Numerical simulation of the water landing process of a light civil helicopter in level 5 sea conditions

A helicopter emergency flotation system can provide flotation capability after the helicopter accidentally falls into the water. To solve the problem of attitude change of a helicopter after landing in water, a numerical simulation was carried out on a light civil helicopter with a weight of 3.5 t. It was simulated in level 5 sea conditions, the traveling speed was 15.4 m/s, and the height of the lowest point of the hydrostatic helicopter from the water surface was 250-260 mm, with or without lift, with or without floats. Landing on the water can be done with either basic or elliptical floats and in three different postures. The simulation results show that equipping a helicopter with pontoons can significantly improve its overturning resistance and flotation capabilities, but the impact on a helicopter equipped with pontoons will increase. Landing a helicopter in the water at a certain elevation angle is beneficial to the stability of the helicopter. A helicopter with a basic pontoon is more stable when it lands in the water. The performance is higher than that of the ellipsoidal pontoon, but the pitch stability of the basic pontoon is lower than that of the ellipsoidal pontoon.


Introduction
Because of its vertical take-off, landing, and good flight control advantages, helicopters are popular for water activities.As the number of helicopters for maritime activities increases, the flight time increases, the number of uses increases, and the number of failures will also increase.Helicopters usually have poor water tightness.Therefore, according to the requirements of the General Aviation Administration of China, helicopters operating at sea must undergo compliance verification with relevant provisions for ditching on water.The analysis of ditching characteristics is to obtain the aircraft's ability to resist overturning and changes in landing attitude, which is necessary for the pilot to escape safely [1] .
The United States has conducted early research on emergency flotation systems for helicopters.The U.S. Department of Transportation (U.S.DOT) analyzed the forced landing accidents at sea from 1982 to 1989 [2] , focusing on the causes of the accidents, the damage to the helicopter structure during the water impact process, and the performance of the emergency flotation system during ditching.The British Civil Aviation Authority (CAA) [3] conducted static and dynamic (under the action of waves and wind) tests on helicopter models of various models, studying the factors affecting the stability of helicopters and the impact of emergency airbags on helicopters.The Civil Aviation Authority [4] investigated and studied some helicopter forced landing accidents that occurred in the UK, tested a helicopter vertically entering water, and established a numerical model of a helicopter vertically entering IOP Publishing doi:10.1088/1742-6596/2764/1/012039 2 water based on LS-DYNA3D.The results were in good agreement with the test results.Cartwright et al. [5] and Groenenboom and Cartwright [6] conducted numerical simulations of the cylinder's water entry process based on PAM-CRASH, which agreed with the experimental results.It also simulated the deployment of the helicopter's emergency flotation airbag.Finally, it applied the SPH method to simulate the helicopter's forced landing process and its floating in waves, verifying the feasibility of the SPH method.Hughes et al. [7] conducted a numerical simulation of the water impact process of the metal plate structure of the helicopter belly, and the simulation results were in good agreement with the test results.Li [8] analyzed the water impact of emergency floating airbags based on LS-DYNA and experiments.He found that the load on the airbag during an impact would be concentrated near the connection of the airbag.Zhou [9] conducted numerical simulation and experimental research on the deployment process of emergency flotation airbags.He divided the airbag deployment process into three parts: rapid inflation, deep inflation, and overinflation.Jiang et al. [10] combined experiments and analyzed the water slamming process of helicopter floats based on LS-DYNA, and obtained the curves of the speed, acceleration, and other state parameters of helicopter floats changing with time; and analyzed the curves of helicopter floats at different elevation angles and deflections.Under the heading angle and vertical speed, the water impact load of the airframe and the speed change after slamming.Liu and Huang [11] established a rigid flex coupling model of the helicopter emergency airbag experimental unit in ADAMS, carried out dynamic simulation, and obtained the vibration displacement of the effective point of the experimental device rail in the vertical direction, which provided a theoretical basis for demonstrating the reliability of the experimental unit.
The above scholars or institutions have analyzed and studied the emergency floating system but rarely simulate the floating performance of small civil helicopters.Through numerical calculation, a numerical simulation was carried out for the helicopter's forced landing on the water in level 5 sea conditions.It was concluded that whether it has lift or not, whether it has pontoons, two different configurations of pontoons, and three different landing postures, the relative motion of the waves and the helicopter situations include the initial velocity of the helicopter, overturning, impact, attitude change, etc. of the helicopter at a certain altitude.

Helicopter and float parameters
The appearance of the helicopter used is shown in Figure 1.

Figure 1. Helicopter appearance.
The location of the center of gravity is determined by measuring its vertical distance from three datum planes, which are as follows: 1) The Z datum plane is parallel to the cockpit floor datum plane and is located 3.080 m above it.Dimensions above the Z plane are positive, and dimensions below are negative.
2) The Y datum plane is the vertical plane perpendicular to the cabin floor datum plane.This datum is the plane of symmetry of the helicopter.The right dimension of the Y plane is positive, and the left dimension is negative.
3) The X datum plane is a vertical plane orthogonal to the above two planes.It is located 3.997 m forward of the rotor centerline.The dimensions after the X plane are positive, and the ones before are negative.
IOP Publishing doi:10.1088/1742-6596/2764/1/0120393 The coordinate system OXYZ formed by the above reference plane is the structural coordinate system.In addition, taking the helicopter's center of gravity O 1 as the origin and parallel to the three datum planes, we establish O 1 X 1 Y 1 Z 1 as the center of gravity coordinate system.The schematic diagram is shown in Figure 2. The maximum take-off weight of the helicopter is 3850 kg.The moment of inertia in the X, Y, and Z directions is shown in Table 1.
Table 1 The main function of the float is to provide buoyancy for helicopters that are forced to land on water and to improve the helicopter's ability to resist overturning and float.The helicopter used for simulation weighs less and has a track skid.The float can be installed on the track skid of the helicopter.The installation diagram of the float on the helicopter is shown in Figure 3.The pontoon used has two states: state one is the basic shape, and state two is the ellipsoid shape.Both status pontoons meet the following conditions: (1) pontoon volume; (2) single volume of left/right pontoon: ≥1.9 m 3 ; (3) Float working pressure: (15±5) kPa.The diameter is not larger than 0.8 m.The appearance of the pontoon in state 1 is shown in Figure 4, and the pontoon in state 2 is shown in Figure 5.

Helicopter forced landing conditions
The simulation conditions include the helicopter's falling state, wave conditions, lift conditions, material settings, helicopter forward speed, and height.
Through fluid-solid coupling numerical simulation, the impact on the helicopter and the attitude change trend of the helicopter after falling into the water was obtained.
The state of the helicopter falling into the water includes the attitude of the helicopter when it falls into the water (yaw angle α, pitch angle β, roll angle γ) and the forward speed of the helicopter.There are three types of attitude when the helicopter falls into the water.The attitude and speed of the helicopter when it falls into the water are shown in Table 2.
Table 2. Attitude and speed of helicopter when falling into the water.

Stance
Yaw angle α Pitch angle β Roll angle γ Velocity (m/s) 15 The sea state level when the helicopter touched down was level 5, and the direction of waves was opposite to that of the helicopter.The lift situation is divided into lift and no lift.The lift is 2/3 gravity, which is 25153.3N.
The state one simulation model of the helicopter and the float is shown in Figure 6.The state two simulation model is similar to Figure 6.The difference is that the state two float replaces the state one float.

Simulation model settings
In LS-DYNA software, the surface of the helicopter fuselage is set to the same material.The helicopter model consists of a body, a flat tail, a vertical tail, a beam, a landing gear, a reinforcement belt, and an airbag, of which the airbag and the reinforcement belt are flexible bodies, and the rest are set as rigid bodies.The airbag and reinforcement belt are flexible bodies using the membrane element algorithm.The material model is *MAT_FABIRC and the material model of air and water is *MAT_NULL.The equation of state for air is a polynomial equation of state, and the equation of state for water is based on the Gruneisen equation of state.
Air, water, airbag, and reinforcement belt materials are shown in Table 3. Helicopter landing height is the lowest point of the float closest to the water surface.The height from the still water surface is 250-260 mm.

Numerical simulation of the basic configuration buoy landing process
The numerical simulation of the basic configuration buoy landing process includes helicopter landing with/without basic buoys and helicopter landing with basic buoys with/without lift.
For helicopter landing with or without basic floats, a water landing simulation was carried out in three postures (Cases 1-3).The acceleration history curve of the center of mass Z 1 direction is shown in Figure 7.It can be seen from Figure 7 that when other landing conditions are the same, the changing trend of the helicopter's z-direction acceleration is the same for the combination of the three dangerous landing attitude angles.
Figure 8 shows the helicopter landing in the water without floats at t=0 s, t=35.0 s, and t=37.8 s. t=0 s t=35.0 s t=37.8 s Figure 8. Case 2 helicopter hits the water without floats.Figure 9 shows the helicopter belt status -the float hits the water at t=0 s, t=35.0 s, and t=40.5 s. t=0 s t=35.0 s t=40.5 s Figure 9. Case 2 Helicopter with status one float hits the water.It can be seen from Figures 7, 8, and 9 that when the basic configuration buoy is installed, although the overload peak value during landing increases due to the increase in the water contact area, the attitude angle of the helicopter after landing in the water will not be the same.It has a good effect on the stability control and prevents the helicopter from rolling over.
Simulations were carried out to land a basic pontoon helicopter with and without lift belts in three attitudes, and the lift force was 2/3 gravity (i.e., 25153.3N).The Z 1 -direction acceleration time curve of the helicopter's center of mass with or without a lift is shown in Figure 10, and the changes in yaw angle α, pitch angle β, and roll angle γ are shown in Figure 11.As for the yaw angle, when there is no lift, and the initial yaw angle, pitch angle, and roll angle are 10°, 10°, and 5°, the yaw angle hardly changes during the landing process and finally stabilizes at about 10°.When the initial yaw angle, pitch angle, and roll angle are -10°, 10°, and -5°, the yaw angle first increases in the negative direction, reaches a negative peak of -15° at about 35.4 seconds and then begins to decrease in the negative direction.It decreased to -6° at about 36.6 seconds.The yaw angle showed a slightly negative increasing trend in the subsequent process.When the initial yaw angle, pitch angle, and roll angle are 10°, 10°, and -5°, the yaw angle gradually decreases after landing on the water.It decreases to about 0° at about 36 seconds, then almost constant.When carrying lift, the initial yaw, pitch, and roll angles are 10°, 10°, and 5°.The yaw angle continues to increase slowly after landing in the water.At 37.7 seconds, the yaw angle is around 12°.After that, the yaw angle has a clear increasing trend and reaches around 40° at 39 s.The changing trend of yaw angle in the working condition with initial yaw angle, pitch angle, and roll angle of 10°, 10°, and -5° is the same as that in the working condition with initial yaw angle, pitch angle and roll angle of 10°, 10° and 5°.The situation is almost the same: When the initial yaw angle, pitch angle, and roll angle are -10°, 10°, and -5°, the changing trend of the yaw angle is the same as when the initial yaw angle, pitch angle, and roll angle are 10°, 10°.The working condition of 5° is almost symmetrical.It can be seen from Figure 11 that when there is a lift, the change range of the yaw angle will increase, and there will be no recovery trend.When the helicopter-buoy moves for a certain period, the final x-axis will be perpendicular to the direction of wave advancement.
Regarding the pitch angle, when the lift conditions are the same, the effects of each initial attitude angle on the pitch angle change are almost equivalent.When there is no lift after landing in the water, the area under the front belly of the helicopter that is in contact with the water body is larger than the rear belly.The force exerted by the water body is relatively large, thus forming a positive pitching moment of the center of mass, causing the pitch angle to increase.It reaches about 20° at 35.4 s, and then after the pitch angle decreases to 0° in the positive direction.It begins to increase in the negative direction, reaching about -10° at 36.4 s, and then decreases in the negative direction and increases in the positive direction.When there is a lift, after landing on the water, the pitch angle first increases positively, reaching about 20° at 35.5 s.Then, after the pitch angle decreases to 0° in the positive direction, it increases negatively, reaching -18° at 37.5 s around, and then decreases in the negative direction and increases in the positive direction, reaching around 18° at 38.4 s, and then decreases.Generally speaking, the yaw angle changes sinusoidally when lift is applied.

Numerical simulation of the ellipsoid float landing process
The numerical simulation of the ellipsoidal buoy landing process includes helicopter landing with/without ellipsoidal buoys and helicopter landing with ellipsoidal buoys with/without lift.Cases 1-3 show the three attitudes and speeds of the helicopter when it falls into the water in Table 2.
Simulation calculations were carried out for helicopters with and without ellipsoidal floats landing in the water.The acceleration in the Z 1 direction is shown in Figure 12.  12 that when other landing conditions are the same, the changing trend of the helicopter's z-direction acceleration is the same for the three combinations of dangerous landing attitude angles.
The helicopter landing in the water with/without ellipsoidal floats in Case 3 attitude is shown in Figure 13 and Figure 14.It can be seen from Figure 12, Figure 13, and Figure 14 that when an ellipsoid float is installed, although the overload peak value during landing increases due to the increase in the water contact area, the attitude angle of the helicopter after landing in the water will not change.Stability control and prevention of secondary water landing due to the helicopter buoy rushing out of the wave crest have obvious effects.
A simulation was carried out for a helicopter landing in the water with/without lift and ellipsoidal buoy.The Z1 direction acceleration curve of the helicopter with/without lift and ellipsoidal buoy landing in the water is shown in Figure 15.The change curves of the yaw angle α, pitch angle β, and roll angle γ of the ellipsoidal pontoon helicopter with/without lift are shown in Figure 16.For the yaw angle, when there is no lift and the initial yaw angle, pitch angle, and roll angle are 10°, 10°, and -5°, the yaw angle decreases slightly after contacting the water surface.During the subsequent landing process, the yaw angle decreases slightly.The navigation angle almost does not change and stabilizes at about 10°.In contrast, when the initial yaw angle, pitch angle, and roll angle are -10°, 10°, and -5°, the yaw angle first increases negatively, reaching around 35.4 seconds.After reaching the negative peak of -15°, it begins to decrease in the negative direction and decreases to -6° at about 36.6 seconds.In the subsequent process, the yaw angle has a slightly negative trend of increasing.When the roll angle is 10°, 10°, and 5°, the yaw angle gradually increases after landing on the water, and there is no recovery trend.When the lift is provided, and the initial yaw angle, pitch angle, and roll angle are 10°, 10°, and 5°, the yaw angle continues to increase slowly after landing in the water, and its trend is similar to that without lift.When the initial yaw angle, pitch angle, and roll angle are 10°, 10°, and -5°, the yaw angle shows a slowly increasing trend initially.It increases to about 15° at 37.6 seconds.After being affected by the water body, the yaw angle increases rapidly, increasing to 40° at 39.3 s; and in the operating conditions where the initial yaw angle, pitch angle, and roll angle are -10°, 10°, and -5°, the changing trend of the yaw angle is consistent with the initial yaw angle.The working conditions of pitch angle and roll angle of 10°, 10°, and 5° are almost symmetrical.It can be seen from Figure 16 that when there is a lift, the change amplitude of the yaw angle will increase, and there is no recovery trend.
Regarding the pitch angle, when the helicopter buoy hits the water, the area under the helicopter's front belly and the front of the buoy that contacts the water body is larger than the water contact area of the rear belly and the back of the buoy, so the force exerted by the water body is relatively large, so about the center of mass.The formation of a positive pitching moment causes the pitch angle to increase.When there is a lift, the impact force of the helicopter-buoyant body on the water body is smaller than that of the working condition without lift, and the pitching moment formed is also smaller, so the increase in pitch angle will also be smaller.When there is no lift and the initial attitude angles are 10°, 10°, 5° and -10°, 10°, -5°, after crossing the wave crest, the helicopter buoy slides along the wave surface, IOP Publishing doi:10.1088/1742-6596/2764/1/01203910 and the belly and the rear of the buoy are in contact with the water surface.The contact area is large, resulting in a negative pitching moment about the center of mass of the aircraft, which reduces the helicopter's elevation angle.When the belly of the aircraft and the front of the pontoon touch the water surface, the decreasing trend of the elevation angle slows down until it disappears.When the helicopter advances to the trough of the second wave, the advancement of the wave will have a lifting effect on the nose of the aircraft, causing the elevation angle to increase again.When carrying lift, the helicopter buoy glides in the air after crossing the crest, and the pitch angle decreases and then increases in the negative direction until it touches the water again.Due to the force of the water body on the helicopter buoy, a positive pitching moment is formed about the center of mass, and the pitch angle begins to decrease in a negative direction.When the initial attitude angle is 10°, 10°, -5°, and with lift, the pitch angle changes the most.The positive peak value of the pitch angle is 18° at around 35.4 s, and the negative peak is 18° around 37.2 s.

Comparison of numerical calculations of the water landing process of basic configuration buoy and ellipsoid configuration
The landing process of the basic configuration float and ellipsoid configuration was simulated, and the landing process of the two types of float helicopters without lift was compared.Its acceleration change curve in the Z 1 direction is shown in Figure 17. in water without lift.When the helicopter buoy was in the initial stage of landing on the water, the belly and the buoy hit the wave surface, which caused the helicopter's center of mass in the z-direction to experience a sharp increase in acceleration to a peak within 20 ms and then a sharp decrease.Comparing the overload changes of the basic configuration float and the ellipsoid float before and after touching the water, it can be found that the overload curve of the ellipsoid float is narrow and sharp, indicating that the impact time is shorter and the impact energy is smaller at this time.The overload curve of the basic configuration pontoon changes in a triangle, indicating that the impact time is longer and the impact energy is larger.Afterward, helicopters equipped with floats of different configurations showed different movement trends.Case 1 is used as an example for analysis.When equipped with a basic configuration pontoon, after the helicopter buoy crosses the wave crest, there is no water below it, and it is only affected by gravity in the air.Therefore, the z-direction acceleration experienced by the center of mass at this time is a constant value; at 36.3 s, the helicopter hit the water surface again, and the slamming force generated by the water caused a secondary peak in the z-direction acceleration of the helicopter's center of mass, with a value of 38.5 m/s -2 .Subsequently, due to the change in the angle between the helicopter's x-axis direction and the wave water surface, the z-direction acceleration fluctuated; in the end, the z-direction acceleration remained stable.When equipped with an ellipsoidal buoy, since the IOP Publishing doi:10.1088/1742-6596/2764/1/01203911 helicopter buoy is always affected by the water after crossing the wave crest and does not fly away from the wave surface, the z-direction acceleration experienced by the center of mass is relatively stable without much fluctuation.
Case 1 non-lift basic shape/elliptical float helicopter landing in the water is shown in Figure 18 20, for the yaw angle, it can be seen that when the initial angle is 10°, 10°, and 5°, the ellipsoid buoy will cause the yaw angle to significantly increase.In contrast, for the other two dangerous postures, Angle, the two configurations of pontoons have roughly the same impact on the change of yaw angle.Regarding the pitch angle, both configurations of floats caused the helicopter to experience a process of first increasing, then decreasing and then increasing.The basic configuration of the float will cause a second large fluctuation in the helicopter's pitch angle.However, when the ellipsoid float is installed, the helicopter's pitch angle will not fluctuate significantly for the second time, and the helicopter will maintain a certain elevation attitude to complete subsequent operations.During the IOP Publishing doi:10.1088/1742-6596/2764/1/01203912 taxiing stage, a certain elevation angle is beneficial to the stability of the helicopter, so the ellipsoid type is beneficial to the pitch stability of the helicopter.The roll angle is the main basis for judging the stability of a helicopter landing in water.Regarding the roll angle, it can be seen that the roll angle of a helicopter equipped with basic configuration pontoons changes slowly and has smaller fluctuations.In contrast, the roll angle of a helicopter is equipped with ellipsoidal pontoons.The changing trend is steep, and the fluctuations are large.This shows that the heel recovery performance of the basic configuration buoy when waves hit the water is slightly better than that of the ellipsoid buoy.

Conclusion
Through simulation calculations, simulation calculations were carried out for a light helicopter traveling in the opposite direction of the wave to that of the helicopter, with or without lift, with or without pontoons, 2 pontoon states, 3 helicopter falling postures, and forced landing on water in level 5 sea conditions.The simulation results show the yaw angle α, pitch angle β, roll angle γ, and the change of the center of mass in the Z direction of the axis of the helicopter under the above conditions, which has reference significance for the design of the shape of the helicopter pontoon and the adjustment of the lift size.In the future, it is necessary to change the α of the helicopter's yaw angle, pitch β angle, roll angle γ, and center of mass in the axis Z direction under the conditions of a variety of pontoon configurations, multiple lifts, and even lift changes.

Figure 2 .
Figure 2. Schematic diagram of helicopter coordinates.The maximum take-off weight of the helicopter is 3850 kg.The moment of inertia in the X, Y, and Z directions is shown in Table1.Table1.Helicopter center of gravity moment of inertia in X, Y, and Z directions.

Figure 3 .
Figure 3. Helicopter float installation.The pontoon used has two states: state one is the basic shape, and state two is the ellipsoid shape.Both status pontoons meet the following conditions: (1) pontoon volume; (2) single volume of left/right pontoon: ≥1.9 m 3 ; (3) Float working pressure: (15±5) kPa.The diameter is not larger than 0.8 m.The appearance of the pontoon in state 1 is shown in Figure4, and the pontoon in state 2 is shown in Figure5.

Figure 4 .
Figure 4.The appearance of the float in the first state.

Figure 5 .
Figure 5.The appearance of the float in the second state.

Figure 6 .
Figure 6.Simulation model of helicopter and float.

Figure 7 .
Figure 7. Z 1 -direction acceleration time history curve of helicopter mass center with/without basic pontoons.It can be seen from Figure7that when other landing conditions are the same, the changing trend of the helicopter's z-direction acceleration is the same for the combination of the three dangerous landing attitude angles.Figure8shows the helicopter landing in the water without floats at t=0 s, t=35.0 s, and t=37.8 s.

Figure 10 .
Figure 10.Z 1 -direction acceleration time history curve of the center of mass of the basic pontoon helicopter with/without lift.

Figure 11 .
Figure 11.Changes in yaw angle α, pitch angle β, and roll angle γ of a basic pontoon helicopterwith/without lift.As for the yaw angle, when there is no lift, and the initial yaw angle, pitch angle, and roll angle are 10°, 10°, and 5°, the yaw angle hardly changes during the landing process and finally stabilizes at about 10°.When the initial yaw angle, pitch angle, and roll angle are -10°, 10°, and -5°, the yaw angle first increases in the negative direction, reaches a negative peak of -15° at about 35.4 seconds and then begins to decrease in the negative direction.It decreased to -6° at about 36.6 seconds.The yaw angle showed a slightly negative increasing trend in the subsequent process.When the initial yaw angle, pitch angle, and roll angle are 10°, 10°, and -5°, the yaw angle gradually decreases after landing on the water.It decreases to about 0° at about 36 seconds, then almost constant.When carrying lift, the initial yaw, pitch, and roll angles are 10°, 10°, and 5°.The yaw angle continues to increase slowly after landing in the water.At 37.7 seconds, the yaw angle is around 12°.After that, the yaw angle has a clear increasing trend and reaches around 40° at 39 s.The changing trend of yaw angle in the working condition with initial yaw angle, pitch angle, and roll angle of 10°, 10°, and -5° is the same as that in the working condition with initial yaw angle, pitch angle and roll angle of 10°, 10° and 5°.The situation is almost the same: When the initial yaw angle, pitch angle, and roll angle are -10°, 10°, and -5°, the changing trend of the yaw angle is the same as when the initial yaw angle, pitch angle, and roll angle are 10°, 10°.The working condition of 5° is almost symmetrical.It can be seen from Figure11that when there is a lift, the change range of the yaw angle will increase, and there will be no recovery trend.When the helicopter-buoy moves for a certain period, the final x-axis will be perpendicular to the direction of wave advancement.Regarding the pitch angle, when the lift conditions are the same, the effects of each initial attitude angle on the pitch angle change are almost equivalent.When there is no lift after landing in the water, the area under the front belly of the helicopter that is in contact with the water body is larger than the rear belly.The force exerted by the water body is relatively large, thus forming a positive pitching moment of the center of mass, causing the pitch angle to increase.It reaches about 20° at 35.4 s, and then after the pitch angle decreases to 0° in the positive direction.It begins to increase in the negative direction, reaching about -10° at 36.4 s, and then decreases in the negative direction and increases in the positive direction.When there is a lift, after landing on the water, the pitch angle first increases positively, reaching about 20° at 35.5 s.Then, after the pitch angle decreases to 0° in the positive direction, it increases negatively, reaching -18° at 37.5 s around, and then decreases in the negative direction and increases in the positive direction, reaching around 18° at 38.4 s, and then decreases.Generally speaking, the yaw angle changes sinusoidally when lift is applied.

Figure 12 .
Figure 12.Z 1 -direction acceleration time history curve of helicopter mass center with/without ellipsoidal float.It can be seen from Figure 12 that when other landing conditions are the same, the changing trend of the helicopter's z-direction acceleration is the same for the three combinations of dangerous landing attitude angles.The helicopter landing in the water with/without ellipsoidal floats in Case 3 attitude is shown in Figure13and Figure14.

9 Figure 15 .
Figure 15.Time history curve of Z 1 -direction acceleration of the center of mass of ellipsoidal pontoon helicopter with/without lift.

Figure 16 .
Figure 16.Variation curves of yaw angle α, pitch angle β, and roll angle γ of helicopter with/without lift ellipsoidal float.For the yaw angle, when there is no lift and the initial yaw angle, pitch angle, and roll angle are 10°, 10°, and -5°, the yaw angle decreases slightly after contacting the water surface.During the subsequent landing process, the yaw angle decreases slightly.The navigation angle almost does not change and stabilizes at about 10°.In contrast, when the initial yaw angle, pitch angle, and roll angle are -10°, 10°, and -5°, the yaw angle first increases negatively, reaching around 35.4 seconds.After reaching the negative peak of -15°, it begins to decrease in the negative direction and decreases to -6° at about 36.6 seconds.In the subsequent process, the yaw angle has a slightly negative trend of increasing.When the roll angle is 10°, 10°, and 5°, the yaw angle gradually increases after landing on the water, and there is no recovery trend.When the lift is provided, and the initial yaw angle, pitch angle, and roll angle are 10°, 10°, and 5°, the yaw angle continues to increase slowly after landing in the water, and its trend is similar to that without lift.When the initial yaw angle, pitch angle, and roll angle are 10°, 10°, and -5°, the yaw angle shows a slowly increasing trend initially.It increases to about 15° at 37.6 seconds.After being affected by the water body, the yaw angle increases rapidly, increasing to 40° at 39.3 s; and in the operating conditions where the initial yaw angle, pitch angle, and roll angle are -10°, 10°, and -5°, the changing trend of the yaw angle is consistent with the initial yaw angle.The working conditions of pitch angle and roll angle of 10°, 10°, and 5° are almost symmetrical.It can be seen from Figure16that when there is a lift, the change amplitude of the yaw angle will increase, and there is no recovery trend.Regarding the pitch angle, when the helicopter buoy hits the water, the area under the helicopter's front belly and the front of the buoy that contacts the water body is larger than the water contact area of the rear belly and the back of the buoy, so the force exerted by the water body is relatively large, so about the center of mass.The formation of a positive pitching moment causes the pitch angle to increase.When there is a lift, the impact force of the helicopter-buoyant body on the water body is smaller than that of the working condition without lift, and the pitching moment formed is also smaller, so the increase in pitch angle will also be smaller.When there is no lift and the initial attitude angles are 10°, 10°, 5° and -10°, 10°, -5°, after crossing the wave crest, the helicopter buoy slides along the wave surface,

Figure 17 .
Figure17.Acceleration change curves in the Z 1 direction of two types of pontoon helicopters landing in water without lift.When the helicopter buoy was in the initial stage of landing on the water, the belly and the buoy hit the wave surface, which caused the helicopter's center of mass in the z-direction to experience a sharp increase in acceleration to a peak within 20 ms and then a sharp decrease.Comparing the overload changes of the basic configuration float and the ellipsoid float before and after touching the water, it can be found that the overload curve of the ellipsoid float is narrow and sharp, indicating that the impact time is shorter and the impact energy is smaller at this time.The overload curve of the basic configuration pontoon changes in a triangle, indicating that the impact time is longer and the impact energy is larger.Afterward, helicopters equipped with floats of different configurations showed different movement trends.Case 1 is used as an example for analysis.When equipped with a basic configuration pontoon, after the helicopter buoy crosses the wave crest, there is no water below it, and it is only affected by gravity in the air.Therefore, the z-direction acceleration experienced by the center of mass at this time is a constant value; at 36.3 s, the helicopter hit the water surface again, and the slamming force generated by the water caused a secondary peak in the z-direction acceleration of the helicopter's center of mass, with a value of 38.5 m/s -2 .Subsequently, due to the change in the angle between the helicopter's x-axis direction and the wave water surface, the z-direction acceleration fluctuated; in the end, the z-direction acceleration remained stable.When equipped with an ellipsoidal buoy, since the

Figure 19 .
Figure 19.No-lift ellipsoidal float helicopter landing in water.

Figure 20 .
Figure 20.Change curves of yaw angle α, pitch angle β, and roll angle γ of basic shape/elliptical float helicopter without lift.As shown in Figure20, for the yaw angle, it can be seen that when the initial angle is 10°, 10°, and 5°, the ellipsoid buoy will cause the yaw angle to significantly increase.In contrast, for the other two dangerous postures, Angle, the two configurations of pontoons have roughly the same impact on the change of yaw angle.Regarding the pitch angle, both configurations of floats caused the helicopter to experience a process of first increasing, then decreasing and then increasing.The basic configuration of the float will cause a second large fluctuation in the helicopter's pitch angle.However, when the ellipsoid float is installed, the helicopter's pitch angle will not fluctuate significantly for the second time, and the helicopter will maintain a certain elevation attitude to complete subsequent operations.During the

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Helicopter center of gravity moment of inertia in X, Y, and Z directions.