant velocity in both the horizontal and vertical directions. The horizontal and vertical displacements are as follows:

[0315]

[0316]

[0317] After climbing to an altitude of 10.5m, the engine is switched to 30min OEI power mode, and the helicopter accelerates forward to an economical speed by reducing the angle of attack; the rotor thrust T during this process is calculated in step S4. This is achieved through a predetermined rotor disk angle of attack. The calculation shows that at this time along OY V Rotor lift in the direction Y and along OX V The forward thrust X of the rotor in the direction of:

[0318]

[0319]

[0320] Similarly, considering the helicopter's horizontal and vertical motion separately, the helicopter experiences drag during forward flight and horizontal thrust from the rotor in the horizontal direction. In the vertical direction, it experiences downward drag and vertical thrust from the rotor during ascent. The drag experienced at a certain moment during forward flight is:

[0321]

[0322]

[0323] The horizontal acceleration at this moment can be obtained by the following formula:

[0324]

[0325]

[0326] The changes in horizontal and vertical velocity are calculated by superimposing the velocity changes over infinitesimal time intervals, and the forward velocity after the infinitesimal time interval is obtained by calculating the velocity at the previous moment.

[0327]

[0328]

[0329] In the formula: The time interval is 0.1s.

[0330] Similarly, the horizontal and vertical displacements after a infinitesimal time interval are calculated using the forward velocity at the current moment:

[0331]

[0332]

[0333] The helicopter's speed and displacement are continuously iterated at every moment until the forward speed is greater than or equal to the economic speed or the advantageous speed. ,

[0334] When the helicopter's forward speed reaches an economical or favorable speed, the horizontal and vertical displacements after a single engine failure are as follows:

[0335]

[0336]

[0337] Accelerate forward to the target speed. At this point, the helicopter adjusts its angle of attack, maintaining an economical speed horizontally and continuing to climb vertically.

[0338]

[0339]

[0340]

[0341] Since the helicopter is still climbing, the drag force is:

[0342]

[0343] The vertical acceleration at this moment can be obtained by the following formula:

[0344]

[0345] By using the initial velocity and acceleration of each infinitesimal time interval, we can calculate the velocity after each infinitesimal time interval and the height of descent during each infinitesimal time interval:

[0346]

[0347]

[0348] The horizontal and vertical displacements of the helicopter during this time period are as follows:

[0349]

[0350]

[0351] Climb to an altitude of 300m above the ground, complete the go-around, and then climb to the target altitude according to the specific flight mission requirements, and complete the flight at the corresponding forward speed.

[0352] The following example is provided:

[0353] The UH-60A helicopter was selected as a case study for calculation. The takeoff trajectory of the UH-60A helicopter in Category A flight was calculated when the total mass of the UH-60A helicopter was 9185kg.

[0354] The parameters of the helicopter and the engine it uses are shown in Table 1 below:

[0355] Table 1

[0356] Helicopter gross weight G 9185kg Rotor rotational angular velocity Ω 27 rad / s Number of blades k 4 pieces Rotor airfoil SC1095, SC1094R8 Rotor radius R 8.1778m Rotor realism σ 0.0826 Minimum rotor speed Ωmin1 after single-engine failure 0.97Ω Minimum rotor speed Ωmin2 after complete engine failure 0.95Ω The maximum vertical landing speed V1 that the landing gear can withstand 1.524m / s The maximum horizontal landing speed that the landing gear can withstand is V2 12.192m / s Number of engines 2 units PAEO full power engine 3780hp Engine 30s single-engine power POEI 1985hp Engine 2min single-engine power POEI 1650hp Engine 30min single-engine power POEI 1573hp

[0357] Calculate the power requirement curve for forward flight of the UH-60A helicopter:

[0358] The power requirement curve for forward flight of the UH-60A helicopter is saddle-shaped. As forward speed increases, the required power initially decreases and then increases, reaching its minimum at approximately 140 km / h, at about 1180 kW. (See also...) Figure 4 As shown;

[0359] Calculate the safe takeoff speed V of the UH-60A helicopter. toss :

[0360] Airworthiness standards for takeoff safety speed V toss The definition is: under given combinations of helicopter takeoff weight, center of gravity and altitude, and temperature, the minimum flight speed at which a stable climb rate of at least 0.5 m / s can be achieved using the remaining power after the failure of a critical engine.

[0361] Based on the established power requirement model for a twin-engine helicopter, the power requirement curve of the twin-engine helicopter as a function of forward flight speed is calculated. Furthermore, the power requirement curve for the helicopter with a climb rate of 0.5 m / s is calculated. Figure 5 We can obtain the relationship between the emergency power of a single helicopter engine and the power required at this time: When the forward speed is low, the helicopter's power requirement is greater than the emergency power of a single engine, and the helicopter cannot climb; as the forward speed increases, the helicopter's power requirement gradually decreases. When it equals the emergency power of a single engine, the helicopter can achieve a stable climb rate of 0.5 m / s. The forward speed corresponding to this is the safe takeoff speed V for a helicopter in the corresponding state of single-engine failure. toss The calculated safe takeoff speed is 78.214 km / h.

[0362] Based on the helicopter takeoff critical decision point model and helicopter OEI state flight trajectory calculation model established above, the safe takeoff speed V of a twin-engine helicopter is known. toss Calculate the critical takeoff decision point for a single-engine failure of a UH-60A helicopter with a total mass of 9185kg and the corresponding Category A takeoff trajectory.

[0363] Calculate the critical takeoff decision point curve for the UH-60A helicopter:

[0364] The critical takeoff decision point is defined as: for a Category A helicopter, on a fixed takeoff path, the first point at which it has the capability to continue takeoff after a single engine failure, and the last point at which it can safely abort takeoff. In other words, the critical takeoff decision point speed is the maximum speed at which takeoff can be aborted after a critical engine failure, and the minimum speed at which takeoff can continue.

[0365] The critical takeoff decision point for a helicopter is a combination of altitude and speed, with different speeds corresponding to different altitudes. The critical takeoff decision speed can be calculated from the time required to accelerate from the engine failure speed to the safe takeoff speed and the duration of emergency power from a single engine. The critical takeoff decision point altitude can be calculated using altitude loss and the minimum ground clearance required by regulations. It is related to the helicopter's available energy just before engine failure and the energy loss during the subsequent acceleration to the safe takeoff speed.

[0366] The altitude-velocity curve formed by the critical takeoff decision points of the UH-60A is as follows: Figure 6 As shown, a specific takeoff critical decision point was selected to verify the optimization of the helicopter's flight trajectory under OEI (Outcome-of-Intake) conditions. When the forward speed was chosen to be 19.75 km / h, the corresponding altitude of the decision point was 144.1 m. Substituting this into the flight trajectory optimization model, the calculated flight trajectory curve of the UH-60A after a single-engine failure at the corresponding takeoff critical decision point was obtained. It can be seen that when the helicopter's descent rate equals 0, i.e., the lowest point above the ground, the altitude is 4.752 m, which meets the expectations.

[0367] Calculate the takeoff trajectory of a UH-60A helicopter in Category A flight:

[0368] Specific flight paths such as Figure 7 As shown, after a single engine failure, the pilot begins to control the helicopter after a 1-second delay, and then initiates collective pitch control after 2 seconds. The helicopter reduces collective pitch, maintains rotational speed, and provides maximum longitudinal control to the rotor disc. The helicopter gains kinetic energy by reducing potential energy, which reduces the power required during this process. The helicopter's lowest point of altitude is 4.752m. When the horizontal speed reaches the safe takeoff speed, the rotor disc angle of attack is adjusted to maintain a constant horizontal speed, while the helicopter climbs vertically at a speed of not less than 0.5m / s. When the altitude increases from 4.752m to 10.5m, the helicopter engine power is switched from V... toss Accelerate to economic speed to achieve maximum climb rate. At this point, the altitude is 60m above the ground. Maintain the forward speed at this moment and climb at the maximum climb rate from 60m to 300m to complete the go-around.

[0369] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method for calculating the takeoff trajectory of a helicopter in Category A flight, characterized in that, The calculation steps include the following: S1: Statistics on the parameters of twin-engine helicopters and the parameters of the engines they use; S2: Based on the statistical parameters, calculate the power N required for forward flight of the twin-engine helicopter. xu And plot N xu -V0 curve; S3: Based on the power N required for forward flight of the twin-engine helicopter. xu And the statistical data on the single-engine emergency power P OEI Calculate the safe takeoff speed V for a twin-engine helicopter. toss ; S4: Based on the statistical parameters, calculate the upward rotation force and forward thrust provided by the helicopter rotor; S5: Based on the safe takeoff speed and the upspin force and forward thrust provided by the helicopter rotor, calculate the critical takeoff decision point for the twin-engine helicopter and plot the critical takeoff decision point curve for the helicopter. S6: Based on the calculated critical decision point for takeoff of the twin-engine helicopter, and according to the location of the failure point, calculate the takeoff trajectory of the twin-engine helicopter in Category A flight, and plot the Category A takeoff trajectory curve of the helicopter. The definition of safe takeoff speed in step S3 includes: Within the threshold altitude range, calculate the power required by the helicopter when it is flying stably at different speeds and a climb rate of 0.5 m / s, obtain the speed-power curve, and then calculate the single-engine emergency power P. OEI Find the left intersection point of the single-engine emergency power versus speed-power curve; the corresponding speed is the safe takeoff speed V. toss ; Calculate the climb power factor m of a twin-engine helicopter using the following formula. kp : In the formula C G This refers to the weight coefficient of a twin-engine helicopter. The relative climb rate of a twin-engine helicopter; In the formula, V y For a twin-engine helicopter, R is the rotor radius; Ω is the rotor angular velocity. Calculate the climbing power P of a twin-engine helicopter using the following formula. kp : In the formula: ρ represents atmospheric density; When the twin-engine helicopter flies at a certain forward speed and maintains a stable climb rate, the algebraic sum N of the required power for level flight and climb is... sum for: Find the safe takeoff speed V for a twin-engine helicopter. toss : In the formula, P OEI This refers to the emergency power output of a single engine.

2. The method for calculating the takeoff trajectory of a helicopter in Category A flight according to claim 1, characterized in that: The parameters of the twin-engine helicopter in step S1 include: total helicopter weight G, rotor rotational angular velocity Ω, number of blades k, rotor airfoil, rotor radius R, and rotor solidity σ. The engine parameters used in the twin-engine helicopter include: single-engine emergency power P. OEI 30s single-engine emergency power P OEI-30s Engine 2-minute single-engine emergency power P OEI-2min Engine 30-minute single-engine emergency power P OEI-30min ; In step S2, the power N required for the twin-engine helicopter to fly forward is... xu Specifically, this includes: the required power P of the rotor. r The tail rotor requires power P TR Power loss P in reducer and transmission system RET Engine installation loss P SET .

3. The method for calculating the takeoff trajectory of a helicopter in Category A flight according to claim 2, characterized in that: The required power P of the rotor r The calculation is as follows: S21: Calculate the atmospheric density; The solution for atmospheric density under non-standard atmospheric conditions is as follows: In the formula, H is the flight altitude, t is the atmospheric temperature, and ρ0 is the standard atmospheric density at sea level; S22: Calculate the tensile coefficient C T and lift coefficient C y : In the formula, T is the rotor lift; R is the rotor radius; Ω is the rotor rotation angular velocity; V0 is the helicopter forward speed; μ is the forward ratio; B is the blade tip loss coefficient, B≈0.92; σ is the rotor solidity; S23: Calculate the rotor-type drag power N x Specifically, it includes: The type resistance power factor m is calculated using the following formula. kx : In the formula, K P K is the power correction factor for hovering state. P0 ≈1.0-1.1, considering the non-uniformity of the drag distribution along the span; C x7 The drag coefficient at the characteristic profile of the blade; Rotor-type resistance power N x for: S24: Calculate the rotor induced power N i Specifically, it includes: The induced power coefficient m is calculated using the following formula. ki : In the formula, J is the hovering state induced power correction coefficient; J0≈1.05-1.10, varying with C. T σ changes; This represents the relative value of the induced velocity at the propeller disk plane during hovering. In the formula: C T B is the tension coefficient; B is the tip loss coefficient. Rotor induced power N i for: S25: Calculate the waste resistance power N f Specifically, it includes: Calculate the exhaust drag Q of the helicopter using the following formula: In the formula, C x S and S represent the drag coefficient and frontal area of ​​each windward component on the helicopter, respectively. Find the waste resistance power N f for: The required power P of the rotor r for: .

4. The method for calculating the takeoff trajectory of a helicopter in Category A flight according to claim 3, characterized in that: The tail rotor requires power P TR The calculation specifically includes: for a single-rotor helicopter with a tail rotor, when flying forward, the power required by the tail rotor consists of shape drag power and induced power; S26: Calculate the tail rotor type resistance power N tx Specifically, it includes: The type resistance power factor m is calculated using the following formula. tkx : In the formula, K P K is the power correction factor for hovering state. P0 ≈1.0-1.1, considering the non-uniformity of the drag distribution along the span; C tx7 The drag coefficient at the characteristic profile of the tail rotor blade; Tail rotor type resistance power N tx for: S27: Calculate the tail rotor induced power N ti Specifically, it includes: The induced power coefficient m is calculated using the following formula. tki : In the formula, J is the correction coefficient for induced power in hovering state; J0≈1.05-1.10; The relative value of the induced velocity at the tail rotor plane; In the formula: C Tt B is the tail rotor thrust coefficient; t The tail rotor tip loss coefficient; Tail rotor induced power N ti for: Tail rotor required power P TR for: .

5. The method for calculating the takeoff trajectory of a helicopter in Category A flight according to claim 4, characterized in that: The power loss of the reducer and transmission system refers to the loss caused by friction between gears and within bearings, as well as aerodynamic resistance or wind resistance, accounting for 2%-4% of the engine power. The engine installation loss P SET This refers to the fact that when the engine is installed on a helicopter, its output power is less than the power during bench testing, accounting for 3%-6% of the engine's total power. The power required for the helicopter to fly forward is calculated as follows: Calculate the power N required for forward flight at different forward flight speeds V0. xu Draw N xu -V0 curve.

6. The method for calculating the takeoff trajectory of a helicopter in Category A flight according to claim 5, characterized in that: The calculation of the upward rotation force and forward thrust provided by the rotor in step S4 includes: S41: Describe the aerodynamic resultant force T of the rotor. R The rotor aerodynamic force is decomposed into an upspinning force T. Y and forward tension T X Furthermore, a force diagram of the rotor disk based on slipstream theory was constructed, along with a helicopter power curve; S42: Calculate the rotor aerodynamic force T under effective forward flight conditions with dual engines. R and its upward rotation force T Y and forward tension T X : Calculate the hovering curve: Selecting the tensile coefficient C T The series of calculation points, take C T =0.006~0.020; Calculate the lift coefficient C at the characteristic profile of the blade using the following formula. y7 ; Based on the calculated C y7 The shape drag coefficient C is obtained by referring to the blade polar curve. y7 ; Calculate the power factor using the following formula: Calculate the relative value of the induced velocity at the propeller disk plane during hovering using the following formula: The induced power coefficient during hovering was obtained as follows: The required power factor for wave impedance is calculated as follows: In the formula: The critical Mach number M for sudden increase in blade airfoil drag and lift coefficient C y The relationship is obtained; Calculate the total power demand factor using the following formula: According to the corresponding C T m K , make C T -m K curve; When a single engine fails, the following formula shall be used for calculation: The corresponding power is the single-engine emergency power P. OEI Calculate the corresponding tensile coefficient C. T Calculate the relative value of the induced velocity at the propeller disk plane during single-engine hovering using the following formula. ; The induced velocity at the propeller disk during forward flight is v1: In the formula, represents the relative value of the induced velocity at the propeller disk; Given the forward velocity V0, calculate the resultant aerodynamic force T of the helicopter rotor after single-engine failure using the following formula. R : In the formula, V1 is the deflection airflow velocity value after passing through the propeller disk; Calculate the rotor's spinning force T using the following formula. Y The forward thrust T of the rotor X : In the formula α E This is the maximum rotor disk angle of attack.

7. The method for calculating the takeoff trajectory of a helicopter in Category A flight according to claim 6, characterized in that: The takeoff critical decision point in step S5 is a combination of flight altitude and speed. The takeoff critical decision point forms a critical decision curve during flight. The intersection of the critical decision curve and the helicopter takeoff trajectory is the takeoff critical decision point for the corresponding takeoff mode.

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