Project Bellerophon 491
A.5.0 Structures
A.5.1 Introduction
Before igniting the first engine, a launch vehicle must prove that it can withstand the basic structural forces during flight. Through iterative math models produced in MATLAB, we are able to appropriately size all components of the launch vehicles to combat buckling, bending, and shear forces. The propellant tanks, inter-stage skirts, inter-tank couplers, and nose cone are designed in this manner. Whether it results in adding internal structural members (stringers and support rings) or increasing the thickness of certain components (tanks, inter-stage skirts), our launch vehicle’s structural success is justified in the following sections.
Prior to the final launch vehicle configuration, we had to be very flexible with our design. At a moment’s notice we were able to create launch vehicles employing different materials for different propellant types, without losing any confidence in mission success. As certain options were eliminated, our analysis became more detailed and thorough. When the final mission specifications were selected, we branched out to other investigations such as finite element analysis and the design of the gondola that carries the launch vehicle to a 30 km altitude.
The design process, methods used, and research performed are presented in the subsequent pages. We anticipate that the work accomplished by this group will be useful for anyone looking to advance this design further.
Author: Brandon White
Project Bellerophon 613
A.5.2 Design Methods
A.5.2.1 Propellant Tanks
A.5.2.1.1 Overview
Our launch vehicle contains a number of propellant storage tanks, which comprise much of its inert mass. The final launch vehicle configuration has a pressurant tank and an oxidizer tank in the first stage of the rocket and a Liquid Injection Thrust Vector Control (LITVC) tank in the second stage. The tanks are subjected to pressure loading as well as axial and bending loads in flight and on the ground. In the preliminary design phase, liquid and cryogenic rocket fuels were also considered, so we also designed fuel tanks. Collectively, we refer to the fuel and oxidizer tanks as propellant tanks in this report.
The tanks are considered to be pressure-flight stabilized structures. This means that they are designed to be strong enough to withstand ground loads while unpressurized, but are pressurized while in flight, meaning that the launch vehicle may be transported and assembled while unpressurised, resulting in safer and less complicated (and thus cheaper) ground logistics. At the same time, treating the tanks as pressurized structures while in flight allows us to make the tanks lighter and more structurally efficient.
Author: Chii Jyh Hiu
Project Bellerophon 613
A.5.2.1.2 Tank Material
The primary materials that we are considering for our launch vehicle are aluminum, steel, titanium, and composites. Research proved that these are the most common materials employed in space flight. Our analysis involves finding different alloys of these materials and figuring out which alloys give us the best results for cost, strength, weight, and manufacturability.
After compiling information on physical properties of the materials, we contacted manufacturing companies to find out the costs associated with producing a tank. The data we obtained helps us compare the materials suitably. These costs include: welding, riveting, and labor hours required for production. These cost numbers are then placed into Matlab codes to give an overall cost for the tank.
We looked at several different alloys for each of the materials. The strength of each of these alloys is compiled into a database. These strengths are then compared to the costs output by the code in order to figure out the best cost-to-strength ratio of the material. Along with the strength, the manufacturability of the alloys is also considered. We looked at the time it would take to weld or rivet the material, as well as the formability of each material. The alloys that we analyzed were Aluminum 7075, Stainless Steel, Isotropic Carbon Fiber, and Titanium Ti-5Al-2.55Sn. Table A.5.2.1.2.1 through Table A.5.2.1.2.4 show the database for each of the materials considered for the tanks.
Table A.5.2.1.2.1 Materials Database for Aluminum 70751 TanksVariable / Value / Units
Yield Stress / 4.61*108 / Pa
Shear Stress / 3.00*108 / Pa
Density / 2.8*103 / kg/m3
Young’s Modulus / 6.79*1010 / Pa
Poisson’s Ratio / 0.333 / --
Table A.5.2.1.2.2 Materials Database for Stainless Steel3 Tanks
Variable / Value / Units
Yield Stress / 9.99*108 / Pa
Shear Stress / 9.99*108 / Pa
Density / 7.83*103 / kg/m3
Young’s Modulus / 1.97*1011 / Pa
Poisson’s Ratio / 0.3 / --
Table A.5.2.1.2.3 Materials Database for Isotropic Carbon Fiber4 Tanks
Variable / Value / Units
Yield Stress / 8.95*108 / Pa
Shear Stress / 4.00*108 / Pa
Density / 1.55*103 / kg/m3
Young’s Modulus / 1.50*1011 / Pa
Poisson’s Ratio / 0.4 / --
Table A.5.2.1.2.4 Materials Database for Titanium Ti-5Al-2.55Sn2 Tanks
Variable / Value / Units
Yield Stress / 8.14*108 / Pa
Shear Stress / 5.00*108 / Pa
Density / 4.48*103 / kg/m3
Young’s Modulus / 1.07*1011 / Pa
Poisson’s Ratio / 0.333 / --
Our propellant tanks are designed with Aluminum 7075. We chose this material because it has been incorporated for many historical launch vehicle tank materials. Our analysis of strength-to-weight ratios favors aluminum. The cost also favors aluminum due to the ease of manufacturability. This material is used for all three stages on all three launch vehicle configurations.
References
1 Setlak, Stanley J., “Aluminum Alloys; Cast,” Aerospace Structural Metals Handbook, Purdue University, Indiana, 2000.
2Setlak, Stanley J., “Titanium Alloys; Cast,” Aerospace Structural Metals Handbook, Purdue University, Indiana, 2000.
3Setlak, Stanley J., “Stainless Steel; Cast,” Aerospace Structural Metals Handbook, Purdue University, Indiana, 2000.
4Callister, W.D. Jr, Fundamentals of Materials Science and Engineering, 2nd Ed., Wiley & Sons, 2005
Author: Sarah Shoemaker
Project Bellerophon 613
A.5.2.1.3 Preliminary Design
Preliminary design for the propellant tanks and pressurant tanks is carried out by sizing the tanks to contain the required amount of propellant and designing the tanks to withstand maximum in-flight internal pressure. We use a safety factor of 1.25 to account for transient spikes in pressure and to cover other failure modes. We also add 5% additional volume to the propellant tanks to account for internal structure and dead space. We specify a minimum tank wall thickness of 0.75mm in the preliminary design algorithms for manufacturability and practicality.
A.5.2.1.3.1 Tanks
The propellant tanks for liquid fuel/oxidizers are designed as cylindrical tanks with hemispherical ends for the purposes of structural efficiency and ease of manufacture. The hemispherical end configuration is stronger and lighter than using elliptical ends, but takes up more space.1 Due to the small size of the launch vehicle, the space savings from using an elliptical-end tank are negligible, so we incorporate the hemispherical end configuration instead. Should a spherical tank be small enough to fit into the stage, we choose a spherical tank instead of a cylindrical tank for structural efficiency. For cylindrical tanks, a maximum length to diameter (L/D) ratio of 6.0 is chosen in preliminary design as a tradeoff between drag and structural efficiency/dynamic stability. This value is later refined to 3.0 in final design based on scaling from existing launch vehicle designs; provided more time to analyze the interaction between size and drag/controllability, a more optimal aspect ratio range could have been determined via simulation runs. However, since the final designs do not reach anywhere near the maximum L/D ratio, we regard this exercise as not crucial to our current design and do not pursue it any further.
Propellant tanks for solid propellants (and the solid components of hybrid rockets) are designed as an open-ended cylinder with an elliptical cap. The same maximum L/D ratio is applied as with the liquid propellant tank design. Spherical tanks are not appropriate for solid rocket fuel, so the tanks were kept cylindrical.
The pressurant tank is designed as a spherical tank, as it is rated to a much higher internal pressure (12 MPa) compared to the propellant tanks (typically ~ 2.0 MPa for liquid propellant tanks and ~ 6.0 MPa for solid propellant tanks). The spherical tank configuration provides the highest structural efficiency for a pressure vessel1 and is the ideal layout for a small, high-pressure tank.
A.5.2.1.3.2 Inter-tank Couplers
The inter-tank couplers connect the pressurant tank to the oxidizer tank, and the oxidizer tank to the fuel tank. They are designed as cylindrical skin sections with longitudinal and hoop stiffeners, and are designed to carry axial and shear load at maximum flight g-loading.
Author: Chii Jyh Hiu
Project Bellerophon 613
A.5.2.1.4 Stress Analysis
A.5.2.1.4.1 Tanks
For the purpose of our analysis, we assume that the tanks carry only axial and bending loads, and that the inter-tank couplers and inter-stage skirts carry only axial and shear loads. Tanks are analyzed as thin-walled structures. We consider these assumptions to be a conservative and reasonable approximation of the actual loads seen in the vehicle.
The oxidizer tank is manufactured from Aluminum 7075 spun in two halves, with a full-thickness circumferential weld at the butt. This provides the optimal weld conditions for strength, as the hoop stress in a cylindrical pressure vessel is twice the axial stress (Eqs.(A.5.2.1.4.1) and (A.5.2.1.4.2)). Assuming a weld strength factor of 0.851 for a spot-examined joint, this ensures that the tank wall thickness is designed entirely by the hoop stress due to pressure, as the reserve factor for axial loading will consequently always be greater than for hoop loading.
As mentioned above, the propellant tank is designed to the hoop stress seen due to pressure loading due to internal pressure and hydrostatic pressure at maximum flight g-loading.
/ (A.5.2.1.4.1)/ (A.5.2.1.4.2)
where sox_hoop is the hoop stress in the oxidizer tank (Pa), sox_axial is the axial stress in the oxidizer tank (Pa), Pox is the internal pressure in the oxidizer tank (Pa), gmax is the maximum in-flight acceleration (m/s2), h is the height of the fluid level (m), ttank_ox is the thickness of the tank wall (m) and Dox.is the diameter of the oxidizer tank (m).
We then subject the model to further failure mode analyses, buckling and bending, and either add structure or increase the wall thickness as needed to meet our strength requirements.
Tank buckling strength is calculated by using Baker’s buckling criteria3 (Eqs. A.5.2.1.4.3) for unpressurized tanks, and using experimental data from Bruhn Figure C8.114 for pressurized cylinders to determine the proportional increase in strength due to pressurization.
/ (A.5.2.1.4.3a)/ (A.5.2.1.4.3b)
/ (A.5.2.1.4.3c)
/ (A.5.2.1.4.3d)
where Pcr is the critical buckling stress of the structure (Pa), ks is the buckling coefficient, E is the Young’s Modulus of the material (Pa), u is the Poisson’s Ratio of the material, t is the thickness of the inter-tank coupler (m), L is the length of the inter-tank coupler (m), D is diameter of the tank (m), DPcr is the non-dimensionalized increase in critical buckling strength (see Section A.5.2.1.6.2) and Pcr_press is the critical buckling stress of a pressurized tank, (Pa).
Tank bending strength is assessed using test data from Bruhn Figure C8.13a4 for unpressurized cylinders and deriving the increase in tank bending allowable due to pressurization from Bruhn Figure C8.144 for pressurized vessels.
Similar to the oxidizer tank, the pressurant tank is manufactured from spun Aluminum 7075 in two hemispheres and joined together with a full thickness weld. Due to the higher criticality of the tank, the weld of the pressurant is to be fully radiographically tested after manufacture. Fortunately, as the pressurant feed tank is smaller than the oxidizer tank, this is easily achieved.
The pressurant tank is designed to withstand a wall stress calculated from Eq. (A.5.2.1.4.4).
/ (A.5.2.1.4.4)where spress is the stress in the pressurant tank (Pa), Ppress is the internal pressure in the pressurant tank (Pa), gmax is the maximum in-flight acceleration in (m/s2), h is the height of the fluid level (m), ttank_press is the thickness of the tank wall (m), and Dpress.is the diameter of the pressurant tank (m).
The LITVC tank is found in the second stage of the rocket, and is designed as a spherical tank to similar principles as the pressurant tank. We place the tank near the nozzle throat. If the need arises, the LITVC tank could be redesigned as a toroidal tank, but this will require additional work not covered in this report.
The LITVC tank is designed to withstand a wall stress calculated from Eq. (A.5.2.1.4.5).
/ (A.5.2.1.4.5)where sLITVC is the stress in the LITVC tank (Pa), PLITVC is the internal pressure in the LITVC tank (Pa), gmax is the maximum in-flight acceleration (m/s2), h is the height of the fluid level (m), ttank_LITVC is the thickness of the tank wall (m) and DLITVC is the diameter of the LITVC tank (m).
A.5.2.1.4.2 Inter-tank Couplers
The inter-tank couplers are designed to carry axial and shear load at maximum flight g-loading.
Fig. A.5.2.1.4.2.1: Inter-tank coupler showing internal supports, 1kg payload
(Chii Jyh Hiu)
The inter-tank couplers are manufactured from rolled Aluminum sheet welded at the seams, with equally spaced I-section hoops and z-section stringers riveted to the inside walls.
We design the inter-tank couplers to withstand axial loads by satisfying the Baker buckling criteria3:
/ (A.5.2.1.4.6)where Pcr is the critical buckling stress of the structure (Pa), ks is the buckling coefficient, E is the Young’s Modulus of the material (Pa), u is the Poisson’s Ratio of the material, t is the thickness of the inter-tank coupler (m) and L is the length of the inter-tank coupler (m).