Very Low Drag Aerospike Projectile

Abstract

A projectile is provided for firing from a launcher, including an ogive nose; a cylindrical midsection joined to the nose; and a base curvature shaped as a modified aerospike nozzle. The aerospike base is created using a modified method of characteristics nozzle design process. The aerospike base allows for the efficient expansion of air behind the projectile to recover base pressure and reduce the overall drag of the projectile.

Description

CROSS REFERENCE TO RELATED APPLICATION

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STATEMENT OF GOVERNMENT INTEREST

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BACKGROUND

The invention relates generally to a projectile having a base, or rear, section designed as a modified inverted short bell nozzle commonly referred to as aerospike design.

SUMMARY

A projectile with an aerospace base design, such that a projectile is provided for firing from a launcher, including an ogive nose; a cylindrical midsection joined to the nose; and concave curvature base with the shape of a modified inverted short bell nozzle.

BRIEF DESCRIPTION OF THE DRAWINGS

These and various other features and aspects of various exemplary embodiments will be readily understood with reference to the following detailed description taken in conjunction with the accompanying drawings, in which like or similar numbers are used throughout, and in which:

FIG. 1 is an elevation view of a comparative projectiles.

FIG. 2 is an isometric view of a comparative projectiles;

DETAILED DESCRIPTION

In the following detailed description of exemplary embodiments of the invention, reference is made to the accompanying drawings that form a part hereof, and in which is shown by way of illustration specific exemplary embodiments in which the invention may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention. Other embodiments may be utilized, and logical, mechanical, and other changes may be made without departing from the spirit or scope of the present invention. The following detailed description is, therefore, not to be taken in a limiting sense, and the scope of the present invention is defined only by the appended claims.

The shape of a projectile is critical in determining how it flies. The flow of air around the base of the projectile is the most critical in determining the overall drag on the projectile. Because of the lack of accurate theoretical models of this flow, the base is one of the least studied and innovated parts of the projectile. A new base design based on a modified inverted rocket nozzle design method commonly called the short bell nozzle design based upon the method of characteristics is proposed to improve on projectile performance.

The aerodynamic drag force on a supersonic projectile can be divided into three components; wave, friction, and base drag. The wave drag is due to the oblique shockwave that is created in front of the projectile. This component of drag is relatively well understood and can be evaluated with simple shock-expansion theory, computational fluid dynamics (CFD), or wind tunnel testing. With these multiple methods of design, the shape of the nose of a projectile (the ogive) is well designed.

The friction drag is caused by viscosity in the air and is well understood with modern boundary layer theory. This theory dictates the smooth skin of the projectile and competes with stability considerations to determine the overall length of the projectile.

Base drag can be summed up by the d'Alembert's paradox. In a perfect inviscid fluid, a projectile should have no drag due to the ‘recovery’ of pressure on the back side of the projectile perfectly balancing the pressure on the front of the projectile. Real projectiles only partially recover the base pressure and the difference between the front pressure and the back pressure is called base drag.

Although extensive empirical models have been proposed to calculate base drag, no theoretical model exists that explain the phenomena. See D. R. Chapman: “An Analysis of Base Pressure at Supersonic Velocities and Comparison with Experiment”, NACA Report 1051, 1951 (available at https://digital.library.unt.edu/ark://167531/metadc65505/m2/1/high_res_d/19930090963.pdf). See W. K. Lockman: “Free-Flight Base Pressure and Heating Measurements on Sharp and Blunt Cones in a Shock Tunnel”, AIAA Journal, October 1967. See B. M. Bulmer: “Study of Base Pressure in Laminar Hypersonic Flow, Re-entry Flight Measurements”, AIAA Journal, October 1975.

The method of characteristics is a mathematical method for the solution of hyperbolic partial differential equations (PDE). The flow of air can be modeled using the Euler equation which for supersonic flow is a hyperbolic PDE. A common use of the method of characteristics with the Euler equation is the design of supersonic nozzles to efficiently expand the exhaust gasses out of a rocket motor. It is often desirable to have the shortest nozzle possible to expand the gasses from approximately Mach 1 at the throat of the rocket motor to the design exit Mach number of approximately Mach 3. The resulting nozzle design is called the short bell nozzle or minimum length nozzle design.

An aerospike rocket nozzle is an inverted (inside-out) short bell nozzle where the nozzle curvature is designed and then inflected about the inlet wall axis. The exhaust gasses exit from a ring around the edge of spike and expand over the surface. Due to the effect of compressible gasses called choked flow, the gasses exit again at approximately Mach 1 and are expanded to approximately Mach 3.

FIG. 1 and FIG. 2 shows a graphical view of a projectile with an exemplary aerospike base. The short bell nozzle design method was modified to allow for inlet Mach numbers higher than 1 to match the Mach number that commonly is seen entering the base flow section of a projectile. For this embodiment, the Mach number entering the base was taken as Mach 2 and the exit was set at Mach 3. The aerospike base isentropically (efficiently) expands the flow around the base to recover as much pressure as possible between the inlet and exit Mach numbers.

The curvature of the aerospike base can be further modified to account for the viscous boundary layer. This technique is common in the design of airfoils and slightly adjusts the outline of the airfoil to account for the viscous sub-layer of flow as a boundary wall.

These exemplary embodiments employ the exemplary method to design projectile bases so that the flow does not separate into a recirculation zone behind the projectile but is carefully compressed after flow around the edge of the base. The increase in base pressure reduces the base drag and therefore the overall drag of the projectile.

This projectile design could potentially be used in every sized projectile to reduce drag and increase accuracy from small arms for civilian or military use to large caliber artillery and naval guns.

The aerospike base has the additional benefit of streamlining the projectile for low Mach number flow and reducing the base drag for this case as well. The projectile with the aerospike base is improved over all Mach numbers as the projectile is slowed from the initial velocity until impact.

While certain features of the embodiments of the invention have been illustrated as described herein, many modifications, substitutions, changes and equivalents will now occur to those skilled in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the embodiments.

Claims

1. A projectile for firing from a launcher, said projectile comprising:

a fore nose;

a cylindrical midsection joined to said nose; and

a base curvature shaped as a modified aerospike nozzle.

2. The projectile according to claim 1, wherein said nose is an ogive.

3. The projectile according to claim 1, wherein the projectile contains explosives and fuse.

4. The projectile according to claim 1, wherein the projectile is spin stabilized by launch from a rifled launcher.

5. The projectile according to claim 1, wherein the projectile material is selected from the group consisting of copper or copper alloy-jacketed lead, tungsten, tantalum, alloys thereof and composites thereof.

6. The projectile according to claim 1, wherein said nose is a hollow point.

7. The projectile according to claim 1, wherein the projectile is launched in a sabot configuration.

8. The projectile according to claim 1, wherein the flat end of said base is filled with energetic material to illuminate the trajectory of the projectile (tracer).

9. The projectile according to claim 1, wherein the projectile is mounted into a bullet case.

10. The projectile according to claim 1, wherein the base curvature is approximated as an aerospike by a polynomial, exponential, inverse power series, or trigonometric mathematical models.

11. The projectile according to claim 1, wherein the base curvature is corrected from the modified short bell nozzle curvature by application of boundary layer theory to offset the curvature by the thickness of the viscous boundary layer created by the interaction of the air with the curvature.