Multi-Disciplinary System Design Optimization of a Launch Vehicle Upper-Stage

ABSTRACT:

The design method presented in this paper is related to the upper-stage system and its instrumentation, expedition and facilitation so as to transfer the satellite from the destination orbit to the target orbit. We used an integrated design method with a structure based on multidisciplinary system design optimization and developed a simple systematic interference method for designing aerospace products. The subsystems' convergence in an optimized environment, matrix relationship, and integration of the subsystems' parameters and presentation of design give results while meeting all requirements and considering the limitations of the design were the main aims of the research. Instead of a merely mathematical optimization design, in the present study a new design method with a systematic multipurpose optimization approach was designed. In this context, the optimization means the parameters are optimized as a result of the design convergence coefficients. Validation of the design method was not only obtained through comparison with a specific product but also with the systematic parameters of all upper-stage systems with a similar operation through the results of statistical design graphs. The approximate similarities of the results indicate an acceptable and genuine design with a quite systematic approach which is better than an unreal and merely optimized design.

KEYWORDS:
Upper stage; Systems design; Multidisciplinary design optimization; Systems integration

INTRODUCTION

In a article named "Technologies for future precision strike missile systems - missile design technology" (Fleeman 2001), there is a survey of missile technology concepts, influential parameters in design, and balance among subsystems, using new technologies with lower weight and cost communicating with the launcher. Overall configuration as well as missile simulation results from such a design method. The detailed explanations for the study are available in his book of Tactical Missiles Design. It needs to be mentioned that design depth is limited in the method yet the functional area is high while lack of integration and systemic communications implementation are the biggest weak points in this method which he explains and completes in his 2012 edition of the book. It is claimed in the study that all main parameters of a missile at conceptual design are taken into consideration while the missile has operational capability. Operational capability as well as systemic relation integration is the first act in the current study.

The history of transition from classic design to modern design is not accountable in this study, however, some developed countries have been able to take advantage of system design and multidisciplinary optimization methods to improve conceptual design process through considerable savings in design time and costs (Olds 1993).

Brown and Olds (2006) surveyed multi-objective optimization techniques of collaborative optimization (CO), modified collaborative optimization (MCO), bi-level integrated system synthesis (BLISS), and all at once (AAO) on a reusable satellite. The study claims that the best design method cannot be chosen since such activities are for research purposes only and require various studies on the results. Systemic design activities are briefly mentioned in this study while most of the activities are focused on comparing 3 design techniques. In the final conclusion, a comparison is made among design methods based on running time as well as quality comparisons, which could be said that BLISS designed outputs have higher quality.

Balesdent et al. (2011) surveyed various multipurpose optimization methods in space systems design quantitatively. Various MDO methods to design satellite missiles are surveyed in the study and some features, such as strength, price calculations, flexibility and convergence speed and problem implementation are taken into consideration so as to select the most suitable design method in designing launch vehicle. Mathematical equations of optimization of every method as well as main profile of the algorithm with optimization activities of every method are mentioned briefly. Selection of the optimal method to design space system based on the mission and various situations such as implementation time, cost, complexity, etc. is the final conclusion of the study (Balesdent et al. 2011).

Riddle (1998) states that using MDO in designing complex systems comes with 2 obstacles. One of them originates from disconnected and nonlinear essence of design process most of mathematical optimization methods are facing. One other unattractive point of MDO methods is design teams' unwillingness to use it and similarity of automatic decisionmaking with creative process of innovative design.

Tsuchiya and Mori (2002) claimed that in spite of the higher speed of MDO with parametric methods, and based on which studies are reported to improve system and destination optimization for reusable launch vehicles (RLV), they are still recognized unsuitable for space systems design, especially satellite-carrying missiles which are essentially more complicated in configuration steps and trajectory design.

The need to design with a systematic approach in addition to design implementation based on physics of an aerospace product attracts some researchers to optimized systematic design. Aldheeb et al. (2012) tried to create an optimized design for a Micro Air Launch Vehicle.

In the present study, optimization and trajectory design are done through a design algorithm with systematic approach to reduce payload mass. The look on functional design physics in the main algorithm of the article and model of subsystems is clear. Villanueva et al. (2013) used a systematic approach in an article to design solid fuel engine. Conceptual design in the current study is optimized through a genetic algorithm.

It could be claimed that creation of a systematic approach and transforming MDO to multi-disciplinary system design optimization (MSDO) includes development of MDO methods which develops operational capability based on MDO. MSDO approach is available in a limited number of the articles.

According to Wronski and Gray (2004), one can verify a comprehensive MSDO implementation in a specific case in the Massachusetts Institute of Technology (MIT). The specific importance of the study is that it gives a true expression of MSDO systematic design, multipurpose optimization and an obvious process of the algorithm.

Additionally, design and multipurpose optimization of an aircraft was studied through implementation and integrated design tools so as to predict and optimize the implementation and related expenditures of commercial aircrafts design and production with the aim of reducing the noise through accurate selection of configuration and mission parameters (Diedrich et al. 2006). After surveying some design samples, a brief look to upper stage activities are made.

Engine and trajectory design in Casalino and Pastrone (2010) is optimized simultaneously. Systematic design is brief in the study and it could be included among the optimization articles with systematic approach for propulsion engine.

An upper stage activity is presented with a brief look at upper stage engine of solid fuel engine (Casalino and Pastrone 2010). Adami et al. (2015) designed an upper stage performed through three forms of MDO. Mathematically, a detailed comparison among the three design methods is presented. The optimal proof of choice is surveyed mathematically.

After considering the aforementioned articles in addition to their quantitative and qualitative analyses, Table 1 presents a summary of their features.

Table 1
Distribution of mass components.

Design methods	Physics-based methods	Mathematical-based methods	Full configuration	Balanced subsystems (converge)	Requirement meeting between subsystems	Subsystems design depth	Imbedded baseline statistics data
Conceptual design classic	×	_	×	_	_	×	×
System design optimization	×	×	_	×	_	×	×
MDO	_	×	×	_	×	_	×
MSDO (this study)	×	×	×	×	×	×	×

METHODOLOGY

Designing an optimized multidisciplinary system is a modern example of aerospace product design. MSDO can be complex product design process and multidisciplinary engineering systems. In this method, the subsystems are related to each other and to a system in an optimized and converging space. Also the main feature of this method is the presence of human expert in the Designing tool environment and integration of all designing subdivisions. The aim of this approach is the creation of sophisticated and advanced engineering systems that are competitive not only in terms of performance but also in terms of value of life cycle.

The most important properties of MSDO method can be stated as follows:

• Deal with design models of realistic size and fidelity that will not lead to erroneous conclusions.

• Reduce the tedium of coupling variables and results from disciplinary models.

• Allow for creativity while leveraging rigorous, quantitative tools in the design process. Hand-shaking: qualitative versus quantitative.

• Data visualization in multiple dimensions.

• Incorporation of higher-level upstream and downstream system architecture aspects in early design: staged deployment, safety and security, environmental sustainability, platform design, etc.

In this procedure, design algorithm similar to other design algorithms is not of tree type or merely a mathematical optimization. The MSDO algorithm is designed to link all the subdivisions directly to each other and the best convergence is applied according to physics and subdivisions. In this way, the designer can easily put all the limitations and restrictions of design to work. In this paper, the concepts of design and multistep optimization are used in a strategic computing environment to design upper-stage which transfers from parking orbit to the target orbit. Presented parameters in this procedure are classified as:

• Design or independent variables: including fuel mass ratio, engine structural mass ratio to the whole engine, etc.

• Simple limitations: including mass ratios, I_sp, etc.

• Restrictions: diameter, orbital altitude, payload.

• Combined merit functions: aiming at minimizing the total mass and designing the best way of sending the satellite to the target orbit.

The most important specifications of the MSDO algorithm are as follows:

• Offering new approaches in systematic design derived from MSDO designing method.

• Using statistical processing in the design process (increasing accuracy and rapid convergence).

• Offering innovative convergence methods.

• Optimizing system and subsystems' design parameters by using communication matrixes.

• Convergence of designing upper stage with previous stages of the rocket.

• Integrating all the design parameters and meeting all the restrictions and requirements.

• Ability to enter any new special requirement in the way of designing.

Algorithm design of upper stage includes the following:

• Statistical designing and analysing statistical data.

• Designing the layout of subsystems and subdivisions.

• Dynamics and trajectory design.

• Propulsion system design and tank design.

• Feeding system design.

• Analysis of mass-dimensions and mass associated with the previous stage of launch vehicle design.

• Structural design and stiffener.

• Systematic analysis (configuration, integrating and optimization).

All the requirements and limitations of designing the upper stage is done based on the objectives, bottlenecks, and administrative constraints. These constraints are applied in all the phases with the presence of the designer in the design environment. All the requirements and restrictions can be classified as follows:

• The requirements of trajectory.

• The requirements of the launch vehicle and launch.

• The requirements of subsystems and subdivisions.

• The requirements of construction and assembly.

• The limitations in choosing the hardware.

Basic hypotheses regarding the design of upper stage are as follows:

• Payload.

• Parking orbit and target.

• Mechanical properties.

• Helium mechanical properties.

• The characteristics of the chosen fuel.

• Safety factors.

• Temperature of tanks and the flame.

The main body of the communication among subsystems, within each other, and the system is created according to the design matrix. Design matrixes are the designer's guide for displaying design communications and the effects of the parameters on each other (Peoples and Schuman 2003). The communicative matrix between the components of propulsion system is shown in Fig. 1 due to the importance of the communication of the propulsion system components. The most important design matrix is the comprehensive design matrix which is shown in Fig. 2. Only the main parameters of design are mentioned in the matrixes.

Figure 1
Propulsion system matrix.

Figure 2
Design correlations matrix.

In designing the MSDO algorithm, several optimization and convergences were used. The goal of optimization is to achieve the least amount of goal parameters; however, the goal of convergence is to converge all design parameters within each other as well as meeting all the requirements and limitations. Optimization includes:

• Optimizing comprehensive design matrix based on the MSDO and through genetic algorithm.

• Optimizing trajectory through genetic algorithm.

• Optimizing propulsion system through genetic algorithm.

• Optimizing total mass through genetic algorithm.

• Optimizing the thickness of the crust and stiffener based on the buckling test and through genetic algorithm.

In Table 2, one can see the above-mentioned optimization properties. Design convergence items in MSDO algorithm include the acceleration of design process according to the statistical equations (reducing the time while increasing accuracy).

Table 2
Optimization properties.

System optimizer	Subjected to	Generations	Population	Crossover	Mutation
MSDO optimization	Min: Mt and L/D	100	100	Scattered	Uniform (0.2)
Orbital optimization	Min: Mp	100	20	Scattered	Uniform (0.2)
Propulsion optimization	Min: Msp and Le /De	100	100	Scattered	Uniform (0.2)
Total mass optimization	Min: Mt	100	20	Scattered	Uniform (0.2)
Structure optimization	Min: Mst	100	20	Scattered	Uniform (0.2)

Primary values for design are obtained with statistical equations. Propulsion system convergence through propulsion system mass factor is defined as (Motlagh et al. 2013):

(1) $\mathit{\beta }\mathit{=}{M}_s/\left(M_s\mathit{+}{M}_p\right)$

(2) ${\mathit{\beta }}_n={\mathit{\beta }}_{n-1}<\epsilon$

The convergence of upper stage compared with the previous stage launch vehicle is:

(3) $\alpha \mathit{=}{M}_{p1}{/M}_{p2}$

(4) ${\alpha }_n-{\alpha }_{\mathrm{n-}1}<\epsilon$

In Fig. 3, it is presented the interference between convergence and optimization of the algorithm (Fig. 4). Design variables are described in Table 3.

Figure 3
Interference between convergence and optimization.

Figure 4
MSDO algorithm.

Table 3
Design variables.

System optimizer	Subjected to	Design variables	Name	Unit	Limitation	Description
MSDO Optimization	Min: Mt and L/D	Pc	Chamber pressure	bar	5 < Pc < 15	-
		OF	Oxide to fuel ratio	-	3.5 < OF < 4.5	According to fuel
		Nħ	Number of helium tanks	-	2 < Nh < 12
		N	Thrust to weight ratio	-	1.5< n <4.5	According to configuration
Orbital Optimization	Min: Msp	rpt	Transfer orbit Perigee	km	200 ...36000	According to orbit design
		rαt	Transfer orbit Apogee
Propulsion Optimization	Min: Mspand Le/De	re	Nozzle exit	m	re < D	-
		Rox	Oxidizer tank profile		Rox < D - ts
		Rf	Fuel tank profile		Rf < D - ts
Total mass Optimization	Min: Mt	-	Selection of components	-	-	According to data feasibility
Structure Optimization	Min: Mst	ts	Body thickness	m	tsm - 2 < ts < tsm	-
		J	Stiffener rigidity	m4	- -	Stiffener selection
		-	Structural Materials	-		-
Propulsion system convergence	βn - βn -1 < ε	β	Propulsion Mass factor	-	0.8 < β < 1.5	According to statistical data
Stages fuel mass ratio	αn - αn-1 < ε	α	Stages mass factor	-	0.08 < α < 0.3	According to statistical data

Design output includes the following:

• Systematic parameters of upper stage.

• Subdivisions' mass-dimension distribution.

• Systematic data of subdivisions.

However, the most important outputs of the algorithms include the following:

• Multidisciplinary optimization system.

• Adaptation of all design parameters.

• Meeting all the requirements and limitations.

DESIGN METHODOLOGY OF SUBSYSTEMS

Statistical Design

Preliminary estimation of systematic parameters in upper stage design process is of utmost importance due to the following reasons: creating a basic configuration for upper stage and faster convergence and more optimal design.

In statistical design via obtained data, the created population and needed graphs were extracted to create initial input (Mirshams and Khaladjzadeh 2010). For instance, 2 sample graphs are given in Figs. 5 and 6. The payload mass is the first and the most important input in designing an upper stage.

Figure 5
Dry mass versus payload mass.

Figure 6
Thrust/weight versus burn time.

(5) $M_k=1.58+1.2M_{\mathrm{pay}}\left(R^2=0.96\right)$

where: M_k and M_pay are the final and payload mass.

The thrust to weight relative to burn time is represented by:

(6) $\begin{array}{c}n=19.38-0.035t+2.6\times {10}^{-5}{t}^2-6.88\times {10}^{-9}{t}^3\hfill \\ \left(R^2=0.98\right)\hfill \end{array}$

Statistical equations are derived as follows: µ_p and µ_f payload mass ratio and dry mass ratio.

(7) $M_F=0.026M_{\mathrm{pay}}^2+0.799M_{\mathrm{pay}}+2.546$

(8) $M_0=-0.066M_F^2+3.439M_F+3.004$

(9) $M_P=0.91M_0{}^{0.917}$

(10) ${\mu }_p=3.267{\mathit{\mu }}_f^2-0.559{\mathit{\mu }}_F+0.273$

(11) $n=2880t^{-0.94}$

(12) $T=3.668n^2-20.21n+107.7$

(13) $\dot{m}=0.525n^2-0.937n+14.45$

(14) $T=4422\left(\dot{m}=\frac{M_P}{t}\right)-0.497$

(15) $L\mathit{=}109.5e^{\mathit{-}2.33D}$

(16) ${\mathrm{LD}}^2=0.323M_0^2-7.997M_0+116.6$

Trajectory Simulation and Design

In this study, trajectory design (Fig. 7) is done based on Hahman's approach as well as 2 references (Chobotv 1996; Curtis 2005).

Figure 7
Trajectory design algorithm.

Mass Analysis

Acc ording to statistical studies, linear relationship between the dry mass of the rocket block with the portable mass of the same rocket block represents the similarity of mass ranges of the whole subsystems and their subcategories in each block with the same objectives. Thus, determining mass ranges of the main subcategories based on the main effective parameters is viable. In Table 4, all the objects and the way to achieve them are illustrated. Final mass of the upper stage is achieved via the table and considering all the mass parameters. The final mass of upper stage can be achieved with all mass parameters presented in Table 4.

Table 4
Distribution of the mass components.

Upper Stage		Estimated mass	Computational mass	Selective mass
Structure	Satellite installation stand	×
	Body structure		×
	Tank protector	×
	Motor holder	×
	Nacelle	×
	Motor front and back flange		×
	Separation equipment	×
Feeding system	Helium		×
	Helium tank		×
	Other equipment	×
Propulsion	Fuel tank		×
	Oxidant tank		×
	Connection tunes	×
	Motor elements	×
	Combustion chamber		×
	Nozzle		×
	Other components of motor	×
Guidance and control hardware	Flight computer			×
	Guidance control block			×
	Inertia measurement block			×
	Valves	×
	Accessories	×
	Telemetric system	×
Actuators	Electromechanical actuators			×
	Cables and electrical connections	×
	Thrusters			×
	Braking motor			×
	Acceleration motor			×
Cases guidance	Central computer			×
	Sensors			×
	Gyro planes			×

Propulsion Subsystem Analysis

Different specifications of a space propulsion system with other propulsion systems of a rocket are summarized as (Friedman and Kenny 1965):

• Different outside conditions (space conditions).

• On-Off numbers (based on the trajectory design).

• Less thrust-to-weight ratio.

• The use of pressure feed system (high accuracy but low thrust) (Sutton and Biblarz 2001).

Figure 8 shows the propulsion analysis algorithm.

Figure 8
Propulsion sub-algorithm.

Propulsion System Convergence

In the first design loop, the amount of fuel mass and the final mass of upper stage in every burning is calculated through the following equations:

(17) $M_{f1}\mathit{=}{M}_0{e}^{\mathit{-}\left(\raisebox{1ex}{$\mathit{\Delta }{V}_1$}\!\left/ \!\raisebox{-1ex}{$I_{\mathrm{sp}}{g}_0$}\right.\right)}$

(18) $M_{P1}\mathit{=}{M}_0\mathit{-}{M}_{f1}$

(19) $M_{\mathrm{fi}}\mathit{=}\left(M_0\mathit{-}\sum _{k\mathit{=}1}^{i\mathit{-}1}{M}_{\mathrm{pk}}\right)e^{\left(\raisebox{1ex}{$\Delta V_i$}\!\left/ \!\raisebox{-1ex}{$I_{\mathrm{sp}}{g}_0$}\right.\right)}$

(20) $M_{\mathrm{Pi}}\mathit{=}{M}_0\mathit{-}\sum _{k\mathit{=}1}^{i\mathit{-}1}{M}_{\mathrm{pk}}\mathit{-}{M}_{\mathrm{fi}}$

(21) $M_P\mathit{=}\sum _{k\mathit{=}1}^i{M}_{\mathrm{Pi}}$

After propulsion system design convergence, the amount of optimal fuel mass in every engine-on status is achieved. In the present study, the optimal propulsion system design is achieved through converging the structural convergence factor (β). Using upper stage mass in every design loop, all subsystems' propulsion design is achieved and then the new value for fuel mass and convergence factor is obtained.

(22) $M_{pj}\mathit{=}\frac{1\mathit{-}\mathit{\beta }}{\mathit{\beta }}\left(M{}_{\mathrm{sh}j}\mathit{+}M{}_{\mathrm{se}j}\mathit{+}M{}_{\mathrm{sT}j}\right)$

where: j is the integration loop counter design; M_sh, M_se, and are dry mass of subsystems. The equation for convergence M_sT coefficient (β) is defined as follows:

(23) $\mathit{\beta }\mathit{=}\frac{M_s}{M_s\mathit{+}{M}_p}$

The internal relations of the propulsion system are shown in Fig. 1.

Feeding System Analysis

Controlling pressure in fuel tanks is easily possible using the pressure system feed. Furthermore, the simplicity of adjusting pressure in pressure system feed determines its high reliability, thus the process of switching and flow control is easily possible. Output flow could be controlled with installing a heater or pressure control valves. Generally, the concurrent process of disembarkation of capsules containing compressed gas and filling propellant tanks could be shown via Eqs. 24 and 25 (Huzel et al. 1992).

High-pressure tanks (capsules):

(24) $I\left\{\begin{array}{c}\frac{\mathrm{dp}}{\mathrm{dt}}\mathit{=}\frac{\left(k\mathit{-}1\right)Z}{V}\left(\frac{\mathrm{dQ}}{\mathrm{dt}}\mathit{-}{\dot{m}}_d{h}_d\mathit{-}\frac{\mathrm{PV}}{\left(k\mathit{-}1\right)Z^2}\frac{\mathrm{dZ}}{\mathrm{dt}}\right)\hfill \\ \frac{d\mathit{\rho }}{\mathrm{dt}}\mathit{=}\frac{{\dot{m}}_d}{V}\hfill \\ T\mathit{=}\frac{P}{R\mathit{\rho }}\hfill \end{array}\right.$

Propellant tanks:

(25) $\mathrm{II}\left\{\begin{array}{c}\frac{\mathrm{dp}}{\mathrm{dt}}\mathit{=}\frac{\left(k\mathit{-}1\right)}{V\left(t\right)}\left(\frac{\mathrm{dQ}}{\mathrm{dt}}\mathit{-}{\dot{m}}_i{h}_i\mathit{-}\frac{k}{\left(k\mathit{-}1\right)}P\frac{\mathrm{dV}\left(t\right)}{\mathrm{dt}}\right)\hfill \\ \frac{d\mathit{\rho }}{\mathrm{dt}}\mathit{=}\frac{1}{V\left(t\right)}\left({\dot{m}}_i\mathit{-}\mathit{\rho }\frac{\mathrm{dV}\left(t\right)}{\mathrm{dt}}\right)\hfill \\ T\mathit{=}\frac{P}{R\mathit{\rho }}\hfill \end{array}\right.$

where: Q is heat transfer between the gas blowing and its environment; Z is the gas compressibility factor; V is the volume control; T is the temperature; P is the pressure; ͘m_i . ͘m_d are blowing gas mass flow rate input and output volume control; h_i and h_d are blowing gas enthalpy entry and exit control volume.

The sub-algorithm of feeding system is shown in Fig. 9.

Figure 9
Blow system sub-algorithm.

Volume, thickness, and the mass of every helium tank is obtained from the following equations (Humble et al. 1995):

(26) $V_h\mathit{=}\frac{\mathit{\gamma }{P}_{\mathrm{po}}}{P_{\mathrm{boo}}\mathit{-}{P}_{\mathrm{boe}}}{V}_{\mathrm{To}}\mathit{+}\frac{\mathit{\gamma }{P}_{\mathrm{pf}}}{P_{\mathrm{bfo}}\mathit{-}{P}_{\mathrm{bfe}}}{V}_{\mathrm{Tf}}$

(27) $t_G\mathit{=}\frac{P_{\mathrm{ho}}}{2{\mathit{\sigma }}_{\mathrm{hw}}}{R}_h$

(28) $M_{\mathrm{Th}}\mathit{=}\frac{3}{2}\frac{{\rho }_{\mathrm{hw}}}{{\mathit{\sigma }}_{\mathrm{hw}}}\frac{2\mathit{\gamma }{V}_b}{1\mathit{-}\left(\frac{P_{\mathrm{Ge}}}{P_{\mathrm{Go}}}\right)}$

where: V_h, t_G and M_Th are volume, thickness, and mass of blowing tanks; σ_hw and ρ_hw are the mechanical properties.

According to blow subsystem sub-algorithm, numbers of blow tanks are selected considering configuration and layout. The final mass of feeding system is calculated by the following equation:

(29) $m_{\mathrm{hellium}}\mathit{=}{m}_h\mathit{+}{m}_{\mathrm{line}}\mathit{+}{m}_{\mathrm{he}}\mathit{+}{m}_{\mathrm{valve}}\mathit{+}{m}_{\mathrm{heater}}$

Tanks Analysis

The shape of the tank is a function of weight, leakage rate, tank volume, and locating restrictions. Spherical tanks have the best empty weight-to-loaded weight ratio (Hutchinson and Olds 2004). Tank design sub-algorithm is shown in Fig. 10. Other elements such as control valves are selected according to input pressure and flow rate.

Figure 10
Tank design sub-algorithm.

Structure Analysis

In structural analysis, providing stability and structural strength to deal with all external pressures is the main goal. In order to determine the mass of the structure, at first, the loads on each section of the structure shall be determined via different stages of preparation to the end of the flight. Loads on each section mean axial force, shear force and bending torque which is applied under external loads during structure mission. Critical load for each section is occurred based on existing experiences in any of the selected above stages. Loading sub-algorithm and the thickness of the body structure is shown in Fig. 11.

Figure 11
Body structure sub-algorithm.

After calculating longitudinal and lateral load flow, equivalent stresses are obtained and exerted to the structure which determines the thickness of the body (Ardema et al. 1996; Crawford and Burns 1963).

(30) $N_x\mathit{=}{N}_{\mathrm{xbend}}\mathit{+}{N}_{\mathrm{xaxial}}\mathit{+}{N}_{\mathrm{xullage}}\mathit{+}{N}_{\mathrm{xhead}}$

(31) ${\mathit{\sigma }}_n\mathit{=}\frac{1}{\mathit{\pi }\mathrm{Dt}}\left(N\mathit{+}\frac{4M}{D}\right)$

(32) $N_{\mathrm{equ}}\left(x\right)\mathit{=}N\left(x\right)\mathit{+}\frac{4M\left(x\right)}{D\left(x\right)}$

(33) $t\mathit{=}\frac{N_{\mathrm{equ}}}{\mathit{\pi }D{\sigma }_n}$

where: N is the axial force; M is the bending moment.

According to the critical situation exerted on the upper stage structure, lateral stiffeners with low number could be used to strengthen body structure. Design algorithm for strengthening stiffeners is shown in Fig. 12.

Figure 12
Stiffener structure sub-algorithm.

Stiffener rigidity and then the shape of the stiffener profile can be selected through the following equation:

(34) $J\mathit{=}\frac{{\left(N\mathit{+}1\right)}^{\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\mathit{-}1}{\left(N\mathit{+}1\right)}\frac{t^3}{12\left(1\mathit{-}{\mathit{\mu }}^2\right)}$

where: J is the rigidity stiffener.

Dimension Design

Dimension design is achieved with 2 different assumptions which, in one, upper stage diameter was determined and, in the other, it was calculated in the output. The calculation of the length and diameter can be achieved through the following equation:

(35) $L_t\mathit{=}{L}_f\mathit{+}{L}_o\mathit{+}{L}_{\mathrm{of}}\mathit{+}{L}_e\mathit{+}{L}_s$

(36) $D_t\mathit{=}{D}_p\mathit{+}2\left(t_s\mathit{+}{t}_t\mathit{+}{t}_r\right)$

RESULTS

SAMPLE SOLUTION

A sample solution for upper stage design is presented in this section to generally introduce the design method:

1. Mission definition

   • Payload mass is 1.5 tones with parking orbit which is 200 KMs and destination orbit is 36000 KMs with inclination of 45 degrees change.

   • Other design inputs are based on requirements and limitations.

2. Results of supplying design initial inputs are shown in Table 5.

   Table 5
   Initial input.
   

   Input variable	Values
   β	0.162
   T (kn)	48.36
   µp	0.75
   MP (ton)	10.23
   MF (ton)	3.47
   M0 (ton)	13.70

3. Trajectory design:

   • Hohmann's transfer (3 times Re burn).

   • Determining transfer orbit (according to energy limitation and optimized mode).

4. Determining material and construction inputs of the subsystem:

   • Used mechanical properties, environmental conditions, used fluid properties.

   • Determining fuel and oxidizer (hydrogen/oxygen).

5. Initial feasibility based on ability to transport about 13 tones to the parking orbit through stages of launcher rocket.

6. System design:

   • Determining configuration parameters according to Table 4.

   • Selecting initial mass factor.

7. Propulsion design parameters (Table 6).

   Table 6
   Propulsion engine parameters.
   

   Parameter name	Input variable	Values
   Thrust factor	Cf	1.68
   Nozzle expansion ratio	ε	37
   Specific impulse	Isp	326
   Burning time	tb (s)	680
   Thrust	T (kn)	60
   Propulsion flow rate	ṁ (kg/s)	20.52
   Motor mass	mm (m)	497
   Motor diameter	dm (m)	0.852
   Motor length	Lm (m)	2.04
   Nozzle length	Ln (m)	1.14
   Nozzle outlet diameter	de (m)	0.78

8. Feeding system design (Table 7):

   Table 7
   Feeding system parameters.
   

   Parameter name	Input variable	Values
   Blowing system mass	mh (kg)	66
   Cases blowing mass	MTh (kg)	34.5
   Helium mass	mhe (kg)	20.6
   Thickness of helium tanks	th (mm)	4.45
   Radius of helium tanks	rh (mm)	257
   Number of helium tank	Nh	6

   1. Selecting pressure-feed system.

   2. Calculating pressure drop in fuel flow which is 3.2 bars and for oxidant is 4 bars.

   3. Fuel tank pressure 11.2 bars and oxidant 12 bars.

9. Design of tanks: mass and volume of tanks (Table 8).

   Table 8
   Tank parameters.
   

   Parameter name	Values
   Oxidant volume	7.050 m2
   Oxidant mass	9.669 ton
   Fuel volume	4.2827 m2
   Fuel mass	3.581 ton
   Oxidant tank radius	1.1895 m
   Fuel tank radius	1.1895 m
   Oxidant tank pressure	12 bar
   Fuel tank pressure	11.2 bar
   Fuel tank thickness	0.72257 m
   Oxidant tank thickness	3.801 mm
   Fuel tank thickness	3.5485 mm

10. Body structure: determining body thickness and stiffener which requires determining critical modes properties of previous steps, fairing and types of stiffener.

11. Mass distribution:

    • Determining mass distribution (Table 9).

      Table 9
      Other components mass distribution.
      

      Parameter name	Values (kg)
      Control block	245.88
      Actuators	94.56
      Cables	113.48
      Body	189.1397
      Telemetry	151
      Stand	150
      Disposal system	60
      Engine maintenance	28.28
      Control segments	18.91
      Long tube	31
      Flanges	28.28
      Separation	75
      Gyro planes and IMU	35

    • Upper stage primary masses.

12. Upper stage mass and dimensions:

    • • Upper stage dimensions (Table 10).

      Table 10
      Diameter and total length.
      

      Parameter name	Values
      Dimensional ratio	2.7812
      Diameter (m)	2.4921
      Total length (m)	6.9314

    • • Upper stage primary masses (Table 11).

      Table 11
      Mass parameters.
      

      Parameter name	Values
      Fuel mass	13.249
      Final mass	3.391
      Structure mass	1.891
      Total mass	16.64

DIFFERENT VARIANTS AND VALIDATION

Technology for constructing a launch vehicle in countries varies from each other, however, the statistical graphs indicate the approximate similarity of systematic parameters for upper-stage systems. For instance, Fig. 13 shows the relationship of payload mass and dry mass in the upperstage system. The real samples are circular and the samples derived from this paper for UDMH/N204 fuel are squareshaped. The comparative curve of burn time due to thrust/weight is presented in Fig. 14. Convergence factors (α and β) are illustrated in Figs. 15 and 16.

Figure 13
Final mass versus payload mass .

Figure 14
Comparative curve of burn time due to T/W.

Figure 15
Convergence factor α.

Figure 16
Convergence factor β.

The close similarity of these graphs is the main reason to validate the results derived from the study. At this point another validation was compared with Cent.D-5 upper-stage of Atlas V (401) which is presented in Table 12. Problem inputs: M_pay = 4.75 ton; D = 3.05m and I_sp = 4378 N*s/kg.

Table 12
Comparation of validation to Cent D-5 upper-stage.

Output data	Mp (ton)	M0 (ton)	µf	µp	β	n (N/kg)
System parameters Cent. D-5	19.65	26.78	0.266	0.18	0.10	3.64
Statistical design	16.8	23.66	0.29	0.2	0.11	3.88
MSDO	18.93	26.01	0.27	0.182	0.109	3.61

In Table 13, the errors in the statistical design methods and MSDO compared to the systematic data of Cent. D-5 upper stage system. As shown in Table 5, errors of fuel mass, dry mass and total mass in MSDO design are decreased by 9 to 16% compared with Cent. D-5. Furthermore, the accuracy of primary data derived from the statistical design is obvious in this table.

Table 13
Methods errors compared to the systematic data of Cent. D-5 upper stage system

Design type method	Propellant weight [%]	Dry weight [%]	Lift off weight [%]
Statistical	11.6	11.3	14.5
MSDO	0.2	2.1	3.66
0.27	0.182	0.109	3.61

CONCLUSION

Design processes of all elements are done simultaneously in this paper. In each design loop, calculations become more accurate and results of each section, more suitable according to other systems. In this design method, a mistake can be found by system (because it affects all elements) and it would be easier to fix it. The main results are:

• Proportional with technology and ability for construction.

• Logical relation of all segments and subsystems.

• Developing a national design and method.

• Presenting a sample upper stage according to different inputs.

• Logical convergence of parameters to logical values.

• Ability of performing general feasibility.

• Extensibility to accurate initial design.

• Ability of networking the design under supervision of the system.

• Designing systematic sample of upper stage.

• General guideline based on implementation of detail design (limitations of methods and range of parameters).

• All the important design points are specified in order to divide the algorithm for performing different projects.

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Publication Dates

• Publication in this collection
  Jan-Mar 2017

History

• Received
  07 May 2016
• Accepted
  08 Sept 2016