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Project RAND Publication: RA-15022 , , ,-.. ,'. --. - ~.-~~ UNCLASSIFIED (rA) AERODYNAMICS, GAS DYNAMICS AND HEAT TRANSFER PROBLEMS OF A SATELLITE ROCKET RA-15022 February 1, 1947 UNCLASSI FI ED DOUGLAS AIRCRAFT COMPANY, INC. == DECLASSIFIED lAW E012958 BY EO Review Team DATE &' - ) r; --- :J-cJl r} This document contains information affecting the national defense of the United States within the meaning of the Espionage Act, SO U.S.C., 31 and 32, as amended. Its transmission or the revelation of its contents in any manner to an unauthorized person is prohibited by law. SECRET TABLE OF CONTENTS LIST OF FIGURES ...... , ......................................................... v SUMMARy .........................................................................vii LIST OF SyMBOLS ............................................................... ix I. AERODYNAMICS .............................................................. I A. Drag ....................................................................... l 1. The Drag Forces Exerted on a Supersonic Rocket ......................... 1 2. Approximations Used in the Drag Analysis ............................... 4 3. Methods Employed in Evaluating the Drag ................................ 6 4. The Optimum Shape for a Satellite Rocket ......... , ..................... 8 5. Rarefied Gas Dynamics (Superaerodynamics) ............................. 20 B. Aerodynamics of Stability and Control. .. , ..............•.... : ............. 20 L Control Manent ..................................... '............ , ...... 21 2. Body Moment ........................................................... 23 3. Tail Moment ............................................................ 25 4. Control ............................................................... 27 5. Damping Moment ........................................................ 28 6. Rolling Moment ........................................................ 29 7. Stability of the Second Stage ......................................... 29 I L GAS DyNAMICS .............................................................30 A. Rocket Motor Gas Dynamics and Design ...................................... 30 B. Lift Forces on a Flat Plate at High Mach Numbers for Use in Winged Rocket Calculations ........................................ 42 I I I. HEAT TRANSFER ...........................................................46 A. Skin Temperatures During Ascent of the Satellite Rocket and Descent of the Satellite Body .......................................... 46 B. Temperature of the Satellite Body During Its Orbital Motion ............... 53 1. The Temperature of the Earth Side of the Satellite .................... 53 2. The Temperature of the Space Side of the Satellite .................... 54 APPENDIX. AERODYNAMIC FORCES ON A CONE AT VERY HIGH MACH NUMBERS............... ............................... 57 RE FERENCES ...................................................................... 59 *Initlal External Distribution Lists ................................................ 62 ·This initial external distribution list includes the distrihution of all related technical re­ ports on the satellite vehicle iii SECRET LIST OF FIGURES Figure L Schematic Diagram of Rocket .................................................... 2 2. Correction to the Subsonic Friction Drag-Coefficient to Obtain Total Subsonic Drag Coefficient. After GOthert .................................... 5 3. Friction Drag Coefficient of a Flat Plate as a FWlction of Reynolds Number and Mach Number .. ; .................................................... 9 4. Total Friction and Wave Drag Coefficient of ~y as a FWlction of Fineness Ratio and Relative Length of the Diverging Section .......................... 12 5. Propellant-Gross Weight Parameter v as a Function of Fineness Ratio and ~lative Length of Diverging Section .................................... 13 6. Gross Weight of the Three Stage Hydrazine-Oxygen Satellite Rocket as a Function of Fineness Ratio and Relative Length of Diverging Section ......... 14 7. Drag Coefficient for the First Stage of the Satellite Rocket .................. 16 7a. Drag Coefficient for the Second Stage of the Satellite Rocket .................. 16 KC 8. The Drag Factor D as a FWlction of Height and Mach Number for the First Stage of the Three Stage Hydrazine-Oxygen Satellite Rocket .................. 17 8a. The Drag Factor KCD as a FWlction of Height and Mach Number for the Second Stage of the Three Stage Hydrazine-Oxygen Satellite Rocket .................. 17 9. Variation with Time and Mach Number of the Trajectory Drag Term D/'rt for the Three Stage Hydrazine~ygen Satellite Rocket ....................... 18 10. Diagram of the Three Stage Hydrazine-Oxygen Satellite Rocket .................. 19 11. Moment Stope for Ekdy and Control Motors of the Three Stage Hydrazine- Oxygen Satellite Rocket During the First Stage .............................. 22 12. Lift Slope of Various Cone-Shaped Ekdies ...................................... 24 13. Lift Slope for a Delta Wing ................................................... 25 14. Angle of Attack and Motor Deflection for the Three Stage Hydrazine-Oxygen Satellite Rocket During the First Burning Period ....................... , .... 29 15. Schematic Diagram of Rocket Motor ............................................. 31 16. Variation of Several Rocket Motor Parameters with Combustion Chamber Pressure During the First Burning Period of a Hydrazine-Oxygen Propellant System ........................................................... 36 17. Variation of Several Rocket Motor Parameters with C~ustion Chamber Pressure During the First Burning Period of a Hydrazine-Fluorine Propellant System ........................................................ ' ... 38 v SECRET Figure 18. Variation with Canbustion Chamber Pressure of Spe~ific Impulse and Throat Area Factor: During Second Burning Period of a Hydrazine- Oxygen Propellant System .................................................... 40 19. Variation with Combustion Chamber Pressure of Specific Impuls~ and 1hroat Area Factor During Second Burning Period for a Hydrazine- Fluorine Propellant System .................................................. 40 20. Variation of Specific Impulse with Height ,During the First Stage Burning Period for the Hydrazine~ygen Propellant System .................. 41 21. Schematic Diagram of Flat Plate Inclined at an Angle to Supersonic Flow ....... 42 22. Lift Coefficient of a Flat Plate as a Function of Angl~ of Attack and Mach Number ................................................................. 45 23. Variation with Temperature of the Specific Heat of Stabilized 18-8 type Stainless Steel ............................................................. 47 24. Time Variation of the Skin Temperature Corresponding to the Optimum Trajectory of the Three Stage Hydrazine~Oxygen Satellite Rocket ............. 50 25. Temperature of the Earth and Space Sides of the Satellite ..................... 55 26. Schematic Diagram of Body of ~volution Inclined at an Angle to the Flow ...... 57 VI SECRET SUMMARY. Consideration is given to the problems of a satellite rocket which involve the motion of high speed gases. These include the flow over the external surface of the rocket (drag), the flow through the rocket motor, and heat transferred to the skin of the rocket by forced convection. The skin temperatures of the satellite during its orbital motion, which depend entirely upon thermal radiation processes, are also evaluated. The discussions, although kept as general as possible, revolve around a three stage rocket employing hydrazine-liquid oxygen propellants and designed to place a 500 pound instrumentation payload on a stable orbit 350 miles above the earth. For the analyses of various features of the satellite rocket which are not covered In this report, see refs. 7, 8, 12, 18, 28 and 31. The analysis of the drag of a satellite rocket may be considerably simplified if certain small effects are neglected, and since this allows the drag to be evaluated with an error not exceeding 10 per cent, which is sufficiently accurate for present purposes, the drag is calculated on this basis. Using these drag results, an optimum shape for the rocket is determined from the combined considerations of drag, flight mechanics, and structural weight such that the rocket has a minimum gross weight. It is found that the optimum body shape is defined by the skeleton parameter values dl.£o = 0.20 and i.lt-o = 0.80, where d is the maximum diameter, La is the total length, and J is the length of the diverging (nose) section. However, since this result became available only during the latter part of the investigation, it was necessary to proceed on the basis of a design which resulted from an earlier study and which had the skele­ ton parameter values dl.£a 0.218 and~(~o = 0.643 (see Fig. 10). The drag calcula­ tions are carried out for this body shape. To provide aerodynamic stability the first stage of the rocket is equipped with four fins having a delta planform and a modified double wedge profile. In accordance with a required lift program for the rocket, the corresponding angle of attack program is calculated, and from this the deflection of the control motor necessary to produce the required angle of attack is determined (Fig. 14). From a consideration of the rolling moments and the damping moments in pitch and yaw it is concluded that the damping moments are negligible and that the rolling ~ents may be adequately controlled
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