Research & Development  Wind Tunnel Testing –Needs to be applicable for subsonic, transonic, and supersonic velocities –Scaled down model Associated costs Dimensions to minimize error due to scale effects, flow blockage, and wall boundary layers –Possible testing locations NASA Glenn Research Center – Cleveland, OH NASA Langley Research Center - Hampton, VA Purdue’s Mach-6 supersonic tunnel – West Lafayette, IN AAE 450 Spring 2008 Aerothermal 1

AAE 450 Spring 2008 Aerothermal 2 Assumptions: -Used Historical Values for large variety of similar shaped rockets and scaled the drag coefficient accordingly to determine C D at α=0. -Also attempted CFD to determine C D at α=0. -Then used C D at α=0 in order to generate plots of C D versus AoA. -”Normal” Geometry indicates all upper stages are smaller in diameter than their predeceasing lower stage and only a total of 1 to 2 shoulders.

AAE 450 Spring 2008 Aerothermal 3 Assumptions: -Used pressure coefficient to calculate the axial and normal force coefficients. -Used the axial and normal force coefficients to calculate the drag coefficient.

Coefficient of Drag 2 Plot Authors: Woods, Zott AAE 450 Spring 2008 Aerothermal

Vanguard Check – subsonic case using Fluent Velocity Vectors Red – 401 m/s Green – 225 m/s Static Pressure Red – 1.18 atm Blue –.364 atm AAE 450 Spring 2008 Aerothermal 5

Vanguard Check – subsonic case using Fluent Static Temperature Red – 300 K Blue – 220 K AAE 450 Spring 2008 Aerothermal 6

1 kg launch vehicle – Mach 1 case using Fluent Pressure Red – 1.56 atm Blue –.373 atm AAE 450 Spring 2008 Aerothermal 7

1 kg launch vehicle – Mach 1 case using Fluent Velocity Red – 411 m/s Green – 208 m/s AAE 450 Spring 2008 Aerothermal 8

200 g Aerodynamic Loads Table Summary of Maximum Aerodynamic Loading 200 g. Aerodynamic LoadSubsonicSupersonic Bending Moment [Nm] Pitching Moment [Nm] Normal Force [N] Axial Force [N] Shear Force [N] Center of Pressure [% length] Coefficient of Drag C D Dynamic Pressure [Pa] C D % error [%] AAE 450 Spring 2008 Aerothermal 9

1 kg Aerodynamic Loads Table Summary of Maximum Aerodynamic Loading 1 Kg. Aerodynamic LoadSubsonicSupersonic Bending Moment [Nm] Pitching Moment [Nm] Normal Force [N] Axial Force [N] Shear Force [N] Center of Pressure [% length] Coefficient of Drag C D Dynamic Pressure [Pa] C D % error [%] AAE 450 Spring 2008 Aerothermal 10

5 kg Aerodynamic Loads Table Summary of Maximum Aerodynamic Loading 5 Kg. Aerodynamic LoadSubsonicSupersonic Bending Moment [Nm] Pitching Moment [Nm] Normal Force [N] Axial Force [N] Shear Force [N] Center of Pressure [% length] Coefficient of Drag C D Dynamic Pressure [Pa] C D % error [%] AAE 450 Spring 2008 Aerothermal 11

Creation of the Pressure Distribution AAE 450 Spring 2008 Aerothermal 12

Linear Perturbation  Forces are found by an integration of pressure distribution over the launch vehicle exterior  Integrations are done numerically within the code  Phi is the geometric angle w/respect to the freestream  S is a reference area, taken to be the area of the base of the launch vehicle  Validated by comparison to Vanguard results and other related geometries AAE 450 Spring 2008 Aerothermal 13

Important Assumptions in Theory  Small changes in geometry  Small angle of attack ~ 0 – 14 degrees  Valid for subsonic or supersonic flow 0 < M < < M < 5  Axial force neglects viscous effects AAE 450 Spring 2008 Aerothermal 14

Stresses due to Aerodynamic Force  Shear Stress –Differential of Normal Force between stages  Axial Loading –A*q ∞ *S  Bending Moment  Picture by Jayme Zott and Alex Woods AAE 450 Spring 2008 Aerothermal 15

Pictures AAE 450 Spring 2008 Aerothermal 16

Pictures AAE 450 Spring 2008 Aerothermal 17

Heating Rate  Heating Rate Analysis –Primarily done to design a TPS (Thermal Protection System) –Stagnation Point Theoretical analysis using methods outlined by Professor Schneider Nose cone heating Determine best material and thickness for the structure of the nose cone –Alternative methods and materials SODDIT (Sandia One-Dimensional Direct and Inverse Thermal) Ablative materials AAE 450 Spring 2008 Aerothermal 18

Heating Rate Lumped Heating at Solid Nosetip Method  Assumptions –Constant specific heats –No heat transfer within the body –Treat whole nosetip as one solid heat sink –Laminar flow at point 2 –No convective heating at point 3, only radiative –Wall temperature is the same at all 4 points AAE 450 Spring 2008 Aerothermal 19

Equations M = 3, N = 0.5 for fully catalytic surface M 2 = 3.2 for laminar, flat plate = nose body radius = volume of solid nosetip Heating rate at point 2 on the nose cone = radiation from fluid to surface AAE 450 Spring 2008 Aerothermal 20

Heating Rate Matlab code: *help from Vince Teixeira AAE450_Stag_heat_analysis.m Uses trajectory outputs (.mat files) Input: d - diameter (m) v - velocity (m/s) r - position from the center of the earth (m) c_p - specific heat of material (J/kg*K) rho_w - density of material (kg/m 3 ) emiss - emissivity of material Output: q_dot - heating rate (W/m 2 ) tw - thickness (mm) Tw - wall temperature (K) AAE 450 Spring 2008 Aerothermal 21

Heating Rate AAE 450 Spring 2008 Aerothermal 22

Backup Slides- Sizing Code Tables  Initial Sizing Code Table of Results Table Created by Chris Strauss AAE 450 Spring 2008 Aerothermal 23

Backup Slides-CFD  Models to be used for GAMBIT griding of project rocket Initial models of project rocket Model would have been used to simulate each stage of flight in Fluent Models Created by Chris Strauss AAE 450 Spring 2008 Aerothermal 24

Backup Slides-CFD  CMARC Model Model of aircraft launched rocket initially conceived Model was flexible enough so that multiple configurations could be made quickly Model was scrapped after it was discovered CMARC results are only valid to Mach 0.9 Model Created by Chris Strauss AAE 450 Spring 2008 Aerothermal 25

Drag Coefficient Standard Deviation  Method –Create a randomizer that produces random values of angle of attack from 0-10 degrees –Fed angles of attack into C d code to obtain values for C d C d code created by Jayme Zott –Entered values for C d into Excel to calculate standard deviation with standard deviation function AAE 450 Spring 2008 Aerothermal 26

Top Down View Fig. by Kyle Donohue AAE 450 Spring 2008 Aerothermal 27 Though an aircraft launch was not put into operation. A wing would be beneficial if it were. A wing creates an additional nose up pitching moment allowing the launch vehicle to pitch from an initial horizontal configuration (α=0°) into a final vertical configuration (α=90°). Wing Moment Coefficient versus AoA Fig. by Brian Budzinski

Shear on Launch Vehicle from Wing Fig. by Brian Budzinski Shear on Launch Vehicle from Fins Fig. by Brian Budzinski Shear Coefficient on Launch Vehicle from Wing Fig. by Brian Budzinski The shear created through the addition of a wing or fins is assumed to be equal to the normal force caused by the corresponding part. AAE 450 Spring 2008 Aerothermal 28

Wing Normal Force Coefficient versus AoA Fig. by Brian Budzinski Wing Axial Force Coefficient versus AoA Fig. by Brian Budzinski ASSUMPTIONS: Initial Horizontal Launch Configuration Final Vertical Configuration Newtonian Model Delta Wing AAE 450 Spring 2008 Aerothermal 29

Wing Lift Coefficient versus AoA Fig. by Brian Budzinski Wing Drag Coefficient versus AoA Fig. by Brian Budzinski AAE 450 Spring 2008 Aerothermal 30 ASSUMPTIONS: Initial Horizontal Launch Configuration Final Vertical Configuration Newtonian Model Delta Wing

Drag Coefficient versus Lift Coefficient Fig. by Brian Budzinski AAE 450 Spring 2008 Aerothermal 31 ASSUMPTIONS: Initial Horizontal Launch Configuration Final Vertical Configuration Newtonian Model Delta Wing Once the lift and drag coefficients are determined, the lift versus drag curve can be created.

Side View Fig. by Kyle Donohue Launch vehicle with a pair of fins. Beneficial for: Stability Control Ground Launch Aircraft Launch Balloon Launch Fins were not implemented because D&C was able to successfully control the launch vehicle without them. AAE 450 Spring 2008 Aerothermal 32

Wing Analysis Divide the wing up into two sections: leading edge and lower surface. These two are chosen because they are the two portions exposed to the relative wind once given an angle of attack. AAE 450 Spring 2008 Aerothermal 33

Wing Analysis Continued Lower Surface Eqns. A similar analysis can be done for a pair of fins. AAE 450 Spring 2008 Aerothermal 34

References  Ashley, Holt, Engineering Analysis of Flight Vehicles, Dover Publications Inc., New York, 1974, pp  Anderson, John D., Fundamentals of Aerodynamics, Mcgraw-Hill Higher Education, 2001  Professor Colicott, in reference to linearized theory applications AAE 450 Spring 2008 Aerothermal 35

References  Barrowman, James and Barrowman, Judith, "The Theoretical Prediction of the Center of Pressure" A NARAM 8, August 18,  Klawans, B. and Baughards, J. "The Vanguard Satellite Launching Vehicle - an engineering summary" Report No , April 1960  Morrisette, E. L., Romeo D. J., “Aerodynamic Characteristics of a Family of Multistage Vehicles at a Mach Number of 6.0”, NASA TN D-2853, June 1965  Professor Williams, concerning the use of pressure coefficients to determine aerodynamic forces  The entire Aerothermodynamics group for their invaluable help and support

 Anderson Jr., John D., “Hypersonic and High-Temperature Gas Dynamics”, 2 nd ed., AIAA, Reston, VA,  Schneider, Steven P., “Methods for Analysis of Preliminary Spacecraft Designs”, AAE450, Spacecraft Design, Purdue University  Schneider, Steven P., personal conversation   pdf pdf  pdf pdf References

 Wade, M., “Vanguard”, [  Tsohas, J., “AAE 450 Spacecraft Design Spring 2008: Guest Lecture Space Launch Vehicle Design”, 2008  “The Vanguard Report”, The Martin Company, Engineering Report No , April AAE 450 Spring 2008 Aerothermal

AAE 450 Spring 2008 Aerothermal 39 References  Hankey, Wilbur L., Re-Entry Aerodynamics, AIAA, Washington D.C., 1988, pp  Rhode, M.N., Engelund, W.C., and Mendenhall, M.R., “Experimental Aerodynamic Characteristics of the Pegasus Air-Launched Booster and Comparisons with Predicted and Flight Results”, AIAA Paper , June  Anderson, John D., Fundamentals of Aerodynamics, Mcgraw-Hill Higher Education, 2001  Ashley, Holt, Engineering Analysis of Flight Vehicles, Dover Publications Inc., New York, 1974, pp  The Martin Company, “The Vanguard Satellite Launching Vehicle”, Engineering Report No , April 1960.