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A.5.4 User’s Guide for Structures Code 1

A.5.4 User’s Guide for Structures CodesCompiled and Edited by Brandon White

The structures code is a conglomeration of 15 MATLAB scripts and functions. The following

document is meant to be a guide to anyone wishing to use the structures code. Each script or

function in the structures code folder is briefly described here, with a listing of inputs needed

and outputs generated.

Indexbendtank.m C. Hiu page 2InertiaFinal.m B. White page 3intertank.m C. Hiu page 6intertank_str.m J. Doyle page 7mass.m D. Childers page 8nose_cone_def.m V. Teixeira page 10press_tank.m C. Hiu page 11shear_calc.m J. Doyle page 12skirt_analysis_v3_str.m J. Doyle page 13skirt_v3.m J. Doyle page 15tank_material_properties.m C. Hiu page 17tanks.m C. Hiu page 19tanksv2.m C. Hiu page 22gond_strength.m S. Shoemaker Page 24

Written and Compiled by Brandon White


bendtank.mWritten by Chii Jyh HiuRevision 1.0 - 20 February 2008

Description:

bendtank.m is a function file that analyses the propellant tanks in bending. It is called by

tanks.m or tanksv2.m.

Assumptions:

Tank bending allowable from Bruhn Figure C8.13a and bending allowable improvements for

pressurized tank from Bruhn Figure C8.14.

Input Section:

The call line of the function is:[Fbcr,Fbcr_press] = bendtank(E,D,t,L,P)

All of the variables that are passed into the m-file are described below:

Variable Name DescriptionE Tank material Young’s modulus (3-vector) [Pa]D Stage diameter(3-vector) [m]t Tank wall thickness (3-vector) [m]L Length of tank (3-vector) [m]P Tank internal pressure (3-vector) [Pa]

Output Section:

Variable Name DescriptionFbcr Unpressurized tank bending allowable [Pa]Fbcr_press Pressurized tank bending allowable [Pa]

Written by Chii Jyh Hiu and Compiled by Brandon White


InertiaFinal.mWritten by Brandon WhiteRevision 1.0 - 1 March 2008

Description:InertiaFinal.m is a function embedded within tanks.m. The function calculates principal

moments of inertia for entire launch vehicle at various stages of flight. InertiaFinal.m uses

inputs from tanks.m and mass.m. InertiaFinal.m is a culmination of previous revisions under

various names (Inertia.m, Inertia1.m, Inertia2.m).

Assumptions:

All products of inertia are zero, launch vehicle is axisymmetric. LITVC is a point mass located at

the top of the second stage nozzle. Payload and avionics in the third stage are point masses at

the base of the nose cone. Nose cone is a perfect, right cone (not blunted). Avionics in the first

and second stages are wall mounted to the inter-stage skirts, utilizing a constant thickness of 10

cm. This thickness assumption for the avionics is extremely conservative and probably should

be updated.

Input Section:

The call line of the function is:[I1_full I1_empty I2_full I2_empty I3_full I3_empty] = InertiaFinal(Xcm, L_cone, M_cone, M_Ox, M_tank_Ox, L_Ox, t_Ox, M_Fuel, M_tank_Fuel, L_Fuel, t_Fuel, M_tank_press, D_tank_press, t_tank_press, D_tank_press, s_len, s_mass, D, M_Engine, L_Nozzle, payload, mass_avionics, LITVC_prop, LITVC_mt, Length_stage)

All of the variables that are passed into the function are described below:

Variable Name Description

Xcm Launch Vehicle Center of mass at the 6 time steps, measured from nose cone [m]

L_cone Vertical length of the Nose Cone [m]M_cone Mass of the Nose Cone [kg]M_Ox Oxidizer mass for each stage [kg]M_tank_Ox Oxidizer tank mass for each stage [kg]L_Ox Length of Oxidizer tank for each stage [m]t_Ox Oxidizer tank thickness for each stage [m]



M_Fuel Fuel mass for each stage [kg]M_tank_Fuel Fuel tank mass for each stage [kg]L_Fuel Length of Fuel tank for each stage [m]t_Fuel Oxidizer tank thickness for each stage [m]M_tank_press Mass of the Pressurant tank [kg]D_tank_press Diameter of Pressurant tank [m]t_tank_press Pressurant tank thickness [m]

D_tank_press Diameter of Pressurant tank [m], yes it is input twice. This is a mistake.

s_len Inter-stage skirt vertical length [m]s_mass Inter-stage skirt mass [kg]D Diameter for each stage [m]M_Engine Engine mass for each stage [kg]L_Nozzle Vertical length of the engine nozzle for each stage [m]payload Mass of payload [kg]mass_avionics Mass of the avionics [kg]LITVC_prop Mass of the LITVC [kg]LITVC_mt Mass of the LITVC tank [kg]Length_Stage Vertical length of each stage [m]

Output Section:

InertiaFinal.m outputs six 3-element arrays. These arrays represent the principle moments of

inertia at different phases of flight. The arrays are output in row format with the Ixx value being

the first element, the Iyy value being the second element, and the Izz value being the third

element.




I1_full Principle moments of inertia with: All three stages, all full propellant [kg*m2]

I1_empty Principle moments of inertia with: All three stages, no propellant in the first stage [kg*m2]

I2_full Principle moments of inertia with: Second and Third stages, both with full propellant [kg*m2]

I2_empty Principle moments of inertia with: Second and Third stages, no propellant in the second stage [kg*m2]

I3_full Principle moments of inertia with: Third stage only, full propellant [kg*m2]

I3_empty Principle moments of inertia with: Third stage only, no propellant [kg*m2]


intertank.mWritten by Chii Jyh HiuRevision 1.0 - 17 February 2008

Description:

intertank.m is a function file that analyzes the inter-tank couplers for axial compressive

strength. It is called by tanks.m or tanksv2.m.

Assumptions:

Intertank buckling theory from Baker, E.H., Kovalevsky, L., Rish, F.L., Structural Analysis of Shells,

Robert E. Krieger Publishing Company, Huntington, NY, 1981, pgs. 229-240.

Important Notes:

Unlike most other MAT-derived functions, intertank.m accepts inputs as scalars

Input Section:

The call line of the function is:[mass_int, t, numhoop] = intertank(E,Sigma_y,Density,v,m_above,max_g,D,L)


Variable Name DescriptionE Inter-tank material Young’s modulus [Pa]Sigma_y Inter-tank material yield stress [Pa]Density Inter-tank material density [kg/m^3]v Inter-tank material Poisson’s ratiom_above Mass of rocket above inter-tank [kg]max_g Maximum g-loading [g’s]D Stage diameter [m]L Length of intertank [m]

Output Section:

Variable Name Descriptionmass_int Inter-tank mass [kg]t Inter-tank wall mass [kg]numhoop Number of hoops


intertank_str.mWritten by Jesii DoyleRevision 1.0 - 27 February 2008

Description:

Intertank_str.m is a function file that determines the number of stringers needed in the inter-

tank coupler. It is called by tanks.m or tanksv2.m.

Input Section:

The call line of the function is:[nsi,mass_str _int] = intertank_str(D,Sy,t_skin,tank_material,L_intertank)


Variable Name DescriptionD Inter-tank Diameter [m]Sy Inter-tank material yield stress [Pa]t_skin Inter-tank wall thickness [kg/m^3]tank_material Inter-tank materialL_intertank Length of inter-tank section [m]

Output Section:

Variable Name Descriptionnsi Number of stringers required mass_str_int Inter-tank stringer mass [kg]

Written by Jesii Doyle and Compiled by Brandon White

mass.mWritten by David ChildersRevision 2.0 - 5 March 2008

Description:

Calculates the center of mass for the launch vehicle.

Assumptions:

Point mass system. Mass is symmetric (located in center of launch vehicle). Locations are

approximated for avionics, engines, and LITVC because actual locations cannot be determined

based on the theoretical aspect of the project. Reference point is the top of the launch vehicle.

Stage numbering is from the bottom up.

Input Section:

The call line of the function is:

[CM_Full_3 CM_Emp_3 CM_Full_2 CM_Emp_2 CM_Full_1 CM_Emp_1]=mass(payload, M_Fuel,M_Ox,M_Engine,M_cone,M_tank_Fuel,M_tank_Ox,Mass_tank_press,LITVC_mt, s_mass,Mass_inert,D,D_tank_press,L_Nozzle,L_Ox,L_Fuel,Length_stage,s_len, L_cone,LITVC_prop,pressmass,Mass_intertank,mass_avionics)


Variable Name DescriptionStages Number of stagespayload Payload mass [kg]M_Fuel Fuel mass for each stage [kg]M_Ox Oxidizer mass for each stage [kg]M_engine Engine mass for each stage [kg]M_tank_Ox Oxidizer tank mass of each stageM_tank_Fuel Fuel tank mass of each stageMass_inert Inert mass/stageM_cone Nose cone massMass_tank_press Pressurant tank mass [kg]LITVC_mt Mass of the LITVC tank [kg]s_mass Mass of the inter-stage skirts [kg]D Diameter of each stage [m]D_tank_press Pressurant tank diameter [m]L_Ox Oxidizer tank length/stage [m]L_Fuel Fuel tank length/stage [m]

Written by David Childers and Compiled by Brandon White

s_len Skirt length/stage [m]L_cone Nose cone length [m]Length_stage Total length of each stage [m]LITVC_prop Mass of the LITVC [kg]Mass_intertank Mass of material between the tanks [kg]mass_avionics Mass of the avionics [kg]

Output Section:

Variable Name DescriptionCM_Full_3 Center of mass for full third stage [m]CM_Emp_3 Center of mass for empty third stage [m]CM_Full_2 Center of mass for full second stage [m]CM_Emp_2 Center of mass for empty second stage [m]CM_Full_1 Center of mass for full first stage [m]CM_Emp_1 Center of mass for empty first stage [m]

Written by David Childers and Compiled by Brandon White

nose_cone_def.mWritten by Vince TeixeiraRevision 1.0 - 24 February 2008

Description:

nose_cone_def.m is a function file that integrates the surface area of the nose cone using a

power-law body relationship.

Assumptions:

A one quarter sphere at the blunted tip at 30% of the nose cone length back from the tip.

Input Section:

The call line of the function is:[L_nose M_nose] = nose_cone_def(D_body)


Variable Name DescriptionD_body Diameter of the final stage of the launch vehicle [m]

Output Section:

Variable Name DescriptionL_nose Length of the nose cone [m]M_nose Mass of the nose cone [kg]

Written by Vince Teixeira and Compiled by Brandon White

press_tank.mWritten by Chii Jyh HiuRevision 1.1 - 20 February 2008

Description:

press_tank.m is a function file that analyses analyzes the buckling strength of a pressurized

cylindrical tank. It is called by tanks.m or tanksv2.m.

Assumptions:

Tank buckling allowable from Baker and buckling allowable improvements for pressurized tank

from Bruhn Figure C8.11.

Input Section:

The call line of the function is:[Fcr_press,Fcr,DF]= press_tank(E,v,D,t,L,P)


Variable Name DescriptionE Tank material Young’s modulus (3-vector)[Pa]v Poisson’s Ratio (3-vector)D Stage diameter (3-vector) [m]t Tank wall thickness (3-vector) [m]L Length of tank (3-vector) [m]P Tank internal pressure (3-vector) [Pa]

Output Section:

Variable Name DescriptionFcr_press Unpressurized tank bending allowable [Pa]Fcr Pressurized tank bending allowable [Pa]


shear_calc.mWritten by Jesii DoyleRevision 1.0 - 27 February 2008

Description:

shear_calc.m is a function file that determines the maximum shear loading (applied through the shear center) allowable by the launch vehicle. It is called by tanks.m or tanksv2.m.

Input Section:


[shear] = shear_calc(D,n_str,A_str,tskin,Sy,stages)


Variable Name DescriptionD Stage diameter [m]n_str Number of Stringers in each stageA_str Cross sectional area of each stringer [m2]t_skin Tank wall thickness [m]Sy Stringer material yield stress [Pa]Stages Number of stages in the launch vehicle

Output Section:

Variable Name Descriptionshear Maximum Shear Force Capability of Launch Vehicle [N]


A.5.4 User’s Guide for Structures Codes 13

skirt_analysis_v3_str.mWritten by Jesii DoyleRevision 2.0 - 24 March 2008

Description:

This function performs the analysis on the inter-stage skirt with stringers and ring

supports, and outputs the option with minimized cost. This code is called by skirt_v3.m.

Assumptions:

Constant taper angle of 10º

Constant skin thickness 4mm

Number of stringers is 1/6th of total possible stringers per radius

Important Notes:

This code is only called by the skirt_v3.m code, and should not need to be revised.

Input Section:

The call line of the function is:[mass,length,cost,ns,ring,yes_no,t_str] =

skirt_analysis_v3_str(P,r_bottom,r_top,l_noz,shear_f)


Variable Name DescriptionP Vertical Load [N]r_bottom Radius of the bottom of the inter-stage skirt [m]r_top Raius of the top of the inter-stage skirt [m]l_noz Length of the nozzle [m]shear_f Applied shear force [N]



Output Section:

Variable Name Descriptionmass Mass of the inter-stage skirt [kg]length Vertical length of the inter-stage skirt [m]cost Cost of the inter-stage skirt [USD]ns Number of stringersring Number of support ringsyes_no Shear stress check outputt_str Stringer thickness [m]



skirt_v3.mWritten by Jesii DoyleRevision 3.0 - 24 March 2008

Description:

This code calculates the mass, vertical length and cost of the skirts between each stage.

This code is run within tanks.m and tanksv2.m.

Assumptions:

The skirt shape is a truncated cone.

Only loads are maximum axial loads applied from mass above skirt and g-loading, and

maximum shear force.

Skirt material: Aluminum

Stringer material: Aluminum

Input Section:

The call line of the function is:[s_mass,s_len,s_cost,ns,ring,yes_no_s,t_str] =

skirt_v3(L_Nozzle,M_Ox,M_Fuel,M_tank_Ox,M_tank_Fuel,M_Engine,D,payload_m

ass,max_g,stages,m_press,M_tank_press,M_Cone,Sy)


Variable Name DescriptionL_Nozzle Length of the nozzle for each stage [m]M_Ox Mass of the oxidizer for each stage [kg]M_Fuel Mass of the fuel for each stage [kg]M_tank_Ox Mass of the oxidizer tank for each stage [kg]M_tank_Fuel Mass of the fuel tank for each stage [kg]M_Engine Mass of the engine for each stage [kg]D Diameter for each stage [kg]payload_mass Mass of the payload [kg]max_g Max g-loading [kg]stages Total number of stagesm_press Mass of the pressurant for each stage [kg]M_tank_press Mass of the pressurant tank for each stage [kg]M_cone Mass of the nose cone [kg]Sy Maximum shear force [N]



Output Section:

Variable Name Descriptions_mass Mass of inter-stage skirt for each stage [kg]s_len Length of inter-stage skirt for each stage [m]s_cost Inter-stage skirt cost for each stage [USD]ns Number of stringers in inter-stage skirt for each stagering Number of support rings in inter-stage skirt for each stageyes_no_s Yes/No outputt_str Stringer thickness [m]



tank_material_properties.mWritten by Chii Jyh HiuRevision 1.0 - 20 February 2008

Description:

tank_material_properties.m is a function file that returns material physical properties

for use in other calculations.

Assumptions:

Material strengths use B-basis, LT values where available. Tensile strengths are at yield,

shear stresses are at ultimate.

Important Notes:

Material properties for Carbon fiber are not authoritative. An isotropic carbon fiber

layup was assumed. As carbon fiber was abandoned early in the design process for cost

reasons, there was no incentive to refine the existing figures, which are kept for historic

purposes.

Input Section:

The call line of the function is:[Sigma_y,Sigma_s,Density,E,Cost_kg,v] = tank_material_properties(tank_material)



tank_material Tank material - S: Steel, A: Aluminum, C: Composite, T: Titanium, X: n/a. (3-vector, string) [unitless]

Written by Chii Jyh Hiu and Complied by Brandon White


Output Section:

Variable Name DescriptionSigma_y Yield stress allowable [Pa]Sigma_s Shear stress allowable [Pa]Density Density [kg/m^3]E Young’s modulus [Pa]Cost_kg Material raw cost [USD/kg]v Poisson’s ratio [unitless]



tanks.mWritten by Chii Jyh HiuRevision 1.7 - 20 February 2008

Description:

tanks.m calculates the required propellant and pressurant tank dimensions to meet

propellant storage and flight load requirements. It passes function calls to subsidiary

functions to calculate tank bending and buckling in-flight, as well as stresses on inter-

tank couplers. It also calls cost functions to calculate the manufacturing cost of the

tanks. It is used in the Material Analysis preliminary design level, where it is called by the

mainloop.m master function and forms an iterative loop with the various propulsion

codes to optimize the inert mass fraction of the launch vehicle.

Assumptions:

A Reserve Factor of 1.25 is applied across all stress analysis. We assume that hoop

stresses in the propellant tanks will always be greater than axial stresses. Max in-flight g-

loading is applied across all components. Inter-stage skirt function calls were disabled to

speed iteration during preliminary design runs.

Important Notes:

tanks.m expects 3-vector inputs for most variables. Exceptions are listed in the table

below

Input Section:


[M_tank_press, t_tank_press, M_tank_Ox, M_tank_Fuel, t_Ox, t_Fuel, inert_mass_fraction_struct, Mass_inert, Length_stage, yes_no, COST_stage, Tot_Cost, D, L_Ox, L_Fuel] = tanks.m(Mat, Prop_Type, M_Ox, Ox_Vol, P_Ox, M_Fuel, Fuel_Vol, P_Fuel, D, L_Nozzle, M_Engine, g, inert_mass, m_press, vol_press, P_press, payload_mass, shear, bending)





Mat Tank material - S: Steel, A: Aluminum, C: Composite, T: Titanium, X: n/a. (3-vector, string) [unitless]

Prop_Type Propellant type - 1: Cryogenic, 2: Storable, 3: Hybrid, 4: Solid, 0: n/a (3-vector, string) [unitless]

M_Ox Mass of oxidizer (3-vector) [kg]Ox_Vol Volume of oxidizer (3-vector) [m^3]P_Ox Oxidizer tank operating pressure (3-vector) [Pa]M_Fuel Mass of fuel (3-vector) [kg]Fuel_Vol Volume of fuel (3-vector) [m^3]P_Fuel Fuel tank operating pressure (3-vector) [Pa]D Stage diameter (3-vector) [m]L_Nozzle Length of Nozzle and Engine (3-vector) [m]M_Engine Mass of Nozzle and Engine (3-vector) [kg]g Max in-flight acceleration (scalar) [g’s]inert_mass Target inert mass (3-vector) [kg]m_press Mass of pressurant (3-vector) [kg]vol_press Volume of pressurant (3-vector) [kg]P_press Pressurant tank max pressure (3-vector) [Pa]payload_mass Payload mass (scalar) [kg]shear Max shear (3-vector) [N]bending Max bending (3-vector) [Nm]



Output Section:


M_tank_press Pressurant tank mass [kg]

t_tank_press Pressurant tank wall thickness [m]

M_tank_Ox Oxidizer tank mass [kg]

M_tank_Fuel Fuel tank mass [kg]t_Ox Oxidizer tank wall thickness [m]t_Fuel Fuel tank wall thickness [m]inert_mass_fraction_struct Inert mass fraction [kg]Mass_inert Inert mass [kg]Length_stage Length of stage [m]yes_no Success/Failure flag for target mass [unitless]COST_stage Cost of stage [USD]Tot_Cost Total Cost [USD]D Stage Diameter [m]L_Ox Length of oxidizer tank [m]L_Fuel Length of fuel tank [m]



tanksv2.mWritten by Chii Jyh HiuRevision 2.4 - 1 March 2008

Description:

tanksv2.m is a m-file that calculates the required propellant, pressurant and LITVC tank

dimensions to meet propellant storage and flight load requirements. It passes function

calls to subsidiary functions to calculate tank bending and buckling in-flight, as well as

stresses on inter-tank couplers and inter-stage skirts. It has calls to center of mass and

inertia matrix functions. It also calls cost functions to calculate the manufacturing cost of

the tanks. It is used in final analysis design, and calls input variables from the workspace

that are calculated by running mainonce.m and LITVC.m.

Assumptions:

A Reserve Factor of 1.25 is applied across all stress analysis. Max in-flight g-loading of

6gs is applied across all components.

Input Section:



tank_material Tank material - S: Steel, A: Aluminum, C: Composite, T: Titanium, X: n/a. (3-vector, string) [unitless]

propellant_type Propellant type - 1: Cryogenic, 2: Storable, 3: Hybrid, 4: Solid, 0: n/a (3-vector, string) [unitless]

prop_mass Mass of propellant (3-vector) [kg]p_ox_tank Oxidizer tank operating pressure (3-vector) [Pa]p_fuel_tank Fuel tank operating pressure (3-vector) [Pa]diameter_final Stage diameter (3-vector) [m]nozzle_length Length of Nozzle and Engine (3-vector) [m]engine_mass Mass of Nozzle and Engine (3-vector) [kg]g Max in-flight acceleration (scalar) [g’s]payload_mass Payload mass (scalar) [kg]



Output Section:

Variable Name DescriptionM_tank_press Pressurant tank mass [kg]t_tank_press Pressurant tank wall thickness [kg]M_tank_Ox Oxidizer tank mass [kg]M_tank_Fuel Fuel tank mass [kg]t_Ox Oxidizer tank wall thickness [m]t_Fuel Fuel tank wall thickness [m]inert_mass_fraction_struct Inert mass fraction [kg]Mass_inert Inert mass [kg]Length_stage Length of stage [m]yes_no Success/Failure flag for target mass [unitless]COST_stage Cost of stage [USD]Tot_Cost Total Cost [USD]D Stage Diameter [m]L_Ox Length of oxidizer tank [m]L_Fuel Length of fuel tank [m]CM_Full Center of mass of fully fueled stage [m]CM_Empty Center of mass of empty stage [m]In_Full Mass moment of inertia of full nth stage [kgm^2]In_Empty Mass moment of inertial of empty stage [kgm^2]



gond_strength.mWritten by Sarah ShoemakerRevision 1.1 - 19 March 2008

Description:

This code generates the strength the base of the gondola experiences.

Important Notes:

The gondola weight is acquired from the CATIA model.

Input Section:


[stress] = gon_strength.m ( GLOW, area, gond_weight )


Variable Name DescriptionGLOW Gross lift off weight of the launch vehicle [kg]area Area of the gondola base [m2]

gond_weight Mass of the guide rails, support rings, and avionics/avionics bay [kg]

Output Section:

Variable Name Descriptionstress Stress on the gondola base [Pa]

Sample Output:

ans =

7.5479e+004

The stress the gondola base experiences.

Written by Sarah Shoemaker and Complied by Brandon White

user’s guide to running the trajectory code using … · web viewtank bending allowable from...

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