WO1989006778A1

WO1989006778A1 - Lightweight weapon stabilizing system

Info

Publication number: WO1989006778A1
Application number: PCT/US1989/000177
Authority: WO
Inventors: William Arthur Mraz; Martin Edwy Buttolph; Michael James Farney
Original assignee: Phoenix Engineering Inc.
Priority date: 1988-01-22
Filing date: 1989-01-23
Publication date: 1989-07-27
Also published as: DK465689D0; CA1336237C; DK465689A; DE68910042D1; AU615041B2; EP0354242B1; JPH02503350A; FI894479A; BR8904796A; AU3191289A; KR900700844A; JP2752208B2; DK166638B1; EP0354242A1; KR950007639B1; DE68910042T2; FI894479A0

Abstract

A gun system comprising a recoiling cannon portion (32), a stationary carriage portion (12), and a campath (64, 66) and cam follower (54, 56) mechanism for movably mounting the cannon portion (32) on the carriage portion (22) for travel along a curvilinear path. The path has two stages, a curved first stage which accelerates the cannon assembly upwards and a second stage which decelerates the cannon assembly's upward motion, and which is either straight or curved in either the same or the opposite direction as the first stage, or some combination of these, as necessary. The second stage, if curved in the same direction as the first, has a shallower curve than the first stage. The first stage has a decreasing radius of curvature in the direction of travel (i.e. recoil) of the cannon portion. The campath mechanism can be fixedly mounted on the cannon portion, with the cam follower mechanism fixedly mounted on the carriage portion, or the campath mechanism can be fixedly mounted on the carriage portion with the cam follower mechanism being fixedly mounted on the cannon portion.

Description

International Bureau

INTERNATIONAL APPLICATION PUBLISHED UNDER THE PATENT COOPERATION TREATY (PCT)

(51) International Patent Classification ^**■^* (11) International Publication Number : WO 89/ 067 F41F 19/00 Al (43) International Publication Date: 27 July 1989 (27.07.8

(21) International Application Number: PCT/US89/00177 (81) Designated States: AT, AT (European patent), AU, B (European patent), BR, CH, CH (European paten

(22) International Filing Date: 23 January 1989 (23.01.89) DE, DE (European patent), DK, FI, FR (Europe patent), GB, GB (European patent), IT (Europe patent), JP, KR, LU (European patent), NL, NL (E

(31) Priority Application Number : 147,317 ropean patent), NO, SE, SE (European patent).

(32) Priority Date: 22 January 1988 (22.01.88)

Published

(33) Priority Country : US With international search report. Before the expiration of the time limit for amending t claims and to be republished in the event of the recei

(71) Applicant: PHOENIX ENGINEERING INC. [US/ of amendments.

US]; 23 Second Street, Newport, VT 05855 (US).

(72) Inventors: MRAZ, William, Arthur ; 22 Seminary

Street, Middlebury, VT 05753 (US). BUTTOLPH, Martin, Edwy ; 32 Oak Street, Newport, VT 05855 (US). FARNEY, Michael, James ; Route 100, Newport Center, VT 05857 (US).

(74) Agent: SHAPIRO, Linda, J.; Mason, Fenwick & Lawrence, 1225 Eye Street, N.W., Suite 1000, Washington, DC 20005 (US).

(54) Title: LIGHTWEIGHT WEAPON STABILIZING SYSTEM

(57) Abstract

FOR THE PURPOSES OFINFORMAπON ONLY

Codes used to identify States party to the PCT on the front pages of pamphlets publishing international appli- cations under the PCT.

AT Austria FR France ML Mali

AU Australia GA Gabon MR Mauritania

BB Barbados GB United Kingdom MW Malawi

BE Belgium HU Hungary NL Netherlands

BG Bulgaria IT Italy NO Norway

BJ Benin JP Japan RO Romania

BR Brazil KP Democratic People's Republic SD Sudan

CF Central African Republic ofKorea SE Sweden

CG Congo KR Republic of Korea SN Senegal

CH Switzerland LI Liechtenstein SV Soviet Union

CM Cameroon LK Sri Lanka TD Chad

DE Germany, Federal Republic of LU Luxembourg TG Togo

DK Denmark MC Monaco US United States of America

FT Finland MG Madagascar

LIGHTWEIGHT WEAPON STABILIZING SYSTEM Background of the Invention

The present invention is directed to the field of gun systems, and more specifically directed to a stabilizing system using curvilinear recoil energy management to improve weapon stability for gun systems, especially towed artillery.

Recoil systems currently in use for artillery, and particularly towed artillery, are strictly rectilinear. In other words, the axis of motion during recoil is coaxial with the tube axis. Retardation of the recoiling parts is provided by one or more hydropneumatic cylinders, in which a working fluid is forced through one or more orifices. In these currently used systems, the moment of retarding force tends to tip the gun over backwards. Opposing this is the moment of weapon weight about the trail ends. If the overturning moment exceeds the downward weight moment, the weapon will momentarily lift about its trail ends. This condition is termed "instability," and is undesirable because of (1) possible damage to the weapon and (2) gross weapon movement requiring resighting.

An alternative, non-rectilinear, recoil system is disclosed in U.S. Patent No. 3,114,291 to Ashley. As shown in Ashley's Figure 1, the system makes use of levers and guides. There are two guideways 8 and 23 and two levers 6 and 7. Levers 6 and 7 connect slide 9 and guideway 8 to barrel 5. Lever 7 extends to a second guideway 12, which can be curved, so that during recoil the barrel is forced to a rearward and upward position. The barrel is moved so that the recoil force is directed down, rather than only back. However, Ashley does not address the problem of deceleration of upward velocity, so that the lightweight weapon stability problem remains unsolved.

U.S. Patent No. 439,570 to Anderson and U.S. Patent No. 463,463 to Spiller disclose "disappearing" guns which, after being fired, rotate vertically so that they descend behind a wall. This motion is caused by recoil. Anderson and Spiller also do not solve the problem of lightweight weapon stability. Also, Anderson and Spiller disclose gun mountings which are suitable for use only with heavy ordnance.

In summary, no system exists which addresses the problem of deceleration of upward velocity or solves the stability problem in a manner applicable to lightweight towed weapons. It is the solution of these and other problems to which the present invention is directed.

Summary of the Invention

Therefore, it is the primary object of this invention to provide a system for providing improved weapon stability for gun systems.

It is another object of this invention to provide a system for providing improved weapon stability for towed artillery.

It is still another object of this invention to provide a weapon stabilizing system for use with lightweight artillery.

It is still another object of this invention to provide a weapon stabilizing system which imposes a transient stabilizing moment during time of high destabilizing recoil loads.

It is yet another object of this invention to provide a weapon stabilizing system in which the transient stabilizing moment is tailored to overcome the destabilizing recoil loads to assure that the weapon never lifts off the ground.

It is yet another object of this invention to provide a weapon stabilizing system which does not rely solely on the static moment of weapon weight about the trail ends, so that a lighter structure can be employed without fear of instability.

The foregoing and other objects of the invention are achieved by provision of a gun system comprising a recoiling cannon portion, a stationary carriage portion, and a mounting mechanism for movably mounting the cannon portion on the carriage portion for travel along a curvilinear path. The path has two stages, a curved first stage which accelerates the cannon assembly upward and a second stage which decelerates the cannon assembly's upward motion, and which is either straight or curved in either the same or the opposite direction as the first stage, or some combination of these, as necessary. The second stage, if curved in the same direction as the first, has a shallower curve than the first stage. In one aspect of the invention the first stage has a decreasing radius of curvature in the direction of travel (i.e. recoil) of the cannon portion. In another aspect of the invention, the mounting mechanism comprises a campath mechanism and a cam follower mechanism associated with the campath mechanism, the campath mechanism having a first, curved stage and a second stage, which is either curved or straight, or both. The campath mechanism can be fixedly mounted on the cannon portion, with the cam follower mechanism fixedly mounted on the carriage portion, or the campath mechanism can be fixedly mounted on the carriage portion with the cam follower mechanism being fixedly mounted on the cannon portion.

A better understanding of the disclosed embodiments of the invention will be achieved when the accompanying detailed description is considered in conjunction with the appended drawings, in which like reference numerals are used for the same parts illustrated in the different figures.

Brief Description of the Drawings

Figure 1 is a right elevational view of a light weight towed Howitzer incorporating a first embodiment of the stabilizing system of the invention;

Figure 2 is a partial, top plan view of Figure 1;

Figure 3 is a partial perspective view of the mounting mechanism of the cannon shown in Figure 1; Figure 4 is an exploded perspective view of a right side roller set and campath of the mounting mechanism shown in Figure 3;

Figure 5 is a perspective view of a left side roller set and campath of the mounting mechanism shown in Figure 3;

Figure 6 is a cross-sectional view of the stabilizing system, taken along line 6-6 of Figure 1;

Figure 7 is a top plan view of Figure 6;

Figure 8 is a partial, right elevational view of a light weight towed Howitzer incorporating a second embodiment of the stabilizing system of the invention;

Figure 9 is a top plan view of Figure 8;

Figure 10 is a cross-sectional view of the stabilizing system shown in Figure 8, taken along line 10-10 of Figure 8;

Figure 11 is a cross-sectional view of the mounting mechanism of the cannon, taken along line 11-11 of Figure 10; Figure 12 is a graph plotting the path of the center of mass of the recoiling parts;

Figure 13 is a graph plotting cannon reaction forces versus recoil length; Figures 14a and 14b are graphs plotting axial and normal force, respectively, versus time;

Figures 15a and 15b are graphs plotting the tube- axial and tube-normal recoil velocities, respectively, versus time; Figure 15c is a graph plotting maximum tube-normal displacement versus maximum tube-axial displacement;

Figure 16 is a diagrammatic representation of the general gun configuration; Figure 17 is a diagrammatic representation of the forces acting on the cannon assembly;

Figure 18 is a diagrammatic representation of the forces acting on the carriage and cradle assembly;

Figures 19a - 19c are free body diagrams of the cannon showing the forces acting on the cannon;

Figures 20a and 20b are vector diagrams showing the forces acting on the cannon; and

Figure 21 is a graph plotting orifice areas for long and short recoils; Figure 22 is a graph plotting moments versus recoil time;

Figure 23 is a graph plotting vertical reaction on the firing platform versus recoil length;

Figure 24 is a graph showing the effect of charge on stability (i.e. vertical ground force);

Figure 25 is a graph plotting cannon velocities versus recoil length;

Figure 26 is a graph plotting cannon accelerations versus recoil length; Figure 27 is a graph plotting track angle versus recoil length; and

Figure 28 is a graph plotting recoil height versus recoil length.

Description of the Preferred Embodiments

In the present invention, curvilinear recoil is used to provide stability to a lightweight towed Howitzer. As will be described in greater detail below, curvilinear recoil works as follows: the recoiling parts travel rearwardly and upwardly during recoil in curved tracks mounted to the recoil cradle.

Weapon stability requires the balancing of the destabilizing (recoil) moment by an equal and opposite stabilizing moment. In conventional towed weapons, e.g. an M198 Howitzer which weighs 15,000 pounds, this stabilizing moment is derived from gravity acting upon the weapon's mass. In the lightweight towed Howitzer, the weapon weight is 9,000 pounds, just over one-half that of existing large caliber weapons; the available stabilizing moment therefore is substantially reduced compared with that of the conventional weapon.

Our invention involves generating an additional vertical force which produces a supplemental stabilizing moment, counteracting the destabilizing moment of the recoil force. This vertical force acts upon the recoiling parts, resulting in a recoil path which is both rearward and upward. From the shape of this path, we have termed it "curvilinear" in contrast to conventional straight-line or "rectilinear," recoil motion. The application of a vertical upward force to the recoiling parts causes an equal and opposite downward reaction force on the non-recoiling parts in accordance with Newton's Third Law. This downward reaction supplements the gravitational force, and acts as a stabilizing moment about the trail ends, permitting recoil loads to be higher without an unstable condition resulting. The vertical force on the recoiling parts results in an upward velocity, and this velocity must be returned to zero by the end of the recoil stroke. This results in a two stage recoil cycle, which is described with respect to a lightweight towed 155 millimeter Howitzer incorporating a first embodiment of the invention.

Referring now to Figures 1-7, there is shown a conventional lightweight towed 155 millimeter Howitzer 10 modified to incorporate a first embodiment of the stabilizing system of the invention. Howitzer 10 comprises a conventional stationary carriage 12 supported by conventional left and right wheels 14 and 16 and conventional left and right trails 18 and 20. A cradle 22 having left and right sides 24 and 26 held together at the top by cross members 27 and modified according to the invention as will be described in greater detail hereinafter is pivotally mounted on carriage 12. Cradle 22 is rotated up or down by a conventional balancing/elevating mechanism, shown here as left and right pistons 28 and 30. As shown in Figure 1, a cannon 32 having a longitudinal tube axis A is mounted in cradle 22 for reciprocating movement between a first, forward and downward position (solid lines) and a second, rearward and upward position (dashed lines). Most of the recoil energy is absorbed and the cannon is returned to battery by a conventional recoil recuperator mechanism, such as left and right recoil/recuperator cylinders 34 and 36 pivotally mounted between cradle 22 and cannon 32. The mounting mechanism for cannon 32 includes a forward yoke 38 positioned forward of the tube center of mass and a rearward yoke 40 positioned rearward of the tube center of mass. Yokes 38 and 40 comprise cylindrical central collars 42 and 44, respectively, for supporting and housing cannon 32 and forward left and right ears 46a and 46b and rearward left and right ears 48a and 48b, respectively, in the form of tapered structures extending from either side of central collars 42 and 44. Each collar includes a torque key 50 to prevent spinning between the yoke and the cannon tube, and a doubler 52 enveloping torque key 50. Forward left and right twin roller sets 54a and 54b are mounted on forward left and right ears 46a and 46b and rearward left and right twin roller sets 56a and 56b are mounted on rearward left and right ears 48a and 48b, respectively, via stub axles 62. Left twin rollers 54a and 56a preferably are flat, i.e., have rectangular longitudinal cross-sections, while right twin rollers 54b and 56b are trapezoidal, i.e., have trapezoidal longitudinal cross-sections.

The left and right sides 24 and 26 of cradle 22 are provided with forward left and right parallel campaths 64a and 64b, respectively, for movably engaging forward left and right roller sets 54a and 54b, and rearward left and right parallel campaths 66a and 66b, respectively, for movably engaging rearward roller sets 56a and 56b, respectively. Forward and rearward left campaths 64a and 66a have rectangular cross-sections, while forward and rearward right campaths 66a and 66b have cross-sections which are rectangular with a necked in portion at the outer face to better accommodate lateral thrust loads. The precise location of yokes 38 and 40 and their appended roller sets 54a and 54b and 56a and 56b is determined by convenience with respect to the overall weapon design. The locations will affect the division of force between the forward and rearward roller sets.

As shown in Figures 1 and 3, campaths 64a, 64b, 66a, and 66b have identical configurations, consisting of a first, curved stage and a second, straight stage. Most of the energy of the recoiling parts in a tube-axial direction, i.e. along tube axis A, is absorbed during the first stage of the recoil cycle. During this period, weapon stability is ensured by accelerating the recoiling parts (i.e., cannon 32 and its mounting mechanism) in a direction normal to the tube axis A. The normal force is generated by the action of roller sets 54a and 54b and 56a and 56b attached to the recoiling parts on curved campaths 64a and 64b and 66a and 66b, which are part of non- recoiling cradle 22.

The hydropneumatic recoil system (i.e. recoil cylinders 34 and 36) brakes the recoiling parts along tube axis A. When the recoil velocity has been reduced to an appropriate level by the recoil system, the recoiling parts will have both a small axial and small normal velocity. At this time (stage II), the high initial recoil force is reduced, and simultaneously the tube-normal force is removed by straightening campaths 64a, 64b, 66a, and 66b. Gravitational forces, plus a small component from recoil/recuperator cylinders 34 and 36, and a possible small contribution from the campaths 64a, 64b, 66a, and 66b, slow the recoiling parts to rest in a tube- normal direction by the end of the recoil stroke, as shown in Figure 13.

More specifically, as Figure 12 shows, the interaction of the cam followers (i.e. roller sets 54a, 54b, 56a, and 56b) and curved campaths (64a, 64b, 66a, and 66b, respectively) causes the center of mass of recoiling parts to follow a like curved path. A centrifugal force is generated whose magnitude is

and whose direction is along the local radius vector. V_inst is the instantaneous velocity of the center of mass of the recoiling parts. R_inst is tne corresponding radius of curvature of the campath at the point of contact between roller sets 54a, 54b, 56a, and 56b and campaths 64a, 64b, 66a, and 66b, respectively.

When fired, the specific combination of projectile and propelling charge will produce a predictable firing recoil impulse, determinable by testing of the specific combination of projectile and propelling charge or through tables. This in turn will cause the recoiling parts of the gun to move rearwardly at a predetermined velocity, likewise determinable by testing or from tables. The recoil system causes this velocity to be diminished in a controlled manner by applying a retardation force, determined by choice of the orifice size through which the recoil working fluid is forced. Again, the retardation force is determinable either by testing of the cylinder or through tables. In this manner, the force applied by the recoil system is known and predictable at any point in the recoil stroke. Additionally, the remaining velocity of the recoiling part is also known and predictable. The overturning moment is thus known and predictable at all points in the recoil stroke.

The difference between the overturning and the stabilizing moment gives the minimum additional stabilizing moment required to maintain the gun in contact with the ground. This additional moment (plus any additional safety factor) is provided by the centrifugal force generated by the cam followers/campath interaction. Since the required instantaneous centrifugal force, together with the mass of the recoiling parts and their instantaneous velocity is now known, the corresponding value for radius of curvature can be predetermined. That is,

In this manner, the "y" coordinates of each of campaths 64, 66, 68, and 70 can be determined for all corresponding values of "x" (tube-axial) coordinates. At all points in the recoil stroke, the recoiling parts will have a velocity component in both the "y" direction (normal to tube axis A) and in the "x" direction (along tube axis A). Both of these velocities must be reduced to zero by the end of the recoil stroke. At some point in the recoil stroke, the centrifugal force is reduced to 0 by making the radius of curvature infinite (i.e., each of campaths 64, 66, 68, and 70 becomes a straight line). Accordingly, the recoiling parts now cease their upward acceleration. The recoil system continues to apply a gentle retardation force, eventually bringing the recoiling parts to rest in both the "x" and "y" axes.

The final retardation force causes a small destabilizing moment, but its magnitude is such that it can be overcome by the s. jilizing moment of the static weight of the complete weapon. In effect, the curvilinear recoil motion gives Howitzer 10 an apparent weight greater than the static weight of the weapon during the period of high recoil forces. The curvilinear campath is designed to assure that the stabilizing moment of the apparent weight of the gun is sufficient to overcome the overturning moment of the recoil retardation forces, maintaining ground contract. During the latter part of recoil travel, when the curvilinear recoil force has been discontinued, the apparent weight of Howitzer 10 is diminished but ground contact is still maintained.

An alternate, equally viable stability solution exists if, as shown in Figures 8-11, the positions of the campaths and the cam followers are reversed. Thus, referring now to Figures 8-11, there is shown a lightweight towed 155 millimeter Howitzer 10' incorporating a second embodiment of the stabilizing system of the invention. Howitzer 10' also comprises a carriage 12, wheels 14 and 16, and trails 18 and 20. A cradle 22' having left and right sides 24' and 26' and modified according to a second embodiment of the invention as will be described in greater detail hereinafter is pivotally mounted on carriage 12. Cradle 22' is pivoted up and down by left and right pistons 28 and 30.

As shown in Figure 8, cannon 22 is mounted in cradle 22' for reciprocating movement between a first, forward and downward position (solid lines) and a second, rearward and upward position (dashed lines). The mounting mechanism for cannon 32 according to the second embodiment of the invention is the reverse of mounting mechanism for cannon 32 according the first embodiment of the invention, in that the campaths are positioned on cannon 32, while the cam followers are positioned on cradle 22'. Specifically, the mounting mechanism for cannon 32 comprises forward left and right campaths 64a' and 64b' and rearward left and right campaths 66a' and 66b', welded or bolted or otherwise attached to track support collars 72 mounted on cannon 32. Left and right sides 24' and 26' of cradle 22' are provided with forward left and right roller sets 54a' and 54b' of twin rollers and rearward left and right twin roller sets 56a' and 56b', respectively for movable engagement with forward left and right campaths 64a' and 64b' and rearward left and right campaths 66a' and 66b', respectively. Each of roller sets 54a', 54b', 56a', and 56b', consists of four rollers, an upper twin roller set and a lower twin roller set, housed in a circular housing 74. Placement of the roller sets in a circular housing is important in that the housing provides the walking beam structure and strength required to make the roller (follower) system work. Circular housings 74 allow the rollers to stay perpendicular to the resultant tangent of the twin rollers to the campath, as the campath curves and angles upward or downward.

Choice of the design of either the first embodiment or the second embodiment of the invention does not affect the function of the stabilizing system, and is dictated by overall weapon design. In a further alternate design, the campath of either the first or the second embodiment can be curved in the opposite direction during the second stage of recoil; that is, towards tube axis A to achieve a greater retardation in the "y" axis (the tube-normal direction). Use of this alternate construction is limited by the requirement to keep ground contact during the second stage of recoil travel.

In a still further alternate design, the campath of either the first or the second embodiment can be curved in the same direction during the second stage of recoil. In this case the curve of the second stage is shallower than that of the first stage. Stylized tube-axial and tube-normal force-time curves for the first embodiment of the stabilizing system of the invention are shown in Figures 14a and 14b. Superimposing these two force-time curves gives a net force vector and a resultant acceleration. Integration leads to a velocity-time history, resolvable into vertical and horizontal components. Further integration produces the horizontal and vertical displacement of the recoiling parts' center of mass. In stylized form, velocity-time is shown in Figures 15a and 15b and displacements shown in Figure 15c. In the configuration of the invention represented by Figures 15a and 15b, stage I accounts for 60% of the recoil distance and 40% of the recoil time, while stage II accounts for 40% of the recoil distance and 60% of the recoil time.

The preceding description of our curvilinear system and the following dynamic (stability) analysis directly support the campath location on the cradle as described with respect to the first embodiment shown in Figures 1-7, and the stability achieved thereby.

The preceding discussion on stability and the recoil system as well as the development of the governing equations and the dynamic analysis are all based on modeling the gun system as two planar rigid bodies: one recoiling and the other fixed. The recoiling body (mass) will hereafter be referred to as the "carriage." Actually, the carriage is made up of two masses or weights, one that elevates (WE) and one that remains fixed (WF). This is to allow for the movement of the carriage center of gravity associated with elevating and depressing the gun.

The general gun configuration is shown diagrammatically in Figure 16. There are two coordinate systems associated with the cannon model. The first is a ground fixed coordinate system (X-Y) centered at the end of the trail at ground level. The second is a coordinate system (U-Z) which rotates with the gun tube as the cannon elevates and which is centered at the in-battery location of the recoiling mass. This reference frame does not recoil with the cannon. The recoil displacement of the cannon (center of gravity) is measured from the U-Z coordinate system and the horizontal and vertical displacements are U and Z, respectively. The coordinate directions U and Z and the displacements U and Z should not be confused. Similarly the position (X,Y) of the cannon center of gravity can be found relative to the X-Y coordinate system. The two rigid bodies are shown separately in Figures 17 and 18 to facilitate the illustration of the forces that act between these two bodies and to make clear their equal and opposite effect. the cannon experiences forces from the carriage, parallel to the tube primarily from the recoil mechanism, and normal to the tube from cradle support points. In the case shown in Figures 1-7, the support is provided by rollers 54a and 54(b) and 56a and 56b constrained in campaths 64a and 64b and 66a and 66b, respectively, both fore and aft. The force from the recoil mechanism is referred to here as the "rod pull" and is the sum of both the recoil (cylinder) force and the recuperator force. To simplify the analysis and discussion, all the forces between the carriage and the cannon are lumped into two force components F_u parallel to the tube and Fz normal to the tube. F_u and F_z are reaction forces that support the cannon. F_x and F_y are equivalent to F_u and F_z yet based on the ground fixed X-Y coordinate system. At zero quadrant elevation F_x = F_u and F_y = F_z. F_x = +F_u(cos ɸ) - Fz(sin ɸ) F_y = +F_u(cos ɸ) + Fu(sin ɸ) ɸ = Quadrant Elevation

The criterion for stability can be derived from a consideration of Figure 18. Stability is the condition when the carriage does not rotate about the trail ends. This condition is satisfied if the vertical reaction on the firing platform (R2Y) remains positive. R2Y will remain positive and the gun stable if the stabilizing moment Mgt remains larger than the overturning moment Mov. At zero quadrant elevation, the overturning moment is the horizontal force F_x times its moment arm:

M_ov = F_u(h + z + hsp) Eq. 1 The stabilizing moment is the vertical force Fz and the fixed weights WF and WE times their respective moment arms:

M_st = F_z(A + B + U) + WF(A + AF) + WE(A + AE) Eq. 2

For stability M_st > M_ov Eq. 3

The degree of stability can be found by defining the excess stability moment Mex as

M_ex = M_st - Mov Eq. 4 also R2Y - M_ex/C Eq. 5

The larger Mex and R2Y are, the more stable the gun system is.

For a conventional recoil system, F_u would be equal to the rod pull (RP), and the force F_z would support the portion (WRZ) of the recoiling weight WR that was acting normal to the tube and cradle. At zero quadrant elevation, F_z would be equal to the entire recoiling weight, i.e., F_z - WRZ = WR. Because the sum of WF, WE and WR is limited to 9000 pounds, the stabilizing moment is greatly reduced.

M_St = F_z(A + B + U) + WF(A + AF) + WE(A + AE) (For a conventional gun) F_z = WR

M_st = WR(A + B + U) + WF(A + AF) + WE(A + AE)

Curvilinear recoil increases the stabilizing moment by increasing F_z. With curvilinear recoil F_z does not simply support the weight of the cannon but acts also to accelerate the cannon upward (normal to the tube) when greater stability is needed. Accelerating the tube upward ( Z direction) increases F_z by the inertial force associated with this acceleration:

F_z = M(A_z) + WRZ Eq. 6

The application of this increased F_z and resulting acceleration of the cannon in the z-direction gives the cannon a displacement ( z ) and velocity (V_z) in the z-direction. At some point in the latter part of the stroke, this velocity (V_z) must be returned to zero. To accomplish this, F_z must be reduced sufficiently to switch the sign of A_z, in effect to pull down on the cannon. If F_z is reduced in the latter portion of the recoil stroke as required, then the overturning moment must also be reduced to prevent instability during this portion of the recoil. This gives rise to two distinct stages during curvilinear recoil: stage one, defined as the portion of recoil when the tube normal acceleration A_z is positive ("upward"), and characterized by a large tube axial force F_u (rod pull large) and a commensurate tube normal force F_z for stability; and stage two, defined as the portion of recoil when the tube normal acceleration A_z is negative ("downward"), characterized by a reduced or even negative tube normal force F_z and a necessarily greatly reduced tube axial force F_u (rod pull small).

In the transition from stage one to stage two, the recoil force is greatly reduced so that during stage two, the rod pull is primarily provided by the recuperator force.

The dynamic analysis models the gun system as two planar rigid bodies; one recoiling, the other fixed. Both rigid bodies are initially at rest; at time equals zero, the time varying forces from firing impulse is applied. This accelerates the cannon in the negative U-direction while it is being acted upon by retarding forces from the recoil mechanism as modeled. Any of several firing impulse functions can be applied to the gun including (but not limited to) M203 PIMP, M203 nominal, and M119, all matched to the cannon tube with 0.7 index muzzle brake and M483 projectile. The recoil force acts to prevent the cannon from attaining free recoil velocity and continues to act to return the recoiling mass to rest. The cannon is constrained in the cradle to follow a pre-defined curvilinear campath. The path is curved upward, which forces the cannon to be displaced and accelerated normally to the tube center-line as it recoils axially. This acceleration "generates" the force that contributes the stability during stage one recoil.

The magnitudes of F_u and F_z at all time steps are found by solving the differential equations of motion set forth below for the recoiling mass. Once the dynamic forces are found, the firing loads on all major components are statically determined at each time step using the known system geometry.

Figure 19a is the free body diagram of the cannon (recoiling mass). From this diagram comes the two differential equations that describe the motion of the gun system. The carriage is assumed stationary, a condition satisfied if the vertical firing platform reaction R2Y remains positive. Summing forces in the u direction yields the first differential equation.

Tube axial: ΣF(u) = M(A_U) = F_u - (-)FIMPU - WRU

M(A_u) = F_u + FIMPU - WRU A_u = (F_u + FIMPU - WRU)/M Eq. 7

Summing forces in the z direction yields the second differential equation Tube normal: ΣF(z) = M(A_Z) = F_z - WRZ

A_z = (F_z - WRZ)/M Eq. 8

As shown in Figure 19a the center of gravity may be displaced from the center line of the tube. This introduces a moment from the firing impulse force (FIMPU) which is balanced by moving the point of application of the reaction forces F_u and _Fz axially, providing a countering moment.

Sum of the moments about the center of gravity yields ΣMOM = 0 = (-) FIMPU(ZEIMP) - F_z(-UEFZ)

UEFZ = FIMPU(ZEIMP)/F_z

when the firing force has gone to zero, the "eccentricity" UEFZ will be zero and the reaction forces F_u and F_z will act through the center of gravity.

F_u and F_z are the reactions on the cannon from the carriage of the gun; specifically, these forces are supplied by the cradle. The cradle applies these forces by two means, the recoil mechanism and the cam tracks. The recoil mechanism pulls on the cannon via the breech band (see Figures 19b and 19c), and has two components that are related by the geometry of the recoil mechanism. Although as shown in Figure 3 there are two pairs of tracks, a front pair and a rear pair, a single equivalent track force (TR) will be used (a single force on a rigid body can be replaced by two different forces located at any two locations, here the fore and aft roller contact points).

The point of action of the track force (TR) is not fixed; rather it moves such that the sum of the moments about the center of gravity remains equal to zero. This ensures that the cannon translates only.

Figures 19a, 19b, and 19c are all equivalent. So,

F_u = TRU + RPU Eq. 9 and F_z = TRZ - RPZ Eq. 10

The total recoil force (RP) is found from the mathematical recoil model and components are found from using the recoil mechanism inclination angle oζ. RP = (C) (VS VS)/(A_o A_o) = (Recup. Force), where C is a constant that includes effective piston area, orifice discharge coefficient, and oil density.

RPU = RP cos a α RPZ = RP sin aα The track force TR is not known, but the relationship between the components can be determined. The track force results from constraining the cannon to follow a pre-determined path. The path can be represented by a function of u, pf(u), such that: Z = pf(u) or Z = pf

The track angle (β) is defined as positive CW so: tan β = -slope = -dz/du = -pf' Referring to Figures 20(a) and 20(b): tan β = TRU/TRZ = -pf'

TRU = -(TRZ)pf' Eq. 11

Two differential equations were developed.

Equations 7 and 8. The constraint of the recoil track couples these two equations, resulting in the first equation 7 being the only independent equation. The displacement Z is strictly a function of U (i.e. Z = pf) so the following relationship can be developed:

Z = pf Eq. 12 dz/du = pf'

V_z = pf' .VU Eq. 13

and

A_z = pf"(V_u)² = pf'.(A_u) Eq. 14

Now defined are position, velocity, and acceleration in the z-direction, all as functions of position, velocity, and acceleration in the u-direction. From Eq. 7 A_u = (F_u + FIMPU - WRU)/M 8 A_z = (F_z - WRZ)/M 9 F_u = TRU + RPU

10 F_z = TRZ - RPZ

11 TRU = -(TRZ) pf From Eq. 9 and 11 F_u = -TRZ(pf') + RPU From Eq. 10 TRZ = F_z + RPZ

Combine Fu = -pf' (F_z + RPZ) + RPU From Eq. 8 F_z = MA_Z + WRZ

Combine F_u = -pf' (MA_Z + WRZ + RPZ) + RPU From Eq. 14 A_z = pf'.A_u + pf".V_u ² F_u - -pf (M[pf'A_u + pf"V_u ²] + WRZ + RPZ)

+ RPU Add Eq. 7 for A_u F_u = -pf (M[pf (F_u + FIMPU-WRU)/M + pf"V_u ²] + WRZ + RPZ) + RPU Solve for F_u:

Also from Eq. 8 F_z = M.A_Z + WRZ Combining with Eq. 14 F_Z = MpfA_u + Mpf" V_u.V_u + WRZ Combining with Eq. 7 F_z - pf' (F_u + FIMPU - WRU) + Mpf" V_u.V_u + WRZ Eq. 16

The track campath used for the dynamic analysis was matched to the current configuration and recoil mechanism model to ensure weapon stability at zero quadrant elevation. In the present example, a positive ground force on the firing platform was specified to decay from 2000 to a minimum of 1000 lbf. An additional factor of safety for stability was included by designing the campath in the present example for the M203 PIMP charge. This results in even greater stability when a nominal M203 is fired. The path description consists of pairs of points U and Z (Table 1). One can see that the point pairs do not extend the full length of recoil. The path beyond the data is defined as a straight line tangent to the last portion of the track, and as such does not need to be explicitly tabulated.

The driving function for the dynamic analysis is the force applied to the cannon by the firing of the projectile. This time dependent force is calculated from the tables of total impulse supplied to the recoiling mass versus time. the force is calculated by:

FIMPU = (change in IMPULSE)/(change in TIME) The effects of different charges on the curvilinear system are determined by using a different firing impulse table as input. The tables are produced from internal ballistics calculations and include the gas action on a muzzle brake with a momentum index of 0.7. Three different tables were used:

Table 2: M203 PIMP - M483 projectile Table 3: M203 nominal - M483 projectile

Table 4: Ml19 nominal - M483 projectile

The recoil force is provided by a recoil cylinder model where the recoil force (F-recoil) is given by: F-recoil - C (V_s · V_S)/(A_o · A_o) The transition between stage one recoil and stage two is accompanied by a rapid drop in F-recoil. This is accomplished by rapidly enlarging the orifice areas. The enlarging of the orifice areas is modeled as a smooth, albeit rapid, transition rather than as an abrupt change. This should more closely represent the response of a real system. This more protracted transition provides for a more forgiving match between the recoil mechanism and the campath profile. Additionally, the recoil force is not removed entirely during stage two but rather is designed to a nominal value of 1000 lbf. This has several advantages over letting the recuperator alone control stage two: (1) the orifice areas are now defined in stage two rather than being infinity; (2) the active recoil cylinder can now be used to fine tune the stage tow recoil; and (3) a velocity dependent retarding force is now present in stage two to help dissipate the energy from an overpressure. Two orifice profiles are developed for the recoil model; one for long recoil, and one for short recoil. These orifice areas are plotted in Figure 21 and tabulated in Tables 5 and 6. These orifice areas are equivalent areas, and do not correspond directly to the orifice areas for the actual recoil cylinder.

The total recoil mechanism force RP includes a linear spring representation of the recuperator function. So,

RP = F-recoil + FRCP + DFRCP(S), where S is the magnitude of extension of the recoil mechanism in feet.

The exact gun configuration and all remaining data are contained in the input data file shown in Table 7, and tabulated in Table 8. The primary objective of the preceding dynamic analysis was to demonstrate the stability of the gun system using curvilinear recoil. Stability is ensured if the stabilizing moment about the trail ends M_st is greater than the overturning moment M_ov. M_ex = M_st- M_ov. If M_st is greater than M_ov then M_ex is positive and the forward vertical ground reaction (R2Y) will remain positive and the gun will not "hop." For the condition of zero quadrant elevation and the M203 (nominal) charge. Figure 22 illustrates that M_st is greater than M_ov and Figure 23 illustrates that R2Y remains positive. The gun system was designed to be stable, even with a M203 PIMP charge. Figure 24 shows that indeed, the gun is stable with the PIMP charge. Figure 24 also shows that the gun system gets progressively more stable as the charge is reduced, the M119 charge being the most stable of the three shown.

For each dynamic analysis run, there are provided up to four files or tables of output with suffixes ".CP1," ".CP2," ".CP3," and ^M.CP4." Each run has a file name associated with it, beginning first with the prefix "XI" which identifies all files used by, and generated for, this analysis. The remainder of the file name identifies the charge and the quadrant elevation of the gun in degrees. All plots are generated from the tables provided, and the file name of the source is printed in the right-most portion of the title.

Additional data is plotted in Figures 13 and 25-28 for the case of the M203 (nominal charge) and a quadrant elevation equal to zero, because this is the worst condition at which the gun must remain stable.

Table 9 describes all of the headings for Tables 10-16. In addition to the plotted results are tables containing all the data for a variety of quadrant elevations and charges. The tabulated results include:

Table 10.1 X1M203QE00.CP1 long recoil/M203

Table 10.2 X1M203QE00.CP2 long recoil/M203 Table 10.3 X1M203QE00.CP3 long recoil/M203

Table 10.4 X1M203QE00.CP4 long recoil/M203 Table 11.1 X1SRQE45.CP1 short recoil/M203

Table 11.2 X1SRQE45.CP2 short recoil/M203

Table 11.3 X1SRQE45.CP3 short recoil/M203

Table 11.4 X1SRQE45.CP4 short recoil/M203

Table 12.1 X1SRQE70.CP1 short recoil/M203

Table 12.2 X1SRQE70.CP2 short recoil/M203

Table 12.3 X1SRQE70.CP3 short recoil/M203

Table 12.4 X1SRQE70.CP4 short recoil/M203

Table 13 X1M203QE05.CP1 long recoil/M203

Table 14 X1M203QE20.CP1 long recoil/M203

Table 15 X1PIMPQE00.CP1 long recoil/PIMP

Table 16 X1M119QE00.CP1 long recoil/M119

Thus, it can be seen that curvilinear recoil will ensure stability for a 9000 pound, 155 mm towed Howitzer Demonstrator under all firing conditions. While preferred embodiments of the invention have been disclosed, it should be understood that the spirit and scope of the invention are to be limited solely by the appended claims, since numerous modifications of the disclosed embodiments will undoubtedly occur to those of skill in the art.

20 .0000 000. .0023 - 502. .0031 -1073. .0040 -2051. .0047 -3016. .0054 -4075. .0060 -4994. .0067 -6025. .0075 -7096. .0085 -8076. .0100 -9035. .0123 -9913. .0133 -10006. .0163 -10211. .0203 -10406. .0271 -10602. .0337 -10704. .0514 -10806. .1711 -10843. 10.00 -10843.

M203 SHOT IMPULSE DATA (PIMP) M483 0.7 M.B.

TABLE 2

14 .0000 000. .0030 -763. .0042 -1797. .0048 -2473. .0069 -5079. .0090 -7291. .0108 -8550. .0129 -9434. .0150 -9677. .0195 -9955. .0315 -10286. .0665 -10443. .1365 -10455. 10.00 -10455.

M203 SHOT IMPULSE DATA (NOMINAL) M483 0.7 M.B

TABLE 3 16

.0000 000.

.0040 -949.

.0050 -1601.

.0060 -2396.

.0070 -3261.

.0080 -4123.

.0100 -5675.

.0120 -6709.

.0140 -7361.

.0155 -7712.

.0203 -7952.

.0253 -8104.

.0453 -8322.

.0803 -8373.

.2803 -8379.

10.00 -8379.

M119 SHOT IMPULSE DATA

(NOMINAL) M483 0.7 M.B.

TABLE 4

r_ !*^*!^■-• -n-^r-".!!--.^ ύ 3240. 1430. 4330. 2000. 16.08 8.00 19 33 3.833 -1.43 4.00 .001 5 1

0.854 6.813 0.854 8.792 700. 0.2 0.0 1000.

0.0 0.0 2.646 -1.688 6000. 500. 1

2.0 0.8333 2.25 -0.250 0.0 0.0 0.0 0.0 0.0

2.417 -1.625 4.833 1.017 4.0 4.0

***** MAY 14, 1986 CONFIGURATION WITH SPADE REACTION OFFSET. WF WE WR - A B C H AF AE TIME PRINT - STEP FREQ. R01 RD1 R02 RD2 - - STAGE 2 F-RECOIL I ll__.J

I ETRl ETR1 DTR1 DTR2 FRCP DFRCP

T1 02 T3 HSP AEY FX_2 A3 BY HTB T4 T5 T6 T7 - - ***** VARIABLE NAMES ARE LISTED AS THEIR VALUES APPEAR IN THE DATA FILE.

TABLE 7

LWTH SYSTEM DIMENSIONS

DATE OF DISTR IBUTION

OF THIS I NFORMATION - May 20 , 1986

DATE OF ASSOCIATED COMPUTER RUNS - May 17,18, 1986

Ibf

WR 4330.0

WF 3240.0

WE 1430.0

FRCP 6000.0 DFRCP 500.0 (Ibf/foot)

Inches

A 193.0

B 96.0

BY 0.0

C 232.0

H 46.0

HTB 0.0

HSP 3.0

A3 0.0

AF -17.2

AE 48.0

AEY 0.0

R01 10.25

RD1 81.75

TABLE 8 R02 10.25

RD2 105.5

ETR1 0.0

DTR1 31.75

ETR2 0.0

DTR2 -20.25

T1 24.0

T2 10.0

T3 29.0

T4 27.0

T5 -19.5

T6 58.0

T7 12.2

TABLE 8 (Continued)

FORCES DESCRIPTIONS FOR COMPUTER PRINT-OUTS

All forces are in Ibf. And forces printed-out are the sum for both sides of the gun.

All forces and dimensions are drawn on diagrams in the direction that was assumed positive for the dynamic analysis and resulting computer print-outs except where noted by a "(-)" which means that direction shown is negative.

Displacements, Velocities and Accelerations

NAME DESCRIPTION UNITS

U recoil displacement of cannon parallel ft to cradle (and tube)

Z recoil displacement of cannon perpendicular ft to cradle (and tube)

VU recoil velocity of cannon parallel ft/s/s to cradle (and tube)

VZ recoil velocity of cannon perpendicular ft/s/s to cradle (and tube)

AU recoil acceleration of cannon parallel ft/s/s to cradle (and tube)

AZ recoil acceleration of cannon perpendicular ft/s/s to cradle (and tube)

TABLE 9 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

WR Weight of recoiling mass centered at

WF Weight of non-recoiling non-elevating mass centered at

WE Weight of non-recoiling elevating mass centered at - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

NAME DESCRIPTION COMPONENT DIRECTION

RRU Rod pull force U

RP Z R o d p u l l f o r c e Z

TRU1 Breech end track force U

TRZ1 Breech end track force Z

TRU2 Muzzle end track force U

TRZ2 Muzzle end track force Z

F14_U Trunnion force on cradle U

F14_Z Trunnion force on cradle Z

TABLE 9 (Continued) F13_U El evating/equilibrator mech force U

F13_Z El evati ng/equilibrator mech force Z

F12_X Trunnion force on upper carriage X F12_Y Trunnion force on upper carriage Y

F11_X El evator/equilibrator force X on upper carriage

F11_Y El evator/equilibrator force Y on upper carriage

F9_Y Support force on upper carriage Y from lower carriage

F3_Y Recoil pad support force on upper Y carri age

*F2_X Lower pintle shear force X from spade assembly

* The presence of this second pintle shear (F2_X) force makes the upper carriage statically indeterminate. So (F2_X) must be chosen prior to running the computer solution. The value for (F2_X) is dependent upon the design of the pintle-spade assembly interface and upon the deflections of all associated parts.

TABLE 9 (Continued) NAME DESCRIPTION COMPONENT DIRECTION

F2 Y Pintle column load from spade Y assembly

Fl X Upper pintle shear force from X spade assembly

F10_Y=-F9_Y Force on trail/lower carriage Y from upper carriage

F8 Y=-F3 Y Force on recoil pads from Y upper carriage

F7_Y Force from spade assembly Y

M2 Moment (force couple(s)) from Ibf-ft spade assembly . F-FLOAT_Y Vertical ground force on float Y (=R2Y) (vertical reaction number 2)

R2X Horizontal ground force on spade/ X float (horizontal reaction number 2)

R1Y Vertical ground forces on trail end Y

(vertical reaction number 1)

FTRACK Total (Net) track force

RP Total rod pull (recoil + recup.)

TABLE 9 (Continued) OR COE F = 14 . 40 Q . E . = 0 . 00 ( D E GR E E S )

T I ME R P FTR AC K F - F L OAT Y U Z V U VZ AU AZ

0.000 0. 4330. 9335. 0.000 0.000 0.00 0.00 0.00 0.00 0.

0.005 42736. 8587. 5592. -0.032 0.000 -19.44 0.05 -7829.01 31.63 0.

0.010 70652. 11431. 3100. -0.232 0.001 -56.47 0.23 -4671.30 52.71 0.

0.015 92648. 14813. 2328. -0.548 0.003 -65.87 0.57 -170.42 77.66 0.

0.020 96579. 15270. 1703. -0.874 0.006 -64.51 0.96 387.27 80.72 0.

0.025 97058. 15690. 1720. -1.190 0.012 -61.93 1.37 518.74 83.37 0.

0.030 97169. 16363. 2070. -1.494 0.020 -59.33 1.79 520.66 87.75 0.

0.035 95061. 15715. 1342. -1.783 0.030 -56.15 2.21 677.53 82.22 0.

0.040 91826. 15652. 1533. -2.055 0.042 -52.82 2.62 654.66 80.99 0.

0.045 88312. 15360. 1530. -2.311 0.056 -49.61 3.02 629.72 78.00 0.

0.050 84575. 15001. 1516. -2.551 0.072 -46.53 3.40 603.14 74.50 0.

0.055 80672. 14979. 1919. -2.777 0.090 -43.58 3.77 575.59 73.49 0.

0.060 80631. 15342. 1855. -2.987 0.110 -40.71 4.14 577.23 75.00 0.

0.065 80583. 15921. 1986. -3.184 0.132 -37.81 4.52 579.36 77.97 0.

0.070 79205. 15521. 1371. -3.365 0.155 -34.82 4.90 603.18 73.69 0.

0.075 76722. 15402. 1297. -3.532 0.181 -31.84 5.26 587.31 71.48 0.

0.080 78470. 16458. 1345. -3.684 0.208 -28.87 5.63 605.04 77.11 0.

0.085 79147. 17303. 1316. -3.820 0.237 -25.81 6.03 615.86 80.82 0.

0.090 77645. 17667. 1217. -3.942 0.268 -22.74 6.43 611.17 80.73 0.

0.095 73804. 17643. 1197. -4.048 0.301 -19,73 6.83 589.77 77.52 0.

0.100 67804. 17600. 1559. -4.139 0.336 -16.86 7.20 553.63 73.66 0.

0.105 10363. -315. 959. -4.218 0.373 -14.94 7.35 74.65 -36.70 0.

0.110 9053. 249. 1723. -4.292 0.409 -14.61 7.18 66.77 -32.82 0.

0.115 9085. 260. 1681. -4.364 0.445 -14.27 7.02 67.02 -32.95 0.

0.120 9114. 270. 1641. -4.434 0.480 -13.94 6.85 67.27 -33.07 0.

0.125 9143. 279. 1601. -4.503 0.513 -13.60 6.69 67.51 -33.19 0.

0.130 9171. 289. 1563. -4.570 0.546 -13.26 6.52 67.74 -33.30 0.

0.135 9197. 299. 1526. -4.636 0.579 -12.92 6.35 67.96 -33.41 0.

0.140 9222. 232. 1431. -4.699 0.610 -12.58 6.18 69.19 -34.01 0.

0.145 9245. 242. 1398. -4.762 0.641 -12.23 6.01 69.39 -34.11 0.

0.150 9268. 251. 1365. -4.822 0.670 -11.89 5.84 69.58 -34.20 0.

0.155 9288. 261. 1335. -4.880 0.699 -11.54 5.67 69.75 -34.29 0.

TABLE 10, 1

0.160 9307. 270. 1306. -4.937 0.727 -11.19 5.50 69.92 -34.37 0.

0.165 9326. 279. 1278. -4.992 0.754 -10.84 5.33 70.08 -34.45 0.

0.170 9341. 289. 1252. -5.046 0.780 -10.49 5.16 70.22 -34.52 0.

0.175 9357. 298. 1227. -5.097 0.805 -10.14 4.98 70.36 -34.59 0.

0.180 9370. 307. 1204. -5.147 0.830 -9.78 4.81 70.47 -34.64 0.

0.185 9382. 316. 1182. -5.195 0.854 -9.43 4.64 70.59 -34.70 0.

0.190 9394. 325. 1161. -5.241 0.876 -9.08 4.46 70.70 -34.75 0.

0.195 9402. 335. 1143. -5.286 0.898 -8.72 4.29 70.78 -34.79 0.

0.200 9410. 344. 1125. -5.328 0.919 -8.37 4.11 70.86 -34.84 0.

0.205 9415. 353. 1109. -5.369 0.939 -8.02 3.94 70.93 -34.87 0.

0.210 9418. 364. 1097. -5.409 0.959 -7.66 3.77 70.96 -34.88 0.

0.215 9419. 373. 1084. -5.446 0.977 -7.31 3.59 71.01 -34.91 0.

0.220 9417. 384. 1075. -5.482 0.995 -6.95 3.42 71.02 -34.91 0.

0.225 9413. 395. 1068. -5.516 1.011 -6.60 3.24 71.01 -34.91 0.

0.230 9406. 405. 1061. -5.548 1.027 -6.24 3.07 71.01 -34.91 0.

0.235 9395. 418. 1060. -5.578 1.042 -5.89 2.89 70.96 -34.88 0.

0.240 9383. 431. 1059. -5.607 1.056 -5.53 2.72 70.90 -34.85 0.

0.245 9367. 444. 1061. -5.633 1.069 -5.18 2.54 70.82 -34.81 0.

0.250 9346. 458. 1066. -5.658 1.081 -4.82 2.37 70.71 -34.76 0.

0.255 9323. 473. 1074. -5.682 1.093 -4.47 2.20 70.58 -34.70 0.

0.260 9297. 487. 1083. -5.703 1.103 -4.12 2.02 70.44 -34.63 0.

0.265 9266. 504. 1097. -5.723 1.113 -3.77 1.85 70.25 -34.54 0.

0.270 9232. 521. 1112. -5.741 1.122 -3.41 1.68 70.06 -34.44 0.

0.275 9197. 538. 1129. -5.757 1.130 -3.07 1.51 69.85 -34.34 0.

0.280 9158. 556. 1149. -5.771 1.137 -2.72 1.34 69.62 -34.22 0.

0.285 9118. 574. 1169. -5.784 1.143 -2.37 1.16 69.39 -34.11 0.

0.290 9078. 591. 1191. -5.795 1.149 -2.02 0.99 69.14 -33.99 0.

0.295 9041. 608. 1212. -5.804 1.153 -1.68 0.82 68.91 -33.87 0.

0.300 9006. 622. 1230. -5.812 1.157 -1.33 0.66 68.70 -33.77 0.

0.305 8977. 634. 1247. -5.818 1.160 -0.99 0.49 68.52 -33.68 0.

0.310 8955. 643. 1259. -5.822 1.162 -0.65 0.32 68.39 -33.62 0.

0.315 8942. 648. 1267. -5.824 1.163 -0.31 0.15 68.31 -33.58 0.

0.320 8938. 650. 1269. -5.825 1.163 0.04* -0.02 68.28 -33.56 0.

TABLE 10. 1 (Continued)

ORCOEF = 14.40 Q.E. = 0.00 (DEGREES)

TIME U Z RPU RPZ TRU1 TRZ1 TRU2 TRZ2 FU FZ

0.000 0.000 0.000 0. 0. 0. 1686. 0. 2644. 0. 4330.

0.005 -0.032 0.000 42736. 0. 31. 11766. -8. -3179. 42758. 8587.

0.010 -0.232 0.001 70652. 6. 76. 18384. -29. -6953. 70699. 11425.

0.015 -0.548 0.003 92648. 30. 207. 24073. -80. -9260. 92775. 14783.

0.020 -0.874 0.006 96579. 74. 373. 25093. -146. -9824. 96806. 15195.

0.025 -1.190 0.012 97057. 135. 562. 25447. -215. -9761. 97404. 15551.

0.030 -1.494 0.020 97169. 215. 781. 25855. -287. -9500. 97663. 16140.

0.035 -1.783 0.030 95060. 306. 998. 25327. -379. -9625. 95679. 15397.

0.040 -2.055 0.042 91825. 402. 1232. 24814. -456. -9181. 92601. 15231.

0.045 -2.311 0.056 88310. 502. 1471. 24162. -538. -8830. 89244. 14829.

0.050 -2.551 0.072 84573. 603. 1714. 23440. -620. -8479. 85667. 14358.

0.055 -2.777 0.090 80668. 702. 1972. 22812. -682. -7888. 81959. 14221.

0.060 -2.987 0.110 80627. 838. 2353. 23150. -802. -7886. 82178. 14425.

0.065 -3.184 0.132 80577. 984. 2819. 23582. -929. -7773. 82467. 14825.

0.070 -3.365 0.155 79197. 1121. 3284. 23354. -1123. -7985. 81358. 14248.

0.075 -3.532 0.181 76712. 1245. 3798. 22991. -1288. -7795. 79223. 13951.

0.080 -3.684 0.208 78457. 1445. 4686. 24023. -1535. -7869. 81608. 14708.

0.085 -3.820 0.237 79130. 1642. 5775. 24736. -1841. -7886. 83064. 15208.

0.090 -3.942 0.268 77624. 1803. 7002. 24751. -2193. -7751. 82433. 15197.

0.095 -4.048 0.301 73779. 1908. 8320. 24031. -2548. -7359. 79552. 14764.

0.100 -4.139 0.336 67777. 1942. 9700. 22712. -2787. -6526. 74689. 14244.

0.105 -4.218 0.373 10358. 327. 1202. 2445. -1341. -2727. 10219. -609.

0.110 -4.292 0.409 9048. 311. 1160. 2360. -1050. -2136. 9158. -88.

0.115 -4.364 0.445 9078. 338. 1185. 2410. -1070. -2177. 9193. -105.

0.120 -4.434 0.480 9107. 363. 1209. 2459. -1090. -2217. 9226. -121.

0.125 -4.503 0.513 9135. 387. 1232. 2507. -1109. -2256. 9258. -137.

0.130 -4.570 0.546 9162. 411. 1255. 2553. -1128. -2294. 9289. -152.

0.135 -4.636 0.579 9187. 434. 1277. 2597. -1145. -2329. 9319. -166.

0.140 -4.699 0.610 9211. 457. 1285. 2614. -1183. -2406. 9313. -248.

0.145 -4.762 0.641 9233. 478. 1305. 2656. -1199. -2438. 9339. -261.

0.150 -4.822 0.670 9254. 499. 1325. 2696. -1214. -2471. 9365. -274.

0.155 -4.880 0.699 9274. 519. 1344. 2735. -1229. -2501. 9389. -285.

TABLE 10.2

0.160 -4.937 0.727 9292. 538. 1363. 2772. -1243. -2530. 9411. -296.

0.165 -4.992 0.754 9309. 557. 1380. 2808. -1257. -2557. 9432. -307.

0.170 -5.046 0.780 9323. 575. 1397. 2842. -1270. -2583. 9451. -316.

0.175 -5.097 0.805 9338. 592. 1413. 2875. -1282. -2608. 9470. -325.

0.180 -5.147 0.830 9350. 609. 1429. 2906. -1293. -2631. 9486. -333.

0.185 -5.195 0.854 9361. 624. 1443. 2936. -1304. -2653. 9501. -341.

0.190 -5.241 0.876 9372. 639. 1458. 2965. -1314. -2674. 9515. -348.

0.195 -5.286 0.898 9380. 654. 1471. 2993. -1323. -2692. 9527. -353.

0.200 -5.328 0.919 9386. 667. 1484. 3018. -1332. -2710. 9538. -359.

0.205 -5.369 0.939 9391. 680. 1496. 3043. -1340. -2726. 9547. -363.

0.210 -5.409 0.959 9392. 692. 1507. 3066. -1346. -2739. 9553. -365.

0.215 -5.446 0.977 9393. 703. 1517. 3087. -1353. -2752. 9558. -368.

0.220 -5.482 0.995 9390. 714. 1527. 3106. -1358. -2762. 9559. -369.

0.225 -5.516 1.011 9385. 723. 1536. 3124. -1362. -2770. 9559. -369.

0.230 -5.548 1.027 9378. 732. 1544. 3141. -1365. -2777. 9557. -368.

0.235 -5.578 1.042 9366. 740. 1551. 3155. -1367. -2780. 9551. -365.

0.240 -5.607 1.056 9353. 748. 1558. 3169. -1368. -2782. 9543. -361.

0.245 -5.633 1.069 9336. 754. 1563. 3180. -1368. -2782. 9532. -356.

0.250 -5.658 1.081 9315. 759. 1568. 3189. -1366. -2778. 9517. -348.

0.255 -5.682 1.093 9292. 764. 1572. 3197. -1363. -2773. 9500. -340.

0.260 -5.703 1.103 9265. 768. 1575. 3203. -1360. -2766. 9480. -331.

0.265 -5.723 1.113 9234. 771. 1577. 3208. -1354. -2755. 9456. -318.

0.270 -5.741 1.122 9199. 773. 1578. 3211. -1348. -2743. 9429. -305.

0.275 -5.757 1.130 9164. 775. 1579. 3212. -1342. -2729. 9401. -292.

0.280 -5.771 1.137 9125. 776. 1579. 3212. -1333. -2713. 9371. -276.

0.285 -5.784 1.143 9085. 776. 1578. 3210. -1325. -2695. 9338. -261.

0.290 -5.795 1.149 9045. 775. 1577. 3208. -1316. -2677. 9306. -245.

0.295 -5.804 1.153 9008. 775. 1575. 3205. -1307. -2660. 9276. -229.

0.300 -5.812 1.157 8973. 774. 1574. 3202. -1300. -2644. 9247. -216.

0.305 -5.818 1.160 8944. 773. 1572. 3199. -1293. -2630. 9224. -204.

0.310 -5.822 1.162 8922. 772. 1571. 3196. -1288. -2619. 9205. -195.

0.315 -5.824 1.163 8908. 771. 1570. 3194. -1284. -2613. 9194. -190.

0.320 -5.825 1.163 8904. 771. 1570. 3194. -1283. -2611. 9191. -188.

TABLE 10 .2 (Continued] 1

FORCES ON CRADLE AND TRAIL/LOWER CARRIAGE *************** ORCOEF = 14.40 q.E. = 0.00 (DEGREES)

TIME F14 U F14 Z F13 U F13 Z F7_Y R2_X R2_Y R1_Y M2

0 000 -9456. -4581. 9456. 10341. 4607. 0. 9335. -335. 0.

0 005 25388. -8978. 17370. 18995. 21023. 42758. 5592. 7665. 96206. 0 010 48576. -11338. 22123. 24193. 31913. 70699. 3100. 12994. 159073. 0, 015 65683. -13414. 27093. 29627. 41107. 92775. 2328. 17125, 208745. 0, 020 70243. -12422. 26563. 29048. 43020. 96806. 1703. 18163. 217814. 0.025 71532. -11311. 25872. 28292. 43720. 97404. 1720. 18501. 219158. 0.030 72179. -10298. 25484. 27868. 44410. 97663. 2070. 18741. 219743. 0.035 72586. -8426. 23093. 25253. 43759. 95679. 1342. 18725. 215278. 0.040 70963. -7001. 21638. 23662. 42941. 92601. 1533. 18368. 208353. 0.045 69317. -5532. 19927. 21791. 41900. 89244. 1530. 17969. 200798. 0.050 67451. -4131. 18215. 19919. 40724. 85667. 1516. 17512. 192750. 0.055 64950. -2949. 17009. 18600. 39639. 81959. 1919. 16972. 184407. 0.060 66017. -1818. 16162. 17673. 40123. 82178. 1855. 17240. 184902. 0.065 66943. -721. 15523. 16975. 40735. 82467. 1986. 17509. 185550. 0.070 67507. 531. 13851. 15147. 40331. 81358. 1371. 17547. 183056.

0 075 66632. 1613. 12591. 13769. 39683. 79223. 1297. 17324. 178251.

0 080 69369. 2755. 12239. 13384. 41253. 81608. 1345. 18033. 183618.

0 085 71446. 3932. 11619. 12706. 42355. 83064. 1316. 18562. 186895.

0 090 71824. 5025. 10609. 11602. 42405. 82433. 1217. 18649. 185474.

0 095 70158. 5921. 9394. 10273. 41368. 79552. 1197. 18236. 178992.

0 100 66353. 6557. 8337. 9116. 39515. 74689. 1559. 17355. 168051.

0, 105 10312. 923. -93. -102. 6845. 10219. 959. 3101. 22992.

0, 110 8773. 921. 385. 421. 6695. 9158. 1723. 2859. 20605.

0, 115 8900. 1005. 293. 320.. 6719. 9193. 1681. 2884. 20684. 0.120 9023. 1088. 203. 221. 6743. 9226. 1641. 2909. 20758. 0.125 9144. 1168. 114. 125. 6766. 9258. 1601. 2932. 20831.0.130 9260. 1247. 28. 31. 6787. 9289. 1563. 2955. 20900.0.135 9373. 1323. -54. -60. 6854. 9319. 1526. 2977. 20967.0.140 9496. 1382. -183. -200. 6924. 9313. 1431. 2991. 20955.0.145 9599. 1453. -260. -284. 7006. 9339. 1398. 3011. 21014.0.150 9699. 1522. -334. -365. 7086. 9365. 1365. 3031. 21072.

TABLE 10.3

0.155 9794. 1588. -406. -444. 7163. 9389. 1335. 3050. 21124.

0.160 9886. 1653. -475. -520. 7238. 9411. 1306. 3068. 21175.

0.165 9974. 1716. -542. -593. 7310. 9432. 1278. 3085. 21222.

0.170 10057. 1777. -606. -663. 7378. 9451. 1252. 3102. 21264.

0.175 10138. 1835. -668. -731. 7445. 9470. 1227. 3118. 21307.

0.180 10213. 1892. -727. -795. 7509. 9486. 1204. 3133. 21343.

0.185 10284. 1946. -784. -857. 7570. 9501. 1182. 3147. 21376.

0.190 10354. 1999. -838. -917. 7629. 9515. 1161. 3161. 21410.

0.195 10417. 2050. -889. -973. 7684. 9527. 1143. 3174. 21436.

0.200 10477. 2098. -939. -1026. 7737. 9538. 1125. 3186. 21460.

0.205 10531. 2144. -985. -1077. 7787. 9547. 1109. 3198. 21480.

0.210 10580. 2188. -1027. -1123. 7833. 9553. 1097. 3208. 21494.

0.215 10626. 2230. -1068. -1168. 7877. 9558. 1084. 3218. 21505.

0.220 10665. 2269. -1105. -1209. 7918. 9559. 1075. 3226. 21509.

0.225 10699. 2307. -1139. -1246. 7955. 9559. 1068. 3234. 21508.

0.230 10728. 2342. -1171. -1281. 7989. 9557. 1061. 3240. 21503.

0.235 10749. 2375. -1198. -1310. 8020. 9551. 1060. 3245. 21489.

0.240 10766. 2406. -1223. -1338. 8047. 9543. 1059. 3250. 21472.

0.245 10777. 2435. -1245. -1361. 8072. 9532. 1061. 3253. 21447.

0.250 10779. 2462. -1262. -1380. 8091. 9517. 1066. 3255. 21413.

0.255 10777. 2486. -1277. -1396. 8109. 9500. 1074. 3256. 21375.

0.260 10768. 2508. -1288. -1409. 8122. 9480. 1083. 3256. 21330.

0.265 10752. 2528. -1296. -1417. 8132. 9456. 1097. 3255. 21276.

0.270 10729. 2546. -1300. -1422. 8138. 9429. 1112. 3252. 21216.

0.275 10703. 2562. -1302. -1424. 8141. 9401. 1129. 3249. 21153.

0.280 10671. 2575. -1300. -1422. 8141. 9371. 1149. 3245. 21084.

0.285 10635. 2587. -1296. -1418. 8139. 9338. 1169. 3240. 21011.

0.290 10596. 2596. -1290. -1411. 8134. 9306. 1191. 3234. 20938.

0.295 10559. 2605. -1284. -1404. 8129. 9276. 1212. 3229. 20870.

0.300 10524. 2610. -1277. -1396. 8123. 9247. 1230. 3224. 20807.

0.305 10494. 2615. -1270. -1389. 8117. 9224. 1247. 3219. 20753.

0.310 10470. 2618. -1265. -1383. 8112. 9205. 1259. 3216. 20712.

0.315 10456. 2620. -1261. -1379. 8109. 9194. 1267. 3214. 20687.

0.320 10451. 2620. -1260. -1378. 8108. 9191. 1269. 3213. 20680.

TABLE 10.3 (Continued)

FORCES ON UPPER CARRIAGE ********************************

ORCOEF = 14.40 Q.E. = 0.00 (DEGREES) F2 X CHOSEN= 0 .

T I M E F 12_X F 12_Y F 11_X F 11_Y F9_Y F1_X F2_Y F3_Y

0.000 9456. 4581. -9456. -10341. 10341. 0. 4728. -9309.

0.005 -25388. 8978. -17370. -18995. 18995. 42758. -15431. 6452.

0.010 -48576. 11338. -22123. -24193. 24193. 70699. -28813. 17475.

0.015 -65683. 13414. -27093. -29627. 29627. 92775. -38779. 25365.

0.020 -70243. 12422. -26563. -29048. 29048. 96806. -41317. 28895.

0.025 -71532. 11311. -25872. -28292. 28292. 97404. -42000. 30689.

0.030 -72179. 10298. -25484. -27868. 27868. 97663. -42340. 32042.

0.035 -72586. 8426. -23093. -25253. 25253. 95679. -42417. 33991.

0.040 -70963. 7001. -21638. -23662. 23662. 92601. -41408. 34407.

0.045 -69317. 5532. -19927. -21791. 21791. 89244. -40370. 34838.

0.050 -67451. 4131. -18215. -19919. 19919. 85667. -39208. 35077.

0.055 -64950. 2949. -17009. -18600. 18600. 81959. -37720. 34771.

0.060 -66017. 1818. -16162. -17673. 17673. 82178. -38268. 36450.

0.065 -66943. 721. -15523. -16975. 16975. 82467. -38749. 38029.

0.070 -67507. -531. -13851. -15147. 15147. 81358. -38960. 39491.

0.075 -66632. -1613. -12591. -13769. 13769. 79223. -38386. 39999.

0.080 -69369. -2755. -12239. -13384. 13384. 81608. -39907. 42662.

0.085 -71446. -3932. -11619. -12706. 12706. 83064. -41039. 44971.

0.090 -71824. -5025. -10609. -11602. 11602. 82433. -41187. 46212.

0.095 -70158. -5921. -9394. -10273. 10273. 79552. -40170. 46092.

0.100 -66353. -6557. -8337. -9116. 9116. 74689. -37956. 44514.

0.105 -10312. -923. 93. 102. 0. 10219. -5886. 6706.

0.110 -8773. -921. -385. -421. 421. 9158. -4972. 5893.

0.115 -8900. -1005. -293. -320. 320. 9193. -5038. 6044.

0.120 -9023. -1088. -203. -221. 221. 9226. -5102. 6190.

0.125 -9144. -1168. -114. -125. 125. 9258. -5165. 6333.

0.130 -9260. -1247. -28. -31. 31. 9289. -5225. 6471.

0.135 -9373. -1323. 54. 60. 0. 9319. -5327. 6591.

0.140 -9496. -1382. 183. 200. 0. 9313. -5493. 6675.

0.145 -9599. -1453. 260. 284. 0. 9339. -5608. 6777. TABLE 10. .4

0.150 -9699. -1522. 334. 365. 0. 9365. -5721. 6877.

0.155 -9794. -1588. 406. 444. 0. 9389. -5828. 6973.

0.160 -9886. -1653. 475. 520. 0. 9411. -5932. 7065.

0.165 -9974. -1716. 542. 593. 0. 9432. -6031. 7155.

0.170 -10057. -1777. 606. 663. 0. 9451. -6126. 7240.

0.175 -10138. -1835. 668. 731. 0. 9470. -6218. 7323.

0.180 -10213. -1892. 727. 795. 0. 9486. -6305. 7402.

0.185 -10284. -1946. 784. 857. 0. 9501. -6388. 7477.

0.190 -10354. -1999. 838. 917. 0. 9515. -6468. 7550.

0.195 -10417. -2050. 889. 973. 0. 9527. -6541. 7618.

0.200 -10477. -2098. 939. 1026. 0. 9538. -6612. 7683.

0.205 -10531. -2144. 985. 1077. 0. 9547. -6677. 7744.

0.210 -10580. -2188. 1027. 1123. 0. 9553. -6736. 7801.

0.215 -10626. -2230. 1068. 1168. 0. 9558. -6793. 7855.

0.220 -10665. -2269. 1105. 1209. 0. 9559. -6843. 7904.

0.225 -10699. -2307. 1139. 1246. 0. 9559. -6888. 7949.

0.230 -10728. -2342. 1171. 1281. 0. 9557. -6928. 7989.

0.235 -10749. -2375. 1198. 1310. 0. 9551. -6960. 8025.

0.240 -10766. -2406. 1223. 1338. 0. 9543. -6989. 8057.

0.245 -10777. -2435. 1245. 1361. 0. 9532. -7011. 8085.

0.250 -10779. -2462. 1262. 1380. 0. 9517. -7025. 8107.

0.255 -10777. -2486. 1277. 1396. 0. 9500. -7035. 8125.

0.260 -10768. -2508. 1288. 1409. 0. 9480. -7039. 8138.

0.265 -10752. -2528. 1296. 1417. 0. 9456. -7035. 8146.

0.270 -10729. -2546. 1300. 1422. 0. 9429. -7025. 8150.

0.275 -10703. -2562. 1302. 1424. 0. 9401. -7012. 8150.

0.280 -10671. -2575. 1300. 1422. 0. 9371. -6993. 8146.

0.285 -10635. -2587. 1296. 1418. 0. 9338. -6969. 8138.

0.290 -10596. -2596. 1290. 1411. 0. 9306. -6943. 8123.

0.295 -10559. -2605. 1284. 1404. 0. 9276. -6917. 8118.

0.300 -10524. -2610. 1277. 1396. 0. 9247. -6892. 8106.

0.305 -10494. -2615. 1270. 1389. 0. 9224. -6870. 8096.

0.310 -10470. -2618. 1265. 1383. 0. 9205. -6853. 8088.

0.315 -10456. -2620. 1261. 1379. 0. 9194. -6842. 8082.

0.320 -10451. -2620. 1260. 1378. 0. 9191. -6839. 8081.

TABLE 10.4 (Continued)

ORCOEF = 14.40 Q.E. = 45.00 (DEGREES) TIME RP FTRACK F-FLOAT_Y U Z VU VZ AU AZ

0.000 3062. 3062. 8724. 0.000 0.000 0.00 0.00 0.00 0.00 0.

0.005 44063. 7308. 31602. -0.032 0.000 -19.54 0.05 -7841.92 31.55 0.

0.010 87934. 10105. 53965. -0.232 0.001 -56.40 0.23 -4565.70 52.27 0.

0.015 105563. 13268. 65080. -0.547 0.003 -65.27 0.56 -97.32 75.57 0.

0.020 104530. 13596. 64737. -0.869 0.006 -63.64 0.94 423.40 77.67 0.

0.025 102663. 13924. 64003. -1.181 0.012 -60.92 1.33 537.32 79.63 0.

0.030 102178. 14470. 64090. -1.479 0.020 -58.25 1.73 534.65 83.06 0.

0.035 100779. 13603. 62236. -1.762 0.029 -55.00 2.13 696.58 75.89 0.

0.040 99304. 13367. 61038. -2.028 0.041 -51.54 2.50 686.53 73.31 0.

0.045 98165. 12608. 59435. -2.278 0.054 -48.13 2.86 678.78 66.75 0.

0.050 97313. 11698. 57809. -2.510 0.069 -44.74 3.17 673.05 58.98 0.

0.055 97201. 10714. 56435. -2.725 0.086 -41.38 3.44 672.66 50.57 0.

0.060 97560. 9942. 55495. -2.924 0.104 -38.01 3.67 675.83 43.63 0.

0.065 98288. 9047. 54590. -3.105 0.123 -34.63 3.87 681.58 35.68 0.

0.070 98770. 6941. 52344. -3.270 0.142 -31.10 4.01 716.32 18.79 0.

0.075 99371. 4627. 49947. -3.416 0.163 -27.51 4.06 719.19 0.37 0.

0.080 100752. 1543. 47096. -3.545 0.183 -23.89 4.00 726.32 -23.71 0.

0.085 98736. -1065. 43345. -3.655 0.202 -20.29 3.83 707.95 -43.71 0.

0.090 103914. -5717. 40466. -3.748 0.221 -16.69 3.53 739.09 -79.32 0.

0.095 103908. -10366. 35478. -3.822 0.237 -12.99 3.04 730.27-113.77 0.

0.100 101118. -14393. 30032. -3.878 0.251 -9.44 2.40 700.69-142.80 0.

0.105 84250. -14147. 23339. -3.917 0.261 -6.18 1.68 574.27-138.38 0.

0.110 57031. -9483. 17089. -3.941 0.268 -3.80 1.07 380.43-100.38 0.

0.115 35237. -4820. 13079. -3.956 0.272 -2.31 0.67 227.72 -63.31 0.

0.120 21947. -1714. 10916. -3.965 0.275 -1.42 0.42 135.38 -38.84 0.

0.125 14649. 67. 9809. -3.971 0.277 -0.88 0.26 84.92 -24.87 0.

0.130 10778. 1035. 9248. -3.974 0.278 -0.53 0.16 58.24 -17.30 0.

0.135 8823. 1531. 8971. -3.976 0.278 -0.28 0.08 44.78 -13.43 0.

0.140 8040. 1681. 8811. -3.977 0.279 -0.07 0.02 40.57 -12.22 0.

TABLE 11 .1

ORCOEF = 14.40 Q.E. = 45.00 (DEGREES)

TIME U Z RPU RPZ TRU1 TRZ1 TRU2 TRZ2 FU FZ

0.000 0.000 0.000 3062. 0. 0. 1796. 0. 1266. 3062. 3062.

0.005 -0.032 0.000 44063. 0. 30. 11529. -11. -4221. 44082. 7308.

0.010 -0.232 0.001 87934. 8. 88. 21275. -46. -11170. 87976. 10097.

0.015 -0.547 0.003 105563. 34. 224. 26022. -110.* -12755. 105677. 13233.

0.020 -0.869 0.006 104530. 79. 384. 26016. -183. -12421. 104731. 13516.

0.025 -1.181 0.012 102663. 141. 565. 25872. -261. -11952. 102967. 13780.

0.030 -1.479 0.020 102178. 222. 778. 26115. -347. -11652. 102609. 14242.

0.035 -1.762 0.029 100779. 316. 992. 25649. -466.* -12056. 101304. 13277.

0.040 -2.028 0.041 99303. 422. 1236. 25431. -587. -12080. 99952. 12929.

0.045 -2.278 0.054 98163. 540. 1489. 25094. -742. -12508. 98910. 12046.

0.050 -2.510 0.069 97311. 668. 1755. 24770. -928. -13101. 98138. 11001.

0.055 -2.725 0.086 97198. 809. 2045. 24583. -1157. -13906. 98086. 9868.

0.060 -2.924 0.104 97555. 962. 2377. 24589. -1420. -14693. 98512. 8934.

0.065 -3.105 0.123 98282. 1126. 2756. 24638. -1751. -15647. 99287. 7865.

0.070 -3.270 0.142 98762. 1294. 3116. 24175. -2229. -17291. 99649. 5590.

0.075 -3.416 0.163 99360. 1466. 3491. 23666. -2815. -19089. 100035. 3112.

0.080 -3.545 0.183 100739. 1652. 3856. 23040. -3601. -21518. 100994. -130.

0.085 -3.655 0.202 98720. 1775. 4117. 21835. -4315. -22881. 98522. -2822.

0.090 -3.748 0.221 103895. 2021. 4536. 21471. -5717. -27065. 102713. -7615.

0.095 -3.822 0.237 103886. 2158. 4662. 19931. -7024. -30025. 101525. -12252.

0.100 -3.878 0.251 101094. 2210. 4571. 17962. -8121. -31910. 97544. -16158.

0.105 -3.917 0.261 84228. 1910. 3870. 14281. -7570. -27935. 80528. -15564.

0.110 -3.941 0.268 57016. 1323. 2758. 9761. -5336. -18887. 54438. -10450.

0.115 -3.956 0.272 35227. 830. 1869. 6443. -3211. -11072. 33884. -5459.

0.120 -3.965 0.275 21940. 521. 1328. 4502. -1812. -6147. 21456. -2166.

0.125 -3.971 0.277 14645. 350. 1031. 3461. -1012. -3397. 14664. -286.

0.130 -3.974 0.278 10775. 258. 874. 2915. -577. -1924. 11072. 733.

0.135 -3.976 0.278 8821. 212. 795. 2642. -354. -1176. 9262. 1254.

0.140 -3.977 0.279 8037. 193. 758. 2515. -273. -905. 8523. 1417.

TABLE 11.2

FORCES ON CRADLE AND TRAIL/LOWER CARRIAGE *************** ORCOEF = 14.40 Q.E. = 45.00 (DEGREES)

TIME F14_U F14_Z F13_U F13_Z F7_Y R2_X R2_Y R1_Y M2

0.000 -4406. -3616. 8479. 7689. 8444. 0. 8724. 276. 0.

0.005 26595. -8457. 18499. 16776. 45659. 26003. 31602. 9406. 58508.

0.010 64503. -11096. 24484. 22204. 84218. 55068. 53965. 20053. 123904.

0.015 76268. -13344. 30420. 27588. 100946. 65367. 65080. 23672. 147076.

0.020 76106. -12350. 29636. 26877. 100139. 64498. 64737. 23546. 145122.

0.025 75228. -11282. 28750. 26073. 98625. 63065. 64003. 23219. 141895.

0.030 75426. -10316. 28194. 25569. 98403. 62485. 64090. 23206. 140591.

0.035 77393. -8314. 24923. 22602. 96522. 62245. 62236. 23455. 140051.

0.040 78040. -6848. 22923. 20789. 94989. 61534. 61038. 23451. 138452.

0.045 79838. -5156. 20083. 18213. 93416. 61422. 59435. 23693. 138199.

0.050 82028. -3514. 17120. 15526. 91996. 61615. 57809. 24034. 138633.

0.055 84936. -1963. 14160. 12842. 91151. 62379. 56435. 24570. 140353.

0.060 87885. -609. 11638. 10554. 90836. 63341. 55495. 25152. 142517.

0.065 91279. 696. 9019. 8180. 90753. 64645. 54590. 25848. 145452.

0.070 95819. 2211. 4841. 4391. 89696. 66509. 52344. 26742. 149646.

0.075 100441. 3574. 605. 549. 88581. 68535. 49947. 27659. 154204.

0.080 106460. 4922. -4456. -4041. 92039. 71505. 47096. 28896. 160886.

0.085 107899. 5776. -8366. -7587. 92426. 71661. 43345. 28996. 161237.

0.090 118883. 7144. -15159. -13747. 100165. 78013. 40466. 31449. 175530.

0.095 123702. 7955. -21167. -19196. 102775. 80452. 35478. 32318. 181017.

0.100 124417. 8307. -25862. -23454. 102163. 80400. 30032. 32187. 180900.

0.105 105468. 7148. -23929. -21701. 86445. 67947. 23339. 27267. 152881.

0.110 71182. 4830. -15733. -14269. 59261. 45882. 17089. 18686. 103235.

0.115 42994. 2896. -8098. -7344. 37157. 27820. 13079. 11691. 62596.

0.120 25614. 1700. -3147. -2854. 23596. 16703. 10916. 7394. 37581.

0.125 16021. 1039. -346. -314. 16130. 10571. 9809. 5027. 23786.

0.130 10919. 688. 1165. 1056. 13333. 7311. 9248. 3770. 16450.

0.135 8338. 510. 1935. 1755. 12101. 5662. 8971. 3134. 12740.

0.140 7344. 442. 2189. 1986. 11573. 5025. 8811. 2887. 11306.

TABLE 11.3

FORCES ON UPPER CARRIAGE ********************************

ORCOEF = 14.40 Q.E. = 45.00 (DEGREES) F2 X CHOSEN** 0.

TIME F12_X F12_Y F11_X F11_Y F9_Y F1_X F2_Y F3_Y

0.000 558. 5672. -558. -11432. 11432. 0. 279. -5951.

0.005 -24786. -12825. -1218. -24943. 24943. 26003. -14057. 26882.

0.010 -53456. -37764. -1612. -33014. 33014. 55068. -30253. 68017.

0.015 -63365. -44494. -2003. -41018. 41018. 65367. -35866. 80360.

0.020 -62547. -45083. -1951. -39960. 39960. 64498. -35402. 80484.

0.025 -61172. -45216. -1893. -38766. 38766. 63065. -34622. 79838.

0.030 -60629. -46040. -1856. -38016. 38016. 62485. -34313. 80353.

0.035 -60604. -48846. -1641. -33605. 33605. 62245. -34286. 83132.

0.040 -60025. -50340. -1509. -30909. 30909. 61534. -33951. 84291.

0.045 -60100. -52808. -1322. -27080. 27080. 61422. -33981. 86789.

0.050 -60488. -55518. -1127. -23085. 23085. 61615. -34187. 89705.

0.055 -61447. -58672. -932. -19093. 19093. 62379. -34716. 93387.

0.060 -62575. -61714. -766. -15693. 15693. 63341. -35341. 97055.

0.065 -64052. -65037. -594. -12162. 12162. 64645. -36163. 101200.

0.070 -66191. -69318. -319. -6528. 6528. 66509. -37352. 106670.

0.075 -68495. -73550. -40. -816. 816. 68535. -38634. 112184.

0.080 -71798. -78760. 293. 6008. 0. 71505. -44944. 117695.

0.085 -72212. -80381. 551. 11280. 0. 71661. -49081. 118182.

0.090 -79011. -89114. 998. 20440. 0. 78013. -59699. 128374.

0.095 -81846. -93096. 1394. 28540. 0. 80452. -67297. 131853.

0.100 -82102. -93850. 1703. 34872. 0. 80400. -72131. 131109.

0.105 -69522. -79632. 1575. 32266. 0. 67947. -63106. 110472.

0.110 -46918. -53749. 1036. 21215. 0. 45882. -42173. 74707.

0.115 -28353. -32449. 533. 10920. 0. 27820. -24078. 45608.

0.120 -16910. -19314. 207. 4244. 0. 16703. -12680. 27750.

0.125 -10594. -12063. 23. 467. 0. 10571. -6321. 17918.

0.130 -7234. -8207. -77. -1570. 1570. 7311. -4085. 12292.

0.135 -5535. -6257. -127. -2609. 2609. 5662. -3130. 9386.

0.140 -4881. -5506. -144. -2952. 2952. 5025. -2762. 8268. TABLE: 11.4

ORCOEF = 14.40 Q.E. = 70.00 (DEGREES) TIME RP FTRACK F-FLOAT Y U Z VU VZ AU AZ

0.000 4069. 1481. 7961. 0.000 0.000 0.00 0.00 0.00 0.00 0.

0.005 44111. 5725. 40176. -0.033 0.000 -19.58 0.05 -7849.08 31.53 0.

0.010 88123. 8545. 73841. -0.233 0.001 -56.47 0.23 -4571.82 52.42 0.

0.015 105873. 11730. 89074. -0.548 0.003 -65.37 0.56 -102.59 75.89 0.

0.020 104929. 12076. 88499. -0.871 0.006 -63.76 0.94 418.71 78.12 0.

0.025 103168. 12416. 87322. -1.183 0.012 -61.07 1.34 533.35 80.17 0.

0.030 102798. 12984. 87308. -1.481 0.020 -58.41 1.74 531.45 83.75 0.

0.035 101524. 12149. 85473. -1.766 0.030 -55.17 2.14 694.22 76.82 0.

0.040 100180. 11921. 84104. -2.033 0.041 -51.73 2.52 685.05 74.28 0.

0.045 99182. 11173. 82558. -2.283 0.055 -48.32 2.88 678.25 67.79 0.

0.050 98450. 10302. 81109. -2.516 0.070 -44.94 3.20 673.30 60.29 0.

0.055 98536. 9277. 80116. -2.732 0.087 -41.57 3.48 674.25 51.55 0.

0.060 99126. 8534. 79710. -2.932 0.105 -38.19 3.72 679.01 44.79 0.

0.065 100129. 7617. 79457. -3.114 0.124 -34.78 3.92 686.65 36.65 0.

0.070 100958. 5476. 78090. -3.279 0.144 -31.23 4.06 723.75 19.44 0.

0.075 102032. 3026. 76633. -3.426 0.164 -27.60 4.11 729.78 -0.05 0.

0.080 103554. -160. 74862. -3.555 0.185 -23.92 4.05 737.56 -24.90 0.

0.085 101469. -2816. 71023. -3.666 0.204 -20.26 3.87 718.32 -45.23 0.

0.090 108365. -8029. 71179. -3.758 0.223 -16.56 3.55 760.96 -85.14 0.

0.095 107697. -12786. 66477. -3.831 0.240 -12.76 3.03 746.55- 120.19 0.

0.100 105620. -17179. 61099. -3.886 0.253 -9.10 2.34 721.16- 151.88 0.

0.105 84323. -15821. 47577. -3.923 0.263 -5.82 1.59 563.78- 138.66 0

0.110 55479. -10556. 32384. -3.946 0.269 -3.53 1.00 359.09 -96.04 0

0.115 34046. -5845. 21834. -3.959 0.273 -2.14 0.62 209.20 -58.67 0

0.120 21525. -2875. 15877. -3.968 0.276 -1.33 0.39 122.30 -35.29 0

0.125 14764. -1207. 12721. -3.973 0.277 -0.85 0.25 75.58 -22.22 0

0.130 11149. -296. 11053. -3.977 0.278 -0.54 0.16 50.68 -15.10 0

0.135 9228. 195. 10173. -3.979 0.279 -0.32 0.10 37.45 -11.26 0

0.140 8268. 393. 9692. -3.980 0.279 -0.15 0.04 32.03 -9.69 0,

0.145 7992. 464. 9567. -3.980 0.279 0.01 0.00 30.13 -9.13 0

TABLE 12 .1

ORCOEF = 14.40 Q.E. = 70.00 (DEGREES)

TIME U Z RPU RPZ TRU1 TRZ1 TRU2 TRZ2 FU FZ

0.000 0.000 0.000 4069. 0. 0. 1379. 0. 102. 4069. 1481.

0.005 -0.033 0.000 44111. 0. 29. 10922. -14.-5197. 44126. 5724.

0.010 -0.233 0.001 88123. 8. 86. 20705. -50.-12160. 88158. 8537.

0.015 -0.548 0.003 105873. 34. 219. 25485. -118.-13755. 105974. 11696.

0.020 -0.871 0.006 104929. 79. 377. 25503. -199.-13429. 105107. 11995.

0.025 -1.183 0.012 103168. 142. 555. 25387. -284.-12973. 103439. 12271.

0.030 -1.481 0.020 102798. 224. 766. 25662. -379.-12684. 103185. 12754.

0.035 -1.766 0.030 101523. 320. 979. 25236. -508.-13096. 101995. 11820.

0.040 -2.033 0.041 100179. 428. 1222. 25050. -641.-13144. 100760. 11479.

0.045 -2.283 0.055 99180. 549. 1475. 24750. -810. 13596. 99845. 10605.

0.050 -2.516 0.070 98447. 680. 1742. 24470. -1011. -14194. 99179. - 9596.

0.055 -2.732 0.087 98533. 826. 2034. 24314. -1260. -15069. 99306. 8419.

0.060 -2.932 0.105 99121. 984. 2373. 24387. -1546. -15893. 99947. 7510.

0.065 -3.114 0.124 100123. 1156. 2761. 24493. -1908. -16924. 100976. 6413.

0.070 -3.279 0.144 100949. 1333. 3134. 24102. -2428. -18672. 101655. 4097.

0.075 -3.426 0.164 102021. 1518. 3524. 23656. -3078. -20662. 102467. 1475.

0.080 -3.555 0.185 103540. 1713. 3897. 23033. -3924. -23191. 103513. -1871.

0.085 -3.666 0.204 101452. 1840. 4164. 21807. -4692. -24573. 100924. -4606.

0.090 -3.758 0.223 108344. 2127. 4633. 21635. -6314. -29486. 106663. -9978.

0.095 -3.831 0.240 107674. 2256. 4723. 19917. -7673. -32358. 104723. -14697.

0.100 -3.886 0.253 105594. 2326. 4635. 17984. -8922. -34619. 101307. -18961.

0.105 -3.923 0.263 84301. 1923. 3749. 13690. -7927. -28950. 80123. -17182.

0.110 -3.946 0.269 55464. 1293. 2565. 9008. -5457. -19160. 52573. -11445.

0.115 -3.959 0.273 34037. 804. 1689. 5786. -3326. -11397. 32399. -6415.

0.120 -3.968 0.276 21519. 513. 1177. 3973. -1994. -6729. 20702. -3269.

0.125 -3.973 0.277 14760. 354. 902. 3014. -1248. -4170. 14414. -1510.

0.130 -3.977 0.278 11146. 268. 755. 2507. -840. -2791. 11061. -551.

0.135 -3.979 0.279 9225. 222. 677. 2240. -621. -2053. 9282. -35.

0.140 -3.980 0.279 8266. 199. 633. 2089. -519. -1713. 8380. 177.

0.145 -3.980 0.279 7990. 193. 622. 2050. -487. -1606. 8125. 251.

TABLE 12.2

0.170 9412. 419. 2018. -5.065 0.790 -10.77 5.29 68.36 -33.61 0.

0.175 9433. 426. 1990. -5.118 0.816 -10.43 5.13 68.53 -33.69 0.

0.180 9451. 434. 1965. -5.169 0.841 -10.08 4.96 68.69 -33.77 0.

0.185 9471. 440. 1938. -5.219 0.865 -9.74 4.79 68.85 -33.85 0.

0.190 9489. 448. 1914. -5.266 0.889 -9.40 4.62 68.99 -33.92 0.

0.195 9505. 456. 1892. -5.313 0.911 -9.05 4.45 69.12 -33.98 0.

0.200 9520. 462. 1869. -5.357 0.933 -8.71 4.28 69.26 -34.05 0.

0.205 9532. 469. 1850. -5.400 0.954 -8.36 4.11 69.37 -34.10 0.

0.210 9545. 477. 1831. -5.440 0.974 -8.01 3.94 69.47 -34.15 0.

0.215 9555. 484. 1813. -5.480 0.994 -7.66 3.77 69.57 -34.20 0.

0.220 9563. 491. 1797. -5.517 1.012 -7.32 3.60 69.64 -34.24 0.

0.225 9569. 499. 1783. -5.553 1.030 -6.97 3.43 69.70 -34.27 0.

0.230 9571. 507. 1771. -5.587 1.046 -6.62 3.25 69.75 -34.29 0.

0.235 9574. 515. 1760. -5.619 1.062 -6.27 3.08 69.79 -34.31 0.

0.240 9572. 524. 1752. -5.649 1.077 -5.92 2.91 69.80 -34.31 0.

0.245 9568. 534. 1746. -5.678 1.091 -5.57 2.74 69.79 -34.31 0.

0.250 9561. 544. 1742. -5.705 1.104 -5.22 2.57 69.77 -34.30 0.

0.255 9547. 555. 1742. -5.730 1.117 -4.87 2.40 69.70 -34.26 0.

0.260 9534. 566. 1743. -5.754 1.128 -4.53 2.22 69.64 -34.23 0.

0.265 9513. 580. 1748. -5.776 1.139 -4.18 2.05 69.52 -34.18 0.

0.270 9485. 596. 1758. -5.796 1.149 -3.83 1.88 69.36 -34.10 0.

0.275 9457. 610. 1768. -5.814 1.158 -3.48 1.71 69.20 -34.02 0.

0.280 9419. 629. 1785. -5.831 1.166 -3.14 1.54 68.97 -33.91 0.

0.285 9372. 649. 1806. -5.845 1.173 -2.79 1.37 68.70 -33.77 0.

0.290 9325. 670. 1829. -5.859 1.180 -2.45 1.21 68.41 -33.63 0.

0.295 9269. 694. 1858. -5.870 1.185 -2.11 1.04 68.06 -33.46 0.

0.300 9207. 718. 1889. -5.880 1.190 -1.77 0.87 67.69 -33.27 0.

0.305 9143. 743. 1923. -5.888 1.194 -1.43 0.70 67.29 -33.08 0.

0.310 9085. 765. 1953. -5.894 1.197 -1.10 0.54 66.94 -32.91 0.

0.315 9034. 785. 1980. -5.899 1.200 -0.76 0.38 66.63 -32.75 0.

0.320 8997. 800. 2001. -5.902 1.201 -0.43 0.21 66.39 -32.64 0.

0.325 8979. 806. 2010. -5.903 1.202 -0.10 0.05 66.29 -32.59 0.

TABL E 13 ( Continued )

0.170 9380. 686. 4417. -5.021 0.768 -10.72 5.27 60.80 -29.89 0.

0.175 9404. 692. 4392. -5.074 0.794 -10.42 5.12 60.99 -29.98 0.

0.180 9427. 698. 4368. -5.125 0.819 -10.11 4.97 61.18 -30.07 0.

0.185 9447. 704. 4345. -5.175 0.844 -9.81 4.82 61.35 -30.16 0.

0.190 9471. 710. 4323. -5.224 0.868 -9.50 4.67 61.53 -30.25 0.

0.195 9492. 715. 4301. -5.270 0.891 -9.19 4.52 61.69 -30.33 0.

0.200 9512. 720. 4280. -5.315 0.913 -8.88 4.37 61.85 -30.41 0.

0.205 9532. 725. 4260. -5.359 0.934 -8.57 4.21 62.01 -30.48 0.

0.210 9550. 732. 4242. -5.401 0.955 -8.26 4.06 62.14 -30.55 0.

0.215 9569. 735. 4222. -5.442 0.975 -7.95 3.91 62.30 -30.63 0.

0.220 9584. 740. 4204. -5.481 0.994 -7.64 3.75 62.43 -30.69 0.

0.225 9600. 745. 4188. -5.518 1.012 -7.33 3.60 62.54 -30.75 0.

0.230 9615. 749. 4171. -5.554 1.030 -7.01 3.45 62.67 -30.81 0.

0.235 9625. 755. 4158. -5.588 1.047 -6.70 3.29 62.76 -30.85 0.

0.240 9639. 759. 4143. -5.621 1.063 -6.38 3.14 62.87 -30.91 0.

0.245 9649. 764. 4130. -5.652 1.078 -6.07 2.98 62.95 -30.95 0.

0.250 9658. 769. 4118. -5.682 1.093 -5.76 2.83 63.03 -30.98 0.

0.255 9665. 774. 4107. -5.710 1.107 -5.44 2.67 63.10 -31.02 0.

0.260 9667. 780. 4098. -5.736 1.120 -5.12 2.52 63.13 -31.04 0.

0.265 9674. 785. 4089. -5.761 1.132 -4.81 2.36 63.19 -31.06 0.

0.270 9673. 792. 4083. -5.784 1.143 -4.49 2.21 63.19 -31.07 0.

0.275 9671. 798. 4077. -5.806 1.154 -4.18 2.05 63.20 -31.07 0.

0.280 9667. 805. 4073. -5.826 1.164 -3.86 1.90 63.19 -31.06 0.

0.285 9652. 815. 4073. -5.844 1.173 -3.54 1.74 63.11 -31.02 0.

0.290 9643. 823. 4072. -5.861 1.181 -3.23 1.59 63.06 -31.00 0.

0.295 9621. 836. 4076. -5.877 1.189 -2.91 1.43 62.93 -30.94 0.

0.300 9589. 850. 4083. -5.890 1.195 -2.60 1.28 62.75 -30.85 0.

0.305 9558. 865. 4092. -5.903 1.201 -2.29 1.12 62.56 -30.75 0.

0.310 9505. 886. 4108. -5.913 1.207 -1.97 0.97 62.24 -30.60 0.

0.315 9438. 913. 4131. -5.922 1.211 -1.66 0.82 61.83 -30.39 0.

0.320 9366. 941. 4156. -5.930 1.215 -1.36 0.67 61.38 -30.17 0.

0.325 9269. 977. 4191. -5.936 1.218 -1.05 0.52 60.79 -29.88 0.

0.330 9161. 1017. 4230. -5.940 1.220 -0.75 0.37 60.12 -29.55 0.

0.335 9066. 1052. 4265. -5.943 1.222 -0.45 0.22 59.53 -29.26 0.

0.340 9008. 1073. 4286. -5.945 1.222 -0.15 0.08 59.17 -29.09 0.

TAB L E 1 4 ( Continued )

ORCOEF = 14.40 Q.E. = 0.00 (DEGREES)

TIME RP FTRACK F-FLOAT_Y U Z VU VZ AU AZ

0.000 0. 4330. 9335. 0.000 0.000 0.00 0.00 0.00 0.00 0.

0.005 25192. 6696. 6950. -0.022 0.000 -11.33 0.02 -4656.81 17.58 0.

0.010 44619. 8685. 5257. -0.153 0.000 -40.27 0.14 -5433.62 32.34 0.

0.015 59141. 10578. 4381. -0.391 0.002 -52.60 0.32 -1298.65 46.34 0.

0.020 63456. 11187. 4022. -0.656 0.004 -52.84 0.56 100:85 50.73 0.

0.025 64835. 11483. 3878. -0.917 0.007 -51.62 0.81 257.18 52.73 0.

0.030 64434. 11389. 3631. -1.170 0.012 -49.66 1.07 399.56 51.78 0.

0.035 63771. 11539. 3722. -1.414 0.018 -47.67 1.33 395.19 52.59 0.

0.040 62947. 11635. 3773. -1.647 0.025 -45.71 1.60 389.71 52.95 0.

0.045 61972. 11846. 3980. -1.871 0.034 -43.78 1.86 383.18 54.12 0.

0.050 60036. 11235. 3462. -2.084 0.044 -41.57 2.11 439.45 49.18 0.

0.055 57945. 10987. 3400. -2.287 0.055 -39.41 2.35 424.54 46.93 0.

0.060 55775. 10706. 3327. -2.478 0.067 -37.32 2.58 409.04 44.42 0.

0.065 53547. 10451. 3307. -2.660 0.081 -35.32 2.80 393.13 42.10 0.

0.070 51571. 10431. 3495. -2.832 0.095 -33.39 3.01 379.26 41.52 0.

0.075 51475. 10610. 3467. -2.994 0.111 -31.49 3.22 379.60 42.25 0.

0.080 51048. 10701. 3411, -3.147 0.127 -29.60 3.43 377.56 42.31 0.

0.085 50135. 10502. 3159. -3.290 0.145 -27.67 3.63 382.37 40.24 0.

0.090 48873. 10378. 3065. -3.423 0.164 -25.78 3.83 374.17 38.71 0.

0.095 47292. 10254. 3045. -3.548 0.183 -23.94 4.02 363.70 37.18 0.

0.100 47874. 10517. 2887. -3.663 0.204 -22.10 4.21 370.02 38.15 0.

0.105 47888. 10702. 2755. -3.769 0.225 -20.24 4.40 372.37 38.48 0.

0.110 47189. 10793. 2670. -3.865 0.248 -18.39 4.59 369.71 38.05 0.

0.115 45743. 10622. 2486. -3.953 0.271 -16.56 4.77 361.38 35.68 0.

0.120 43574. 10265. 2287. -4.031 0.296 -14.78 4.94 347.60 31.94 0.

0.125 40777. 9820. 2150. -4.101 0.321 -13.09 5.09 329.07 27.53 0.

0.130 37190. 8579. 1536. -4.162 0.346 -11.50 5.21 302.26 17.76 0.

0.135 9356. 38. 1514. -4.216 0.373 -10.53 5.18 69.38 -34.11 0.

0.140 8573. 376. 1968. -4.268 0.398 -10.21 5.02 64.68 -31.79 0.

0.145 8583. 388. 1947. -4.318 0.423 -9.88 4.86 64.78 -31.84 0.

0.150 8592. 399. 1927. -4.367 0.447 -9.56 4.70 64.86 -31.89 0.

0.155 8599. 410. 1907. -4.414 0.470 -9.23 4.54 64.96 -31.93 0.

TABLE 16

Claims

I CLAIM

1. A gun system comprising: a recoiling cannon portion having a longitudinal tube axis; a stationary carriage portion including a cradle portion; and means for movably mounting said cannon portion on said cradle portion for travel along a two-stage curvilinear path, said first stage being curved to produce an upward push of said cannon portion, and said second stage having a configuration different from that of said first stage for causing vertical deceleration of said cannon portion.

2. The gun system of claim 1, said first stage having a decreasing radius of curvature in the direction of travel of said cannon portion, the radius of curvature for both said stages being defined by the equation:

, where

Rinst = the radius of curvature at the point along said path where said cannon portion is mounted to said carriage portion, M = the mass of said cannon portion, vinst = the instantaneous velocity of the center of mass of said cannon portion, and

F = the centrifugal force of said cannon portion.

3. The gun system of claim 2, said second stage being straight.

4. The gun system of claim 2, said second stage being curved in the same direction as said first stage, and the curve of said second stage being shallower than the curve of said first stage.

5. The gun system of claim 2, said second stage being curved in the opposite direction from said first stage.

6. A gun system comprising: a recoiling cannon portion having a longitudinal tube axis and a tube center of mass; a stationary carriage portion including a cradle portion; and campath means and cam follower means associated with said campath means for movably mounting said cannon portion on said cradle portion for travel along said campath means, said campath means having a first, curved stage and said second stage having a configuration different from that of said first stage for causing vertical deceleration of said cannon portion.

7. The gun system of claim 6, said first stage having a decreasing radius of curvature in the direction of travel of said cannon portion, the radius of curvature for both said stages being defined by the equation:

where

R_inst = the radius of curvature at the point along said path where said cannon portion is mounted to said carriage portion, M = the mass of said cannon portion, V_inst = the instantaneous velocity of the center of mass of said cannon portion, and

F = the centrifugal force of said cannon portion.

8. The gun system of claim 6, said second stage being straight.

9. The gun system of claim 6, said second stage being curved in the same direction as said first stage, and the curve of said second stage being shallower than the curve of said first stage.

10. The gun system of claim 6, said second stage being curved in the opposite direction from said first stage.

11. The gun system of claim 6, said campath means being fixedly mounted on said cradle portion and said cam follower means being fixedly mounted on said cannon portion.

12. The gun system of claim 11, said cam follower means comprising left and right forward, cam followers attached to said cannon portion on opposite sides of said tube axis forward of said tube center of mass and left and right rear cam followers attached to said cannon portion on opposite sides of said tube axis rearward of said tube center of mass, and said campath means comprising left and right forward and rear campaths positioned to slidingly engage said left and right forward and rear cam followers, respectively.

13. The gun system of claim 6, said campath means being fixedly mounted on said cannon portion and said cam follower means "being fixedly mounted on said cradle portion.

14. A method for stabilizing a gun system upon firing, the gun system comprising a stationary carriage portion including a cradle portion, a recoiling cannon portion having a longitudinal tube axis and being slidingly mounted on the cradle portion, and a recoil system for braking the cannon portion along the tube axis, said method comprising the steps of: displacing the cannon portion along a first curved path normal to the tube axis as it recoils axially until the recoil velocity of the cannon portion is reduced to a predetermined level by the recoil system and displacing the cannon portion along a second path curved to vertically decelerate the cannon portion.