Research Article
Design and simulation of inner and outer cylinder–type steam catapult Yan Shi, Tiancheng Shi, Weihua Ma
Advances in Mechanical Engineering 2018, Vol. 10(4) 1–7 Ó The Author(s) 2018 DOI: 10.1177/1687814018772363 journals.sagepub.com/home/ade
and Chang Gao
Abstract In order to solve the problem of sealing the cylinder of the steam catapult, a nested structure of inner and outer cylinders is developed. The openings of the inner and the outer cylinders are staggered after the installation. The materials of inner and outer cylinders are the same. The thermal deformations of the two types of cylinders are consistent at high temperature, so that the radial sealing can be guaranteed. Based on the basic working principle of this steam catapult, a dynamic mathematical simulation model is developed with some assumptions; relevant researches are carried out by simulating the dynamics and thermodynamics process of the steam launch system. The result indicates that the radius of cylinder and the initial steam pressure have significant effects on the takeoff speed and the takeoff acceleration. With a constant load, the radius of cylinder is inversely proportional to the initial steam pressure, and it is considered that the optimal choice should be 0.4 m/2 MPa. The headwind helps takeoff and reduces the dependence on the thrust force in the launch process. The simulation result could provide a reference for the design of the inner and outer nested cylinder–type steam catapult. Keywords Steam-powered catapult, inner and outer cylinders, dynamic, simulation, steam pressure
Date received: 9 September 2017; accepted: 23 February 2018 Handling Editor: Jose Antonio Tenreiro Machado
Introduction The carrier-based plane is the core part of an aircraft carrier. Since most basic combat missions are accomplished by the carrier-based plane, the takeoff and landing capability of carrier-based plane is one of the most important indicators of the combat power of the aircraft carrier battle group.1 Currently, there are mainly two takeoff ways for the carrier-based plane: the ‘‘ski jump’’ takeoff and the ‘‘catapult-assisted’’ takeoff. The ski jump takeoff depends mainly on its own power; the takeoff run of the carrier-based plane is on the aircraft carrier deck; finally, the carrier-based plane is launched across the upswept deck at the end of the deck.2,3 Thus, the carrier-based plane can attain a certain climb angle and a vertical upward velocity component at the moment of departure. However, this takeoff mode has some limitations. On the one hand, there are strict requirements of the course and the speed of
aircraft carrier. On the other hand, due to the limitation of the deck length, the load capacity and the combat radius could be greatly reduced, which leads to the decrease in the combat capacity. In Russia, the ski jump takeoff mode is widely used because of the simple structure and the low cost. The catapult-assisted takeoff mode depends on the high-power catapult to supply the sufficient takeoff speed and then launch the plane. This takeoff mode greatly reduces the requirements for the carrier-based plane itself. For example, the latest American-commissioned aircraft carrier, the USS
Traction Power State Key Laboratory, Southwest Jiaotong University, Chengdu, China Corresponding author: Weihua Ma, Traction Power State Key Laboratory, Southwest Jiaotong University, Chengdu 610031, Sichuan, China. Email:
[email protected]
Creative Commons CC BY: This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://www.creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/ open-access-at-sage).
2 George H.W. Bush, CVN-77,4 can load more than 80 carrier-based planes of various types. The aircraft carrier is equipped with four steam catapults, and the aircraft sortie rate can reach 15 s per sortie.5 Moreover, there is no limitation of the deck length, and the plane can take off with full oil, which can greatly improve the combat capacity of the aircraft carrier. The application of the steam catapult can notably shorten the takeoff distance of the carrier-based plane and ensure the high frequency of takeoff and landing. At present, it is the most widely used takeoff device. The steam catapult transforms the steam pressure into the thrust for the plane so as to launch it. It is a mechanical device which cannot generate the strong magnetic field. Therefore, there is no problem of electromagnetic interference from the Electromagnetic Aircraft Launch System, EMALS,6,7 with the carrier-based plane and the carrier-based electronic equipment. In consideration of technical confidentiality, the researches on catapultassisted takeoff are rarely published, and the published researches are quite ancient. For example, GE Clarke and AA Smith et al. determined the minimum speed of the catapult-assisted takeoff for the carrier-based plane in the 1970s. Lawrence8 conducted a preliminary research on the takeoff and landing process of carrierbased plane in the 1950s. CB Lucas9 analyzed the minimum speed of the catapult-assisted takeoff and the flying attitude change in the takeoff run process. C Jing and Zheng-Chun10 simulated and analyzed the effect law of the factors such as the aircraft carrier, the carrier-based plane, and the environment on the takeoff safety. Aiming at the difficulty of sealing the cylinder of the steam catapult, the design of the inner and outer cylinder is proposed and relevant dynamics analysis is carried out.
Advances in Mechanical Engineering
Figure 1. Cross section of launching engine cylinders (typical).
Figure 2. Cross section of the inner and outer cylinders.
Steam catapult structure The steam catapult consists of the steam system, the launch system, the return system, the lubrication system, and the accessory equipment. As shown in Figure 1, the steam system of the US C13 type catapult is composed of the piston assembly, the cylinder, the valve assembly, and the steam accumulator.11 Ao et al.12 explained the working principle of the steam catapult and analyses it based on dynamics and thermodynamics. In order to improve the sealing of the cylinder, a design of the inner and outer cylinders is proposed. To be specific, an opening outer cylinder and several opening cylinders are nested, and the openings of the inner and the outer cylinders are staggered in the initial state. As shown in Figure 2, the sealing structure is made up of the inner cylinder, the outer cylinder, and the piston. In Figure 3, there is a piston neck in the middle of the
Figure 3. Piston diagram.
piston to connect the external mechanism. The guide plate is fixed on the piston neck and composes the opening and closing mechanism with the switch lever of the inner cylinder; the opening and closing mechanism controls the opening of the inner cylinder and that of the outer cylinder to be coincident or staggered. The energy conversion mechanism is shown in Figure 4: the high-pressure steam drives the piston; the piston neck drives the external mechanism to haul the aircraft. With the movement of the piston, the inner cylinder before the piston neck is opened and meanwhile that after the piston neck is closed. At the later stage of
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Figure 4. Energy conversion mechanism assembly.
launch stroke, the water inlet is opened, and a highpressure water wall is formed at the front end of the piston. The delayed opening of the outfall has an effect of hydraulic shock absorber, so the piston finally stops as a result of the hydraulic brake.
Figure 5. Force analysis of aircraft.
Mathematical model In the launch process of carrier-based plane, the plane has to reach the required launch speed with the launch force and then takes off. The whole launch process begins with the acceleration of the carrier-based plane driven by the piston and ends up with the vanishing of the launch force of catapult. In this article, a mathematical model of the process is developed. In the launch process, the forces are complex, and the external force is not constant. The process is a variable acceleration rectilinear motion, so it is necessary to analyze the force of the catapult and the plane before developing the model. The equation of motion is given based on Newton’s second law, and thus the relation between the launch force, the speed, the acceleration, and the launch displacement can be obtained. In this article, environmental factors such as the temperature change, the undulating of wave, and the pitch of carrier are not taken into consideration.
Force analysis of aircraft and piston For the force analysis of the aircraft, the deck plane is considered parallel to sea level. On the horizontal plane and the vertical plane, the forces of the aircraft are shown in Figure 5; the forces of the piston are shown in Figure 6. During the accelerated takeoff run, the aircraft is regarded as a mass point which is in a variable acceleration rectilinear motion in the x-direction. According to Newton’s second law, equation of motion can be expressed as follows13
Figure 6. Force analysis of piston.
D=
1 2 rv SCx 2
Based on the force equilibrium in the y-direction, the resultant force is 0, so the equations are as follows L + N Tc sin u m1 g = 0 L=
1 2 rv SCy 2
ð1Þ
F f = m1 N
ð2Þ
ð4Þ ð5Þ
In the cylinder, the forces of the piston include the gravity, the cylinder wall pressure on the piston, the pressure produced by steam expansion, the tractive reaction force from the aircraft to the piston, as well as the friction force. Compared with the area of area, the area of piston neck is so small that it can be ignored. The differential equations of motion in x-direction are as follows m2
dvt = Fp Tc cos u f dt Fp = pr2 P
dvt = Ft + Tc cos u Ff D m1 dt
ð3Þ
ð6Þ ð7Þ
In y-direction, the equilibrium equations of piston are as follows
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Advances in Mechanical Engineering Np = Tc sin u m2 g
ð8Þ
f = m2 Np
ð9Þ
Thermodynamic analysis of steam launch system The whole launch process is very short, so the work of steam can be regarded as an adiabatic expansion process. When the steam expands and works in the cylinder, the pressure change can be expressed as follows14 P0 V0k = PV k
ð10Þ
V = V0 + xSp
ð11Þ
Therefore, the steam pressure can be expressed as follows k P V0 = V0 + xSp P0 ðt x=
vdt
ð12Þ
ð13Þ
0
Thermodynamic simulation of steam catapult Calculation flow In the modeling process, the force analysis of the aircraft and the piston has been completed; the thermodynamic analysis of steam in the cylinder has also been completed; the required equations for modeling have been obtained. According to equations (1)–(13), it can be seen that the model is very complex, and the analytical solution cannot be found. As a result, the time increment method is adopted for simulation. To be specific, the iterative-loop simulation is used for the steam launch process; the output parameter at the end of the last period serves is used as the input parameter for the next period; the launch force and the piston stroke can be recurrently solved. The calculation flow chart is shown in Figure 7. The main simulation parameters are listed in Table 1. On the basis of Table 1, the minimum takeoff speed of the aircraft is 80 m/s. Only when the takeoff run speed reaches or exceeds the minimum speed, could the aircraft normally take off. Because the inner cylinder can adapt itself to the thermal deformation of the outer cylinder, the cylinder radius can be a little larger. The number of outer cylinder used for calculation in this article is always one.
Effect of initial steam pressure In order to analyze the effect of the initial steam pressure on the catapult-assisted takeoff, without consideration of the steam leakage and the wind speed effect on
Figure 7. Thermodynamic simulation flow chart.
Table 1. Main simulation parameters. Parameter
Value
Mass of aircraft (kg) Mass of piston (kg) Engine thrust (N) Wing area (m2) Angle between Tc and deck (°) Air resistance coefficient Aircraft lift coefficient Deck friction coefficient Piston friction coefficient Cylinder store volume (m3)
24,000 2000 140,000 62 30 0.1 0.78 0.1 0.2 215
the launch process, the curves which describe the change of aircraft acceleration and the velocity with the launch stroke under different initial steam pressures are shown in Figures 8 and 9, respectively. The inner cylinder radius is 0.3 m, and the initial steam pressures are 3, 3.5, 4, and 4.5 MPa, respectively. Under a certain initial steam pressure, the aircraft acceleration decreases, and the velocity increases with the increase in launch stroke. The initial acceleration is
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Figure 10. Change of launch stroke. Figure 8. Speed curve.
Figure 9. Acceleration curve.
Figure 11. Change of maximum acceleration.
the largest, which means that the initial overload of the aircraft is the maximum overload. With the increase in initial steam pressure, the initial aircraft acceleration increases, so the launch stroke shortens. When the initial steam pressure is 3 MPa, the largest acceleration is 35.4 m/s2, and the required launch stroke is 98 m. When the initial steam pressure is 4.5 MPa, the largest acceleration is 50.8 m/s2, and the required launch stroke is 67 m. Therefore, after the cylinder radius is fixed, the overload is large when the launch stroke is short; the overload is small when the launch stroke is long.
launch stroke, the maximum acceleration, the cylinder radius, and the initial steam pressure is shown in Figures 10 and 11, respectively.
Effect of inner cylinder radius For the purpose of finding the effect of cylinder radius on catapult-assisted takeoff, the launch process is numerically simulated by changing the cylinder radius. When the inner cylinder radiuses are set 0.2, 0.28, and 0.4 m, respectively, the area of cylinder multiplies; the initial steam pressures are set 2, 3, 3.5, 4, 4.5, and 5 MPa, respectively. The relation between the minimum
Optimization design In order to reduce the launch stroke and the overload, the inner cylinder radius and the initial steam pressure should match well. If the launch stroke is required less than 100 m and meanwhile the maximum acceleration is required less than 45 m/s2, the optimal combinations of the inner cylinder radius and the steam initial pressure are listed in Table 2. Although the installation dimension of the large-radius cylinder is large, there are still the following advantages: the pressure in the cylinder is low, so the steam is hard to leak; the mechanical load of each part can be reduced; the steam pressure can be increased to launch heavier airplanes; there are more usable working conditions. The initial steam pressure can be changed, but the cylinder radius cannot be changed once it is determined. As a result, the cylinder
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Table 2. Optimal combination of cylinder radius and initial steam pressure. Cylinder radius (m)
Initial steam pressure (MPa)
Launch stroke (m)
0.28 0.28 0.28 0.4
3.5 4 4.5 2
95 84 76 87
Figure 13. Change of aircraft thrust.
Figure 12. Comparison of speed change.
radius of 0.4 m is proposed. Thus, when the initial steam pressure is less than 3.5 MPa, the maximum launch weight is 54,000 kg; when the speed reaches 80.08 m/s with the launch stroke of 98.90 m, the aircraft is qualified for the takeoff condition; and when the initial steam pressure is 2 MPa, the maximum launch weight is 32,000 kg, as shown in Figure 12.
Effect of headwind on launch parameters The headwind helps takeoff and reduces the dependence on the thrust force in the launch process, which has a practical significance for reducing the fuel consumption and increasing the effective takeoff load. The calculation parameters are as follows: the cylinder radius is 0.4 m; the initial steam pressure is 2 MPa; the wind speeds are 0, 5, 10, and 15 m/s, respectively. At different wind speeds, the change of thrust force and that of steam pressure is shown in Figures 13 and 14. Under a fixed initial pressure, with the increase in wind speed, the minimum required thrust force for takeoff gradually decreases. For example, when the wind speed is 0 m/s, the required aircraft thrust force is 140 kN, which is the maximum required aircraft force; when the wind speed is 15 m/s, the thrust force produced by steam is enough for takeoff; and the aircraft thrust force is not required any more. The launch force includes the steam thrust force and the aircraft thrust force.
Figure 14. Change of steam pressure.
When the wind speed increases from 0 to 15 m/s, the launch force decreases from 1145 to 1005 kN, which has a drop of 12%. In any case, the pressure of cylinder decreases on average 0.4 MPa from the beginning to the end. After the launch, about 1.6 MPa of steam is wasted.
Conclusion By developing a single-cylinder steam catapult mathematical model, the dynamics response of launch process has been analyzed, and the following results have been obtained: 1.
The increase in cylinder radius can reduce the length of track, so that the longitudinal dimension of aircraft carrier can be reduced. Moreover, the launch potential of steam catapult is improved. By changing the initial steam pressure, the launch weight can be changed.
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3.
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Consequently, this method is applicable to various aircrafts. Under the normal conditions, the initial steam pressure is low, so the system load is reduced. Under unusual conditions, in order to save the aircraft fuel and increase the cruising radius, the engine is not necessary to boost the aircraft, and the initial steam pressure can be increased to reach the takeoff speed. Increasing the initial steam pressure can increase the aircraft takeoff speed, but it would increase the overload at the same time. During use period, the restrictive relation between the takeoff speed and the overload should be taken into consideration, so that the initial steam pressure can be determined. The headwind helps takeoff. The larger the wind speed is, the smaller aircraft the thrust force is required.
Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
8. Lawrence T. Milestones and developments in US naval carrier aviation. In: AIAA atmospheric flight mechanics conference, Austin, TX, 2003. 9. Zhen Z, Jiang J, Wang X, et al. Modeling, control design, and influence analysis of catapult-assisted takeoff process for carrier-based aircrafts. Proc Inst Mech Eng G J Aerosp Eng 2017. DOI: 0954410017715278 10. Jing C and Zheng-Chun H. Dynamic modeling, simulation and safe boundary evaluation of catapult launch for carrier-based airplane. In: Proceedings of the AIAA modeling and simulation technologies conference Kissimmee, FL, 2015. 11. Eggleston J. Aviation Boatswain’s Mate E. Naval education and training program development and technology center. United States Navy, 2001. 12. Ao L, Hui C, Guolei Z, et al. The thermodynamic simulation and analysis of the aircraft steam catapults. Ship Sci Technol 2016; 9: 136–139. 13. Gang C, He N and Fengrui S. Modeling and simulation research on naval steam-power aircraft launch system. J Wuhan Univ Technol 2010; 34: 301–305. 14. Jinhui C, Shaoli Z, Changliang W, et al. Numerical calculation and analysis of steam catapult launch for carrierbased aircraft. Aeroengine 2017; 43: 71–78.
Appendix 1 Funding
Notation
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Exploration Project of Traction Power State Key Laboratory (2016TPL-T06).
ORCID iD Weihua Ma
https://orcid.org/0000-0002-2315-8981
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Cx Cy D F Ff Fp Ft K L m1 m2 N Np P P0 r S Sp Tc v V V0
air resistance coefficient aircraft lift coefficient air resistance (N) piston friction (N) deck friction (N) steam thrust (N) engine thrust (N) adiabatic index of steam aircraft lift (N) mass of aircraft (kg) piston mass (kg) deck normal force to aircraft (N) normal force of piston (N) steam pressure (MPa) initial steam pressure (MPa) cylinder radius (m) aircraft wing area (m2) piston cross-sectional area (m2) catapult thrust (N) aircraft speed (m/s) steam volume (m3) initial steam volume (m3)
u
angle between catapult thrust and deck plane (°) deck friction coefficient friction coefficient between piston and cylinder air density (kg/m3)
m1 m2 r
