Launch Bar Dynamics Character Analysis of Carrier-Based Aircraft Catapult Launch

applied sciences

Article Launch Bar Dynamics Character Analysis of Carrier-Based Aircraft Catapult Launch

Qidan Zhu 1,*, Peng Lu 1,* , Zhibo Yang 1, Xun Ji 2 , Yu Han 1 and Lipeng Wang 1 1 College of Automation, Harbin Engineering University, Harbin 150001, China 2 School of Marine Electrical Engineering, Dalian Maritime University, Dalian 116026, China * Correspondence: [email protected] (Q.Z.); [email protected] (P.L.)

Received: 25 June 2019; Accepted: 28 July 2019; Published: 30 July 2019

Abstract: The launch bar is a unique device of carrier-based aircraft, which is connected to the nose gear and shuttle. In order to avoid the launch bar striking the flight deck after the launch bar pops out of the shuttle, it is very important to research the dynamics performance of the launch bar. This paper establishes a staged mathematical model of catapult launch including the launch bar, a steam-powered catapult, a holdback bar, and a carrier-based aircraft. This article studied the effect of the mass of the launch bar, restoring moment of the launch bar, and center of gravity position of the launch bar on the dynamics performance of the launch bar. The results showed the following: (1) we could reduce the risk collision of the launch bar and deck by reducing the mass of the launch bar, increasing the restoring moment, and shifting the center of gravity position of the launch bar; (2) under the working condition of this article, we changed the center of gravity position of the launch bar to control the sink of the launch bar end, having the most obvious effect, and we reduced the mass of the launch bar, having the least effect on controlling the sink of the launch bar end; however, reducing the mass of the launch bar could also greatly reduce the risk collision of the launch bar and deck; (3) in order to avoid the launch bar striking the flight deck, the restoring moment of the launch bar must overcome the sum of other moments. The study results can give a theoretical reference for designing and testing the launch bars of carrier-based aircraft. It can also give a theoretical reference for designing and testing the launch bar’s driving mechanisms.

Keywords: catapult launch; launch bar; holdback bar; steam catapult; carrier-based aircraft

1. Introduction The main role of the launch bar is to transmit the catapult force [1–3] to the aircraft, allowing the aircraft to accelerate while taxiing before reaching a safe catapult end airspeed within the limited length deck. At the end of the catapult [4–6], the launch bar pops out of the shuttle. The launch bar, which is in the air, needs a mechanism for controlling and overcoming other damping torque. The launch bar may strike the ﬂight deck if the restoring moment of the launch bar cannot overcome the other damping torque. Therefore, restraining the contrarotation of the launch bar is an important condition when ensuring the secure catapult launch of an aircraft. It is very important to research the characteristics of launch bar dynamics. When researching the launch bar for a catapult launch, Reference [7] indicated that the launching system should consist of launch bar installation, cockpit controls and components, and holdback and release installation. Small [8] studied full-scale tests of nose tow catapulting, and showed that nose wheel tow catapulting was better than a bridle launching system. Reference [9] established a six-degree-of-freedom dynamics model of a catapult launch for carrier-based aircraft taking into consideration aircraft oﬀ-center position, and the launch bar load was calculated. Reference [10] carried out parametric models and optimization analyses of launch bar driving mechanisms. There were

Appl. Sci. 2019, 9, 3079; doi:10.3390/app9153079 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 3079 2 of 17 some patents introduced concerning the installation of launch bars, for example, (a) an improved power-operated launching system for aircraft [11]; (b) launching and holdback gear designed around the nose landing gear of the aircraft [12]; (c) a launch bar pivotally mounted on the oleo strut torque links [13]; (d) a control mechanism for controlling a catapult bar [14]; and (e) a nose gear assembly using one nose wheel for a catapult-launched airplane [15]. However, there is no literature on the characteristics of launch bar dynamics after the launch bar automatically disengages from the shuttle at the end of the power stroke. On the basis of the security of a catapult launch for carrier-based aircraft, Reference [8] indicated that nose wheel tow would increase the safety of the flight deck. Lucas [16] researched catapult criteria for carrier-based airplanes. Many studies were carried out on the problem of the main gear’s off-center location for the catapult launch of carrier-based aircraft [7,9,17–20]. Reference [21] indicated that the catapult minimum end airspeed was the airspeed value that could be safely tested aboard an aircraft carrier. In Reference [22], a total of 39 launching tests were performed during the first test campaign; the conclusion was that the launch bar retraction system had to be improved. Further research on catapult launch mainly focused on the effect of deck motion [23–25], the control problems of the climbing stage [26–29], the effect of nose landing gear’s sudden extension [30–32], the analysis of aircraft–carrier parameter matching [33,34], and so on. However, despite all public documents in regard to catapult launch around the world, there is a lack of research on the effect of the characteristics of launch bar dynamics on the security of the catapult launch after the launch bar automatically disengages from the shuttle at the end of the power stroke. This paper made great efforts toward the goal of analyzing the characteristics of launch bar dynamics. This article built a mathematical model of catapult launch, including a launch bar dynamics model, and analyzed the effect of some factors on the characteristics of launch bar dynamics, such as the mass of the launch bar, the center of gravity position of the launch bar, and the restoring moment of the launch bar. The main contributions of this paper are as follows: (1) a complete mathematical model of catapult launch used for analyzing the characteristics of launch bar dynamics character was established; (2) the effects of some factors on the characteristics of launch bar dynamics were analyzed, providing a theoretical reference for the relevant design of launch bars. The rest of this article is organized as follows: A mathematical model of catapult launch is introduced in Section2. Influence factor analysis of launch bar dynamics is carried out in Section3. Finally, conclusions are presented in Section4.

2. Mathematical Model of Catapult Launch A steam catapult launch system for carrier-based aircraft is made up of a steam-powered catapult, a towing holdback device, and the carrier-based aircraft, and its simpliﬁed model is presented in Figure1. The distinct parameters of the catapult launch process of carrier-based aircraft can be found in Reference [35]. Appl. Sci. 2019, 9, x FOR PEER REVIEW 3 of 18

6 7 5

1 3 4

12−−−−Accumulator,,,LCPiston aunch valve 34ylinder 5 −−Shuttle,,6 Launch bar 7 −Holdback bar ,8 − Aircratf

Figure 1.FigureThe general1. The general steam-powered steam-powered catapult catapult launch launch system system for carrier-based for carrier-based aircraft. aircraft.

2.1. Modeling Assumptions In order to research the basic law of motion for a launch bar during the process of a catapult launch, this article made the following assumptions: 1. The thermodynamic process of the steam catapult is an adiabatic process; the steam in the catapult is not affected by its environment. 2. The accumulator, cylinder, and piston are rigid bodies, neglecting any changes in shape caused by temperature and pressure. 3. The thermodynamic processes of the accumulator and cylinder are quasi-static processes. 4. The steam has no friction with the pipe wall during the progress from accumulator to cylinder. 5. The fuselage of the carrier-based aircraft is a rigid body. 6. The deck motion and airflow interference are neglected. 7. The carrier-based aircraft has no yaw angle during the process of catapult launch. 8. The effects of asymmetric factors are not considered during the process of catapult launch. 9. The nose gear is vertical with the flight deck surface of the carrier during the process of catapult launch. 10. The elevator angle is fixed during the whole process of catapult launch. 11. The force and damper model of the nose gear adopts the classical two-mass spring–damper model which divides the aircraft into two parts: the elastic support mass [36] and the inelastic support mass.

2.2. Mathematical Model of the Launch Bar

2.2.1. The Mathematical Model of the Launch Bar before the Launch Bar Automatically Disengages The launch bar is connected with the nose gear and shuttle before the launch bar automatically disengages, as presented in Figure 2.

Appl. Sci. 2019, 9, 3079 3 of 17

2.1. Modeling Assumptions In order to research the basic law of motion for a launch bar during the process of a catapult launch, this article made the following assumptions:

1. The thermodynamic process of the steam catapult is an adiabatic process; the steam in the catapult is not affected by its environment. 2. The accumulator, cylinder, and piston are rigid bodies, neglecting any changes in shape caused by temperature and pressure. 3. The thermodynamic processes of the accumulator and cylinder are quasi-static processes. 4. The steam has no friction with the pipe wall during the progress from accumulator to cylinder. 5. The fuselage of the carrier-based aircraft is a rigid body. 6. The deck motion and airflow interference are neglected. 7. The carrier-based aircraft has no yaw angle during the process of catapult launch. 8. The effects of asymmetric factors are not considered during the process of catapult launch. 9. The nose gear is vertical with the flight deck surface of the carrier during the process of catapult launch. 10. The elevator angle is fixed during the whole process of catapult launch. 11. The force and damper model of the nose gear adopts the classical two-mass spring–damper model which divides the aircraft into two parts: the elastic support mass [36] and the inelastic support mass.

2.2. Mathematical Model of the Launch Bar

O xo yo zo

On O1

S xs

ys zs

Figure 2. The engagement system of the launch bar, nose gear, and shuttle. Figure 2. The engagement system of the launch bar, nose gear, and shuttle.

In Figure2, Sxs yszs is the carrier-body coordinate system which is ﬁxed with the carrier. The origin In Figure 2, Sx y z is the carrier-body coordinate system which is fixed with the carrier. The S is placed at the centers ss of gravity of the carrier. Axis xs is parallel with the deck surface of the carrier andorigin points S is to placed the prow. at the Axis centerzs is of in thegravity carrier of the symmetry carrier. planeAxis andxs pointsis parallel to the with bottom, the deck and surface axis ys is perpendicular to the carrier symmetry plane and points to the starboard. The point O is the pivot of the carrier and points to the prow. Axis zs is in the carrier symmetry plane and points to the

bottom, and axis ys is perpendicular to the carrier symmetry plane and points to the starboard.

The point O is the pivot point of the launch bar. Oxooo y z is the pivot point coordinate system

which is fixed with the nose gear. Axis xo is perpendicular to the nose gear and points to the front.

Axis zo is parallel with the nose gear and points downward, and axis yo follows the right-hand

rule. Point On is the center of gravity of the tire of the nose gear. Point Dn is the contact point of the deck and the tire of the nose gear. According to the geometrical relationship between the launch bar and nose gear, we can get the equation of the center of gravity (cg) position of the launch bar as follows: =+ θ xxKLcg O launch launchcos c  =+ θ , (1) zzKLcg O launch launchsin c () where xOO, z is the coordinate of the pivot point, Klaunch is a proportionality factor which is defined as the distance from the cg position of the launch bar to the pivot point divided by the θ length of the launch bar, Llaunch is the length of the launch bar, and c is the angle between the launch bar axis and the deck. According to the geometrical relationship between the launch bar and nose gear, we can get the equation of the end of the launch bar as follows: =+ θ xxLend O launchcos c  =+ θ . (2) zzLend O launchsin c

The steam catapult transmits the load to the nose gear via the launch bar; thus, the axial load of

the launch bar can be divided into two parts: the catapult force Flaunch1 which is parallel with the

deck, and the force Flaunch1 which is vertical with respect to the deck; they are given by

Appl. Sci. 2019, 9, 3079 4 of 17

point of the launch bar. Oxo yozo is the pivot point coordinate system which is ﬁxed with the nose gear. Axis xo is perpendicular to the nose gear and points to the front. Axis zo is parallel with the nose gear and points downward, and axis yo follows the right-hand rule. Point On is the center of gravity of the tire of the nose gear. Point Dn is the contact point of the deck and the tire of the nose gear. According to the geometrical relationship between the launch bar and nose gear, we can get the equation of the center of gravity (cg) position of the launch bar as follows: ( x = x + K L cos θ cg O launch launch c , (1) zcg = zO + KlaunchLlaunch sin θc where (xO, zO) is the coordinate of the pivot point, Klaunch is a proportionality factor which is deﬁned as the distance from the cg position of the launch bar to the pivot point divided by the length of the launch bar, Llaunch is the length of the launch bar, and θc is the angle between the launch bar axis and the deck. According to the geometrical relationship between the launch bar and nose gear, we can get the equation of the end of the launch bar as follows: ( x = x + L cos θ end O launch c . (2) zend = zO + Llaunch sin θc

The steam catapult transmits the load to the nose gear via the launch bar; thus, the axial load of theAppl. launch Sci. 2019 bar, 9, x can FOR be PEER divided REVIEW into two parts: the catapult force Flaunch1 which is parallel with the5 deck, of 18 and the force Flaunch1 which is vertical with respect to the deck; they are given by ( = θ F FFlaunch=1 F launchcos c launch1 launch cos θc  = θ , , (3)(3) FlaunchFFlaunch2 =21Flaunch launch1 tantan θ cc wherewhere FFlaunchlaunch is is the the axial axial load load of of the the launch launch bar. bar.

2.2.2. The Mathematical Model of the Launch Bar after the Launch Bar AutomaticallyAutomatically DisengagesDisengages At the end of the catapult,catapult, thethe launchlaunch barbar popspops outout ofof thethe shuttle,shuttle, asas presentedpresented inin FigureFigure3 3..

O xo yo zo

On O1

S xs

ys zs

Figure 3. The system of the launch ba bar,r, nose gear, andand shuttle.shuttle.

The equation of the cg position of the launch bar is as follows: =+ θ xxKLcg O launch launchsin r  =+ θ , (4) zzKLcg O launch launchcos r θ where r is the angle between the launch bar and nose gear. Because the pivot point coordinate system is parallel to the carrier-body coordinate system, the equation of the momentum theorem for the launch bar is given by −−−=θ MrgatMMMJ r, (5)

where M r is the restoring moment of the launch bar, M g is the moment of gravity of the launch

bar, M a is the moment of the force of inertia due to the longitudinal acceleration of the pivot point,

Mt is the moment of the force of inertia due to the nose landing gear’s sudden extension, J is the θ moment of inertia of the launch bar, and r is the angular acceleration of the launch bar. The equation of the angle between the launch bar and nose gear is as follows: θθ=+Δ θ rr0 r, (6) θ Δθ where r0 is the initial angle between the launch bar and nose gear, and r is the change value of the angle between the launch bar and nose gear. The equation of the restoring moment of the launch bar is as follows: = Mrrk , (7)

where kr is the restoring moment of the launch bar, which is a constant in this article.

Appl. Sci. 2019, 9, 3079 5 of 17

The equation of the cg position of the launch bar is as follows: ( x = x + K L sin θ cg O launch launch r , (4) zcg = zO + KlaunchLlaunch cos θr where θr is the angle between the launch bar and nose gear. Because the pivot point coordinate system is parallel to the carrier-body coordinate system, the equation of the momentum theorem for the launch bar is given by

.. Mr Mg Ma Mt = Jθr, (5) − − − where Mr is the restoring moment of the launch bar, Mg is the moment of gravity of the launch bar, Ma is the moment of the force of inertia due to the longitudinal acceleration of the pivot point, Mt is the moment of the force of inertia due to the nose landing gear’s sudden extension, J is the moment of .. inertia of the launch bar, and θr is the angular acceleration of the launch bar. The equation of the angle between the launch bar and nose gear is as follows:

θr = θr0 + ∆θr, (6) where θr0 is the initial angle between the launch bar and nose gear, and ∆θr is the change value of the angle between the launch bar and nose gear. The equation of the restoring moment of the launch bar is as follows:

Mr = kr, (7) where kr is the restoring moment of the launch bar, which is a constant in this article. The equation of the moment of gravity of the launch bar is as follows:

Mg = mlaunch gKlaunchLlaunch sin θr, (8) where mlaunch is the mass of the launch bar, and g is the acceleration due to gravity. The equation of the moment of the force of inertia due to the longitudinal acceleration of the pivot point is as follows: Ma = mlaunchaKlaunchLlaunch cos θr, (9) where a is longitudinal acceleration of the aircraft. The equation of the moment of the force of inertia due to the nose landing gear’s sudden extension is as follows: Mt = mlauncha2KlaunchLlaunch sin θr, (10) where a2 is the vertical acceleration of the elastic support mass. The vertical acceleration of the elastic support mass can be calculated as follows:

 m g Fn f F Yn .  2 − − 3− h− u 0 =  m2 ≥ a2  m g Fn+ f +F Yn . , (11)  2 − 3 h− u < 0 m2 where m2 is the elastic support mass of the nose gear, Fn is the air spring force of the nose gear, f3 is the strut friction force of the nose gear, Fh is the hydraulic damping force of the nose gear, Yn is the . equivalent aerodynamic lift acting on the nose gear, and u is the gear stroking velocity of the nose gear. The air spring force can be calculated as follows:

" !γ # V0 Fn = Aa P0 Patm , (12) V Aa u − 0 − · Appl. Sci. 2019, 9, 3079 6 of 17

where Aa is the eﬀective area of pressure in the air chamber, P0 is the initial pressure of air in the chamber, V0 is the initial volume of air in the chamber, u is the stroke of the damper, γ is gas polytropic index which varies between 1.1 and 1.4, and Patm is the air pressure. The equation for calculating the hydraulic damping force is shown below.

 .  0 u= 0  . 2 . 2 ! =  . A3 u A3 u Fh  u ρ h hs . , (13)  . · + · u 0  |2u| C2 A2 C2 A2 , d· d ds· s where ρ is the density of the oil, Cd is the coeﬃcient of contraction of the main oil chamber, Cds is the coeﬃcient of contraction of the back oil chamber, Ah is the area of oil pressure of the main oil chamber, Ahs is the area of oil pressure of the back oil chamber, Ad is the oil hole area of the main oil chamber, and As is the oil hole area of the back oil chamber. The strut friction force of the nose gear is displayed below.

. u[KmFa + µb(Nu + Nl)] f3 = . , (14) u where Km is the friction coeﬃcient of the leather cup, µb is the bending friction coeﬃcient of the damper, Nu is the normal force of the upper supporting points when the damper bends, and Nl is the normal force of the lower supporting points when the damper bends.

2.3. Mathematical Model of Other Sub-Modules

dP0 κRgT0 Qm1 1 = 1 , (15) dt − V where κ is the ratio of specific heat, Rg is the gas constant of steam, Qm1 = dMs/dt is the mass flow rate, dMs is the outflow mass of steam from the accumulator, T10 is the temperature of the accumulator, and V is the volume of the accumulator. The launch valve is one of the central devices of the steam catapult launch system. The steam catapult launch system can get different catapult energies by adjusting the stroke of the launch valve and the effective launch valve opening area. In order to make the model of the launch valve mostly conform to real conditions, this article uses the test data describing the stroke of a launch valve and the effective launch valve opening area [38]. These test data are illustrated in Figure4. The accumulator and cylinder thermodynamic systems are connected with each other through the mass flow rate. The formula of mass flow rate is given by  s  2 κ+1   P κ κ  10 2κ 1  P1 P1   Aq   P1 > Pk  T κ 1 Rg  P0 P0   √ 10 − 1 − 1 Qm1 = , (16)  r +  P κ 1  10 2 κ 1 κ  Aq − P P  T κ+1 Rg 1 k √ 10 ≤ where Aq is the equivalent effective cross-sectional area of the launch valve and the pipe between the accumulator and cylinder, Pk is the critical pressure, and P1 is the pressure of the cylinder. Appl. Sci. 2019, 9, x FOR PEER REVIEW 7 of 18

2.3. Mathematical Model of Other Sub-Modules

2.3.1. Mathematical Model of the Steam-Powered Catapult The steam catapult is mainly made up of an accumulator, a launch valve, a cylinder, and a piston, as shown in Figure 1. Below, the thermodynamics model of the accumulator, the mathematical model of the launch valve, and the thermodynamics model of the cylinder are described. The thermodynamics models of the accumulator and cylinder were verified by comparison with experimental data [3,37]. We can get the differential equation of steam pressure inside the accumulator from Reference [37]. κ ′ dP′ RgTQ11m 1 =− , (15) dt V κ = where is the ratio of specific heat, Rg is the gas constant of steam, QdMdtms1 / is the mass ′ flow rate, dM s is the outflow mass of steam from the accumulator, T1 is the temperature of the accumulator, and V is the volume of the accumulator. The launch valve is one of the central devices of the steam catapult launch system. The steam catapult launch system can get different catapult energies by adjusting the stroke of the launch valve and the effective launch valve opening area. In order to make the model of the launch valve mostly Appl.conform Sci. 2019 to, 9real, 3079 conditions, this article uses the test data describing the stroke of a launch valve7 of and 17 the effective launch valve opening area [38]. These test data are illustrated in Figure 4.

140 launch valve stroke 0.05 120 launch valve area 0.04 100

80 ) 0.03 2

60 area(m stroke(mm) 0.02

40 0.01 20

0 0 0 1 2 3 4 5 0 20 40 60 80 100 120 140 Time(s) launch valve stroke(mm) (a) (b)

FigureFigure 4. 4.( a(a)) Launch Launch valve valve stroke; stroke; ( b(b)) launch launch valve valve area. area.

TheThe critical accumulator pressure and can cylinder be calculated thermodynamic as follows: systems are connected with each other through

the mass flow rate. The formula of mass flow rate is givenκ by κ 1 2 − P = P0 . (17)  k 1 κ+ 1 21κ +  PPP′ 21κ κκ  A 111−>PP The equivalent effective cross-sectional qk′ κ − area of the′′ launch  valve1 and the pipe between the  T1 1 RPg 11  P =   accumulator and cylinder is givenQm1 by the following equation: , (16)  κ+1  ′ κ −1 κ P1 2 1 ≤ AqkAq =r ,PP1 (18) T′ κ +1 R  1 1 + 1g + 1 S2 S2 S2 g d r where Aq is the equivalent effective cross-sectional area of the launch valve and the pipe between where Sg is the accumulator outlet area, Sd is the effective launch valve opening area, and Sr is the inlet the accumulator and cylinder, Pk is the critical pressure, and P1 is the pressure of the cylinder. area of the cylinder. The critical pressure can be calculated as follows: We can get the differential equation of steam pressure inside the cylinder from Reference [37]. κ κ − κR T Q= ′2 1 (17) dP1 gPPk10 m11κP1. dX = κ +1 , (19) dt A1(X10 + X) − X10 + X dt where A1 is the area of the piston, X is the displacement of the piston, and X10 is the initial displacement of the piston. The equation of the steam pressure of the piston is as follows:

6 FT = 2 10 (P A P A ), (20) × 1 1 − 2 2 where A2 is the area of the non-steam piston, and P2 is the gas pressure of the non-steam cylinder.

2.3.2. Mathematical Model of the Holdback Bar The holdback bar acts on three stages: tensioning, aircraft thrust with the holdback, and catapult force build-up with the holdback. The aircraft is in a static balance condition on the deck during the above three stages, because it is aﬀected by the holdback load of the holdback bar. The holdback bar has a minimum release element load. The holdback bar is broken when the axial load of the holdback bar reaches the minimum release load during the catapult force build-up with the holdback. In Reference [39], the minimum release load was calculated as follows: ! P + f + 0.2G R = 1.35 , (21) min × cos β where P is the maximum thrust of the aircraft, f is the tension load, G is the maximum design weight of the aircraft, and β is the angle between the holdback axis and the deck at release. Appl. Sci. 2019, 9, 3079 8 of 17

The longitudinal component of the axial load of the holdback bar is as follows:

R1 = R cos β. (22)

The vertical component of the axial load of the holdback bar is as follows:

R2 = R1 tan β. (23)

2.4. Staged Mathematical Model of the Catapult Launch The catapult launch process for carrier-based aircraft is mainly divided into nine stages. In this article, the mathematical model of the catapult launch process corresponds to the final eight stages. The mathematical model of the catapult launch process is composed of a static model of tensioning, a static model of full takeoff power, a mathematical model of catapult force build-up with the holdback, a model of release, a dynamics model of the power stroke, a dynamics model of the free deck run, and a dynamics model of fly-away [35]. The mathematical model of the steam catapult launch process of carrier-based aircraft was verified by comparison with experimental data, and the mathematical model of the minimum release load of the holdback bar was consistent with military specifications [37].

3. Results and Discussions The simulation conditions of the catapult launch are shown in Table1.

Table 1. Simulation conditions of the catapult launch.

Simulation Conditions Data The type of aircraft A3 Mass of the aircraft 31,752 kg Thrust angle 0◦ Wing area 72.37 m2 Mean geometric chord 3.55 m Nose tire undeflected radius 0.4 m Main tire undeflected radius 0.559 m Initial steam pressure of accumulator 1.38 MPa The type of steam-powered catapult C7 Mass of piston 3000 kg Catapult stroke 75.3 m Deck edge distance 12 m The initial angle between the launch bar axis and deck 30◦ The initial angle between the holdback axis and deck 25◦ The coefficient of friction between the tire and deck surface 0.17 The coefficient of friction between the piston and cylinder wall 0.17 Air density 1.2254 kg/m3

3.1. The Eﬀect of the Launch Bar Mass on the Launch Bar Dynamics This article selected the masses of the launch bar as 10 kg, 20 kg, 30 kg, and 40 kg when the simulation was carried out. The height of the pivot point of the launch bar, the height of the cg position of the launch bar, the height of the end of the launch bar, and the angle between the launch bar and the nose gear with the change in mass of the launch bar are shown in Figure5. Appl. Sci. 2019, 9, x FOR PEER REVIEW 9 of 18

3. Results and Discussions The simulation conditions of the catapult launch are shown in Table 1.

Table 1. Simulation conditions of the catapult launch.

Simulation Conditions Data The type of aircraft A3 Mass of the aircraft 31,752 kg Thrust angle 0° Wing area 72.37 m2 Mean geometric chord 3.55 m Nose tire undeflected radius 0.4 m Main tire undeflected radius 0.559 m Initial steam pressure of accumulator 1.38 MPa The type of steam-powered catapult C7 Mass of piston 3000 kg Catapult stroke 75.3 m Deck edge distance 12 m The initial angle between the launch bar axis and deck 30° The initial angle between the holdback axis and deck 25° The coefficient of friction between the tire and deck surface 0.17 The coefficient of friction between the piston and cylinder wall 0.17 Air density 1.2254 kg/m3

3.1. The Effect of the Launch Bar Mass on the Launch Bar Dynamics This article selected the masses of the launch bar as 10 kg, 20 kg, 30 kg, and 40 kg when the simulation was carried out. The height of the pivot point of the launch bar, the height of the cg Appl.position Sci. 2019 of, 9the, 3079 launch bar, the height of the end of the launch bar, and the angle between the launch9 of 17 bar and the nose gear with the change in mass of the launch bar are shown in Figure 5.

0.8 0.48 m =40kg m =40kg 0.78 launch launch 0.46 m =30kg m =30kg launch 0.76 launch m =20kg m =20kg launch launch 0.74 m =10kg 0.44 m =10kg launch launch 0.72 0.42 0.7

0.68 0.4

0.66 The height of the pivot point/m The height of the cg position/m 0.38 0.64

0.62 0.36 0 1 2 3 4 5 0 1 2 3 4 5 Appl. Sci. 2019, 9, x FOR PEER Time/sREVIEW Time/s 10 of 18 (a) (b)

0.18 68

m =40kg 0.16 launch 67 m =30kg launch 66 0.14 m =20kg launch m =10kg launch 65 0.12 64 0.1 63 0.08 m =40kg 62 launch m =30kg launch 0.06 61 m =20kg launch The height of the end of launch bar/m launch of end the of height The 0.04 60 m =10kg launch

0.02 The angle between launch bar and nose gear/deg 59 0 1 2 3 4 5 0 1 2 3 4 5 Time/s Time/s (c) (d)

FigureFigure 5.5. ((a)) TheThe heightheight betweenbetween thethe pivotpivot pointpoint ofof thethe launchlaunch barbar andand thethe deckdeck ofof thethe carrier;carrier; ((bb)) thethe heightheight betweenbetween thethe centercenter of of gravity gravity (cg) (cg) position position of of the the launch launch bar bar and and the the deck deck ofthe of carrier;the carrier; (c) the (c) heightthe height between between the end the ofend the of launch the laun barch and bar the and deck the of deck the carrier;of the carrier; (d) the ( angled) the between angle between the launch the barlaunch and bar the and nose the gear. nose gear.

AfterAfter thethe launchlaunch bar bar automatically automatically disengaged disengaged from from the the shuttle shuttle at theat the end end of theof the power power stroke, stroke, the followingthe following values values are recordedare recorded in Table in Table2 for the2 for di thefferent different masses masses of the of launch the launch bar: (1) bar: the (1) peak the value peak andvalue the and final the value final of value the height of the between height between the pivot the point pivot and point the deck and of the the deck carrier; of the (2) thecarrier; peak (2) value the andpeak the value final and value the offinal the value height of between the height the between cg position the ofcg theposition launch of barthe andlaunch the bar deck and of the deck carrier; of (3)the the carrier; peak (3) value the andpeak the value final and value the offinal the value height of between the height the between end of the the launch end of bar the andlaunch the bar deck and of thethe carrier;deck of (4)the the carrier; final (4) value the of final the value angle of between the angle the between launch bar the and launch the nosebar and gear. the nose gear.

Table 2.2. Results of keykey parametersparameters withwith didifferentﬀerent launchlaunch barbar masses.masses.

MassesMasses 10 kg 10 kg 20 20 kg kg 30 kg 30 40 kg kg 40 kg p p hO 0.7693h m0.7693 m 0.7693 0.7693 m 0.7693 m 0.7693 0.7693 m m 0.7693 m p O hcg 0.4649p m 0.4556 m 0.4464 m 0.4372 m p h 0.4649 m 0.4556 m 0.4464 m 0.4372 m h cg end 0.1607 m 0.1420 m 0.1235 m 0.1055 m f p 0.7414hend m0.1607 m 0.1420 0.7414 m 0.1235 m 0.7414 0.1055 m m 0.7414 m hO f f hcg 0.4338hO m0.7414 m 0.7414 0.4164 m 0.7414 m 0.3988 0.7414 m m 0.3817 m f h 0.1266f m 0.0917 m 0.0572 m 0.0212 m end hcg 0.4338 m 0.4164 m 0.3988 m 0.3817 m f θr 63.95f ◦ 62.31◦ 60.72◦ 59.06◦ hend 0.1266 m 0.0917 m 0.0572 m 0.0212 m θ f r 63.95° 62.31° 60.72° 59.06°

p In Table 2, hO is the peak value of the height between the pivot point and the deck of the f p carrier, hO is the final value of the height between the pivot point and the deck of the carrier, hcg is the peak value of the height between the center of gravity (cg) position of the launch bar and the f deck of the carrier, hcg is the final value of the height between the cg position of the launch bar and p the deck of the carrier, hend is the peak value of the height between the end of the launch bar and the f deck of the carrier, hend is the final value of the height between the end of the launch bar and the θ f deck of the carrier, and r is the final value of the angle between the launch bar and the nose gear. The change of the launch bar mass had no effect on the height from the pivot point to the deck, as shown in Figure 5a. This phenomenon occurred because the pivot point and the nose gear were hinged, and the height from the pivot point to the deck changed along with the change in elastic support mass. Due to the mass of the launch bar being smaller than the elastic support mass, it had little effect on the dynamics of the elastic support mass. Therefore, the changeable position of the pivot point was affected by the condition of the launching system, which was at the end of the

Appl. Sci. 2019, 9, 3079 10 of 17

p In Table2, hO is the peak value of the height between the pivot point and the deck of the carrier, f p hO is the final value of the height between the pivot point and the deck of the carrier, hcg is the peak value of the height between the center of gravity (cg) position of the launch bar and the deck of the f carrier, hcg is the final value of the height between the cg position of the launch bar and the deck of p the carrier, hend is the peak value of the height between the end of the launch bar and the deck of the f carrier, hend is the final value of the height between the end of the launch bar and the deck of the carrier, f and θr is the final value of the angle between the launch bar and the nose gear. The change of the launch bar mass had no effect on the height from the pivot point to the deck, as shown in Figure5a. This phenomenon occurred because the pivot point and the nose gear were hinged, and the height from the pivot point to the deck changed along with the change in elastic support mass. Due to the mass of the launch bar being smaller than the elastic support mass, it had little effect on the dynamics of the elastic support mass. Therefore, the changeable position of the pivot point was affected by the condition of the launching system, which was at the end of the catapult, and by the performance of the nose gear after the launch bar automatically disengaged from the shuttle at the end of the power stroke. With the increase in launch bar mass, some values were reduced after the launch bar automatically disengaged from the shuttle at the end of the power stroke, as shown in Table2 and Figure5: (a) the peak value and the final value of the height between the cg position of the launch bar and the deck of the carrier; (b) the peak value and the final value of the height between the end of the launch bar and the deck of the carrier; (c) the final value of the angle between the launch bar and the nose gear. This phenomenon occurred because as the launch bar mass increased, so did the moment of gravity of the launch bar and the moment of the force of inertia due to the longitudinal acceleration of the pivot point. These two moments could affect the equation of the momentum theorem for the launch bar. Finally, the increase of the launch bar mass caused the decrease of the above values. There was an assumption that the initial height from the end of launch bar to the deck was 5 cm. When the mass of the launch bar was 40 kg, the final value of the height between the end of the launch bar and the deck of the carrier decreased by 7.88 cm, whereby the launch bar would strike the deck surface of the carrier. Therefore, the risk of the launch bar striking the deck surface can be decreased by reducing the mass of the launch bar.

3.2. The Eﬀect of the Restoring Moment of the Launch Bar on the Launch Bar Dynamics This article selected the restoring moments of the launch bar as 50 N m, 150 N m, 250 N m, and · · · 350 N m when the simulation was carried out. The height of the pivot point of the launch bar, the · height of the cg position of the launch bar, the height of the end of the launch bar, and the angle between the launch bar and the nose gear with the change in restoring moment of the launch bar are shown in Figure6. After the launch bar automatically disengaged from the shuttle at the end of the power stroke, the key parameters are recorded in Table3 for di ﬀerent restoring moments of the launch bar.

Table 3. Results of key parameters with diﬀerent restoring moments of the launch bar.

Restoring Moments 50 N m 150 N m 250 N m 350 N m · · · · p hO 0.7693 m 0.7693 m 0.7693 m 0.7693 m p hcg 0.4372 m 0.4491 m 0.4618 m 0.4752 m p h end 0.1055 m 0.1289 m 0.1551 m 0.1836 m f 0.7414 m 0.7414 m 0.7414 m 0.7414 m hO f hcg 0.3814 m 0.4035 m 0.4261 m 0.4492 m f h 0.0212 m 0.0655 m 0.1108 m 0.1570 m end f θr 59.04◦ 61.13◦ 62.23◦ 65.33◦ Appl. Sci. 2019, 9, x FOR PEER REVIEW 11 of 18

catapult, and by the performance of the nose gear after the launch bar automatically disengaged from the shuttle at the end of the power stroke. With the increase in launch bar mass, some values were reduced after the launch bar automatically disengaged from the shuttle at the end of the power stroke, as shown in Table 2 and Figure 5: (a) the peak value and the final value of the height between the cg position of the launch bar and the deck of the carrier; (b) the peak value and the final value of the height between the end of the launch bar and the deck of the carrier; (c) the final value of the angle between the launch bar and the nose gear. This phenomenon occurred because as the launch bar mass increased, so did the moment of gravity of the launch bar and the moment of the force of inertia due to the longitudinal acceleration of the pivot point. These two moments could affect the equation of the momentum theorem for the launch bar. Finally, the increase of the launch bar mass caused the decrease of the above values. There was an assumption that the initial height from the end of launch bar to the deck was 5 cm. When the mass of the launch bar was 40 kg, the final value of the height between the end of the launch bar and the deck of the carrier decreased by 7.88 cm, whereby the launch bar would strike the deck surface of the carrier. Therefore, the risk of the launch bar striking the deck surface can be decreased by reducing the mass of the launch bar.

3.2. The Effect of the Restoring Moment of the Launch Bar on the Launch Bar Dynamics This article selected the restoring moments of the launch bar as 50 N·m, 150 N·m, 250 N·m, and 350 N·m when the simulation was carried out. The height of the pivot point of the launch bar, the height of the cg position of the launch bar, the height of the end of the launch bar, and the angle Appl.between Sci. 2019 the, 9, launch 3079 bar and the nose gear with the change in restoring moment of the launch11 bar of 17are shown in Figure 6.

0.8 0.48 M =50N·m r M =50N·m 0.78 r M =150N·m r 0.46 M =150N·m 0.76 r M =250N·m M =250N·m r r 0.74 M =350N·m 0.44 M =350N·m r r 0.72 0.42 0.7

0.68 0.4

0.66 The height of the pivot point/m The height of the cg position/m 0.38 0.64

0.62 0.36 0 1 2 3 4 5 0 1 2 3 4 5 Time/s Time/s (a) (b)

0.2 68

M =50N·m 0.18 r 67 M =150N·m r 0.16 66 M =250N·m r 0.14 M =350N·m 65 r

0.12 64

0.1 63

M =50N·m 0.08 62 r M =150N·m 0.06 61 r M =250N·m

The height of the end of launch bar/m r 0.04 60 M =350N·m r The angle between launch bar and nose gear/deg 0.02 59 0 1 2 3 4 5 0 1 2 3 4 5 Time/s Time/s (c) (d)

Figure 6. (a) The height between the pivot point of the launch bar and the deck of the carrier; (b) the height between the cg position of the launch bar and the deck of the carrier; (c) the height between the end of the launch bar and the deck of the carrier; (d) the angle between the launch bar and the nose gear.

The change in launch bar restoring moment had no effect on the height from the pivot point to the deck, as shown in Figure6a. This phenomenon occurred because the restoring moment of the launch bar was smaller than the load in the catapult launch system. Therefore, the change in launch bar restoring moment had little effect on the dynamics of the elastic support mass. Upon increasing the restoring moment of the launch bar, the following values increased after the launch bar automatically disengaged from the shuttle at the end of the power stroke: (a) the peak value and the final value of the height between the cg position of the launch bar and the deck of the carrier; (b) the peak value and the final value of the height between the end of the launch bar and the deck of the carrier; (c) the final value of the angle between the launch bar and the nose gear. This phenomenon occurred because the launch bar restoring moment could affect the equation of the momentum theorem for the launch bar, whereby a larger launch bar restoring moment resulted in a larger angular acceleration of the launch bar. The risk of collision between the launch bar and the deck can be reduced by increasing the restoring moment. There was an assumption that the initial height from the end of the launch bar to the deck was 5 cm. When the restoring moment of the launch bar was 50 N m, the final value of the height between · the end of the launch bar and the deck of the carrier decreased by 7.88 cm, whereby the launch bar would strike the deck surface of the carrier. Therefore, the risk of the launch bar striking the deck surface can be decreased by increasing the restoring moment of the launch bar. Appl. Sci. 2019, 9, 3079 12 of 17

3.3. The Eﬀect of the Launch Bar CG Position on the Launch Bar Dynamics

This article selected the proportionality factor (Klaunch) of the launch bar as 20%, 40%, 60%, and 80% when the simulation was carried out. The height of the pivot point of the launch bar, the height of the cg position of the launch bar, the height of the end of the launch bar, and the angle between the launch bar and the nose gear with the change in proportionality factor of the launch bar are shown in FigureAppl. Sci.7. 2019, 9, x FOR PEER REVIEW 13 of 18

0.8 0.8 K =20% K =20% launch launch 0.78 K =40% K =40% 0.7 launch launch K =60% 0.76 K =60% launch launch 0.6 K =80% K =80% launch 0.74 launch

0.72 0.5

0.7 0.4

0.68 0.3 The height of cg position/m

The height of the pivot point/m pivot the of height The 0.66 0.2 0.64

0.62 0.1 0 1 2 3 4 5 0 1 2 3 4 5 Time/s Time/s (a) (b)

0.22 68 K =20% 0.2 launch 67 K =40% launch 0.18 66 K =60% launch 0.16 K =80% 65 launch 0.14 64 0.12 63 0.1 62 K =20% 0.08 launch K =40% 61 launch 0.06 K =60% launch The height of the end of launch bar/m 60 0.04 K =80% launch The angle between launch bar and nose gear/deg 0.02 59 0 1 2 3 4 5 0 1 2 3 4 5 Time/s Time/s (c) (d)

FigureFigure 7. 7.(a ()a The) The height height between between the the pivot pivot point point of of the the launch launch bar bar and and the the deck deck of of the the carrier; carrier; (b ()b the) the heightheight between between the the cg cg position position of theof the launch launch bar bar and and the deckthe deck of the of carrier; the carrier; (c) the (c height) the height between between the endthe of end the launchof the launch bar and bar the and deck the of thedeck carrier; of the (d carrier;) the angle (d) betweenthe angle the between launch the bar andlaunch the bar nose and gear. the nose gear. After the launch bar automatically disengaged from the shuttle at the end of the power stroke, the key parametersAfter the arelaunch recorded bar automatically in Table4 for disengaged di ﬀerent proportionality from the shuttle factors at the (K launchend of) of the the power launch stroke, bar. the key parameters are recorded in Table 4 for different proportionality factors ( Klaunch ) of the launch bar. Table 4. Results of key parameter with diﬀerent proportionality factors of launch bar. Proportionality Factors 20% 40% 60% 80% Tablep 4. Results of key parameter with different proportionality factors of launch bar. hO 0.7693 m 0.7693 m 0.7693 m 0.7693 m p hcgProportionality Factors0.6555 m20% 0.529440% m 60% 0.3912 m80% 0.2408 m p h p 0.2035 m 0.1711 m 0.1393 m 0.1085 m end hO 0.7693 m 0.7693 m 0.7693 m 0.7693 m f h p 0.7414 m 0.7414 m 0.7414 m 0.7414 m O hcg 0.6555 m 0.5294 m 0.3912 m 0.2408 m f 0.6327 m 0.5006 m 0.3460 m 0.1697 m hcg p f h 0.2035 m 0.1711 m 0.1393 m 0.1085 m h end 0.1978 m 0.1395 m 0.0824 m 0.0267 m end f h f 0.7414 m 0.7414 m 0.7414 m 0.7414 m θr O 67.15◦ 64.54◦ 61.92◦ 59.30◦ f hcg 0.6327 m 0.5006 m 0.3460 m 0.1697 m f hend 0.1978 m 0.1395 m 0.0824 m 0.0267 m θ f r 67.15° 64.54° 61.92° 59.30°

The change in proportionality factor of the launch bar had no effect on the height from the pivot point to the deck, as shown in Figure 7a. Due to the mass of launch bar being smaller than the elastic support mass, the change in proportionality factor of the launch bar had little effect on the dynamics of the elastic support mass. Therefore, the change in proportionality factor of the launch bar had no effect on the height from the pivot point to the deck.

Appl. Sci. 2019, 9, 3079 13 of 17

The change in proportionality factor of the launch bar had no effect on the height from the pivot point to the deck, as shown in Figure7a. Due to the mass of launch bar being smaller than the elastic support mass, the change in proportionality factor of the launch bar had little effect on the dynamics of the elastic support mass. Therefore, the change in proportionality factor of the launch bar had no effect on the height from the pivot point to the deck. With the decrease in proportionality factor of the launch bar, the following values were reduced after the launch bar automatically disengaged from the shuttle at the end of the power stroke: (1) the peak value and the final value of the height between the cg position of the launch bar and the deck of the carrier; (2) the peak value and the final value of the height between the end of the launch bar and the deck of the carrier; (3) the final value of the angle between the launch bar and the nose gear. The proportionality factor of the launch bar could affect the equation of the momentum theorem for the launch bar by affecting the moment of gravity of the launch bar, the moment of the force of inertia due to longitudinal acceleration of the pivot point, and the moment of the force of inertia due to the nose landing gear’s sudden extension. With the decrease in proportionality factor of the launch bar, the three above moments were reduced. Therefore, the risk of the launch bar striking the deck surface can be decreased by reducing the proportionality factor of the launch bar. There was an assumption that the initial height from the end of the launch bar to the deck was 5 cm. When the proportionality factor of the launch bar was 80%, the final value of the height between the end of the launch bar and the deck of carrier decreased by 7.33 cm, whereby the launch bar would strike the deck surface of the carrier. Therefore, the risk of the launch bar striking the deck surface can be decreased by reducing the proportionality factor of the launch bar.

3.4. Contrastive Analysis of Each Inﬂuence Factor The comparative results of the ﬁnal height values between the end of the launch bar and the deck surface of the carrier are recorded in Table5.

Table 5. Results of ﬁnal values of the launch bar end.

- Mass Increases Restoring Moment Decreases Proportionality Factor Decreases 1 0.1266 m 0.1570 m 0.1978 m 2 0.0917 m 0.1108 m 0.1395 m 3 0.0572 m 0.0655 m 0.0824 m 4 0.0212 m 0.0212 m 0.0267 m

Under the working conditions of this article, we increased the center of gravity position of the launch bar to control the sink of the launch bar end, which had the most obvious effect, and we reduced the mass of the launch bar, which had the least effect when controlling the sink of the launch bar end. Furthermore, reducing the mass of the launch bar could also greatly reduce the risk of collision between the launch bar and the deck, as shown in Table5. It is worth noting that the degree of influence of these factors on the results of the final values of the launch bar end may change if the working conditions change. Each comparative moment of the force of the launch bar is shown in Figure8 under the following conditions: mass of the launch bar = 40 kg; restoring moment of the launch bar = 350 N m; · proportionality factor of the launch bar = 40%. We assumed that the restoring moment was a constant in this article. At the moment of the launch bar automatically disengaging from the shuttle at the end of the power stroke, only the restoring moment played a positive role when the launch bar was affected by four moments of force. In the three negative moments, the longitudinal moment of the force of inertia due to the acceleration of the pivot point worked less, whereas the moment of gravity of the launch bar had a large contribution and the moment of the force of inertia due to the nose landing gear’s sudden extension had a large contribution. Appl.Appl. Sci. Sci.2019 2019, 9,, 9 3079, x FOR PEER REVIEW 1415 of of 17 18

800 M 700 r M 600 t M g 500 M a 400

300

200

100 Moment of force(N·m) of Moment

-100

-200 0 1 2 3 4 5 Time/s FigureFigure 8. 8.The The comparison comparison chart chart of of moments. moments.

TheWe moment assumed of gravitythat the of restoring the launch moment bar changed was a less constant during in the this process article. of theAt the free moment deck run. of We the canlaunch know bar that automatically the momentof disengaging gravity of the from launch the barshuttle changes at the with end the of change the power in angle stroke, between only the the launchrestoring bar moment and the noseplayed gear a positive according role to when the equation the launch of bar the was moment affected of gravity by four of moments the launch of force. bar. TheIn momentthe three of gravitynegative of moments, the launch the bar changedlongitudinal less becausemoment the of angle the betweenforce of theinertia launch due bar to and the theacceleration nose gear changedof the pivot less. point worked less, whereas the moment of gravity of the launch bar had a largeIn contribution the three negative and the moments, moment theof the longitudinal force of inertia moment due ofto thethe forcenose oflanding inertia gear’s due tosudden the accelerationextension had of thea large pivot contribution. point worked less. This phenomenon occurred because the longitudinal accelerationThe moment of the aircraft of gravity was of smaller the launch than thebar acceleration changed less due during to gravity the process and the of acceleration the free deck of therun. elasticWe can support know mass. that the moment of gravity of the launch bar changes with the change in angle betweenThe moment the launch of thebar forceand the of inertianose gear due according to the nose to the landing equation gear’s of suddenthe moment extension of gravity changed of the greatlylaunch during bar. The the processmoment of of the gravity free deck of the run. launch Furthermore, bar changed the first less half because of the moment the angle of thebetween force ofthe inertialaunch due bar to and the the nose nose landing gear gear’schanged sudden less. extension played a negative role, and the second half of it playedIn the a positive three negative role. The moments, moment of the the longitudinal force of inertia moment also changed of the force greatly of uponinertia the due sudden to the dischargeacceleration of the of holdbackthe pivot load point in Figureworked8. Weless. should This phenomenon pay attention tooccurred the nose because landing the gear’s longitudinal sudden extensionacceleration and of the the sudden aircraft discharge was smaller of the than holdback the acceleration load during due the to process gravity of and landing the acceleration gear design, of sothe as elastic to control support launching mass. safety. InThe order moment to avoid of thethe launchforce of bar inertia striking due the to deckthe nose surface, landing the restoring gear’s sudden moment extension must overcome changed thegreatly total negativeduring the moments process upon of the the free launch deck barrun. automatically Furthermore, disengaging the first half from of the the moment shuttle atof thethe endforce ofof the inertia power due stroke. to the nose landing gear’s sudden extension played a negative role, and the second half of it played a positive role. The moment of the force of inertia also changed greatly upon the 4. Conclusions sudden discharge of the holdback load in Figure 8. We should pay attention to the nose landing gear’sThere sudden is no literature extension on and the characteristics the sudden discharg of launche bar of dynamicsthe holdback after theload launch during bar automaticallythe process of disengageslanding gear from design, the shuttle so as to at control the end launching of the power safety. stroke. This paper addressed the problem of the dynamicsIn order of the to launch avoid the bar launch after the bar launch striking bar the pops deck out surface, of the shuttle.the restorin In thisg moment paper, severalmust overcome points werethe summarizedtotal negative as moments follows: upon the launch bar automatically disengaging from the shuttle at the end of the power stroke. 1. A complete mathematical model of catapult launch used to characterize the dynamics of the 4. Conclusionslaunch bar was established. Several experimental data from previous research were used to verify the proposed model. The mathematical model of catapult launch including the launch bar can be usedThere to predictis no literature the dynamic on behaviorthe characteristics of the launch of barlaunch in order bar todynamics avoid the after launch the bar launch striking bar automaticallythe flight deck. disengages from the shuttle at the end of the power stroke. This paper addressed the 2.problemThe changes of the dynamics in launch of bar the mass, launch launch bar after bar restoringthe launch moment, bar pops and out launchof the shuttle. bar proportionality In this paper, severalfactor points had were no eff suectmmarized on the height as follows: from the pivot point to the deck. We can reduce the risk of 1. collisionA complete between mathematical the launch model bar and of the catapult deck by laun reducingch used the to mass characterize of the launch the dynamics bar, increasing of the thelaunch restoring bar was moment, established. and shifting Several the experimental cg position of data the launch from previous bar. research were used to verify the proposed model. The mathematical model of catapult launch including the launch

Appl. Sci. 2019, 9, 3079 15 of 17

3. Under the working conditions of this article, we increased the center of gravity position of the launch bar to control the sink of the launch bar end, which had the most obvious effect, and we reduced the mass of the launch bar, which had the least effect when controlling the sink of the launch bar end. Furthermore, reducing the mass of the launch bar can also greatly reduce the risk of collision between the launch bar and the deck. In order to avoid the risk of collision between the launch bar and the deck after the launch bar automatically disengages from the shuttle at the end of the power stroke, the restoring moment of the launch bar must overcome the sum of the other moments. It is worth noting that the degree of influence of these factors on the results of the final values of the launch bar end may change if the working conditions change. 4. The moment of the force of inertia due to the nose landing gear’s sudden extension changed greatly during the process of the free deck run. Furthermore, the first half of the moment of the force of inertia due to the nose landing gear’s sudden extension played a negative role, and the second half of it played a positive role. The moment of the force of inertia also changed greatly following the sudden discharge of the holdback load. In order to improve launching safety, we should pay attention to the nose landing gear’s sudden extension and the sudden discharge of the holdback load during the process of landing gear design. 5. Selecting the optimal parameters for the launch bar is an important task, so as to control launching safety. The study results can give a theoretical reference for designing and testing the launch bars of carrier-based aircraft. It can also give a theoretical reference for designing and testing the launch bar’s driving mechanisms.

Author Contributions: Software, P.L.; writing—original draft, Q.Z. and P.L.; writing—review and editing, Q.Z., P.L., Z.Y., X.J., Y.H., and L.W. Funding: This research was funded by the International Science & Technology Cooperation Program of China (2013DFR10030). This research was funded by the National Natural Science Foundation of China (61603110, 61803116, U1530119). This research was funded by the fundamental research funds for the central universities (HEUCFM170401, 3072019CFJ0405). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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