Leonardo Pinero-Perez

Design of Hypersonic Lifting Body Vehicle (Lead Chief Engineer’s Report) · Chapter VIII

VIIISynthesis

Author
Leonardo Pinero-Perez
Written
2018 · Report, University of Texas at Arlington
Original
Full report · 120 pages
Contents
Nomenclature · Chapter I · II · III · IV · V · VI · VII · VIII · IX · X · XI · Appendix · References
Ref
MAE 4351-2018

Converted from the original PDF on with Claude Opus 5.5. The wording is unchanged, except: two classmates’ names are replaced by their roles, Figure 54 (an attendance sheet) is omitted, and my name is spelled without accents. Equations, figures and numbering follow the original. Conversion not yet checked against the PDF.

ASizing

The sizing method used is dependent on the industry capability index (ICI), which is constructed by structural weight, mission requirements, and slenderness. Payload and fuel volume fractions available are also drivers of sizing. This index will size the planform area of the vehicle according to mission requirements.

The ICI is a measure of available technology and is defined such that performance can increase with increasing structural or propulsion capabilities [2]. This is very useful for sizing high-performance aircraft where failure of a concept is often due to a lack of available technology, as it was for many spaceplane concepts after the Apollo program [1]. As shown in the MDA, sizing begins with an understanding of the mission requirements, and technological capability will be built off of 176 data. The ICI is calculated as follows:

Propulsive Index:

Ip=(ρpplWR−1)=(ρpplWTOGWWOWE−1)=(1200 kg/m345,500 kg9750 kg−1)=327 kg/m3

Structural Index:

Istr=WstrSwet=8300 kg560 m2=14.82 kg/m2

Industrial Capability Index (ICI):

ICI=10∗IpIstr=10∗327kgm314.82kgm2= 22 m−1

To obtain a starting value, the values for the Model-176 are used in this equation, provided by the disciplines. Other geometric values allowed the team to find sizing parameters:

τ=VtotalSplanform1.5=107 m365.71.5m3=0.20
Kw=SwetSplanform=560 m265.7m2=8.52

We now have the ICI for the 1964 Model-176. This provides a starting point for iteration. Producing a carpet plot with variables of planform area versus industrial capacity will now prove useful. It is desirable for the hypersonic vehicle design to be as small and light as possible, since that will drive down launch costs immensely (this is an upper stage so weight reduction here greatly compounds in the rocket equation).

Sizing is conducted from the mission profiles and completed by synthesis engineer Rashi Jain. The two military variants converged to a proper planform size at the time of presentation, but the civilian variant has yet to converge. Fortunately, this variant is not design critical given its low delta-V mission profile and light payload for a geometry and volume budget equivalent to the other two military variants.

BDisciplinary MATLAB Functions

In order to condense the synthesis script, the disciplines have encapsulated their methods into MATLAB functions. Disciplines have multiple functions called, so user guides are documented in this section. This is an important high-level method which will allow the team to debug any inconsistencies within the hypersonic vehicle’s design script.

Performance Functions [15]:

Function Name: subsonic_perf.m Brief Description:

Inputs: subsonic_perf(LDmaxsub,CLsub,CLmaxsub,Ssub,Wsub,hsub);

Constants:

Outputs: [Range, Vapp, Sg, gammaa] , plot: altitude vs. velocity for optimum glide

Function Name: Dvcalc.m Brief Description:

Inputs: Dvcalc(hi,Vi,h_des)

Constants:

Outputs: dVs

Function Name: AeroInc.m Brief Description:

Inputs: AeroInc(W,S,CL,LD,h,sel)

Constants: For this function all the constants are in freedom units, the inputs and outputs are all converted to proper units as necessary

Outputs: dV,V,hret

Function Name: Thermmap.m Brief Description:

Inputs: Thermmap(W,S,CL,R0,Tmin,Tmax,Tint,points)

Constants:

Outputs: Plot of thermal map. Does not currently output any of the variables (although could be very easily modified to do so)

Aerodynamics Functions [16]:

Function Name: subsonic.m Brief Description:

Inputs: subsonic(WL_sub, l, A_base, b_sub, S_wetsub, S_refsub)

Constants:

Outputs: [C_L, C_D, L_D, L_Dmax], Drag Polar, C_Lalpha,

Function Name: hyper.m Brief Description:

Inputs: hyper(l, A_base, Sw, Sref, W_e)

Constants:

Outputs: [C_L, C_D, L_D, L_Dmax], Drag Polar, C_Lalpha,

Function Name: neutral_point.m (l) Brief Description:

Inputs: neutral_point (l)

Constants:

Outputs: [np, np_sub], neutral point locations for each speed regime as a percent of length

Propulsion Functions [35]:

Function Name: PropulsionSizingFunction.m

Brief Description:

Inputs: PropulsionSizingFunction(T_req)

Constants:

Outputs: [T2W_eng, D_eng, L_eng, m_eng]

Stability and Control Functions: Function Name: StaCon_Function.m Brief Description:

Inputs: StaCon_Function(StaConINPUT) (Currently)

Outputs: [Mstacon, Cma, Cyb, Cnb, Clb, aoaH, Cmah, Cybh, Cnbh, Cybh, Cndr, Cmde, Cydr, Clda], Each output vs M or aoa plots, T/F for long/lat stability

CAD and Layout Functions [20]: Function Name: GeomSizing.m Brief Description:

Inputs: myFunction(S_plan, S_wet, GEOM, VOL)

Constants:

Outputs: [void], plotter

Structures Functions [18]: Function Name: materials.m Brief Description:

Inputs: materials(Nose, WLeading, Leeward, Windward, VTLeading, VT, HTLeading, HT, YieldM, YieldC, rhoM, rhoC, EM, EC, TempM, TempC, NameM, NameC, TExM,TExC)

Outputs: [Mat]

CSynthesis Script: Product Disciplinary Development

The synthesis script will be written by the author as a contribution to the synthesis discipline, and will take the database as an input, as well as a spreadsheet with user-guided parameters to fulfill the mission. The script will import a database first to reduce computation time (this section can be commented out once a mature database has been imported). The script written to date can be found in section B of the appendix.

Early in the project, the stability script was developed for the supersonic and subsonic speed regimes, heavily modified from the previous semesters’ script written by the author. Additionally, load cases were written out in pseudocode as part of structure’s literature research. This function was the first to be integrated into the main synthesis script. Plotting features are suppressed and called outside the function in the main synthesis script.

A weight/balance script was written, modified from a CAD engineer’s old MATLAB code. There has been significant progress in developing performance trajectory plots. The script for the hypersonic trajectory turn is still in development. CAD has also begun their script to build shapes and determine geometric properties from sizing parameters and user shape selection. This will aid in iteration, volume comparison, and trade studies. Aerodynamics is also implementing methods to find angle of attack as a function of Mach number by keeping the craft at maximum lift-to-drag ratio as computed by the speed regime. The author aided in the development of this script, and the resulting plots are shown below. These plots are used as inputs to stability assessment.

Plot titled “L/D vs AOA”: L/D against angle of attack from 0 to 90 degrees for Mach 5, 10, 15, 20 and 25; each curve peaks at an angle of attack of about 10 degrees, highest (about 4.4) at Mach 25 and lowest (about 2.5) at Mach 5.
Figure 72L/D vs AOA for various Mach Numbers [16]
Two plots against Mach number from 5 to 25: the maximum L/D rises from about 2.4 to about 4.4, and the corresponding angle of attack falls from about 15 to about 8.5 degrees.
Figure 73Maximum L/D and Associated Angle of Attack as Function of Mach Number [16]

The organization of the weights is recorded by the author to ensure that there is consistency between the weight calculations and no double-counting.

Tree diagram of the Model 176’s full mass, m_176: propellant (oxidizer and fuel) and empty mass, which splits into structural (cold structure and thermal protection) and payload (equipment, and crew made up of people and life support).
Figure 74Upper Stage Mass Breakdown with Associated Variable Names

The weights shown above represent different methods for obtaining them. The payload weight is straightforwardly provided by the mission, where the crew needed and their associated life support system is easily computed in the mission chapter.

The CAD script is currently under development but will not be ready for the midterm as there is a huge difference between the methods used and the historical values, particularly when computing tau.

Plot titled “Surface Volume Continuum” of K_w against tau from 0 to 0.5: a rising line for geometric shapes, from about 2.45 to 3.6, and two points for the Model 176 and the calculated 176 near K_w = 5.
Figure 75Initial Results from CAD Script [20]

DSynthesis Script: Product Description

The Nassi-Schneiderman diagrams in the methodology chapter describe the process of analysis along with parallel processes, but the author believes it is also necessary to show code structure as it pertains to the various MATLAB subroutines developed by the individual disciplines. This more clearly displays the code hierarchy and the order they appear in the script. This is similarly shown in the table of contents within the script.

The flight profile and Disciplinary Analysis under “Hypersonic Analysis” is further broken down into the respective sub-team’s analysis by the following structure:

Below is a collection of variables which keep track of and standardize some common variables found in many disciplinary scripts.

Tables of common variable names in the synthesis script, grouped as weights, trajectory, geometry, propulsion and aerodynamics, each listing the variable, its name in the script and its units.
Figure 76Common Variable Names in Synthesis Script

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