CH623407A5 - Tubular projectile capable of being fired at a supersonic speed - Google Patents

Description

io The invention is based in part on the observation that, for a tubular projectile to behave satisfactorily, it must be arranged so that supersonic flow conditions are established in its central passage immediately after the launch of so as to obtain a low drag during the first part of the flight path. The configuration of the projectile according to the invention is, moreover, such that, when the speed drops to a certain number of flight Machs, choked flow conditions are suddenly established in the central passage. This constricted flow creates a normal shock wave in front of the projectile which causes a relatively rapid deceleration limiting the range of the projectile.

Preferably, the ratio of the section of the passage in the narrowed region A, to the section of the passage at the anterior inlet end A; is greater than that defined by the equation:

The present invention relates to a tubular projectile capable of being fired at supersonic speed by a muzzle.

Tubular projectiles in accordance with the preamble of claim 1 are usually launched at supersonic speeds by a cannon or the like. They must follow a desired trajectory from a launch site or vehicle to a target or a target area. The desired trajectory is often difficult to obtain. This may be due to stringent requirements imposed on the trajectory, for example a trajectory to

M =

Ai / min

Y 4- 1 \ y + l / 2 (T-l)

H

30 or:

M = Mach number at launch (for M> 1.0);

y = ratio of specific heats at constant pressure and constant volume, respectively.

To allow a normal shock wave to pass through the throttle region in order to establish supersonic flow in the passage and to provide relatively low drag after launch, the AJA- ratio is also less than 1.0 of so that when the speed of the projectile decreases to a predetermined flight Mach number, the shock wave is expelled from the passage to establish strangulated flow conditions therein and to provide a relatively high drag which limits the range of the projectile.

As soon as the ratio A ^ A; was chosen so as to ensure a supersonic flow in the central passage of the projectile at the intended launch speed, it is possible to predict the speed (or 45 the Mach number) for which conditions of choked flow are established in the passage as the speed of the projectile decreases during the flight. The equation which reports the Mach number of flight with theoretical throttling to the AJA: ratio chosen is as follows:

50

A. A, "

M

V — 1 \ Y + 1/2 (Y-1)

(1 + J_LM2 \

2

or:

Y + l

~~ 2 ~

M = Mach number of flight; y = ratio of specific heats.

In a preferred embodiment of the invention, the annular wedge part at the anterior end of the body is a composite part delimiting a generally sharp leading edge of the projectile, the included angle of this composite wedge part being 65 sufficiently small to allow the oblique shock wave to attach itself to the leading edge after launch to help impose drag or poor aerodynamic resistance on the projectile.

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The projectile base can be mounted on the rear end of the tubular body to transform the gas pressures in the muzzle into a driving force exerted on the body and be arranged so as to be separated from this body by to the stagnation pressures acting on the pellet after launch.

The forcing belt mounted on the external surface of the tubular body can be adapted to engage with the scratches of the muzzle to rotate the projectile gyroscopically.

The discharge base can include a front end in the shape of a warhead which, before separation, is enclosed in the tubular body.

The description of several embodiments is given below, by way of example, with reference to the appended drawings in which:

Fig. 1 is a view in axial longitudinal section of a tubular projectile;

Fig. 2 is a view similar to FIG. 1 showing the flight configuration of the projectile;

Fig. 3 is an elevational view of the rear end of the projectile;

Fig. 4 shows the projectile in flight with oblique shock waves attached to its anterior and posterior ends;

Fig. 5 is a view similar to FIG. 4, but showing a normal shock wave situated in front of the projectile;

Figs. 6a to 6d illustrate the phenomena of swallowing and expelling shock waves in a projectile according to the invention;

Fig. 7 is a graph comprising curves which illustrate the effect of the throttling zone: entry zone ratio on the phenomena of expulsion and swallowing of shock waves for various flight Mach numbers;

Fig. 8 is a graph illustrating the variation in the coefficient of drag or typical aerodynamic resistance with respect to the Mach number for various wall thickness ratios and for a typical tubular projectile;

Fig. 9 is a graph illustrating the variation of the ballistic coefficient with the wall thickness ratio for various flight Mach numbers and for a typical tubular projectile;

Fig. 10 is a schematic view of part of a tubular projectile with various symbols illustrating the various dimensions of the projectile;

Fig. 11 is a part of a test report which indicates the points of impact of the projectiles on a target;

Figs. 12a to 12c illustrate various configurations of tubular projectiles used in firing range tests;

Fig. 13 is a graph of the trajectories of various projectiles;

Fig. 14 is a graph of the evolution of the speed of the projectile shown in FIG. 12b;

Fig. 15 illustrates the variation of the drag coefficient with the Mach number of flight for various projectile configurations;

Fig. 16 is a view in longitudinal section of a variant projectile.

Before describing the theoretical considerations governing the design of the tubular projectile, reference is made below to FIGS. 1 to 3 which illustrate a typical embodiment of the invention. Fig. 1 illustrates the complete assembly of the projectile body 10, the forcing belt 12 and the discharge base 14. An anterior protective cover 16 of plastic material breaks up and separates from the body 10 immediately after launch. Figs. 2 and 3 illustrate the projectile in flight, that is to say the body 10 of the projectile alone.

The body 10 of the projectile is of circular section and has a central passage 18 of circular section also. The front part of the body 10 is shaped so as to form an annular wedge-shaped part 20. This wedge-shaped part comprises an internal conical surface comprising an annular wall 22 which forms an angle with the longitudinal axis of the projectile and which therefore tapers towards the interior from the leading edge 26 of the projectile to a narrowed portion 25 which begins at region 24, and an outer conical surface having an annular wall 28 which also forms an angle with the axis of the projectile and which therefore by flaring outwards and backwards from the leading edge 26 to the region 30 where it is connected to the cylindrical outer wall 32 of the projectile. The narrowed portion 25 has a constant diameter from the region 24 to the posterior end 28 of the projectile. The apex of the inner and outer annular cuneiform surfaces is located, in fact, a short distance in front of the leading edge 26 owing to the fact that this leading edge is, for practical reasons, rounded along a very small radius , as shown in cross section.

The posterior end section of the projectile has a rebate 31 and the outer wall of this rebate is knurled to ensure a good grip between the body 10 and the annular forcing belt 12 which is pressed tightly on the surface of the rebate. The forcing belt 12 has an annular groove 32 which retains the discharge base 14 in place. The trailing edge of the forcing belt 12 includes an annular lip 13 which serves as a gas-tight element during launch.

The discharge base 14 bears against the rear end 28 of the body 10 and comprises an annular projection 36 having a groove containing a sealing ring 38. The ring 38 contributes to preventing any passage of gas during the launching of the projectile . In a well known manner, the discharge base serves to transform the pressure of the gases in the launching tube or the muzzle into a driving force which makes the projectile accelerate for launching. The forcing belt 12, which is made of a relatively soft material (for example an adequate plastic), attacks the scratches of the muzzle and makes the projectile rotate on itself so as to contribute to stabilizing it during its flight. After launching, the centrifugal forces separate the forcing belt 12, after which the stagnation pressure which accumulates inside the projectile intervenes to detach the base 14 from the projectile.

The tubular body projectile 10 is intended to be launched at supersonic speeds, usually between Mach 4 and Mach 4.5. Supersonic flow zones are therefore associated with the tubular body 10 and can have two different structures. At the higher speed ranges, illustrated in fig. 4, the flow zone produces an oblique shock wave structure (provided that the ratio of the throttle section to that of the input zone A, / A; is sufficiently large, as explained in more detail more far), in which a compression shock wave 60 is attached to the leading edge 26, is followed by an expansion region, then a recompression shock wave 62 attached to the trailing edge 28. A zone supersonic flow in which an oblique shock wave structure is formed in association with supersonic flow inside the tubular body determines drag or low resistance forces.

The speed of the projectile decreases with the range and, at a predetermined Mach number which depends on the ratio A, / Aj, the flow field associated with the projectile 10 suddenly turns into a field having a powerful normal shock wave (or wave leading edge impact) 64 which is detached from the leading edge 26 of the tubular body 10. This is clear from FIG. 5. The presence of a powerful normal shock wave detached from the leading edge 26 indicates that strangulated flow conditions exist inside this projectile. The constricted flow conditions tend to give the impression that the projectile is a full cylinder and, in any case, impose significant drag forces on the projectile.

The phenomenon of flow throttling in the tubular projectile has been highlighted in tests carried out in an aerodynamic wind tunnel using models and techniques for visualizing flows and has been demonstrated more in real tests carried out at shooting range. It is therefore possible, with the projectile according to the invention, to increase, considerably and suddenly, the drag forces which are exerted on the tubular projectile.

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It is also possible to adapt the configuration of the tubular body so as to obtain a low drag during the first part of the trajectory which must be followed, at a predetermined threshold or at a predetermined critical speed (and Mach number), a natural transition to strangulated flow conditions which impose very high drag forces on the projectile and thus limit the range of its flight. The usefulness of this transition will emerge more clearly below.

The basic functional and structural features of a typical projectile according to the invention have been briefly described above. The following description illustrates various important theoretical and practical considerations involved in the design of a type tubular projectile stabilized by gyrosco-pic rotation known under the acronym STUP (“spin stabilized tubulär projectile”) to be used as an exercise projectile, this projectile 'exercise to be used to simulate an APDS (armor piercing discarding hoof) projectile, with detachable hoof for piercing armor. The description will refer specifically to the design of a 105 mm projectile, but it goes without saying that the invention is not limited to this caliber, but on the contrary extends to all the calibers used in the practice.

Of course, the flow properties of a STUP are a little more critical than those of conventional bullet projectiles. The specific criteria must be well understood and used in the basic design to achieve the desired goals. A STUP projectile designed as an exercise ammunition for training in the firing of 105 mm APDS projectiles, for example, must have several important features such as: a) a trajectory corresponding to the firing of an APDS projectile at distances of exercise up to 2500 m, b) a low safety range, c) a minimum ricochet range, and d) an attractive price.

The most important parameter to consider in the initial design phase is the adaptation of the trajectory to that of an APDS projectile. In theory, this result is achieved by precisely adapting the inertia properties for launch, the aerodynamic properties and the dynamic stability of the exercise projectile to those of combat APDS. In practice, this is not possible, even with a STUP. It is therefore necessary to seek a compromise in the goals which one seeks to achieve and which have been mentioned above in order to obtain an acceptable concordance of the trajectory with that of the APDS. It is a compromise between the initial speed, the ballistic coefficient CDA / W (CD = drag coefficient, A = section of the projectile based on the maximum outside diameter of the flight configuration, W = total weight of the projectile- flight configuration), flight time, inertia properties and dynamic stability. For the cost of the projectile to be interesting, it must be designed with a minimum number of elements, which requires a projectile of normal caliber (the APDS is an under-calibrated projectile and is provided with a complicated and expensive hoof) .

To match the trajectory of the APDS with that of a normal caliber STUP, the drag must be weak and it is essential that the supersonic flow begins in the central passage of the projectile as soon as it leaves the muzzle , otherwise the drag will be too great. The flow initiation process, also called the shock wave swallowing process, will be described below and can be used to establish a minimal relationship between the throttle section and the cross section. inlet end, based on the maximum Mach number at the outlet of the mouth. Reference is made below to FIGS. 6a and 6b and the graphs shown in figs. 6d and 7. FIG. 6 schematically illustrates a tubular projectile according to the invention which comprises a composite annular annular anterior end delimiting an inlet section Ai and a throttling section in the central passage designated by At.

The internal flow process of a STUP is essentially similar to that of a supersonic diffuser and the reverse Laval nozzle. As flow begins from a state of rest in the muzzle of the weapon, a normal shock wave must pass through the throttle section to establish a supersonic flow in the central passage and, thus, drag conditions weak.

The process of starting or swallowing the shock wave 5 involves the pilot equations of mass continuity, inertia and energy. Reference may be made to the following literature: A. Hermann, "Aerodynamics of Supersonic Diffusers"; B. Donovan A.F., Lawrence, H.R., "Aerodynamic Components of Aircraft at High Speed", Princeton University Press, 1957; C. Shapiro, H., io "Compressible Fluid Flow", volume I, The Ronald Press Company, New York.

As the flow (materialized by the arrow) accelerates to supersonic speeds, a normal shock wave appears in front of the inlet, as shown in fig. 6a. As the Mach number increases, the normal shock wave approaches the leading edge. The flow behind the shock wave is subsonic and accelerates towards Mach one at the throttle section. The acceleration of the flow depends on the geometry or the ratio of the sections of the inlet and the throttle. At a slightly higher Mach number, the shock wave attaches to the leading edge. Under these conditions, the Mach number at the throttle level is equal to or less than one. If the shock wave travels inward of the leading edge, even a short distance, it is swallowed, because it can be shown that this region is an unstable region and that flow conditions supersonic settle there. However, if the Mach number in the throttle reaches unity before the shock wave is attached to the leading edge, this means that the Mach number is equal to unity at the throttle and that the flow is choked. The additional mass flow escapes around the leading edge, as shown in FIG. 6b. Even if the Mach number is increased further, the shock wave never reaches the leading edge and the flow does not start. This is the condition producing a significant drag.

The equation which defines the minimum theoretical ratio at the start between the narrowed section and the inlet end section can be derived from the pilot equations which give:

"i / min i + -

-M2J / 2 ^ yM2-

'IT

or:

^ z ± ìm2J + 1/2 (y_1)

Y = ratio between the specific heats at constant pressure and at constant volume of the surrounding gas;

45 M = Mach number (M> 1.0) at launch speed or initial speed.

This equation defines curve A in fig. 7.

The above equation and the curve shown in fig. 7 can be easily used to determine the minimum theoretical-50 ric ratio of the section of the throttle to the inlet end section At / Ai necessary to obtain a supersonic flow in the central passage at the initial speed. However, in practice, the minimum ratio A, / Aj is always chosen so as to be slightly greater than the value indicated by the equation, because the boundary layer has the effect of making the constriction a little narrower. As an example, we will take the ratio A, / Ai necessary for a tubular projectile which is designed so as to correspond (approximately) to the flight characteristics of an APDS 105 mm projectile. The initial speed of the 105 mm APDS is 60 1478.3 m per second, i.e. a Mach number of 4.3. It can be seen from the graph of A, / Ai opposite the Mach number that, for the flow to start, the ratio At / Ai must be at least 0.66. As indicated above, this design criterion does not take into account the thickness of the boundary layer which affects the minimum effective section 65 of the constriction. In the STUP model shown in figs. 1 to 3, the minimum section of the constriction must be at the rear end face of the model, because the thickness of the boundary layer increases with length and depends in a

also some measure of ambient conditions, especially temperature. Therefore, the STUP must be designed to have an At / Aj ratio greater than 0.66 for the flow to start. For the STUP model in question, an A, / Aj ratio of 0.7 was chosen. In general, an A / Aj ratio of some 5 or 6% higher than the theoretical minimum given by the equation is sufficient to take account of the thickness of the boundary layer.

It should be noted that the margin available for the ratio Ai / A-, at the time of design, is relatively small for most of the existing weapon systems. This margin in the ratio A, / Ai for launch Mach numbers from 1 to 4.3 is 1 to 0.66, excluding all considerations regarding the boundary layer. The ratio A, / Ai for launch Mach numbers from 1 to 5 is 1 to about 0.65, also excluding all considerations regarding the boundary layer. For AJAi values below these limits, flow does not start at launch and the drag is high. Since the ratio A, / Aj is the square of the ratio of the diameter of the throttle to the diameter of the inlet end (dt / dä) 2, an examination of the STUP model shown in Figs. 1 to 3, for example, shows that the difference between the diameter of the throttle and the diameter of the inlet end is relatively small.

The ratio A, / Aj is also very important for limiting the range of the projectile. The process by which the projectile according to the invention expels the shock wave, and thus establishes conditions for strangled flow in its central passage at a predetermined Mach number, will be described below.

When the flow has started, the Mach number in the central passage is supersonic, as shown in fig. 6c. Unlike the subsonic flow, the Mach number in the converging section decreases towards the throttle and its value is related to that of the ratio of the throttle section to that of the inlet end. As the Mach number decreases (that is to say as the projectile loses speed in flight) towards the unit, at the level of the constriction, the shock wave appears in this constriction, but it comes from the rear, that is to say from the trailing edge of the projectile. At a slightly lower Mach number, the shock wave enters the converging section and, this being an unstable state, it only stabilizes in front of the projectile, as shown in fig. 6a. This is the condition producing significant drag which is necessary to decrease the range. The equation that defines the process of expelling the shock wave as a function of the Mach number is as follows:

At M

ÄT7 y - 1 \ ï + i / 2 <ï-i>

w where:

M = Mach number of flight;

Y = ratio of specific heats.

This equation defines curve B in fig. 7.

The processes described above of swallowing and expelling the shock wave at selected Mach numbers apply in most direct fire guns where the total range of the weapon is important compared to the distance maximum of the objective (for example a tank gun of 105 mm). In general, these processes provide a low drag (flow started) during the first part of the flight path to the target, which is followed by a sudden transition to high drag conditions (expelled shock wave) aimed at reducing the scope.

Thus, due to the phenomenon of swallowing and expulsion of the shock wave obtained with the projectile according to the invention, a STUP (or tubular projectile) can be designed with a coefficient of drag at high Mach numbers (in A in fig. 6d) which is much lower than that of a conventional projectile (curve D in fig. 6d). At a predetermined Mach number, the drag coefficient CD rises sharply to a high level (at B in fig. 6d). These features make it easier to adapt the STUP design to a chosen drag curve. (For some applications, this adaptation can prove to be relatively easy, while it can be more difficult for other applications which require a very low drag and a high throttle Mach number).

In the practical example of the STUP ammunition intended for a 105 mm tank gun, an At / Ai ratio of 0.7 was chosen to ensure the swallowing of the shock wave at start-up and at launch . It appears from the graph of At / A; next to the Mach number in fig. 7 that, for this model, the flow constriction occurs at around Mach 1.8 or a slightly higher Mach number (depending on the effects of the boundary layer). Reference will be made below to various tests carried out which demonstrate that this choking effect takes place as predicted.

As shown in fig. 7 (curve B), as the At / Ai ratio approaches unity, the Mach number for which a choked flow occurs also approaches unity. If the central passage through the projectile is simply a bore of uniform diameter, that is to say if no constriction is provided, the flow does not constrict at all at supersonic speeds (if it is assumed that the boundary layer effects are zero); therefore, it is essential that the projectile has an internal configuration such that flow throttling phenomena can be obtained. A composite wedge part at the anterior end is very desirable because it can easily be adapted to obtain the desired flow pattern.

Other important considerations are the wall thickness ratio t / R (where t is the maximum wall thickness and R = a maximum half-outside diameter of the projectile) as well as the values of the angles of the wedge-shaped part located at the anterior end of the projectile. These angles must be kept reasonably small to ensure that the oblique shock wave conditions attached to the leading edge are obtained necessary to minimize the pressure drag. For the composite wedge-shaped part as shown in figs. 1 to 3, the included angle 0 (see fig. 2) between the inner and outer wedge faces must be less than about 15 ° or, better still, less than about 10 °. At the same time, the included angle should usually be greater than about 5 °. An excessively blunt leading edge can cause loose shock waves and significant drag, so the leading edge should therefore be reasonably sharp; a knife-like leading edge is not necessary, however, and for all practical purposes, the leading edge can be rounded to a small radius, for example 0.127 mm, to reduce the risk of edge damage. attack during manipulation.

We know that the range of a projectile decreases if we increase the ballistic coefficient CDA / W. In a tubular projectile, the drag coefficient CD is increased by increasing the wall thickness. Increasing the wall thickness also increases the weight. There is, for any particular tubular projectile, a wall thickness ratio t / R for which CDA / W is optimal and braking during flight is minimal. The wall thickness ratio t / R is a parameter which is therefore useful for expressing the various existing relationships.

The wall thickness ratio t / R is chosen so as to determine a minimum CDA / W ballistic coefficient. Curves obtained by plotting the drag coefficient Cd, with respect to the Mach number and for certain values of t / R, were obtained from tests of various tubular projectiles. Fig. 8 illustrates, in general, the type of relationship which exists between these variables for tubular projectiles of the type described. Experience has shown that t / R must be between approximately 0.18 and 0.45 in order for the drag coefficient to remain between acceptable limits. A graph generally illustrating the relationships between the CuA / W ballistic coefficient and the thickness ratio t / R of pro5

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tubular jectiles of the type described is given in fig. 9 which shows the importance of choosing the appropriate thickness ratio so as to minimize the ballistic coefficient. (The curves shown in figs. 8 and 9 vary according to the exact configuration of the projectile and are given here only as an example.)

The flight weight W of the projectile is determined by the limits of the interior ballistics of the muzzle system. In the example considered (the 105 mm STUP exercise ammunition intended for the 105 mm L7A1 tank gun), the maximum weight of the APDS munition (projectile plus sabot) admissible to obtain an initial speed of 1478.3 m per second is about 6 kg. In this case, the weight of the STUP ammunition (projectile plus discharge base and forcing belt, etc.) cannot exceed 6 kg if the initial speed of the tubular projectile must correspond to that of the weapon that she must simulate.

Another important phase of a STUP design process is the estimation of dynamic stability. This stability involves the relationship between the gyroscopic moment and the aerodynamic moment. In summary, the gyro stability factor must be greater than unity for the projectile to be dynamically stable. The gyro stability factor Sg is defined as follows:

I V

Sg = ~ ° ù h = k pd3 V2Cm, and

Ix = axial moment of inertia;

Iy = transverse moment of inertia;

p = angular speed;

p = air density;

d = maximum body diameter;

V = initial speed;

Cm, = coefficient of static moment.

In the 105 mm L7A1 tank gun, for example, the parameters p, p, V must be identical for the STUP and the APDS. But the value of Ix is much higher for a STUP of normal size than for an under-calibrated APDS, while Y is of the same order of magnitude. In this case, the above equation gives a much higher Ix2 / Iy ratio for the STUP than for the APDS. The value of Cmi is very difficult to estimate, but it is of the same order of magnitude for the two projectiles. We can then demonstrate that the 105 mm STUP ammunition has a Sg factor much higher (i.e. Sg> 1) than that of the APDS and this must also intervene in the adaptation of the path. The STUP tends to follow a flatter trajectory, so that its fall is not as vertical as that of the APDS at the end of the range. The fineness ratio - £ / D (where • £ = length of the projectile and D = maximum outside diameter) is theoretically limited by the maximum admissible stability factor Sg. In practice, the -t / D ratio can vary from approximately 2 to approximately 5. Finally, in the process of adapting the trajectory of the APDS and that of the STUP, a compromise is chosen between the initial speed, the time of flight, the ballistic coefficient and the dynamic stability, and we use for this purpose a theoretical estimation and experimental iteration techniques at real scale.

The basic equations used to determine the drag coefficient and the ballistic coefficient are shown below. These equations can be used in simple computer code for example (APL language) to arrive at a design which satisfies the requirements of the trajectory. It should be noted that the ou could use other classical mathematical techniques based on known aerodynamic principles to optimize the design; however, the summary of the pilot equations used and the computer code used are useful to specialists in designing a STUP that meets a particular range of requirements. We can refer to fig. 10.

The basic aerodynamic principles can be obtained in the following references: A. Ames Research Staff, "Equations, Tables and Charts for Compressible Flow", NACA Report 1135.1953; B. Hoerner, S., "Fluid-Dynamic Drag", C. NACA RM L53C02.

The nomenclature to be used in the pilot equations is as follows:

L length of the projectile

D; inlet end diameter

Dt internal diameter or diameter of the throttle

D0 outer diameter t wall thickness

R half outside diameter D „

0 „external angle of the wedge-shaped part

0i interior angle of the wedge-shaped part

With reference section (îtDl / 4)

M Mach number

V speed y ratio of specific heats

CP pressure coefficient

CDpo pressure drag coefficient - external face of the wedge-shaped part

CDP | pressure drag coefficient - internal face of the wedge-shaped part

See coefficient of friction

Re Reynolds number

CpB pellet pressure coefficient p air density

H viscosity of air

The following assumptions are made in mathematical analysis:

a) Two-dimensional fluid flow (only valid for t / R <0.5);

b) oblique shock wave attached to the leading edge of the projectile;

c) No throttling, ie supersonic flow in the central passage of the projectile;

d) Zero angle of attack;

e) Geometry as shown in fig. 10.

The drag coefficient (CD) is expressed as follows:

Cd = Cdp (pressure) + Cdf (friction) + CDb (base)

The coefficients are based on the total projected section (ÎCDo / 4).

a) The pressure drag coefficient (Cd,) is expressed as follows:

from reference A for a bi-monthly wedge-shaped part:

C 2 (y + l) M4—1 (M2—1) 2 1

P (M2 -!) 1'2 2 (M2 - l) 2 (M2 —1) 7/2>

-? + 12J ~ 3Y V + KY + 1) M4—2M2 + f] e3 + ... For the external face of the cuneiform part (0 = 0O):

C- = CP ° [1- ©]

For the internal face of the cuneiform part (0 = 0;):

and CDp — CdPo + CDp.

b) The coefficient of friction drag (CDf) is expressed as follows:

from reference B for turbulent flow: Cf = KCf /

where K = (l + 0.15M2) - ° '432 Cf' - (3.46 Log10Re — 5.6) -2 Re = PVL / (i

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The surface friction is based on the wetted surface Sw = tcL (D „+ Dt)

and CD = Q4L

"Do + D, l

L D02 J

c) The base halftone coefficient (CD „) is determined as follows.

The base pressure coefficient for a two-dimensional body is given in reference C. The base drag data is also obtained in tests carried out in an aerodynamic wind tunnel using 105 mm models. The results of the aerodynamic wind tunnel are perfectly correlated with the data of reference C. The following function has been derived from these data:

CPb = Ao + A1M + A2M2 + A3M3 1.5 £ M £ 4.5 where Ao = 0.6331 Ai = -0.33257 A2 = 0.06619 A3 = -0.004

and CDb = Q

-Pb

"

Other formulas which are well known to specialists are indicated below:

Ballistic coefficient C A

feet2 / pound (1 foot2 / lb = 0.205 m2 / kg).

w

Deceleration dV dX

= (16.1 pVCDA) / W (m / s / m).

The above equations have been used in a computer program (APL language) and, for your convenience, the program list is shown below.

APL list

Input data (lines 1,2 and 4)

L model length (in inches) (1 inch = 25.4 mm)

OD outside diameter of the model (in inches) (1 inch =

25.4 mm)

TOR wall thickness ratio (t / R)

AOR ratio of the inlet section (A, / Ai) (throttle section / inlet end section) TETAO angle of the external face of the wedge-shaped part in degrees

TETAI angle of the internal face of the wedge-shaped part in degrees

DENS material density in pounds / inch3 (1 pound /

inch3 = 27.68 g / cm3)

NOT no scratches of the weapon in feet (1 foot =

30.48 cm)

RHO atmospheric density (0.002378 slugs / ft3)

(1 slug / foot3 = 515 kg / m3)

MU viscosity (3,719 x 10 ~ 7 slugs / foot / s) (1 slug / foot =

47.88 kg / m)

S speed of sound (1117 feet / s) (or 340.5 m / s)

Vel velocity in feet / s (1 foot / s = 30.48 cm / s)

A0, Ai, A2, A3 constants in the polynomial which determines the coefficient of pellet drag

Output data (lines 57 to 62)

T wall thickness in inches (1 inch = 25.4 mm)

DT inside diameter or throttle diameter in inches (1 inch = 25.4 mm) DI inlet end diameter in inches

(1 inch = 25.4mm)

TO diameter of the inlet end to its outer face in inches (1 inch = 25.4 mm) TI diameter of the inlet end to its inner face in inches (1 inch = 25.4 mm)

s LOD model fineness ratio

Li length of external parallel section in inches

(1 inch = 25.4mm)

L2 length of the external face of the wedge-shaped part in inches (1 inch = 25.4 mm) io L3 length of the internal face of the wedge-shaped part in inches (1 inch = 25.4 mm) L4 length of the internal parallel section in inches

(1 inch = 25.4mm)

V volume of material in inches3 (1 inch3 = 16.39 cm3)

i5 W model weight in pounds (1 pound = 0.454 kg)

CPO pressure coefficient - external face of the wedge part

CDPO pressure drag coefficient - external face of the wedge-shaped part 20 CPI pressure coefficient - internal face of the wedge-shaped part

CDPI pressure drag coefficient - external face of the wedge-shaped part CDP pressure drag coefficient

25 RE Reynolds number

CF coefficient of friction

CDF coefficient of friction drag

PPB base pressure coefficient

CDB pellet drag coefficient

30 M Mach number

CD drag coefficient

CDA ballistic coefficient (feet2 / pound) (1 foot2 / pound =

0.205 m2 / kg)

VELD deceleration (m / s / 100 m)

35 SPIN angular speed (revolutions / s)

VT tangential speed (feet / s) (1 foot / s = 30.48 cm / s)

STRESS tangential tension (circumferential in pounds / inch2) (1 pound / inch2 = 0.07 kg / cm2)

40

Note:

The reference area used in aerodynamics is based on the outside diameter.

APL List

Model 26

50

VSTUP2 [D] V VSTUP2

1] L, DO, TOR, AOR, TETAO, TETAI, DENS, PITCH

2] RHO, MU, S, VEL

3] M <-VEL- ^ S

4] A0, Al, A2, A3

5] DELO <-TETAO x ° 1 -180

6] DELI <-TETAI x ° l-rl80

7] T <-TOR x DO-h 2

8] DT <-DO — 2xT

9] DI <-DTx (l-AOR) *. 5

10] TO <- (DO — DI) -r2

11] TI <- (DI — DT) - ^ 2

12] L2 "-TO h- 3 ° DELO

13] L3 <-TI + 3 ° DELI

14] Ll <-L — L2

15] L4 <-L2 — L3

16] VI "- (ol x Ll -f-4) x (DO * 2) —DT * 2

17] V2 <-. 2618 x L2 x (DO * 2) + (DO x DI) + DI * 2

18] V3 <-. 2618 x L3 x (DI * 2) + (DI x DT) + DT * 2

19] V4 <-ol xL4x (DT * 2) -î-4

20] V <-V1 + V2 + (- V3) —V4

21] Wf-DENSxV

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8

[26] M2 <- (M * 2) —1

[27] CPl <-2- ^ M2 * .5

[28] CP2 <- ((2.4xM * 4) -4xM2) -r2xM2 * 2

[29] CP3f- (l (M2 * (7 -r 2))) x (. 36 x M * 8) - {1.493 x M * 6) + + (3.6xM * 4) - (2xM * 2) + 4-r3

[30] CPO <- (CPl x DELO) + (x DELO * 2) + CP3 x DELO * 3

[31] CDPO <-CPO x 1 - (DI DO) * 2

[32] CPIf- (CPl x DELI) + (CP2 x DELI * 2) + CP3 x DELI * 3

[33] CDPI <-CPI x ((DI * 2) —DT # 2) -r DO * 2

[34] CDP-f-CDPO + CDPI

[36] RE “-RHO x VEL x (L-r-12) -rMU

[37] CFP <- ((3.46 x (10®RE)) - 5.6) * - 2

[38] K <- (1+. 15xM * 2) * - .432

[39] CF <-K x CFP

[40] CDF <-CF x 4 x L x (DO + DT) + DO * 2

[41] PPB <-A0 + (A1 x M) + (A2 x M * 2) + A3 x M * 3

[42] CDE <-PPB x 1 - (DT 4- DO) * 2

[43] CD <-CDP + CDF + CDB

[44] CDA <- (CD x o 1 x (DO * 2) 4) W

[45] CDA <-CDA -f-144

[46] VELD <-16.1 x RHO x VEL x CDA x 100

[47] SPIN <-VEL -f- PITCH

[48] SPINR <-SPIN x 2 x ol

[49] VT <- SPINR x DO -r- 24

[50] STRESS “- (LENS x (VT * 2) - 32.2) x 12

[51] LOD <-L - = - DO

[57] T, DT, DI, TO, TI, LOD

[58] LI, L2, L3, L4, V, W, VC, WCS, WCT

[59] CPO, CDPO, CPI, CDPI, CDP

[60] RE, CF, CDF

[61] PPB.CDB

[62] M, CD, CDA, VELD

Model 26

Example

Entrance

(1) 10 4.127 0.2125 0.7 3 3.5 0.282 6.25

(2) 0.002378 3.719E "7 1117 4850 (4) 0.63331 0.33257 0.06619" 0.004

Exit

(57) 0.4385 3.25 3.8845 0.12125 0.31725 2.4231

(58) 7.6863 2.3137 5.1869 "2.8733 40.082 11.303 0.42706 0.12043 0.12043

(59) 0.02835 0.0032339 0.033815 0.0089873 0.012221

(60) 2.584.3E7 0.0013934 0.02414

(61) 0.10973 0.041681

(62) 4,342 0.078042 0.0006414 11.91

By following an iterative process on the input parameters which can be modified, for example TOR, TETAO, TETAI, we obtain the following data:

(see input data)

Lf-10.0 or L = 10.0 inches (25.4 cm)

DO <-4.127 or D0 = 4.127 inch = 105 mm TOR <-O, 213 or t / R = 0.213 AOR <-0.7 or At / Ai = 0.7 TETAO <-3 or 0 „= 3 °

TETAI <-3.5 or 0i = 3.5 °

DENSITY-f-0.282 = material density = 0.282 pounds / inch3 or 7.806 g / cm3

STEP <-6.25 = no streaks of 6.25 feet or 190.5 cm RHO + -0.002378 = (density of atoms in slugs / foot3)

(1 slug / foot3 = 515 kg / m3)

MU "-3.719E" 7 = air viscosity 3.719 x 10 "7 slugs / dry foot (1 slug / dry foot = 47.88 kg / m)

S <-1117 = speed of sound 1117 feet / s or 340.5 m / s VEL <-4850 = initial speed 4850 feet / s or 1478 m / s

A0, Ai, A2, Aaf-0.6331, -0.33257.0.06619, -0.004 and (see output data) (partial list only)

DT <-3.250 or throat diameter = 3.250 inches or 8.255 cm

ID <-3.88 or inlet end diameter = 3.88 inches or 9.855 cm

LOD <-2.42 or speed ratio (L / D) = 2.42 L! <- 7.81 or length of the external parallel section = 7.81 inches or 19.837 cm

L2 <-2.29 or length of the external face of the cuneiform part =

2.29 inches or 5.817 cm L3 <-5.19 or length of the inner face of the wedge part =

5.19 inches or 13.183 cm W "-9.88 or projectile weight = 9.88 pounds or 4.485 kg

The remaining output data is not shown in this memo. The partial list above gives the basic parameters for the design of the 105 mm STUP ammunition which is considered as an example. It should be noted that the optimal wall thickness ratio (t / R) has a value of 0.213; the optimal angles of the wedge-shaped part are 3 ° for the external face of the wedge-shaped part and 3.5 ° for the internal face. Other interesting dimensions are given above. These dimensions have been used in the particular embodiment shown in FIGS. 1 to 3 to produce an effective 105 mm exercise ammunition. The material used for the projectile is highly drawn AISI1018 steel. The leading edge 26 shown in FIG. 2 is rounded by a small radius (for example a radius of 0.127 mm).

The precision of the STUP compared to that of conventional projectiles, for example APDS and TPDS (detachable saber exercise projectile) has been demonstrated in various tests. Below is part of a recording of a 105 mm STUP development test described above.

Weapon used: 105 mm tank gun.

Target: 6.1 x 6.1 m at 1000 m.

Ammunition: 1) STUP 105 mm - ammunition B; 2) APDS / TC35A1 105 mm - R ammunition; 3) TPDS / T C-36 105 mm - W ammunition, fired at a load weight of 5.597 kg.

The test was carried out with the following pointing settings:

site line - 0 thousandths; elevation - 2.0 thousandths. The test is detailed in the following table and the points of impact of the test ammunition are reported in fig. 11. It should be noted that the STUP exercise ammunition in accordance with the invention is at least as precise as conventional APDS and TPDS ammunition.

Board

Muni

Speed'

Speed

Impact point

Final initial rotation

gyrosco

No.

m / s m / s

Hori

Vertical spades

zontal

turns / s

W-l

1500.0

1287.9

3.32

3.51

W-2

1501.4

1,292.4

3.32

3.05

R-l

1468.9

1360.5

2.35

3.44

815

B7L1

1459.0

1316.1

3.11

3.96

774

B7F1

1482.9

1342.2

3.72

5.09

770

B7F2

1478.3

1341.9

3.48

2.74

815

B8L1

1459.2

1327.6

3.20

3.41

789

R-2

1474.6

1378.7

3.35

3.32

811

B8F1

1474.2

1340.7

3.66

3.96

854

B8F2

1466.6

1334.0

3.05

2.65

812

Notes:

1) Aiming point: horizontal: 3.05 m; vertical: 3.05 m;

2) Height of the trunnions: 1.33 m; height of the aiming mark above the ground: 4.01 m;

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3) Coordinates measured from the lower left corner of the target.

The critical nature of the At / A- ratio, including the flow throttling phenomenon, has been demonstrated in various tests. Reference may be made to a series of range tests carried out using conventional APDS projectiles and various varieties of STUP projectiles. Fig. 12 illustrates the various proven models. The models shown in fig. 12a and 12b have composite wedge-shaped parts at their anterior ends, FIG. 12a illustrating a composite wedge-shaped part CW (S) and FIG. 12b a slightly modified wedge-shaped part CW (M), while the model in FIG. 12c only has an internal wedge face (IW)

at its anterior end. The three models of fig. 12a, 12b and 12c also have external wedge-shaped faces at their posterior ends; this helps to somewhat reduce the base halftone coefficient, but has no appreciable effect on general flight behavior. The basic dimensions of the various models in fig. 12 are the following (see fig. 10 which illustrates how to apply these dimensions):

Fig. 12a CW (S)

Fig. 12b CW (M)

Fig. 12c IW

L

25.4 cm

25.4 cm

25.4 cm

U

5.385 cm

3,592 cm

-

U

4.770 cm

5.420 cm

6.706 cm

Sun

9.088 cm

9.274 cm

9.652 cm

D,

7.747 cm

7.747 cm

7.747 cm

D „

9.652 cm

9.652 cm

9.652 cm t

0.953 cm

0.953 cm

0.953 cm

R

4.826 cm

4.826 cm

4.826 cm

9 "

û

3 ° 8 °

3 °

QO

0 °

QO

At / Aj o

0.727

0

0.700

O

0.640

t / R

0.197

0.197

0.197

L / D

2.63

2.63

2.63

The models shown in fig. 12 were all fired at equal speeds and under similar conditions, and the flight paths were followed using a Doppler-Fizeau tracking radar. The flight paths were compared to the trajectory of a conventional ammunition (APDS) fired under the same conditions and at the same weight. The trajectories of the various projectiles are indicated in fig. 13. The model with internal cuneiform surface having an At / A- ratio of only 0.640 was strangled at all times and had a total range of less than 6096 m. The two composite wedge-shaped models, having At / Aj ratios greater than the critical values, were uncoupled immediately after launch, but choked approximately 7 to 7.2 s after launch and had spans of approximately 13,700 m for the CW (M) and around 15250 m for the CW (S). The classic APDS has a range of approximately 21,950 m. The curves for the evolution of the speed of the models with the CW wedge-shaped part (M) are shown in fig. 14. The inflection point on the curve shows that the strangulation has occurred as predicted. The drag coefficients of the various models shown in fig. 12 were calculated with respect to the flight Mach number and the results are shown in fig. 15. The two models with composite cuneiform part having ratios A, / Ai of 0.727 and 0.700 respectively show an abrupt transition from a weak halftone to a strong drag at a speed slightly lower than Mach 2, which is in accordance with the predictions. theoretical. The internal wedge-shaped (IW) model is strangled at all Mach angles and has a high drag for all Mach numbers. As expected, the APDS drag coefficient shows a gradual increase as the Mach number decreases.

As mentioned above, the design of the tubular projectile according to the invention can be modified considerably, provided that the basic criteria of this design which have been established above are observed. For example, the trailing end may be dull, as shown in figs. 1 to 3, or it may have a relatively sharp edge (see for example Figs 12a and 12b). The internal passage of the projectile must not be precisely cylindrical, for example a small progressive increase in the diameter towards the trailing end can be beneficial in certain constructions and, in a similar manner, the diameter of the external surface can gradually decrease ( conically) towards the trailing end. The degree of taper for internal and external surfaces should usually not exceed 2 or 3 °. The front end of the projectile is provided with a wedge-shaped part, preferably composite, as shown for example in FIGS. 1 to 3. The generatrix of each anterior wedge part can be straight, or bent in an adequate manner. In all cases, however, an A, / A ratio; must be large enough to ensure that supersonic flow conditions can be achieved in the center passage at the launch speeds in question. The presence of a trailing edge can be useful in many cases when it is desired to reduce the drag of the base.

The variant shown in FIG. 16 may be useful in some cases. This projectile 50 is essentially identical to that shown in FIGS. 12a, 12b. The embodiment of fig. 16 however has a wedge-shaped rear end section capable of supporting a discharge base 52 in the form of a conventional non-tubular projectile, the front end portion of which is in the form of a conventional warhead. The refouler base 52 is shaped so as to have a radial shoulder 54 suitable for pressing against a support seat 56. Although FIG. 16 does not show it, the wedge-shaped trailing end of the projectile detachably supports at least one forcing belt (not shown) and, preferably, a sealing ring. Such a forcing belt and such a sealing ring function in the same manner as that described with reference to FIGS. 1 to 3. As soon as the tubular projectile 50 has been launched, a normal shock wave forms just upstream of its leading edge. However, high stagnation pressures appear in the central opening of the projectile and these pressures cause the separation of the repressor base 52. Like the drag forces which are exerted on the conventional projectile, that is to say the base repressor 52, exceed those which are exerted on the tubular projectile 50, each projectile follows its own trajectory. This technique can be used to launch a tubular projectile from an airplane, because in this case the repressor base must be designed to follow a stable trajectory, otherwise it could be swallowed by the engines.

The tubular projectiles contemplated in this specification take advantage of the gyroscopic rotation inherent in a projectile stabilized by rotation. This rotation can be used to prevent any ricochet from the tubular projectile beyond the desired target area. By providing adequate scratches in the barrel or the launching tube, the tubular projectile is launched with a rotation speed of between 500 and 1000 t / s (30,000 to 60,000 rpm) and preferably of the order of approximately 750 t / s. Rotational speeds of this order of magnitude produce stresses in the envelope-shaped body, stresses of the order of 4218 to 4570 kg / cm2. Naturally, a projectile in accordance with the invention is made of a material chosen so as to be able to withstand the stresses produced by these high rotational speeds. Successful tubular projectile prototypes have been manufactured from AISI4340 steel, i.e. annealed alloy steel. Another acceptable type of steel, which is preferable given its low price, is AISI 1018 steel. The latter is ordinary carbon steel, highly drawn, with a yield strength of between 4570 and 4921 kg / cm2.

It is very desirable that the material of which the tubular projectile is made can be chosen so that its elastic limit does not

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exceeds only to a small extent the stresses which can be calculated and which are imposed on the surface of the tubular projectile when it is launched with the desired speed of rotation. When such a spinning tubular projectile hits a target or other object in the target area, additional impact loads and stresses are imposed on that projectile and the additional stress produced by the impact causes the projectile to rupture. The body of the tubular projectile has been found to crack, these cracks propagating to cause the projectile to break up in a manner roughly similar to the peeling of a banana. As the body of the projectile fragments in this way, a greatly increased drag is imposed on the fragments produced. However, the fragments 5 slow down rapidly and any tendency for excessive ricochet beyond the target area is severely thwarted and possibly even eliminated. Even more important is the fact that regular control over unwanted ricochets can be obtained beyond the target area.

R

7 sheets of drawings

Claims (8)

623,407 1 + 1__M2J fYM2-IyM "Y 4- 1 V + 1/2 (Y-1) 1. Tubular projectile, capable of being fired at a supersonic speed by a muzzle, comprising a tubular body of circular section comprising a front inlet end and a rear outlet end as well as a central passage which extends to through the body, a refouling base and a forcing belt, characterized in that the interior surface and the exterior surface at the level of the anterior end of the body have a conical shape and delimit a leading edge whose angle is included between 5 and 15 °, the inside diameter of the central passage decreasing from the anterior inlet end towards a narrowed region, the ratio of the section of the passage in the narrowed region At to the section of this passage at the end of input Ai being at least 0.65, but less than 1, the ratio of the thickness of the wall of the tubular body to its radius t / R being between 0.18 and 0.45, where: t = maximum wall thickness; R = maximum radial distance between the axis of the tubular body and the outer surface of the tubular body. 2. Projectile according to claim 1, characterized in that the ratio of the section of the passage in the narrowed region A, to the section of this passage at the inlet end A; is at least 0.66. 2 3. Projectile according to claim 2, characterized in that this ratio of the passage sections is at least 0.7. 4. Projectile according to claim 3, characterized in that this ratio of the passage sections is approximately 0.7. 5. Projectile according to one of claims 1 to 4, intended to be launched at a determined speed in a determined gas, characterized in that the ratio of the section of the passage in the narrowed region A, to the section of the passage to l input front end Ai is greater than that defined by the equation: V-l V'2 / y_1 \ 1 / Y-1 6. Projectile according to one of claims 1 to 5, characterized in that the pressure base is mounted on the rear end of the tubular body to transform the gas pressures in the muzzle into a driving force exerted on the body and in that it is arranged so as to be separated therefrom by the pressures acting on it after launching. 7. Projectile according to one of claims 1 to 6, characterized in that the forcing belt is mounted on an external surface of the tubular body and adapted to engage with the scratches of the muzzle to rotate the projectile on itself. 7 M2 or: M = Mach number at launch, for M> 1.0; Y = ratio between the specific heat at constant pressure and the specific heat at constant volume of the surrounding gas. 8. Projectile according to one of claims 1 to 7, characterized in that the repressor base comprises an anterior end of ogival shape which, before separation, is enclosed in the tubular body. slow deceleration below the target, followed by rapid deceleration with instability beyond the target to reduce range. In another situation, it may be necessary to maximize the range. The trajectory difficulties can also be due to foreign and disruptive forces produced either during launch or during free flight. In order to meet these requirements, the tubular projectile according to the invention has the characteristics set out in claim 1.