Nozzle with Widely-Spaced Thrust Chambers, Engine Including the Nozzle, and Vehicle Including the Engine

Abstract

A nozzle for a vehicle is disclosed. The nozzle includes a plurality of thrust chambers spaced relative to one another. Each thrust chamber has a throat and a nozzle portion extending aft of the throat. The nozzle portion has an exit dimension D.sub.exit at an aft end. Each thrust chamber is spaced away from each adjacent thrust chamber by a respective spacing distance D.sub.space, such that D.sub.spaceM*D.sub.exit, where M1.

Claims

1. A nozzle, comprising: a plurality of thrust chambers spaced relative to one another, each thrust chamber including: a throat; and a nozzle portion extending aft of the throat, the nozzle portion having an exit dimension D.sub.exit at an aft end thereof; wherein each thrust chamber is spaced away from each adjacent thrust chamber by a respective spacing distance D.sub.space, such that D.sub.spaceM*D.sub.exit, where M1.

2. The nozzle of claim 1, wherein the thrust chambers are circumferentially spaced relative to one another.

3. The nozzle of claim 2, wherein each respective spacing distance D.sub.space is an arc length.

4. The nozzle of claim 2, wherein each respective spacing distance D.sub.space is a chord length.

5. The nozzle of claim 2, wherein the thrust chambers are uniformly spaced relative to one another.

6. The nozzle of claim 2, wherein the thrust chambers are non-uniformly spaced relative to one another.

7. The nozzle of claim 1, wherein the exit dimension D.sub.exit is a diameter.

8. The nozzle of claim 1, wherein the nozzle is an aerospike nozzle.

9. The nozzle of claim 1, wherein the nozzle is an annular aerospike nozzle.

10. The nozzle of claim 1, further comprising a centerbody; wherein the thrust chambers are spaced around the centerbody.

11. The nozzle of claim 10, wherein the centerbody includes a centerbody base; and wherein an outer surface defined by the centerbody base has a semi-spherical shape.

12. The nozzle of claim 10, wherein the centerbody includes a centerbody base; and wherein an outer surface defined by the centerbody base has a frustoconical shape.

13. The nozzle of claim 10, wherein the centerbody includes a centerbody base; and wherein an outer surface defined by the centerbody base has a frustoconical shape.

14. The nozzle of claim 10, wherein the centerbody includes a centerbody base; and wherein an outer surface defined by the centerbody base has a multi-conic shape.

15. The nozzle of claim 10, wherein the centerbody includes a centerbody base; and wherein an outer surface defined by the centerbody base has an ellipsoidal shape.

16. An engine, comprising: a plurality of thrust chambers spaced relative to one another, each thrust chamber including: a high pressure chamber that generates a gas for thrust; a nozzle portion that extends aft of the high pressure chamber and exhausts the gas generated by the high pressure chamber; the nozzle portion having an exit dimension D.sub.exit at an aft end thereof; and a throat connecting the high pressure chamber to the nozzle portion; wherein each thrust chamber is spaced away from each adjacent thrust chamber by a respective spacing distance D.sub.space, such that D.sub.spaceM*D.sub.exit, where M1.

17. The engine of claim 16, wherein the thrust chambers are circumferentially spaced relative to one another.

18. The engine of claim 17, wherein each respective spacing distance D.sub.space is an arc length.

19. The engine of claim 17, wherein each respective spacing distance D.sub.space is a chord length.

20. The engine of claim 17, wherein the thrust chambers are uniformly spaced relative to one another.

21. The engine of claim 17, wherein the thrust chambers are non-uniformly spaced relative to one another.

22. The engine of claim 16, wherein the exit dimension D.sub.exit is a diameter.

23. The engine of claim 16, further comprising a centerbody; wherein the thrust chambers are spaced around the centerbody.

24. The engine of claim 23, wherein the centerbody includes a centerbody base; and wherein an outer surface defined by the centerbody base has a semi-spherical shape.

25. The engine of claim 23, wherein the centerbody includes a centerbody base; and wherein an outer surface defined by the centerbody base has a frustoconical shape.

26. The engine of claim 23, wherein the centerbody includes a centerbody base; and wherein an outer surface defined by the centerbody base has a frustoconical shape.

27. The engine of claim 23, wherein the centerbody includes a centerbody base; and wherein an outer surface defined by the centerbody base has a multi-conic shape.

28. The engine of claim 23, wherein the centerbody includes a centerbody base; and wherein an outer surface defined by the centerbody base has an ellipsoidal shape.

29. A vehicle, comprising: an engine including a plurality of thrust chambers spaced relative to one another, each thrust chamber including: a high pressure chamber that generates a gas for thrust, a nozzle portion that extends aft of the high pressure chamber and exhausts the gas generated by the high pressure chamber, the nozzle portion having an exit dimension D.sub.exit at an aft end, and a throat connecting the high pressure chamber to the nozzle portion; wherein each thrust chamber is spaced away from each adjacent thrust chamber by a respective spacing distance D.sub.space, such that D.sub.spaceM*D.sub.exit, where M1.

30. The vehicle of claim 29, wherein the engine further includes a centerbody; wherein the thrust chambers are spaced around the centerbody.

31. The vehicle of claim 30, wherein the centerbody includes a centerbody base; and wherein an outer surface defined by the centerbody base has a semi-spherical shape.

32. The vehicle of claim 30, wherein the centerbody includes a centerbody base; and wherein an outer surface defined by the centerbody base has a frustoconical shape.

33. The vehicle of claim 30, wherein the centerbody includes a centerbody base; and wherein an outer surface defined by the centerbody base has a frustoconical shape.

34. The vehicle of claim 30, wherein the centerbody includes a centerbody base; and wherein an outer surface defined by the centerbody base has a multi-conic shape.

35. The vehicle of claim 30, wherein the centerbody includes a centerbody base; and wherein an outer surface defined by the centerbody base has an ellipsoidal shape.

36. The vehicle of claim 30, further comprising a thruster mount positioned at an aft end of a main body of the vehicle, the thruster mount having a plurality of openings extending therethrough in a direction parallel to a centerline of the main body of the vehicle, wherein each opening is configured to receive one of the thrust chambers.

37. The vehicle of claim 36, wherein the centerbody is non-axisymmetric relative to the centerline of the main body of the vehicle.

38. The vehicle of claim 36, wherein the centerbody and the thruster mount define at least a portion of a heat shield.

39. The vehicle of claim 29, wherein the thrust chambers are circumferentially spaced relative to one another.

40. The vehicle of claim 39, wherein each respective spacing distance D.sub.space is an arc length.

41. The vehicle of claim 39, wherein each respective spacing distance D.sub.space is a chord length.

42. The vehicle of claim 39, wherein the thrust chambers are uniformly spaced relative to one another.

43. The vehicle of claim 39, wherein the thrust chambers are non-uniformly spaced relative to one another.

44. The vehicle of claim 29, wherein the exit dimension D.sub.exit is a diameter.

45. The vehicle of claim 29, wherein the vehicle is an upper stage rocket.

46. The vehicle of claim 29, wherein the vehicle is an atmospheric re-entry vehicle.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0054] FIG. 1 schematically illustrates a prior art aerospike engine and nozzle.

[0055] FIG. 2 schematically illustrates a portion of the prior art aerospike engine and nozzle of FIG. 1.

[0056] FIG. 3 schematically illustrates a prior art vehicle (i.e., the re-entry vehicle of the Apollo spacecraft) with an axisymmetric heat shield in a zero angle of attack orientation.

[0057] FIG. 4 schematically illustrates the prior art vehicle of FIG. 3 in a non-zero angle of attack orientation.

[0058] FIG. 5 is an elevation view of a two-stage rocket system including an upper stage rocket with the present non-axisymmetric heat shield.

[0059] FIG. 6 is an exploded elevation view of the two-stage rocket system of FIG. 5.

[0060] FIG. 7 is a perspective view of the upper stage rocket of FIG. 5.

[0061] FIG. 8 is an elevation view of the upper stage rocket of FIG. 5 in a zero angle of attack orientation.

[0062] FIG. 9 is an elevation view of the upper stage rocket of FIG. 5 in a non-zero angle of attack orientation.

[0063] FIG. 10 is an elevation view of the aft end of the upper stage rocket of FIG. 5.

[0064] FIG. 11 schematically illustrates a portion of the aerospike engine and nozzle of the upper stage rocket of FIG. 5.

[0065] FIG. 12 is a plan view of the aft end of the upper stage rocket of FIG. 5.

[0066] FIG. 13 is an enlarged portion of the plan view in FIG. 12.

DETAILED DESCRIPTION

[0067] Referring to FIGS. 6-9, the present disclosure describes a non-axisymmetric heat shield 10, a nozzle 12 defined by at least a portion of the heat shield 10, an engine 14 including the nozzle 12, and a vehicle 16 including the engine 14.

[0068] The vehicle 16 is a rocket (e.g., a multi-stage rocket, a single-stage-to-orbit (SSTO) rocket, an upper stage rocket, a booster rocket, etc.), a missile, a spacecraft, an aircraft, or another vehicle designed for travel (e.g., flight) up to at least supersonic speeds (e.g., supersonic speeds, hypersonic speeds, re-entry speeds, etc.) in atmospheric, sub-orbital, orbital, extraterrestrial, and/or outer space environments. Referring to FIG. 5, in the illustrated embodiment, the vehicle 16 is a reusable second stage rocket of a two-stage rocket system 18. Referring to FIGS. 6 and 7, the vehicle 16 extends between a forward end 20 and an opposing aft end 22. The vehicle 16 includes a payload housing 24 proximate the forward end 20, and an engine 14 proximate the aft end 22. The aft end 22 defines the windward side of the vehicle 16 during atmospheric re-entry, for example.

[0069] Referring to FIGS. 8 and 9, the vehicle 16 includes a main body portion 26 defining the forward end 20 of the vehicle 16, and a base portion 28 defining the aft end 22 of the vehicle 16. The main body portion 26 is shaped such that the outer surface thereof is at least substantially axisymmetric relative to a main body centerline 30 (e.g., a linear centerline perpendicular to the tangent of the forwardmost point of the main body portion 26) extending in a direction between a forward end of the main body portion 26 (i.e., the forward end 20 of the vehicle 16) and an aft end of the main body portion 26. The base portion 28 includes a heat shield 10 defining a heat shield outer surface, which is on the windward side of the vehicle 16 during atmospheric re-entry, for example. The heat shield 10 is configured such that heat shield outer surface is non-axisymmetric relative to the main body centerline 30, and is non-axisymmetric relative to a heat shield centerline 32 (e.g., a linear centerline perpendicular to the tangent of the aftmost point of the heat shield 10) extending in a direction between a forward end of the heat shield 10 and an aft end of the heat shield 10 (e.g., the aft end 22 of the vehicle 16). The main body portion 26 and the heat shield 10 of the vehicle 16 are therefore configured such that the heat shield centerline 32 is offset relative to the main body centerline 30 by an angle . The angle is typically within the range of 1 to 10. In the illustrated embodiment, the angle is 4. In other embodiments, the angle is approximately 1, 2, 3, 5, 6, 7, 8, 9, or 10, for example. In some embodiments, including the illustrated embodiment, at least one portion of the heat shield outer surface is at least substantially axisymmetric relative to the heat shield centerline 32, as will be discussed in more detail below.

[0070] Referring still to FIGS. 8 and 9, the main body portion 26 of the vehicle 16 includes a nose 34 and a sidewall 36 extending aft of the nose 34. In the illustrated embodiment, the nose 34 includes a rigid wall with a rounded cone shape, and the sidewall 36 includes a rigid wall with a frustoconical shape. The sidewall 36 at least partially defines a payload housing 24 in which a payload (e.g., cargo, munitions, etc.) is stored during transport by the vehicle 16. The sidewall 36 further surrounds one or more internal components of the vehicle 16, such as one or more components of the engine 14 and/or one or more components of a system for actively cooling the heat shield 10 (e.g., a tank, a pump, a turbine, etc.). The sidewall 36 is disposed at an angle (hereinafter the sidewall angle ) relative to planes 38, 39 parallel to the main body centerline 30. In the illustrated embodiment, the vehicle 16 is designed with a relatively shallow sidewall angle (i.e., the sidewall angle has a low high magnitude) in comparison to the prior art vehicle 216 of FIGS. 3 and 4. The sidewall angle is within the range of 0 to 90. In some embodiments, the sidewall angle is within the range of 5 to 15. In the illustrated embodiment, for example, the sidewall angle is 7. The magnitude of the sidewall angle is inversely related to the volume of the vehicle 16, and thus the shallow sidewall angle advantageously allows the vehicle 16, and in particular the payload housing 24, to have a larger volume than that of the prior art vehicle 216.

[0071] Referring to FIGS. 8-10, the base portion 28 of the vehicle 16 includes one or more components that define the heat shield 10 and the outer surface thereof (i.e., the heat shield outer surface). In the illustrated embodiment, the base portion 28 includes a centerbody 40 and a thruster mount 42, which each define portions of the heat shield 10 and the heat shield outer surface. The centerbody 40 is in the form of a truncated toroidal aerospike. The centerbody 40 includes a centerbody sidewall 44 and a centerbody base 46 that collectively form a blunt body. The centerbody sidewall 44 includes a rigid wall with a truncated and oblique cone shape. The centerbody base 46 includes a rigid wall with a semi-spherical shape. In other embodiments, the centerbody base 46 additionally or alternatively includes one or more rigid walls having a frustoconical shape, a multi-conic shape (e.g., bi-conic, tri-conic, etc.), an ellipsoidal shape, and/or another blunt shape. Referring to FIGS. 10 and 11, the thruster mount 42 includes a rigid wall extending annularly about the main body centerline 30, and positioned proximate the aft end of the main body portion 26 of the vehicle 16. The thruster mount 42 includes circumferentially-spaced openings 43 extending therethrough in a direction parallel to the main body centerline 30. Each opening 43 in the thruster mount 42 is configured to receive a thrust chamber 48 of the engine 14, which will be described in more detail below.

[0072] The heat shield outer surface defined by respective outer surfaces of the centerbody sidewall 44, the centerbody base 46, and the thruster mount 42 is non-axisymmetric relative to the main body centerline 30. In some embodiments, at least one portion of the heat shield outer surface is at least substantially axisymmetric relative to the heat shield centerline 32. In the illustrated embodiment, for example, the outer surface defined by the centerbody base 46 has a semi-spherical shape and is axisymmetric relative to the heat shield centerline 32.

[0073] In some embodiments, one or more components of the heat shield 10, including the centerbody sidewall 44, the centerbody base 46, and/or the thruster mount 42 are actively cooled using the heat shielding system disclosed in the commonly-assigned U.S. Provisional Patent Application No. 62/942,886, filed Dec. 3, 2019, and in the International Patent Application No. PCT/US2020/48226 filed Aug. 27, 2020 filed Aug. 27, 2020 and claiming priority to U.S. Provisional Patent Application No. 62/942,886, the contents of which are hereby incorporated by reference in their entirety. In some embodiments, at least a portion of the sidewall 36 of the main body portion 26 of the vehicle 16 is actively cooled in a same or similar manner.

[0074] Referring to FIGS. 10 and 11, the engine 14 includes at least one high pressure chamber 50 (e.g., a combustion chamber) and a nozzle 12.

[0075] The high pressure chamber 50 generates gas that is exhausted through the nozzle 12. The high pressure chamber 50 is in the form of an annular ring, a segmented ring, individual thrust chambers, or any other configuration providing supersonic flow to the nozzle 12.

[0076] The nozzle 12 is an aerospike nozzle having at least one initial nozzle portion 52 through which exhaust gas initially exits at least one high pressure chamber 50, and a secondary nozzle portion 53 (FIG. 11) downstream relative to the initial nozzle portion 52. The initial nozzle portion 52 includes at least one throat 54 and is typically in the form of a converging-diverging nozzle.

[0077] Referring still to FIGS. 10 and 11, the nozzle 12 is defined by at least a portion of the heat shield 10. In the illustrated embodiment, the secondary nozzle portion 53 (FIG. 11) of the nozzle 12 is defined by the centerbody 40. The centerbody sidewall 44 functions as an expansion surface 55 of the nozzle 12 in addition to its function as a portion of the heat shield 10. The centerbody sidewall 44 is non-axisymmetric relative to the heat shield centerline 32, and thus the nozzle 12 is non-axisymmetric relative to the heat shield centerline 32. As shown in FIG. 10, the initial nozzle portion 52 and the centerbody base 46 are separated by respective first and second distances d.sub.1, d.sub.2 on opposing sides of the vehicle 16. The first and second distances d.sub.1, d.sub.2 differ from one another due to the non-axisymmetric shape of the nozzle 12. This in contrast to the prior art aerospike nozzle 112 shown in FIG. 1, in which the initial nozzle portion 52 and the centerbody base 46 are separated by a same distance d.sub.1 on opposing sides of the vehicle 16.

[0078] The engine 14 and the nozzle 12 can be configured in various different ways. In the illustrated embodiment, the engine 14 has a so-called plug cluster configuration. That is, the engine 14 includes a plurality of discrete high pressure chambers 50 spaced relative to one another and a plurality of discrete initial nozzle portions 52 spaced relative to one another.

[0079] Referring to FIGS. 10 and 11, in the plug cluster configuration of the illustrated embodiment, each initial nozzle portion 52 is disposed relative to a corresponding high pressure chamber 50, and is configured to exhaust gas exiting the respective high pressure chamber 50. Each high pressure chamber 50 and initial nozzle portion 52 pair is referred to hereinafter as a thrust chamber 48. The secondary nozzle portion 53 is downstream relative to the thrust chambers 48.

[0080] Referring to FIG. 11, in the illustrated embodiment, the initial nozzle portion 52 of each thrust chamber 48 is in the form of a converging-diverging nozzle and/or a primary nozzle. In particular, the initial nozzle portion 52 of each thrust chamber 48 includes a throat 54 that defines a transition between an upstream converging section with opposing converging surfaces 70, 72, and a downstream diverging section with opposing diverging surfaces 64, 66. The throat 54 of each thrust chamber 48 extends annularly about an axis 74 of the initial nozzle portion 52. The diverging surfaces 64, 66 define an initial nozzle cavity 25 therebetween. The outer aft end 68 of the initial nozzle portion 52 is defined by the aft end of the wall defining the outer diverging surface 66. A radially inner portion of thruster mount 42 extends between the inner aft end 69 of the initial nozzle portion 52 and the centerbody sidewall 44 of the secondary nozzle portion 53. In other embodiments, the inner aft end 69 of the initial nozzle portion 52 meets the expansion surface 55 and an inflection point is defined therebetween.

[0081] Referring to FIG. 11, in the illustrated embodiment, each thrust chamber 48 is configured such that the axis 74 of the initial nozzle portion 52 is parallel to the main body centerline 30 (see FIG. 10). This is in contrast to the prior art aerospike nozzle 112 in FIGS. 1 and 2, for example, in which the axis 174 is angled (i.e., not parallel) relative to the centerline 116 of the vehicle on which the nozzle 112 is disposed. In other embodiments of the present engine 14 and nozzle 12, each thrust chamber 48 is configured such that the axis 74 of the initial nozzle portion 52 is angled (i.e., not parallel) relative to the main body centerline 30.

[0082] Referring still to FIG. 11, each thrust chamber 48 has an exit dimension D.sub.exit. The exit dimension D.sub.exit is a maximum dimension of the initial nozzle cavity 25 in a direction perpendicular to the axis 74. In the illustrated embodiment, the diverging surfaces 64, 66 of the initial nozzle portion 52 define a circular cross-sectional shape in a plane perpendicular to the axis 74, and thus the exit dimension D.sub.exit corresponds to a diameter of the initial nozzle cavity 25 at the outer aft end 68 thereof. In the illustrated embodiment, the plurality of thrust chambers 48 are identical to one another, and thus the exit dimension D.sub.exit of each thrust chamber 48 has a same magnitude as that of every other thrust chamber 48.

[0083] Referring to FIGS. 12 and 13, in the illustrated embodiment, the thrust chambers 48 are circumferentially spaced relative to the main body centerline 30 such that each discrete thrust chamber 48 is separated from a circumferentially-adjacent thrust chamber 48 by a spacing distance D.sub.space that is greater than or equal to the product of the exit dimension D.sub.exit of the thrust chamber 48 and a multiplication factor M having a magnitude greater than or equal to one (1).

[0084] In the illustrated embodiment, the spacing distance D.sub.space is an arc length extending between the axis 74 of the initial nozzle portion 52 of a first thrust chamber 48 and the axis 74 of the initial nozzle portion 52 of a circumferentially-adjacent thrust chamber 48. In other embodiments, the spacing distance D is a chord length between the axis 74 of the initial nozzle portion 52 of a first thrust chamber 48 and the axis 74 of the initial nozzle portion 52 of a circumferentially-adjacent thrust chamber 48.

[0085] Referring still to FIGS. 12 and 13, in the illustrated embodiment, the multiplication factor M is approximately three (3) and the thrust chambers 48 are spaced uniformly around the centerbody 40 such that the spacing distance D.sub.space between a pair of circumferentially-adjacent thrust chambers 48 has a same magnitude as the respective spacing distances D.sub.space between every other pair of circumferentially-adjacent thrust chambers 48. In other embodiments, the thrust chambers 48 are spaced non-uniformly around the centerbody 40 such that the spacing distance D.sub.space between a pair of circumferentially-adjacent thrust chambers 48 has a different magnitude from the spacing distance D.sub.space between at least one other pair of circumferentially-adjacent thrust chambers 48. In other embodiments, the multiplication factor M has a magnitude greater than or equal to 2, 3, 4, 5, 6, 7, 8, 9, 10, etc. In some embodiments, the multiplication factor M has a magnitude within the range of at least of 1 to 2, 2 to 3, 3 to 4, 4 to 5, 5 to 6, 6 to 7, 7 to 8, 8 to 9, 9 to 10, etc. In some embodiments, the multiplication factor M is an integer. In other embodiments, the multiplication factor M is a non-integer. For example, in such embodiments, the multiplication factor M has a magnitude greater than or equal to 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 3.0, 3.1, etc.

[0086] The magnitude of the multiplication factor M can vary based on one or more cost and/or performance factors, including, for example: a dimension and/or geometry of the engine 14, the nozzle 12, the vehicle 16, and/or a component thereof (e.g., a diameter of the vehicle 16, an exit dimension D.sub.exit of the thrust chamber 48, a desired nozzle expansion ratio, etc.); the total number of thrust chambers 48 included in the engine 14; a mass of the engine 14, the nozzle 12, the vehicle 16, and/or a component thereof; and/or a desired performance characteristic (e.g., thrust-to-weight ratio, thrust coefficient C.sub.F, specific impulse I.sub.sp, characteristic velocity c*, etc.).

[0087] The prior art teaches positioning thrust chambers as close as possible to circumferentially-adjacent thrust chambers, such that D.sub.space=M*D.sub.exit, where M is less than one (1). The conventional thought was that positioning thrust chambers very close to one another (e.g., M<<1) would better approximate the flow field of a non-clustered aerospike configuration and/or a traditional bell nozzle, and would thereby achieve optimal thrust performance and flow separation, and minimize efficiency losses. However, Applicant achieved unexpected results (e.g., improved thrust performance, minimized efficiency loss, etc.) when widely spacing thrust chambers 48 relative to one another such that D.sub.spaceM*D.sub.exit, where M is greater than or equal to one (1). For example, Applicant achieved unexpected results in connection with the illustrated embodiment, in which the thrust chambers 48 are spaced relative to one another such that D.sub.space=M*D.sub.exit, where M is approximately three (3). Applicant discovered that, when the number of thrust chambers 48, the spacing distance D.sub.space, between the thrust chambers 48, and the exit dimension D.sub.exit of the thrust chambers 48 are selected as design variables, the thrust coefficient C.sub.F can be optimized by widely spacing thrust chambers 48 relative to one another such that D.sub.spaceM*D.sub.exit, where M is greater than or equal to one (1). The thrust T of the rocket engine 14 can be defined as

[00001]$T\left(\stackrel{}{m}\right)(c\text{*)}\left(C_F\right)$

where {dot over (m)} is the mass flow rate of propellant, c* is the characteristic velocity of the combustion gasses in the chamber 50 and is a measure of the energy generated by combustion, and C.sub.F is the nozzle thrust coefficient. The thrust coefficient determines the amplification of thrust due to gas expansion in the nozzle 12, and can be defined in terms of nozzle parameters using the equation

[00002]$C_F{}_{C_F}\left[\sqrt{\left(\frac{2{}^2}{-1}\right){\left(\frac{2}{+1}\right)}^{\frac{+1}{-1}}\left(1-{\left(\frac{P_e}{P_o}\right)}^{\frac{-1}{}}\right)}+\left(\frac{P_e}{P_o}-\frac{P_a}{P_o}\right)\frac{A_e}{A_t}\right]$

where .sub.CF is the thrust coefficient efficiency, is the ratio of specific heats of the combustion gas, P.sub.o is the total stagnation pressure in the chamber 50, P.sub.e is the static pressure at the exit of the nozzle, P.sub.a is the ambient static pressure in the surrounding environment, and A.sub.e/A.sub.t is the area ratio between the nozzle exit and the throat. Widely spacing thrust chambers 48 relative to one another can trade a reduction in efficiency .sub.CF in exchange for a more significant increase in area ratio A.sub.e/A.sub.t, resulting in an overall more optimal solution.

[0088] During operation, the vehicle 16 moves through an environment (e.g., the atmosphere, space) at freestream Mach numbers that can approach Mach thirty (30). During operation in vacuum conditions, exhaust plumes from the various thrust chambers 48 of the engine 14 merge to form an aerodynamic spike which traps a positive pressure along the centerbody base 46 of the heat shield 10. This generates additional thrust and improves the overall efficiency of the engine 14 and the vehicle 16. Referring to FIG. 10, during atmospheric flight, a bow shock 56 is formed upstream of the vehicle 16, and temperature on the vehicle side of the bow shock 56 can reach thousands of degrees Kelvin. The bow shock 56 generates significant drag to reduce the velocity of the vehicle 16, and also generates significant aerodynamic heating 58 on the heat shield 10, thereby necessitating cooling and/or other thermal protection for reusability, such as the above-mentioned active cooling system.

[0089] Referring again to FIG. 8, the vehicle 16 may initially re-enter the atmosphere at a so-called zero angle of attack (i.e., =0), in which the vehicle 16 is oriented such that the main body centerline 30 is parallel to the direction of travel 60. In this orientation, the heat shield centerline 32 is offset relative to the direction of travel 60 by an angle equal to the angle at which the heat shield centerline 32 is offset relative to the main body centerline 30. In the zero angle of attack orientation, the center of gravity 62 and the center of pressure 64 of the vehicle 16 are in a plane 66 offset relative to the direction of travel 60. The fact that the centerbody base 46 of the heat shield 10 is axisymmetric about the heat shield centerline 32, which is offset at the angle relative to the main body centerline 30, advantageously causes a net lift force on the vehicle 16 relative to the direction of travel 60, even at the zero angle of attack.

[0090] During operation of the vehicle 16 at a zero angle of attack (FIG. 8), the aerodynamic lift and drag forces on the vehicle 16 will generate pitching moments about the center of gravity 62, and the vehicle 16 will naturally adopt an orientation at which those moments are balanced (i.e., the aerodynamic trim point). This orientation, shown in FIG. 9, increases an angle between the centerbody base 46 and the high enthalpy flow 68 that is moving relative to the vehicle 16 in a direction opposite the direction of travel 60. The non-zero angle of attack orientation (FIG. 9) therefore generates additional lift than the zero angle of attack orientation (FIG. 8). In the non-zero angle of attack (FIG. 9), the plane 66 of the center of gravity 62 and the center of pressure 64 will be parallel relative to the direction of travel 60, and opposing sides of the vehicle 16 will be at different respective angles .sub.1, .sub.2 relative to planes 70, 71 parallel to the direction of travel 60. The heat shield centerline 32 is offset relative to the direction of travel 60 by an angle equal to the sum of: (i) the angle between the centerbody base 46 and the high enthalpy flow 68; and (ii) the angle at which the heat shield centerline 32 is offset relative to the main body centerline 30. The angle of attack should not exceed the sidewall angle . Thus, in the illustrated embodiment, the vehicle 16 should not be flown at an angle of attack that exceeds 7. Maintaining the angle of attack below this threshold prevents the high enthalpy flow 68 from impinging on the sidewall 36 of the vehicle 16, eliminating the need for additional heat shielding (and the accompanying additional mass) on those surfaces the sidewall 36. The center of gravity 62 and the center of pressure 64 of the vehicle 16 can be selected to achieve a particular non-zero angle of attack during atmospheric re-entry.

[0091] The non-axisymmetric nature of the heat shield 10 (e.g., the oblique angle of the centerbody base 46 relative to the main body centerline 30) allows the vehicle 16 to achieve a higher lift-to-drag ratio within a certain angle of attack constraint. That is, the vehicle 16 can achieve a certain target lift-to-drag ratio with a lower range of angles of attack . This allows a shallower sidewall angle while still preventing hypersonic flow 68 from impinging on the sidewall 36 of the vehicle 16. This in turn allows for increased volume available for other system uses (e.g., propellant, payload, etc.).

[0092] To minimize the additional mass of the heat shield 10 and aerodynamic controls, the vehicle 16 exposes only the relatively small heat shield 10 of the vehicle 16 to the high enthalpy flow 68, while also generating a sufficient lift-to-drag ratio for precise maneuvering and landing. By adjusting both the angle of the centerbody base 46 relative to the main body centerline 30, and the location of the center of gravity 62, the design of the vehicle 16 can be adjusted to produce different amounts of lift while maintaining the same trimmed angle of attack . This adds freedom in the design space which is not available for traditional axisymmetric vehicle shapes. The combined surfaces of the heat shield 10 and nozzle 12 are advantageous in that they result in a lower mass penalty for the heat shield 10 in a reusable upper stage application.

[0093] While several embodiments have been disclosed, it will be apparent to those having ordinary skill in the art that aspects of the present invention include many more embodiments. Accordingly, aspects of the present invention are not to be restricted except in light of the attached claims and their equivalents. It will also be apparent to those of ordinary skill in the art that variations and modifications can be made without departing from the true scope of the present disclosure. For example, in some instances, one or more features disclosed in connection with one embodiment can be used alone or in combination with one or more features of one or more other embodiments.