AU615041B2 - Lightweight weapon stabilizing system - Google Patents

Description

0 8 4 I OPI DATE 11/08/89 INTERNATIONAL APPLICATI AOJP DATE 07/09/89 (51) International Patent Classification 4 Internati F41F 19/00 Al (43) Internati APPLN. ID 31912 89 PCT NUMBER PCT/US89/00177 onal Publication Number: onal Publication Date: WO 89/ 06778 27 July 1989 (27.07.89) (21) International Application Number: PCT/US89/00177 (22) International Filing Date: 23 January 1989 (23.01.89) (81) Designated States: AT, AT (European patent), AU, BE1 (European patent), BR, CH, CH (European patent), DE, DE (European patent), DK, FI, FR (European patent), GB, GB (European patent), IT (European patent), JP, KR, LU (European patent), NL, NL (European patent), NO, SE, SE (European patent).

Published (31) Priority Application Number: 147,317 (32) Priority Date: 22 January 1988 (22.01.88) 3 3 )r 1 I With intprnation l aparrh rennrt.

ISECTION 34(4)(a) DIRECTION SEE FOLIO (71) NAME DIRECTED Royc pic (72)1 o. ri z .1 p ii Martin, Edwy 32 Oak Street, Newport, VT 05855 FARNEY, Michael, James Route 100, Newport Center, VT 05857 (US).

r amending the 'I oft'-e receipt

WAL

VT

1 (74) Agent: SHAPIRO, Linda, Mason, Fenwick Lawrence, 1225 Eye Street, Suite 1000, Washington, DC 20005 (US).

(54) Title: LIGHTWEIGHT WEAPON STABILIZING SYSTEM (57) Abstract A gun system comprising a recoiling cannon portion a stationary carriage portion 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 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.

W( 89/06778 PcT/US89/001l77 -1- LIGHTWEIGHT WEAPON STABILIZING SYSTEM 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 I 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 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 !7 k^/y PCr/ LS89/OG?77 WO 89/06778 PCT/US89/077 -2deceleration 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.

Sm m fr -tr -h Invnti..

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

It is another object of this invention to provide a system fo: providing improved weapon stability for S| 25 towed artillery.

It is still another object of this invention to provide a weapon stabilizing system for use with lightweight artillery. pre~~rec SIt is still anotherAobject 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 anotherA object of this invention to provide a weapon stabilizing system in which the -3transient stabilizing moment is tailored to overcome the destabilizing recoil loads to assure that the weapon never lifts off the ground.

It is yet another preferred 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.

According to a first aspect of the present invention there is provided a gun system comprising: a recoiling cannon portion having a recoil cycle, a pre-firing orientation, and a longitudinal barrel axis, said recoil cycle having first and second stages; a non-recoiling carriage portion; 15 trail ends for supporting said carriage portion; a cradle portion rotatably mounted on said carriage ooeoo S portion; mounting means for movably mounting said cannon S• portion on said cradle portion for travel during recoil along a curvilinear path having first and second stages defining a direction of recoil travel, said first stage of said curvilinear path having a curved configuration to 55.555 produce an upward vertical component force on said cannon portion during said first stage of recoil, and said second stage of said curvilinear path having a I: 25 configuration different from that of said first stage of ii said curvilinear path for causing vertical deceleration I-i of said cannon portion during said second stage of recoil; and hydropneumatic recoil system means for braking said cannon portion along said barrel axis, said recoil system means having retardation characteristics tailored to said configurations of said first and second stages of said curvilinear path, wherein in said first stage of recoil, the destabilizing moment of recoil force about said trail ends is overcome by the stabilizing moment of the forces resulting from the curved motion of said cannon portion -3 I 910507,rshspe.003,31912cla 3

L,

S

S

S..

*i 5

S

*.S

A -4along said first stage of said curvilinear path and the static weight of said gun system, and wherein in said second stage of recoil, the recoil force is reduced to a small fraction of its value in said first stage of recoil to produce a final gentle retardation of said cannon portion.

According to a second aspect of the present ivention there is provided a gun system comprising: a recoiling cannon portion having a recoil cycle, a pre-firing orientation, a longitudinal barrel axis and a barrel center of mass; a non-recoiling carriage portion; trail ends supporting said carriage portion; a cradle portion rotatably mounted on said carriage portion; campath means and cam follower means associated with said campath means for movably mounting said cannon portion on said cradle portion for travel during recoil along said campath means, said campath means defining a 20 direction of recoil travel and having a first, curved stage for displacing said barrel center of mass during said first stage of recoil, in a direction having an upward vertical component, and a second stage having a configuration different from that of said first stage of 25 said curvilinear path for causing vertical deceleration of said cannon portion during said second stage of recoil; and hydropneumatic recoil system means for braking said cannon portion along said barrel axis, said recoil system means having retardation characteristics tailored to said configurations of said first and second stages of said curvilinear path, wherein in said first stage of recoil, the destabilizing moment of recoil force about said trail ends is overcome by the stabilizing moment of the forces resulting from the curved motion of said cannon portion along said first stage of said curvilinear path and the 910507,rhspe.003,31912ca,4

C

-4astatic weight of said gun system, and wherein in said second stage of recoil, the recoil force is reduced to a small fraction of its value in said first stage of recoil to produce a final gentle retardation of said cannon portion.

According to third aspect of the present invention there is provided a method for stabilizing a gun system upon firing, the gun system comprising a non-recoiling carriage portion, trail ends supporting said carriage portion, a cradle portion rotatably mounted on said carriage portion, a recoiling cannon portion having a longitudinal barrel axis and a barrel center of mass and being movably mounted on the cradle portion for travel 15 during recoil, and a recoil system for braking the cannon portion along the barrel axis, said method comprising the steps of: displacing the barrel center of mass, in a direction having an upward vertical component along a first curved 20 path normal to the barrel 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 configures to vertically decelerate the cannon portion as 25 it recoils, wherein the shape of the first and second paths are tailored to the retardation characteristics of said recoil system.

According to one embodiment of the invention a gun system comprises 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 ~i .1 5

II

-I

91057,rshspe.003,31912cIa,5 ~I u 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 recoil) of the cannon portion.

In anothr. 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 15 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 S S S* with the cam follower mechanism being fixedly mounted on the cannon portion.

Embodiments of the invention will now be described by way of example only with reference to the accompanying drawings in which:- Figure 1 is a right elevational view of a light i weight towed Howitzer incorporating a first embodiment of i 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 S 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 i 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; 910507,rshspe.003,3191Za,6 I

I

-4c- 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 0e e 0 *e 1

C

CC 910507,rshspe.003,31912-cla,8 I WO 89/06778 PCT/US89/00177 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 tubeaxial and tube-normal recoil velocities, respectively, versus time; Figure 15c is a graph plotting maximum tubenormal 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; i 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 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 7 -6recoil length; and Figure 28 is a graph plotting recoil height versus recoil length.

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 m 15 the weapon's mass. In the lightweight towed Howitzer, the weapon weight is 9,000 pounds, just over one-half o oo that of existing larger calibre weapons; the available *.stabilizing moment therefore is substantially reduced compared with that of the conventional weapon.

The various embodiments of the invention described hereafter generate 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 part, resulting in S. 25 a recoil path which is both rearward and upward. From the shape of this path, we have termed it "curvilinear" in contrast to convention 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 S910507,rshspe.003,31912 a,6

T'?

O 89/06778 PCT/US89/001 77 -7reaction 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 modified to incorporate a first embodiment of the stabilizing system of the invention. Howitzer comprises a conventional stationary carriage 12 supported by conventional left and right wheels 14 and 16 and conventional left and right trails 18 and 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 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 PCT/US89/00177 WO 89/06778 -8forward 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 Wi tube, and a doubler 52 enveloping torque key Forward left and right twin roller sets 54a and 54b I are mounted on forward left and right ears 46a and 46b ;i and rearward left and right twin roller sets 56a and 56b are mounted on rearward left and right ears 48a ii and 48b, respectively, via stub axles 62. Left twin rollers 54a and 56a preferably are flat, have rectangular longitudinal cross-sections, while right twin rollers 54b and 56b are trapezoidal, have trapezoidal longitudinal cross-sections.

The left and right sides 24 and 26 of cradle 22 jI 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 i 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 -nd 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 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 nonrecoiling cradle 22.

The hydropneumatic recoil system 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 tubenormal 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 roller sets 54a, 54b, 56a, and 56b) and curved ce-paths (64a, 64b, 66a, and 66b, respectively) causes the center of mass S. PCT/US89/00177 VWO 89/06778 -23- An additional factor of safety for stability was included by designing the campath in the present WO 89/06778 PCT/US89/001'77 of recoiling parts to follow a like curved path. A centrifugal force is generated whose magnitude is F M.V nst Rinst and whose direction is along the local radius vector.

Vinst is the instantaneous velocity of the center of mass of '.ne recoiling parts. Rinst is the 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

I

WO 89/06778 PCT/US89/00 177 -11contact 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, Rinst

M'V

2 1 nst

F

In this manner, the coordinates of each of campaths 64, 66, 68, and 70 can be determined for all corresponding values of (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 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 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 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- ilizing 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 cf the weapon during the period of high recoil forces. The WO 89/06778 PCT/US89/001'77 -12curvilinear 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 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 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 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 WO' 89/06778 PCT/US89/00177 -13otherwise 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 e.ther 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 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.

WO 89/06778 PCT/US89/0077 -14- Stylized tube-axial and tube-normal force-time curves for the first erbodiment 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 10 of mass. In stylized form, velocity-time is shown in Figures 15a and 15b and displacements shown in Figure In the configuration of the invention represented by Figures 15a and 15b, stage I accounts jl 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.

II 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 li recoil system as well as the development of the i governing equations and the dynamic analysis are all based on modeling the gun system as two planar rigid 0 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 30 that remains fixed 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.

W, 89/06778 PCT/US89/00177 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 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 of the cannon center of gravity can be found relative to the X-Y coordinate system.

The two rigid bodies are shown separately in Figur3s 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 i 20 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 l rollers 54a and 54(b) and 56a and 56b constrained in campaths 64a and 64b and 66a and 66b, respectively, 25 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 Srecuperator 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. Fu and F z are reaction forces that support the cannon.

Fx and Fy are equivalent to Fu and Fz yet based on the ground fixed X-Y coordinate system.

At zero quadrant elevation Fx F u and Fy Fz.

WO 89/06778 PCT/US89/00177 -16- Fx +Fu(cos Fz(sin 4) Fy +Fu(cos Fu(sin 4 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 Mst remains larger than the overturning moment Mov. At zero quadrant elevation, the overturning moment is the horizontal force F x i times its moment arm: Mov Fu(h z hsp) Eq. 1 The stabilizing moment is the vertical force Fz and the fixed weights WF and WE times their respective Smoment arms: Mst Fz(A B U) WF(A AF) WE(A AE) Eq. 2 jFor stability Mst Mov Eq. 3 The degree of stability can be found by defining the excess stability moment Mex as Mex Mst Mov Eq. 4 also i 25 R2Y Mex/C Eq. i The larger Mex and R2Y are, the more stable the gun system is.

-For a conventional recoil system, Fu would be equal to the rod pull and the force Fz would support the portion (WRZ) of the recoiling weight WR that was acting normal to the tube and cradle. At zero quadrant elevation, Fz would be equal to the entira recoiling weight, Fz WRZ WR.

WO'89/06778 PCT/US89/00177 -17- Because the sum of WF, WE and WR is limited to 9000 pounds, the stabilizing moment is greatly reduced.

Mst Fz(A B U) WF(A AF) WE(A AE) (For a conventional gun) Fz WR Mst 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, by the inertial force associated with this acceleration: F, M(Az) WRZ Eq. 6 The application of this increased Fz and resulting acceleration of the cannon in the zdirection gives the cannon a displacement and velocity (Vz) in the z-direction. At some point in the latter part of the stroke, this velocity (Vz) must be returned to zero. To accomplish this, Fz must be reduced sufficiently to switch the sign of Ag, in effect to pull down on the cannon. If Fz 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 Fu (rod pull large) and a WO 89/06778 PCT/US89/0077, -18commensurate 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 Fz and a necessarily greatly reduced tube axial force Fu (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 i 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 iupward, which forces the cannon to be displaced and 'i 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 Fu 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 WO 89/06778 PCT/US89/00177 -19major 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: EF(u) M(Au) Fu (-)FIMPU WRU M(Au) Fu FIMPU WRU Au (Fu FIMPU WRU)/M Eq. 7 Summing forces in the z direction yields the second differential equation Tube normal: ZF(z) M(Az) Fz WRZ Az (Fz 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 F z axially, providing a countering moment.

Sum of the moments about the center of gravity yields EMOM 0 FIMPU(ZEIMP) Fz(-UEFZ) UEFZ FIMPU(ZEIMP)/Fz When the firing force has gone to zero, the "eccentricity" UEFZ will be zero and the reaction forces Fu and Fz will act through the center of gravity.

Fu and Fz are the reactions on the cannon from WO 89/06778 PCT/US89/001'77 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 4 15 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, Fu TRU RPU Eq. 9 and

F

z TRZ RPZ Eq. The total recoil force (RP) is found from the i mathematical recoil model and components are found Ifrom using the recoil mechanism inclination angle oc.

RP (VS VS)/(A o Ao) (Recup. Force), where C is a constant that includes effective piston I area, orifice discharge coefficient, and oil density.

RPU RP cos a oc RPZ RP sin a J; 30 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 WO 89/06778 PCT/US89/00177 -21- The track slope dz/du d(pf) pf' du The track angle is defined as positive CW so: tan -slope -dz/du -pf' Referring to Figures 20(a) and tan P 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 Z pf) so the following relationship can be developed: Z pf Eq. 12 dz/du pf' dz dz du pf'. VU dt du dt

V

z pf'.VU Eq. 13 and d 2 z d dz d dz.du du d dz dz d du dt 2 dt dt dt du dt dt dt du du dt dt d 2 z du du d dz dz d 2 u dt dt dt du du du dt d 2 z du 2 d 2 z dz d 2 dt 2 dt du2 u dt4 Az pf"(Vu) 2 pf'.(Au) Eq. 14 Now defined are position, velocity, and acceleration PCT/US89/0 1'77 WO 89/06778 -22in the z-direction, all as functions of position, velocity, and acceleration in the u-direction.

From Eq. 7 Au (Fu FIMPU WRV)/M 8 Az (Fz WRZ)/M 9 Fu -TRU +RPU Fz M TRZ RPZ il TRU -(TRZ) pf' From Eq. 9 and 11 Fu -TRZ(pf') RPU From Eq. 10 TRZ Fz RPZ Combine Fu -pf'(Fz RPZ) RPU From Eq. 8 Fz W MAZ WRZ Combine Fu -pf'(MAz WRZ RPZ) RPU From Eq. 14 Az pf'.Au pftI.Vu 2 Fu- -pf'(M[Pf'Au pf"Vu 2 l WRZ RPZ)

RPU

Add Eq. 7 for Au Fu pf'(M[pf'(Fu FIMPU-WRU)/M pf"Vu 2 WRZ RPZ) RPU Solve for Fu: Fu .pf'(M pf" V,,y 1 pf' (FIMPU -WRU) WRZ RPZ) +RPU (1 pf'. pf') Eq. Also from Eq. 8 Fz M.Az WRZ Combining with Eq. 14 Fz Mpf'Au Mpf" Vu.Vu WRZ Combining with Eq. 7 Fz pf' (Fu FIMPU WRU) Mpf" Vu.Vu 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.

WO 89106778 PCT/US89/00177 -23- 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 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 varsus 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: M119 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 (Vs Vs)/(Ao Ao) 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 W O 89/06778 PCT/US89/00177 -24abrupt 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 Ibf. 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; the active recoil cylinder can now be used to fine tune the stage tow recoil; and a velocity dependent retarding force is now present in stage two to help dissipate the energy from ii an overpressure.

f 15 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 ji jtabulated 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 Sdata are contained in the input data file shown in :1 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 Mst is greater than the overturning moment Mov. Mex Mst- Mov. If Mst is greater than Mov then Mex 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 Mst is greater than Mov 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 and Each run has a file name associated with it, beginning first with the prefix "Xl" 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 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 X1M203QEOO.CP1 long recoil/M203 Table 10.2 X1M203QEOO.CP2 long recoil/M203 Table 10.3 X1M203QE00.CP3 long recoil/M203 Table 10.4 X1M203QE00.CP4 long recoil/M203 WO89/06778 PCT/US89/00177 -39- NAME DESCRIPTION COMPONENT DIRECTION i C i Ii Ii Ii PCT/US89/0OT77, WO 89/06778 -26- Table 11.1 Table 11.2 Table 11.3 Table 11.4 Table 12.1 Table 12.2 Table 12.3 Table 12.4 Table 13 Table 14 Table 15 Table 16 X1SRQE45.CP1 X1SRQE45.CP2 X1SRQE45.CP3 X1SRQE45.CP4 X1SRQE70.CP1 X1SRQE70.CP2 X1SRQE70.CP3 X1SRQE70.CP4 X1M203QE05.CP1 X1M203QE20.CP1 X1PIMPQEOO.CP1 X1M119QE00.CP1 short recoil/M203 short recoil/M203 short recoil/M203 short recoil/M203 short recoil/M203 short recoil/M203 short recoil/M203 short recoil/M203 long recoil/M203 long recoil/M203 long recoil/PIMP 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.

7 wO689/06778 PCT/US89/00I 77 -27- 0.0 -1 .3943355E-02 -3 .3580475E-02 -6.3684531E-02 -0.1042869 -0.1540052 -0.2104911 -0.2717772 -0.3362349 -0.402869 5 -0.470893 3 539 1440 607 1967 67 5 016 0 0.7425436 -0.8097011 -0.8764620 -0.9428217 -1.008725 -1.074094 -1.138907 -1 .203163 -1.266861 -1.330001 -1.392581 454558 -1.515883 -1.576554 -1.636573 -1.695942 -1.754664 -1.812731 -1.870110 -1.926781 -1.982749 -2.038018 -2 .09 2594 146482 -2.199686 252212 304066 -2.355253 -2.405778 -2.455648 -2.504867 53442 -2.601379 -2.648682 -2.695359 74 1403 -2.786800 0.0 0.0 1 .3027527E-05 5 .6624860E-05 1 .3510455E-04 2 .5162366E-04 4. 1052324E-04 6. 17 16477 E-04 8 .7735784E-04 1.197 5885E-03 1.5843266E-03 2.04 39695E-03 2. 5809 486E-03 3. 197 4320E-03 3 .8950406E-03 4.6753157E-03 5.5395346 E-03 6 .4888075E-03 7 .5242161E-03 8 .6467713E-03 9.8571833E-03 1. 1155967E-02 1 .2543593E-02 1. 4020517 E-02 1 .5587180E-02 1 .7244002E-02 1 .8991329E-02 2.0829225E-02 2.2757646E-02 2.4776516E-02 2 .6885740E-02 2 .9085198E-02 3. 13 747 34E-02 3. 3754066E-02 3 .6222722E-02 3.8780171E-02 4. 14 25858E-02 4.4 159204E-02 4.6979610E-02 4.9886454E-02 5.2879095E-02 5 .5956870E-02 5 .9119098E-02 6.2365074E-02 6.5694079E-02 6 .9105372E-02 7.2598197E-02 7 .6171771E-02 7 .9825304E-02 8. 355 799 3E-02 8.7 368988E-02 9 .1257334E-02 0.1064280 0.1409592 0. 1563128 0 .1717640 0. 1937785 0.2249140 0.2614119 0.3080340 0.3572629 0 .4173858 0.4845083 0.5538852 0 .6251525 0.69925 0.7756743 0.853987 3 0.9342385 1.017888 1.104130 1.192294 1 .282417 1.374535 1. 468686 1. 564907 1. 665446 1.768319 1.873283 1. 980368 2.089606 2.201026 2. 315465 2.434139 2.555043 2.678199 2.803630 2 .9 31360 3.061410 3. 193803 3. 3285 59 3.465699 3.605246 3.747216 3.891629 4.038505 4.187860 4.339711 4.494075 4.650968 4.812841 4.978995 TABLE I 0 -Arm-

I

-2 .831550 -2.875655 -2.919115 -2.961929 -3.004096 -3.045615 -3.086488 -3.126714 -3.166293 3.205228 -3.243518 -3.281166 -3.318173 -3.354541 -3.390272 -3.425370 -3.459837 -3.493676 -3.526892 -3.559488 -3 .591464 -3.622815 -3.653537 -3.683624 -3.713072 -3 .741877 -3.770037 -3.797549 -3 .824410 -3.850620 -3.876178 -3.901085 -3.925340 -3.948947 971907 -3.994224 -4.015902 036945 -4.057360 -4.077151 -4.096327 -4.114895 -4.132864 -4.150242 -4.167034 183279 -4.199083 9 .5221981E-02 9 .9262640E-02 0.1033798 0.1075741 0.1118458 0 .1161953 0.1206231 0.1251293 0.1297142 0.1343779 0.1391206 0.1439423 0.1488429 0.1538224 0.1588807 0 .1640174 0.1692324 0.1745252 0.1798956 0.1853429 0.1908675 0.1964707 0 .2021539 0 .2079185 0 .2137657 0 .2196966 0.2257122 0 .2318135 0.2380012 0.2442758 0.2506378 0.2570876 0.2636252 0. 2702507 0.2769639 0.2837644 0.2906516 0.2976250 0.3046835 0.3118262 0.3190518 0.3263590 0.3337463 0.3412120 0.3487554 0.3563679 0. 3640 265 5 .147982 5.322362 5.502657 5.689036 5.881670 6.080730 6.286392 6.498833 6 .718233 6.944769 7 .178625 7.419980 7.669021 7.925926 8.190881 8.464065 8.745662 9.035846 9.334798 9.643009 9 .965417 10.30448 10 .66101 11 .03582 11 .42976 11 .84371 12 .27855 12 .73519 13 .21455 13 .71754 14 .24510 14.79814 15 .37757 15.98427 16 .61910 17 .28289 17.97638 18.70029 19 .45525 20. 24179 21 .06035 21.91125 22. 79468 23.71479 24. 66697 25.52153 26 .12380 TABLE I. (Continued)

SHEET

WO 89/06778 PCT/US89/00 177 -42- U- qtrc 4qrL n t n L r r e 4 R cL n wd I I I I I I I I I -4 -4 .4 -f -4 4 -4 -4 -4 -4 -4 -4 -4 -4 w6 89/06778 C/S9O 7 PCT/US89/00177 -29- .0000 .0023 .0031 .0040 .004 7 .0054 .0060 .0067 .0075 .008 5 .0100 .0123 .0133 .0163 .0203 .0271 .0337 .0514 .1711 10.00 000.

502.

1073.

-2051.

-3016.

-4075.

-4994.

-6025.

-7096 -8076 -9035 -9913.

-10006.

-10211 -10406 -10602 -10704 -10806 -10843.

-10843.

(PIMP) M483 0.7 M.B.

TABLE 2 .0000 .0030 .0042 .0048 .0069 .0090 .0108 .0129 .0150 .01.9 5 0 315 .0665 .1365 10.00 000.

-763 -1797.

-2473.

-5079 -7291.

-8550.

-9434 -9677 -9955.

-10286.

-10443 -10455.

-10455.

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

TABLE 3 PCT/US891001/7 WO 89/06778 16 .0000 .0040 .0050 .0060 .0070 .0080 .0100 .0120 .0140 .0155 .0203 .0253 .0453 .0803 2803 10.00 000.

-949.

-1601 -2396.

-3261 -4123.

-5675.

-6709.

-7361 -7712.

-7952.

-8104.

-8322.

-8373.

-8379.

-8379.

M119 SHOT IMPULSE DATA (NOMINAL) M483 0.7 M.B.

TABLE 4 ~~ULSiTE SEET ,WO 89/06778 PCT/US89/0O1 77 -31- 43 -1 .0 0.0 1 .0980606E-02 2 .9442310E-02 5.8368206E-02 9. 7794533E-02 0.1463418 0.2016678 0.2618084 0.3251381 0.3906655 2.811534 3.551729 4 .144249 4 .162491 4.18 4.20 4.21 4.23 4.24 4.245087 4.260842 4.276539 4.445129 4.620374 4.772849 4 .9 30054 5.065610 5.203977 5.332038 5.440137 5.539235 5.629237 5.710056 .781618 5.843856 .896716 .940156 .974138 5.998644 6.013669 6 .05 7 .05 0. 1000000 0. 1000000 0. 2136773 0. 3697216 0.5307279 0 .6714978 0. 77 19964 0 .8272313 0.8600011 0 .8641519 0.8674879 0.6066884 0 45'50896 0.2584715 0.2494449 0.260 0.310 0.500 1.500 1.800 1.838936 1.830884 1.822829 1.734067 1.636875 1 .547431 1.449455 1 .359271 1.259954 1 .157433 1.063096 0.9684290 0 .8734521 0. 7781891 0.6826680 0.5869220 0.4909886 0.3949136 0. 2987 556 0.2026038 0.1066578 0.060 0.060 -1 .0980375E-02 -2 .9442154E-02 -5 .8368392E-02 7794317E-02 1463419 -0.2016679 -0.2618082 -0.3251382 -0.390665 1 -2.811117 -3.550291 -4 .139841 157892 -4.270426 -4.436337 -4.608381 -4.757758 -4 .911491 -5.043849 178774 -5.303502 -5.408682 -5.505030 -5.592476 670962 -5.740430 -5.800835 -5 .852135 -5.894298 -5.927299 -5.951124 -5.965774 7 .615981 7.634443 7.663369 7.702795 7.751342 7.806668 7.866809 7 .930139 7.995666 10 .41653 11 .15673 11 .74925 11 .76749 11 .88154 12 .05013 12 .22537 12 .37785 12 .53505 12 .67061 12.80898 12.93704 13.04514 13. 14424 13.23424 13.31506 13 .38662 13.44886 13 .50172 13.54516 13 .57914 13 .60364 13 .61867 a

A

TABLE uv TI SHET 7 PCT/US89/00177 WO 89/06778 -32- 29 -1 .0 0.0 1 .1038303E -0 2 2 .9524803 E -0(2 .8463097E-02 9 .7870827E-02 0.1463437 0.2015076 0.2613635 0.3242474 0.3891602 0.4553499 0.5216808 0.9126625 1 .286214 1.638360 1.966563 2.269381 2.547086 2.799577 3.026139 3 .226931 3.402062 3 .551527 3 .675147 3. 772432 3 .8 509 54 3.90 7 .00 0.1000000 0.1000000 0.2141681 0. 365 1744 0.5136756 0.6343604 0 .7107175 0.7425037 0. 7537519 0.7553425 0.7807769 0. 788 53 55 0. 7871751 0 .7689710 0.7367233 0.6977797 0 .6532170 0.6065208 0 .5591587 0.5086938 0.4566602 0.4036990 0.3496875 0.2944165 0.2374927 0.1780574 0.1018210 0.060 0.060 1038204E-02 -2 .9524621E-02 -5 .8463290E-02 -9 .7870767E-02 146 3436 2015076 2613631 -0.324247 1 3891598 4553490 -0.5216795 -0.9126559 -1 .286190 -1.638298 -1 .966431 -2 .269134 -2.546663 -2.798896 -3.025103 225414 -3 .399911 -3.548557 -3 .671132 -3 .767100 843654 7 .616039 7.634525 7.663464 7 .702871 7 .751344 7.806508 7.866364 7.929248 7 .994161 8.060350 8.126681 8.517663 8 .891214 9 .243361 9 .571564 9.874381 10 .15209 10 .40458 10.63114 10 .83193 11 .00706 11 .15653 11 .28015 11 .37743 11 .45595 TABLE 6

T

iT!

T

~SHEET

00 00 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 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 MAY 14, 1986 CONFIGURATION WITH SPADE REACTION OFFSET.

4

C-.

r~

C-,

I

WF

ROI

WE WR- D1 R02 RD2 A B It AF AE TIME PRINT STEP FREQ.

STAGE 2 F-RECOIL ETRI. ETRI DTR1 DTR2 FRCP DFRCP Ti T2 T3 HSP AEY FX 2 A3 B Y HTB T4 T5 T6 T7 ***VARIABLE NAMES ARE LISTED AS THEIR VALUES APPEAR IN THE DATA FILE.

TABLE 7 '-7 PC-/US89OO 177, WO 89/06778 -34- LITEI SYSTEM DIMENSIONS DATE OF DISTRIBUTIO OF THIS INFORMATION DATE OF ASSOCIATED COMPUTER RUNS

WR

WF

WE

FRC P

DFRCP

May 20, 1986 May 17,18, 1986 lbf 4 330 .0 3240.0 1430.0 5000.0 Inches (lbf/foot) 193.0 96.0 0.0 232.0 46.0 0.0 0.0 -17.2 48.0 0.0 10.25 81.75 TABLE 8 SL~iTUTESHEET IWO 89106778 WO 8906778PCT/US89/0O 177 R02 R02 ETR I DTR 1 ETR 2 DTR 2

TI

T2 T3 T4 T6 T7 10.25 105.5 0.0 31.75 0.0 -20.25 24.0 10.0 29.0 27.0 -19.5 58.0 12.2 TABLE 8 (Continued) r tii WO 89/06778 PCT/US89/00f7'/, -36- 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 iid Accelerations

NAME

U

Z

z VU

VZ

AU

DESCRIPTION

recoil displacement of cannon parallel to cradle (and tube) recoil displacement of cannon perpendicular to cradle (and tube) recoil velocity of cannon parallel to cradle (and tube) recoil velocity of cannon perpendicular to cradle (and tube) recoil acceleration of cannon parallel to cradle (and tube) recoil acceleration of cannon perpendicular to cradle (and tube)

UNITS

ft ft ft/s ft/s ft/s/s ft/s/s TABLE 9 SETIiE

SHEET

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

RRU

RPZ

TRU1 TRZ1 TRU2 TRZ2 F14 U F14 Z

DESCRIPTION

Rod pull force Rod pull force Breech end track force Breech end track force Muzzle end track force Muzzle end track force Trunnion force on cradle Trunnion force on cradle TABLE 9 (Continued) COMPONENT DIRECTION

U

Z

U

Z

U

Z

U

Z

j i. SHEET WO 89/06778 -52o 00 o ooo O o0 .oo 00000 CD o csJ' M j i ocr =M M U C)M U" :t LnW o PCT/US89/00 177, 0000000 QI- O Ci Oh r [i WO 89/06778 PCT/US89/00177 -38i 4)

I

I

2 'i g F13 U F13 Z F12 X F12 Y F11 X F11 Y F9 Y F3 Y *F2 X Elevating/equilibrator mech force U Elevating/equilibrator mech force Z Trunnion force on upper carriage X Trunnion force on upper carriage Y Elevator/equilibrator force X on upper carriage Elevator/equilibrator force Y on upper carriage Support force on upper carriage Y from lower carriage Recoil pad support force on upper Y carriage 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) "Olt;T T SHEET WO 89/06778 PCT/US89/00177 -39-

NAME

F2_Y Fl X Y=-F9 Y F8 Y=-F3 Y F7 Y M2 DESCRIPTION COMP Pintle column load from spade assembly Upper pintle shear force from spade assembly Force on trail/lower carriage from upper carriage Force on recoil pads from upper carriage Force from spade assembly Moment (force couple(s)) from spade assembly Vertical ground force on float (vertical reaction number 2) Horizontal ground force on spade/ float (horizontal reaction number 2) Vertical ground forces on trail end (vertical reaction number 1) Total (Net) track force Total rod pull (recoil recup.)

ONENT

Y

DIRECTION

Y

1bf-

F-FLOAT_Y

(=R2Y) R2X R1Y _i-

FTRACK

RP

TABLE 9 (Continued) i C .7 1I6 IEEI ORCOEF =14.40 Q.E. =0.00 (DEGREES) TIME RP FTRACK F-FLOAT Y U Z vI) VZ AU AZ 0 0.000 0. 4330. 9335. 0.000 0.000 0.00 0.00 0.00 0.00 0. 0 0.005 42736. 8587. 5592. -0 .0 32 0.000 -19.44 0.05 -7829.01 31.63 0. ON.

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 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.

C1.0.065 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.

C0.090 77645. 17667. 1217. -3.942 0.268 -22.74 6.43 611.17 80.73 0.

Ir L 0.095 73804 17643. 1197 -4.048 0.301 -19.73 6.83 589.77 77 .52 0.

C130.100 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 v-.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. 00 TABLE 10.1, ml

C;

-~1 -2 0 .10Fl 0.165S 0.170 0.175 0.180 0.185 0.190 0.195 0.200 0.205 0.210 0.215 0.220 0.225 0.230 0.235 0.240 0.245 0.250 0.255 0.260 0.265 0.270 0.275 -3.280 0.285 0.290 0.295 0.300 0.305 0.310 0.315 0.320 9307.

9326.

9341 9357.

9370.

9382.

9394.

9402.

9410.

9415.

9418.

9419.

9417 9413.

9406.

9395.

9383.

9367.

9346.

9323.

9297.

9266.

9232.

9197.

9158.

9118.

9078.

9041.

9006.

8977.

8955.

8942.

8938.

270.

279.

289.

298.

307.

316.

325.

335 344.

353.

364.

373.

384.

395.

405.

418.

431.

444.

458.

473.

487.

504.

521.

538.

556.

574.

591 608.

622.

634 643.

648.

650.

1306.

1278.

1252.

1227.

1204.

1182.

1161.

1143.

1125.

1109.

1097.

1084.

1075.

1068.

1061 1060.

1059.

1061.

1066.

1074.

1083.

1097.

1112.

1129.

1149.

1169.

1191 1212.

1230.

1247 1259.

1267 1269 -4.937 -4.992 -5.046 -5.097 -5.147 -5.195 -5.241 -5.286 -5.328 -5.369 -5.409 -5.446 -5.482 -5.516 -5.548 -5.578 -5.607 -5.633 -5.658 -5.682 -5.703 -5.723 -5.741 -5.757 -5.771 -5.784 -5.795 -5.804 -5.812 -5.818 -5.822 -5.824 -5.825 0.727 0.754 0.780 0.805 0.830 0.854 0.876 0.898 0.919 0.939 0.959 0.977 0.995 1.011 1.027 1.042 1 .056 1.069 1.081 1.093 1 .103 1 .113 1 .122 1 .130 1.137 1 .143 1.149 1 .153 1 .157 1 .160 1.162 1 .163 1.163 -11 .19 -10 .84 -10.49 -10.14 -9.78 -9.43 -9.08 -8.72 -8.37 -8.02 -7 .66 -7.31 -6.95 -6.60 -6.24 -5.89 5.5 3 -5.18 -4.82 -4.47 -4.12 -3.77 -3.41 -3.07 -2.72 -2.37 -2.02 -1 .68 -1.33 -0.99 -0.65 -0.31 5.50 5.33 5.16 4.98 4.81 4.64 4.46 4.29 4.11 3.94 3.77 3.59 3.42 3.24 3.07 2.89 2.72 2.54 2.37 2.20 2.02 1.85 1 .68 1 .51 1.34 1 .16 0.99 0.82 0.66 0.49 0.32 0.15 69.92 -34.37 70.08 -34.45 70.22 -34.52 70.36 -34.59 70.47 -34.64 70.59 -34.70 70.70 -34.75 70.78 -34.79 70.86 -34.84 70.93 -34.87 70.96 -34.88 71.01 -34.91 71.02 -34.91 71.01 -34.91 71.01 -34.91 70.96 -34.88 70.90 -34.85 70.82 -34.81 70.71 -34.76 70.58 -34.70 70.44 -34.63 70.25 -34.54 70.06 -34.44 69.85 -34.34 69.62 -34.22 69.39 -34.11 69.14 -33.99 68.91 -33.87 68.70 -33.77 68.52 -33.68 68.39 -33.62 68.31 -33.58 68.28 -33.56 0.04-0.02 ro It i I Led TABLE 10. 1 bb.-

I

ORCOEF 14.40 Q.E. 0.00 (DEGREES) TIME U Z RPU L i -j3 -21

C-,

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055 0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110 0.115 0.120 0.125 0.130 0.135 0.140 0.145 0.150 0.155 0.000 -0.032 -0.232 -0.548 -0.874 -1.190 -1.494 -1.783 -2.055 -2.311 -2.551 -2.777 -2.987 -3.184 -3.365 -3.532 -3.684 -3.820 -3.942 -4.048 -4.139 -4.218 -4.292 -4.364 -4.434 -4.503 -4.570 -4.636 -4.699 -4.762 -4.822 -4.880 0.000 0.000 0.001 0.003 0.006 0.012 0.020 0.030 0.042 0.056 0.072 0.090 0.110 0.132 0.155 0.181 0.208 0.237 0.268 0.301 0.336 0.373 0.409 0.445 0.480 0.513 0.546 0.579 0.610 0.641 0.670 0.699 0.

42736.

70652.

92648.

96579.

97057.

97169.

95060.

91825.

88310.

84573.

80668.

80627.

80577.

79197.

76712.

78457.

79130.

77624.

73779.

67777.

10358.

9048.

9078.

9107.

9135.

9162.

9187.

9211.

9233.

9254.

9274.

RPZ

0.

0.

6.

30.

74.

135.

215.

306.

402.

502.

603.

702.

838.

984.

1121.

1245.

1445.

1642.

1803.

1908.

1942.

327.

311.

338.

363.

387.

411.

434.

457.

478.

499.

519.

0.

31.

76.

207.

373.

562.

781.

998.

1232.

1471.

1714.

1972.

2353.

2819.

3284.

3798.

4686.

5775.

7002.

8320.

9700.

1202.

1160.

1185.

1209.

1232.

1255.

1277.

1285.

1305.

1325.

1344.

TRUI TRZ1 TRU2 TRZ2 FU FZ 1686.

11766.

18384.

24073.

25093.

25447.

25855.

25327.

24814.

24162.

23440.

22812.

23150.

23582.

23354.

22991.

24023.

24736.

24751.

24031.

22712.

2445.

2360.

2410.

2459.

2507.

2553.

2597.

2614.

2656.

2696.

2735.

0. 2644.

-3179.

-29. -6953.

-80. -9260.

-146. -9824.

-215. -9761.

-287. -9500.

-379. -9625.

-456. -9181.

-538. -8830.

-620. -8479.

-682. -7888.

-802. -7886.

-929. -7773.

-1123. -7985.

-1288. -7795.

-1535. -7869.

-1841. -7886.

-2193. -7751.

-2548. -7359.

-2787. -6526.

-1341. -2727.

-1050. -2136.

-1070. -2177.

-1090. -2217.

-1109. -2256.

-1128. -2294.

-1145. -2329.

-1183. -2406.

-1199. -2438.

-1214. -2471.

-1229. -2501.

0.

42758.

70699.

92775.

96806.

97404.

97663.

95679.

92601.

89244.

85667.

81959.

82178.

82467.

81358.

79223.

81608.

83064.

82433.

79552.

74689.

10219.

9158.

9193.

9226.

9258.

9289.

9319.

9313.

9339.

9365.

9389.

4330.

8587.

11425.

14783.

15195.

15551.

16140.

15397.

15231.

14829.

14358.

14221.

14425.

14825.

14248.

13951.

14708.

15208.

15197.

14764.

14244.

-609.

-88.

-105.

-121.

-137.

-152.

-166.

-248.

-261.

-274.

-285.

TABLE 10.2 II -I I L- 1

I

0.160 -4.937 0.165 -4.992 0.170 -5.046 0.175 -5.097 0.180 -5.147 0.185 -5.195 0.190 -5.241 0.195 -5.286 0.200 -5.328 0.205 -5.369 0.210 -5.409 0.215 -5.446 0.220 -5.482 0.225 -5.516 0.230 -5.548 0.235 -5.578 0.240 -5.607 0.245 -5.633 0.250 -5.658 0.255 -5.682 0.260 -5.703 0.265 -5.723 0.270 -5.741 0.275 -5.757 0.280 -5.771 0.285 -5.784 0.290 -5.795 0.295 -5.804 0.300 -5.812 0.305 -5.818 0.310 -5.822 0.315 -5.824 0.320 -5.825 0.727 0.754 0.780 0.805 0.830 0.854 0.876 0.898 0.919 0.939 0.959 0.977 0.995 1.011 1.027 1 .042 1.056 1.069 1.081 1.093 1.103 1 .113 1.122 1.130 1.137 1.143 1 .149 1.153 1 .157 1.160 1 .162 1 .163 1.163 9292.

9309.

9323.

9338.

9350.

9361 9372.

9380.

9386.

9391 9392.

9393.

9390.

9385.

9378.

9366.

9353.

9336.

9315.

9292.

9265.

9234.

9199.

9164.

9125.

9085.

9045.

9008.

8973.

8944.

8922.

8908.

8904.

538.

557.

575.

592.

609.

624.

639.

654.

667.

680.

692.

7 0 3.

714.

723.

732.

740.

748.

754.

759 764 768.

771.

773 775.

776.

776.

775 775 774 773 772 771 771 1363.

1380.

1397.

1413.

1429.

1443.

1458.

1471.

1484.

1496.

1507.

1517.

1527.

1536.

1544.

1551.

1558.

1563.

1568.

1572.

1575.

1577 1578.

1579.

1579, 1578.

1577 1575.

1574.

1572.

1571 1570.

1570.

2772.

2808.

2842.

2875.

2906.

2936.

2965.

2993.

3018.

3043.

3066.

3087.

3106.

3124.

3141 3155.

3169.

3180.

3189.

3197.

3203.

3208.

3211.

3212.

3212.

3210.

3208.

3205.

3202.

3199.

3196.

3194.

3194 -1243.

-1257.

-1270.

-1282.

-1293.

-1304.

-1314.

-1323.

-1332.

-1340.

-1346.

-1353.

-1358.

-1362.

-1365.

-1367.

-1368.

-1368.

-1366.

-1363.

-1360.

-1354.

-1348.

-1342.

-1333.

-1325.

-1316.

-1307.

-1300.

-1293.

-1288.

-1284 -1283.

-2530.

-2557.

-2583.

-2608.

-2631.

-2653.

-2674.

-2692.

-2710.

-2726.

-2739.

-2752.

-2762.

-2770.

-2777.

-2780.

-2782.

-2782.

-2778.

-2773.

-2766.

-2755.

-2743.

-2729.

-2713.

-2695.

-2677.

-2660.

-2644.

-2630.

-2619.

-2613.

-2611 9411.

9432.

9451.

9470.

9486.

9501.

9515.

9527.

9538.

9547.

9553.

9558.

9559.

9559 9557.

9551 9543.

9532.

9517.

9500.

9480.

9456.

9429.

9401 9371 9338.

9306.

9276.

9247.

9224.

9205.

9194 9191 -296.

-307.

-316.

-325.

-333.

-341 -348.

-353.

-359.

-363.

-365.

-368.

-369.

-369.

-368.

-365.

-361.

-356.

-348.

-340.

-331.

-318.

-305 -292.

-276.

-261.

-245.

-229.

-216.

-204.

-195.

-190.

-188.

0- 00 0 -4 -4 00 1 C00.

TABLE 10.2 (Contiiiued) FORCES ON CRADLE AND TRAIL/LOWER CARRIAGE ORCOEF 14.40 Q.E. 0.00 (DEGREES) TIME F14 U F14 Z F13 U F13 Z

C

I

I

i4; 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055 0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110 0.115 0.120 0.125 0.130 0.135 0.140 0.145 0.150 -9456.

25388.

48576.

65683.

70243.

71532.

72179.

72586.

70963.

69317.

67451.

64950.

66017.

65943.

67507.

66632.

69369.

71446.

71824.

70158.

66353.

10312.

8773.

8900.

9023.

9144.

9260.

9373.

9496.

9599.

9699.

-4581.

-8978.

-1i338.

-13414.

-12422.

-11311.

-10298.

-8426.

-7001.

-5532.

-4131.

-2949.

-1818.

-721.

531.

1613.

2755.

3932.

5025.

5921.

6557.

923.

921.

1005.

1088.

1168.

1247.

1323.

1382.

1453.

1522.

9456.

17370.

22123.

27093.

26563.

25872.

25484.

23093.

21638.

19927.

18215.

17009.

16162.

15523.

13851.

12591.

12239.

11619.

10609.

9394.

8337.

-93.

385.

293.

203.

114.

28.

-54.

-183.

-260.

-334.

10341.

18995.

24193.

29627.

29048.

28292.

27868.

25253.

23662.

21791.

19919.

18600.

17673.

16975.

15147.

13769.

13384.

12706.

11602.

10273.

9116.

-102.

421.

320.

221.

125.

31.

-60.

-200.

-284.

-365.

F7 Y 4607.

21023.

31913.

41107.

43020.

43720.

44410.

43759.

42941.

41900.

40724.

39639.

40123.

40735.

40331.

39683.

41253.

42355.

42405.

41368.

39515.

6845.

S6695.

6719.

6743.

6766.

6787.

6854.

6924.

7006.

7086.

R2 X 0.

42758.

70699.

92775.

96806.

97404.

97663.

95679.

92601.

89244.

85667.

81959.

82178.

82467.

81358.

79223.

81608.

83064.

82433.

79552.

74689.

10219.

9158.

9193.

9226.

9258.

9289.

9319.

9313.

9339.

9365.

R2 Y R1 Y 9335.

5592.

3100.

2328.

1703.

1720.

2070.

1342.

1533.

1530.

1516.

1919.

1855.

1986.

1371.

1297.

1345.

1316.

1217.

1197.

1559.

959.

1723.

1681.

1641.

1601.

1563.

1526.

1431.

1398.

1365.

-335.

7665.

12994.

17125.

18163.

18501.

18741.

18725.

18368.

17969.

17512.

16972.

17240.

17509.

17547.

17324.

18033.

18562.

18649.

18236.

17355.

3101.

2859.

2884.

2909.

2932.

2955.

2977.

2991.

3011.

3031.

M2 0.

96206.

159073.

208745.

217814.

219158.

219743.

215278.

208353.

200798.

192750.

184407.

184902.

185550.

183056.

178251.

183618.

186895.

185474.

178992.

168051.

22992.

20605.

20684.

20758.

20831.

20900.

20967.

20955.

21014.

21072.

TABLE 10.3 Is C A ~1 -2 3

C-,

I

0.155 0.160 0.165 0.170 0.175 0.180 0.185 0.190 0.195 0.200 0.205 0.210 0.215 0.220 0.225 0.230 0.235 0.240 0.245 0.250 0.255 0.260 0.265 0.270 0.275 0.280 0.285 0.290 0.295 0.300 0.305 0.310 0.315 0.320 9794.

9886.

9974', 10057.

10138.

10213.

10284.

10354.

10417.

10477.

10531.

10580.

10626.

10665.

10699.

10728.

10749.

10766.

10777 10779.

10777 10768.

10752.

10729.

10703.

10671 10635.

10596.

10559 10524.

10494 10470.

10456.

10451 1588.

1653.

1716.

1777 1835.

1892.

1946.

1999 2050.

2098.

2144.

2188.

2 2 30 2269 2307 2342 2375 2406 2435.

2462.

2486 2508.

2528.

2546 2562 2575 2587 2596 2605.

2610.

2615.

2618.

2620.

2620.

-406.

-475 -542.

-606 -668.

-727.

-784 -838.

-889.

-939.

-985.

-1027 -1068.

-1105 -1139 -1171 -1198.

-1223.

-1245 -1262 -1277* -1288.

-1296 -1300.

-1302.

-1300.

-1296 -1290.

-1284.

-1277 -1270.

-1265.

-1261 -1260 -44-4.

-520.

-593.

-663.

-731 -795.

-857 -917 -973.

-1026.

-1077.

-1123.

-1168.

-1209.

-1246 -1281.

-1310.

-1338.

-1361 -1380.

-1396 -1409.

-1417 -1422.

-1424.

-1422.

-1418.

-1411 -1404 -1396.

-1389 -1383.

-1379 -1378 7163.

7238.

7310.

7378.

7445 7509 7570.

7629.

7684.

7737 7787 7833.

7877 7918.

7955.

7989.

8020.

8047 8072.

8091 8109.

8122.

8132.

8138.

8141.

8141.

8139.

8134.

8129.

8123.

8117 8112.

8109.

8108.

9389.

9411.

9432.

9451 9470.

9486.

9501 9515 9527 9538.

9547.

9553.

9558.

9559 9559 9557 9551 9543 9532 9517 9500.

9480.

9456 9429 9401 9371 9338.

9306.

9276.

9247 9224 9205 9194 9191 1335.

1306.

1278.

1252.

1227.

1204.

1182.

1161.

1143.

1125.

1109.

1097.

1084.

1075.

1068.

1061.

1060.

1059 1061.

1066.

1074.

1083.

1097 1112.

1129 1149.

1169.

1191 1212.

1230.

1247 1259 1267 1269 3050.

3068.

3085.

3102.

3118.

3133.

3147 3161 3174.

3186.

3198.

3208.

3218.

3226.

3234.

3240.

3245.

3250.

3253.

3255.

3256.

3256 3255.

3252.

3249 3245.

3240.

3234 3229.

3224 3219 3216 3214 3213.

21124.

21175.

2 12 2 2'.

21264.

21307.

21343.

21376.

21410.

21436.

21460.

21480.

21494.

21505.

21509.

21508.

21503.

21489.

21472.

21447 21413.

21375.

21330.

21276 21216.

21153.

21084.

21011.

20938.

20870.

20807.

20753.

20712.

20687.

20680.

TABLE 10.3 (Continued) EN= 0.

FORCES ON UPPER CARRIAGE ORCOEF 14.40 Q.E. 0.00 (DEGREES) F2 X CHOS TIME F12-X F12-Y £11 X FIl Y

I.

C

ci-

I

I

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0 .0:35 0.040 0.045 0.050 0.055 0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110 0.115 0.120 0.125 0. 130 0.135 0.140 0. 145 9456 -25388.

-48576.

-65683.

-70243.

-71532.

-72179 -72586.

-70963.

-69317 -67451 -64950.

-66017.

-66943.

-67507 -66632.

-69369.

-71446.

-71824.

-70158.

-66353.

-10312.

-8773.

-8900.

-9023.

-9144.- -9260.

-9373.

-9496 -9599.

4581 8978.

11338.

13414.

12422 11311 10298.

8426 7001 5532.

4131 2949.

1818.

721 -531 -1613 -2755.

-3932.

-5025.

-5921 -6557 -923.

-921 -1005 -1088.

-1168 -1247.

-1323.

-1382.

-1453.

-9456.

-17370.

-22123.

-27093.

-26563.

-25872.

-25484.

-23093.

-21638.

-19927 -18215.

-17009 -16162.

-15523 -13851 -12591 -12239 -11619 -10609.

-9394 -8337 93.

-385.

-293 -203 -114 -28.

54 183.

260.

-10341 -18995.

-24193.

-29627 -29048.

-28292.

-27868.

-25253 -23662.

-21791 -19919.

-18600.

-17673 -16975 -15147 -13769 -13384.

-12706 -11602.

-10273.

-9116 102 -421.

-320.

-221 -125 -31 60.

200.

284

Y

10341.

18995.

24193.

29627 29048.

28292.

27868.

25253.

23662.

21791 19919.

18600.

17673.

16975 15147 13769 13384 12706 11602 10273 9116 0 421 320.

221 125 31 0.

0.

0.

0.

42758 70699.

92775 96806.

97404.

97663.

95679 92601 89244.

85667 81959.

82178.

82467 81358.

79223.

81608.

03064 82433 79552 74689.

10219.

9158.

9193 9226.

9258 9289 93119.

9313.

9339 4728.

-15431 -28813.

-38779.

-41317 -42000.

-42340.

-42417.

-41408.

-40370.

-39208.

-37720.

-38268.

-38749 -38960.

-38386.

-39907 -41039 -41187 -40170.

-37956.

-5886.

-4972 -5038.

-5102.

-5165 -5225 -5327 -5493 -5608.

F1 IX 2-Y 3_Y -9309.

6452.

17475 25365.

28895.

30689 32042.

33991 34407.

34838.

35077 34771 36450.

38029 39491.

39999.

42662.

44971 46212.

46092.

44514 6706 5893.

6044 6190.

6333.

6471 6591 6675.

6777 TABLE 10.4 rk ri 0.150 0.155 0.160 0.165 0.170 0.175 0.180 0.185 0.190 0.195 0.200 0.205 0.210 0.215 0.220 0.225 0.230 0.235 0.240 0.245 0.250 0.255 0.260 0.265 0.270 0.275 0.280 0.285 0.290 0.295 0.300 0.305 0.310 0.315 0.320 -9699.

-9794.

-9886.

-9974.

-10057.

-10138.

-10213.

-10284.

-10354.

-10417.

-10477.

-10531.

-10580.

-10626.

-10665.

-10699.

-10728.

-10749.

-10766.

-10777.

-10779.

-10777.

-10768.

-10752.

-10729.

-10703.

-10671.

-10635.

-10596.

-10559.

-10524.

-10494.

-10470.

-10456.

-10451.

-1522.

-1588.

-1653.

-1716.

-1777.

-1835.

-1892.

-1946.

-1999.

-2050.

-2098.

-2144.

-2188.

-2230.

-2269.

-2307.

-2342.

-2375.

-2406.

-2435.

-2462.

-2486.

-2508.

-2528.

-2546.

-2562.

-2575.

-2587.

-2596.

-2605.

-2610.

-2615.

-2618.

-2620.

-2620.

334.

406.

475.

542.

606.

668.

727.

784.

838.

889.

939.

985.

1027.

1068.

1105.

1139.

1171.

1198.

1223.

1245.

1262.

1277.

1288.

1296.

1300.

1302.

1300.

1296.

1290.

1284.

1277 1270.

1265.

1261.

1260.

365.

444.

520.

593.

663.

731.

795.

857.

917.

973.

1026.

1077.

1123.

1168.

1209.

1246.

1281.

1310.

1338.

1361.

1380.

1396.

1409.

1417.

1422.

1424.

1422.

1418.

1411.

1404.

1396.

1389.

1383.

1379.

1378.

9365.

9389.

9411.

9432.

9451.

9470.

9486.

9501.

9515.

9527.

9538.

9547.

9553.

9558.

9559.

9559.

9557.

9551.

9543.

9532.

9517.

9500.

9480.

9456.

9429.

9401.

9371 9338.

9306.

9276.

9247 9224.

9205.

9194.

9191.

-5721.

-5828.

-5932.

-6031.

-6126.

-6218.

-6305.

-6388.

-6468.

-6541.

-6612.

-6677.

-6736.

-6793.

-6843.

-6888.

-6 928 -6960.

-6989.

-7011.

-7025.

-7035.

-7039.

-7035.

-7025.

-7012.

-6993.

-6969.

-6943.

-6917.

-6892.

-6870.

-6853.

-6842.

-6839.

6877.

6973.

7065.

7155.

7240.

7323.

7402.

7477.

7550.

7618.

7683.

7744.

7801.

7855.

7904.

7949.

7989.

8025.

8057.

8085.

8107.

8125.

8138.

8146.

8150.

8150.

8146.

8138.

8123.

8118.

8106.

8096.

8088.

8082.

8081.

0- 00

'C

0 -a a 00 TABLE 10.4 Cotne (Continued bbb.- ORCOEF =14 .40 Q.E. 45.00 (DEGREES) T I ME R P FIRACK F-FLOAT_ Y U Z VU v z AU AZ 0 0.000 3062. 3062. 8724. 0.000 0.000 0.00 0.00 0.00 0.00 0.0 0.005 44063. 7308. 31602. -0.032 0.000 -19.54 0.05 -7841.9? 31.55 0. -4 0.010 87934. 10105. 53965. -0.232 0.001 -56.40 0.23 -4565.70 52.27 0. 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. c q0.090 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.

00 TABLEI I0 0RC0EF =14.40 Q.E. =45.00 (DEGREES) 0, 00 TIME U Z RPU RPZ TRUl. TRZL TRU2 TRZ2 FU FZ 0.000 0.000 0.000 3062. 0. 0. 1796. 0. 1266. 3062. 3062. 0 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. 216115. -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.-1L2080. 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 97553. 962. 2377. 24589. -1420.-14693. 98512. 8934.

0.065 -3.105 C-123 982f,2. 1126. 2756. 24638. -1751.-15647. 99287. 7865.

0.070 -3.270 0.142 987L;2. 1294. 3116. 24175. -2229.-17291. 99649. 5590.

0.075 -3.416 0.163 99360. 1466. 3491. 23666. -2815.-19089. 100035. 3!12. 41 -10.080 -3.545 0.183 100739. 1652. 3856. 23040. -3601.-21518. 100994. -13nl.

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.

co)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.

-10.110 -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.C- 00 TABLE 11.

FORCES ON CRADLE AND TRAIL/LOWER CARRIAGE ORCOEF 14.40 4.E. 45.00 (DEGREES) TIME F14 U F14-Z F13-U F13-Z F7 Y CV3 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055 0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110 0.115 C .12 0 0. 125 0.130 0.135 0.140 -4406.

26595.

64503.

76268.

76106.

75228.

75426.

77393.

78040.

79838.

82028.

84936.

87885.

91279.

9S8 19.

100441.

106460.

107899.

118883.

123702.

124417.

105468.

71182.

42994.

25614.

16021.

10919.

8338.

7344.

-3616.

845 7 -11096.

-13344.

-12350.

-11282.

-103 1 c.

-8314.

-6848.

-5156 -3514.

-1963.

-609.

696.

2211 3574 4922.

5776.

7144.

7955.

8307.

7148.

4830.

2896.

1700.

1039 688.

510.

442.

8479.

18499.

24484.

30420.

29636.

28750.

28194.

24923.

22923.

20083.

17120.

14160.

11638.

901i9 4841.

605.

-4456.

-8366.

-15159 -21167 -25862.

-23929.

-15733.

-8098.

-3147.

-346 1165.

1935.

2189.

7689.

16776.

22204.

27588.

26877.

26073.

25569.

22602.

20789.

18213.

15526.

12842.

10554.

8180.

4391 549.

-4041.

-7587.

-13747.

-19196.

-23454.

-21701.

-14269.

-7344.

-2854.

-314.

1056.

1755.

1986.

8444.

45659.

84218.

100946.

100139.

98625.

98403.

96522.

94989.

93416.

91996.

91151.

90836.

90753.

89696.

88581.

92039.

92426.

100165.

102775.

102163.

86445 59261 37157 23596.

16130.

13333.

12101.

11573.

R 2_X 0.

26003.

55068.

65357.

64498.

63065.

62485.

62245.

61534.

61422.

61615.

62379.

63341 64645.

66509.

68535.

71505.

71661.

78013, 80452.

80400.

67947.

45 8821?.

27820.

16703.

10571 7311.

5662.

5025.

8724.

31602.

53965.

65080.

64737 64003.

64090.

62236.

61038.

59435.

57809.

56435.

55495.

54590.

52344.

49947.

47096.

43345.

40466.

35478.

30032.

23339.

17089.

13079.

10916.

9809.

9248.

8971.

8811.

276.

9406.

20053.

23672.

23546.

23219.

23206.

23455.

23451.

23693.

24034.

24570.

25152.

25848.

26742.

27659.

28896.

28996.

31449.

32318.

32187 27267.

18686.

11691.

7394 5027.

3770.

3134.

2887.

R 2_Y Ri IY M2 0.

58508.

123904.

147076 145122.

141895.

140591 140051.

138452.

138199.

138633.

140353.

142517.

145452.

149646.

154204.

160886.

161237.

175530.

181017.

180900.

152881.

103235.

62596.

37581 23786.

16450.

12740.

11306.

TABLE 11I. 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.

r 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.

S0.095 -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 -3j ORCOEF 14.40 Q.E. =70.00 (DEGREES) TIME RP FTRACK F-FLOATY U Z VU VZ AU AZ 0 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.

G1130 102798. 12984. 87308. -1.481 0.020 -58.41 1.74 531.45 83.75 0.

0.035 i01524. 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 99132- 1-1173. 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.

C0.065 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. 2026. 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. V3 0.090 108365. -8029. 71179. -3.758 0.223 -16.56 3.55 760.96 -85.14 0.

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

Col0.100 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. -2,.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 '0 ORCOEF =14.40 Q.E. 70.00 (DEGREES) T IME u Z R PU R PZ TRUl TRZ1 TRIJ2 TRZ2 FUJ F Z 0.000 0.000 0.000 4069. 0. 0. 1379. 0. 102. 4069. 1481.

0.005 -0.033 0.000 44111 G0. 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,, L0.070 -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. 1090924. -4606.

-10.090 -3.758 0.223 108344. 2127. 4633. 21635. -6314.-29486. 106663. -9978. t r~i1 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.

r 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. 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 c 00

J

FORCES ON CRADLE AND ORCOEF 14.40 TRAIL/LOWER CARRIAGE Q.E. 70.00 (DEGREES) TIME F14 U F14 Z F13 U F13 Z F7 Y R2 X R2 Y R1 Y rn- 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055 0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110 0.115 0.120 0.125 0.130 0.135 0.140 0.145 -485.

25148.

60361.

69362.

69363.

68738.

69043.

72304.

73776.

76781.

80165.

84541.

88660.

93434.

100141.

107280.

115739.

118779.

135423.

142129.

146100.

119563.

78956.

47765.

29282.

19228.

13832.

10957.

9585.

9171.

-2127.

-7904.

-11218.

-14184.

-13280.

-12280.

-11409.

-9251.

-7712.

-5861.

-4057.

-2283.

-776.

729.

2601.

4375.

6178.

7353.

9557.

10845.

11713.

9773.

6439.

3815.

2246.

1390.

929.

684.

569.

534.

5898.

20321.

29141.

37956.

37088.

36045.

35486.

31034.

28328.

24407.

20358.

16109.

12631.

8886.

2858.

-3470.

-10883.

-16511.

-27416.

-36062.

-43450.

-38096.

-25039.

-14023.

-7236.

-3471.

-1428.

-331.

139.

298.

4097.

14117.

20244.

26368.

25765.

25041.

24652.

21560.

19679.

16956.

14143.

11191.

8774.

6173.

1986.

-2411.

-7560.

-11470.

-19046.

-25052.

-30185.

-26466.: -17395.

-9741.

-5027.

-2411.

-992.

-230.

96.

207.

8878.

48811.

90851.

109216.

108179.

106373.

105967.

103705.

101859.

99990.

98318.

97313.

96972.

96917.

95972.

98116.

103658.

104822.

116786.

120437.

121980.

99574.

66623.

41582.

26814.

18802.

14507.

12221.

11237.

11047.

0.

9713.

22130.

25255.

24677.

23847.

23306.

23777.

23675.

24183.

24903.

26053.

27127.

28509.

30918.

33659.

37161.

38846.

45857.

49628.

52466.

43549.

28736.

17109.

10153.

6349.

4301.

3208.

2700.

2542.

7961.

40176.

73841.

89074.

88499.

87322.

87308.

85473.

84104.

82558.

81109.

80116.

79710.

79457.

78090.

76633.

74862.

71023.

71179.

66477.

61099.

47577.

32384.

21834.

15877.

12721.

11053.

10173.

9692.

9567.

1039.

7917.

16590.

19179.

19043.

18746.

18687.

19084.

19175.

19562.

20042.

20751.

21448.

22293.

23506.

24829.

26439.

26910.

30309.

31574.

32283.

26507.

17774.

11087.

7128.

4977.

3822.

3207.

2912.

2824.

0.

21854.

49791.

56823.

55522.

53655.

52439.

53498.

53269.

54412.

56033.

58619.

61035.

64145.

69564.

75734.

83613.

87405.

103178.

111662.

118049.

97986.

64655.

38496.

22843.

14285.

9677.

7217.

6075.

5721.

00 c \o 0.

-J

TABLE 12.3 I I FORCES ON UPPER CARRIAGE ORCOEF 14.40 Q.E. 70.00 (DEGREES) F?_X CHOSEN= Fl_-X F 2-Y TIME F12-X F12-Y Fil X FliY F9 Y F 3-Y 0 00~ 0 -1

-I

00 ril

I

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055 0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110 0.115 0.120 0.125 0.130 0.135 0.140 0.145 -1833. 1133.

-16028. -?0928.

-31186. -52884.

-37051. -60328.

-36203. -60638.

-35049. -60392.

-34335.- -60977.

-33422. -64780.

-32479. -66689.

-31768. -70146.

-31230. -73943.

-31060. -78661.

-31052. -83048.

-31271. -88049.

-31806. -94991.

-32581 102307.

-33779 110873.

-33715 114131.

-37336 130525.

-38420.-137 267.

-38963 14 1295.

-31709.-115695.

-20l954. -76397.

-12751. -46190.

-7904. -28284.

-5270. -18544.

-3857. -13316.

-3105. -10530.

-2743. -9201.

-2635. -8800.

1833.

6316.

9057.

11796.

11526.

11202.

11029.

9645.

8804, 7585.

6327.

5007.

3925.

2 76 2.

888.

-1078.

-3382.

-5131 -8521 -11208.

-13504.

-11840.

-7782.

-4358.

-2249.

-1079.

-444.

-103.

43.

92 -6943.

-23924.

-34307.

-44686.

-43663.

-42436.

-41778.

-36537.

-33350.

-28734 -23967 -18966.

-14870.

-10461.

-3365.

4085.

12812.

19439.

32277.' 42456 51153.

44851.

29479 16509.

8518.

4086.

1681.

390.

-164.

-350.

6943.

23924.

34307.

44686.

43663.

42436.

41778.

36537.

33350.

28734 23967.

18966.

14870.

10461.

3365.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

164.

350 0.

9713.

22130.

25255.

24677 23847.

23306.

23777.

23675 24183.

24903.

26053.

27127 28509.

30918.

33659.

37161 38846.

45857 49628.

52466.

43549.

28736.

17109.

10153.

6349 4301 3208.

2700.

2542.

-916.

-8636.

-17009.

-20142.

-19681.

-19051 -18659.

-18233.

-17755.

-17432.

-17209 -17197 -17262.

-17460.

-17882.

-21483.

-28796.

-33800.

-45607.

-53960.

-60882.

-51997.

-34239.

-19748.

-10937 -6080.

-3454.

-2048.

-1544.

-1480.

-267.

29564.

69893.

80470.

80319.

79443.

79636.

83012.

84444.

87578.

91152.

95859 100310.

105509.

112873.

119705.

126857.

128492.

143855.

148772.

151024 122841.

81157.

49429.

30703.

20538.

15089.

12188.

10746.

10281.

TABLE 12. 4 Now 0RC0EF =14.40 Q.E. =5.00 (DEGREES) TIME RP FTRACK F-FLOATY U Z vu VZ AU AZ 0 0.000 377. 4314. 9327. 0.000 0.000 0.00'0.00 0.00 0.00 0.

0.005 42751. 8570. 8832. -0.032 0.000 -19.45 0.05 -7831.71 31.62 0.

0.010 70701. 11423. 8438. -0.232 0.001 -56.50 0.23 -4673.74 52.77 0.

0.015 92753. 14810. 9334. -0.548 0.003 -65.91 0.57 -172.44 77.75 0. 0 0.020 96723. 15273. 9012. -0.875 0.006 -64.56 0.96 385.54 80.86 0.

0.025 97238. 15700. 9082. -1.191 0.012 -61.99 1.37 517.28 83.56 0.

0.030 97385. 16402. 9488. -1.495 0.020 -59.39 1.80 519.47 88.15 0.

0.035 95308. 15741. 8583. -1.784 0.030 -56.22 2.22 676.58 82.53 0..

0.040 92101. 15724. 8593. -2.057 0.042 -52.89 2.63 653.94 81.63 0.

0.045 88611. 15378. 8270. -2.313 0.057 -49.68 3.03 629.16 78.24 0.

0.050 84895. 15084. 8054. -2.554 0.073 -46.60 3.41 602.78 75.21 0.

0.055 81010. 15085. 8202. -2.779 0.091 -43.66 3.78 575.39 74.36 0.

0.060 81078. 15559. 8257. -2.991 0.110 -40.78 4.16 577.93 76.67 0.

0.065 81068. 15853. 8097. -3.187 0.132 -37.89 4.54 580.14 77.52 0.

0.070 79718. 15630. 7573. -3.369 0.156 -34.89 4.92 604.36 74.53 0.

10.075 77249. 15687. 7512. -3.536 0.181 -31.90 5.29 588.85 73.59 0.

0.080 79221. 16671. 7623. -3.688 0.209 -28.92 5.67 608.24 78.61 0.

.0.085 79926. 17501. 7673. -3.825 0.238 -25.84 6.07 619.36 82.15 0.

0.090 78400. 18040. 7686. -3.947 0.270 -22.75 6.49 615.02 83.25 0. u rLJ0.095 74481. 18232. 7636. -4.053 0.303 -19.72 6.90 593.83 81.43 0.

C.400.100 68717. 17632. 7044. -4.144 0.339 -16.84 7 .28 558.23 73.49 0.

0.105 9674. 123. 2205. -4.223 0.376 -15.09 7.42 68.16 -33.51 0.

0.110 9079. 392. 2506. -4.297 0.412 -14.77 7.26 64.63 -31.77 0.

0.115 9113. 402. 2465. -4.370 0.448 -14.45 7.10 64.90 -31.90 0.

0.120 9145. 411. 2424. -4.442 0.483 -14.12 6.94 65.16 -32.03 0.

0.125 9178. 420. 2384. -4.511 0.518 -13.79 6.78 65.42 -32.16 0.

0.130 9208. 428. 2345. -4.580 0.551 -13.47 6.62 65.67 -32.28 0.

0.135 9238. 437. 2308. -4.646 0.584 -13.14 6.46 65.91 -32.40 0.

0.140 9267. 370. 2208. -4.711 0.616 -12.80 6.29 67.17 -33.02 0.

0.145 9294. 378. 2173. -4 .774 0.647 -12.47 6.13, 67 .39 -33.13 0.

0.150 9320. 386. 2140. -4.836 0.677 -12.13 5.96 67.61 -33.23 0.9 0.155 9344. 395. 2108. -4.895 0.706 -11.79 5.80 67.80 -33.33 0.

0.160 9369. 403. 2076. -4.954 0.735 -11 .45 5.63 68.00 -33.43 0. 0 0.165 9391. 411. 2047. -5.010 0.763 -11.11 5.46 68.19 -33.52 0.

TABLE 13 0.170 0.175 0.180 0.185 0.190 0.195 0.200 0.205 0.210 0.215 0.220 0.225 0.230 0.235 0.240 0.245i 0.250 0.255 0.260 0.265 0.270 0.275 0.280 0.285 0.290 0.295 0.300 0.305 0.310 0.315 0.320 0.325 9412.

9433.

9451.

9471 9489.

9505.

9520.

9532.

9545 9555.

9563.

9569.

9571 9574.

9572.

9 56 8.

9561 9547 9534.

9513.

9485.

9457.

9419.

9372.

9325.

9269 9207.

9143.

9085.

9034.

8997.

8979.

419.

426.

434.

440.

448.

456.

462.

469.

477.

484 491.

499.

507.

515.

524.

534.

544.

555.

566.

580.

596.

610.

629.

649.

670.

694.

718.

743.

765.

785.

800.

806.

2018.

1990.

1965.

1938.

1914.

1892.

1869.

1850.

1831.

1813.

179q7 1783.

1771.

1760.

1752 1746.

1742.

1742.

1743.

1748.

1758.

1768.

1785.

1806.

1829.

1858.

1889.

1923.

1953.

1980.

2001.

2010.

-5.065 -5 .118 -5.169 -5.219 -5.266 -5.313 -5.357 -5.400 -5.440 -5.480 -5.517 -5.553 -5.587 -5.619 -5.649 -5.678 -5.705 -5.730 -5.754 -5 .776 -5.796 -5.814 -5.831 -5.845 -5.859 -5.870 -5.880 -5.888 -5.894 -5.899 -5.902 -5.903 0.790 0.816 0.841 0.865 0.889 0.911 0.933 0.954 0.974 0.994 1.012 1 .030 1.046 1.062 1 .077 1.091 1 .104 1 .117 1 .128 1 .1-139 1.149 1 .158 1 .166 1.173 1 .180 1 .185 1.190 1 .194 1 .197 1 .200 1 .201 1 .202 -10.77 -10.43 -10.08 -9.74 -9.40 -9.05 -8.71 -8.36 -8.01 -7.66 -7 .32 -6.97 -6.62 -6.27 -5.92 -5.57 -5.22 -4.87 -4.53 -4.18 -3.83 -3.48 -3.14 -2.79 -2.45 -2.11 -1.77 -1 .43 -1.10 -0.76 -0.43 -0.10 5.29 5.13 4.96 4.79 4.62 4.45 4.28 4.11 3.94 3.77 3.60 3.43 3.25 3.08 2.91 2.74 2.57 2.40 2.22 2.05 1.88 1.71 1 .54 1 .37 1 .21 1 .04 0.87 0.70 0.54 0.38 0.21 0.05 68.36 68.53 68.69 68.85 68.99 69.12 69.26 69.37 69.47 69.57 69.64 69.70 69.75 69.79 69.80 69.79 69.77 69.70 69.64 69.52 69.36 69.20 68.97 68.70 68.41 68.06 67.69 67 .29 66.94 66.63 66.39 66.29 -33.61 -33.69 -33.77 -33.85 -33.92 -33.98 -34.05 -34.10 -34.15 -34.20 -34.24 -34.27 -34.29 -34.31 -34.31 -34.31 -34.30 -34.26 -34.23 -34.18 -34.10 -34.02 -33.91 -33.77 -33.63 -33.46 -33.27 -33.08 -32.91 -32.75 -32 .64 -32.59 TABLE 13 (Continiued) ORCOEF 15.00 Q.E. =20.00 (DEGREES) TIM4E RP FTRACK F-FLOATY U Z VU VZ AU AZ 0.000 1481. 4069. 9209. 0.000 0.000 0.00 0.00 0.00 0.00 0.

0.005 44274 8319 18267 -0 .032 0.000 -19 .47 0.05 -7828.60 31 .58 0. 0.010 73339. 11170. 24253. -0.232 0.001 -56.48 0.23 -4662.35 52.71 0.

0.015 96095. 14518. 30143. -0.548 0.003 -65.82 0.57 -155.83 77 .40 0. 0 0.020 99953. 14929. 30665. -0.874 0.006 -64.39 0.96 401.29 80.11 0.

0.025 100206. 15310. 30805. -1.189 0.012 -61.74 1.36 531.06 82.45 0.

0.030 100078. 15952. 31191. -1.491 0.020 -59.08 1.78 531.17 86.59 0.

0.035 97660. 15244. 29766. -1.779 0.030 -55.85 2.19 685.68 80.62 0.

0.040 94104. 15140. 28969. -2.050 0.042 -52.49 2.60 660.37 79.07 0.

0.045 90293. 14823. 27913. -2.304 0.056 -49.25 2.98 633.16 75.91 0.

0.050 86289. 14451. 26796. -2.543 0.072 -46.16 3.35 604.52 72.32 0.

0.055 82151. 14295. 25932. -2.766 0.089 -43.21 3.71 575.07 70.33 0.

0.060 81684. 14688. 25950. -2.975 0.109 -40.35 4.06 573.45 72.10 0.

0.065 81475. 14989. 25869. -3.169 0.130 -37.48 4.43 574.01 73.06 0.

(0.070 79940. 14749. 25092. -3.349 0.153 -34.52 4.78 596.62 70.01 0.

(0.075 77322. 14622. 24373. -3.515 0.178 -31.57 5.13 579.53 67.81 0.

0.080 78275. 15262. 24677. -3.665 0.204 -28.67 5.47 590.44 70.60 0.

0.085 78893. 16011. 25022 -3.801 0.233 -25.68 5.83 600.09 73.81 0.

0.090 77444. 16441. 24854. -3.922 0.263 -22.69 6.21 595.19 74.48 0.

0.095 73795. 16349. 23966. -4.028 0.295 -19.76 6.57 574.15 71.15 0.

0.100 68133. 15936. 22595. -4.120 0.328 -16.97 6.91 538.37 65.26 0.

0.105 28953. 13871 18423. -4 .198 0.364 -14 .62 7 .18 248 .15 55 .65 0.

0.110 9026. 673. 4847 -4 .270 0.399 -14.26 7 .01 56.95 -28.00 0.

0.115 9061. 681. 4813. -4.341 0.434 -13.98 6.87 57.23 -28.13 0.

rni0.120 9094. 689. 4779. -4.410 0.468 -13.69 6.73 57.49 -28.26 0.

0.125 9127. 697. 4746. -4.478 0.501 -13.40 6.59 57.76 -28.39 0.

0.130 9159. 704. 4714. -4.544 0.534 -13.11 6.45 58.02 -28.52 0.

0.135 9189. 712. 4683. -4.609 0.566 -12.82 6.30 58.26 -28.64 0.

0.140 9220. 644. 4580. -4.672 0.597 -12.53 6.16 59.53 -29.26 0.

0.145 9248. 651 4551 -4.734 0.627 -12.23 6.01 59.76 -29.37 0.

0.150 9277. 658. 4523. -4.795 0.657 -11.93 5.86 59.98 -29.49 0.

0.155 9304. 665 4495 -4 .854 0 .686 -11 .63 5.72 60.20 -29 .59 0.

0.160 9329 673. 4468 -4 .911 0.714 -11 .33 5.57 60.40 -29 .69 0.

0.165 9356. 679. 4142. -4.967 0.741 -11.02 5.42 60.61 -29.80 0. TABLE 14 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 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.CI 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. 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.

r: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 6 3 -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.

C030.285 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 1L59 63.06 -31.00 0.

025 92. 836. 4076. -5.877 1.189 -2.91 1.43 62.93 -30.94 0.

0.0 59. 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 60.1? -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. 0

II

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 62799. 10019. 3133. -0.034 0.000 -24.66 0.07-10074.72 42.26 0.

0.010 84048. 13064. 2251. -0.272 0.001 -63.31 0.29 -4125.08 64.82 0.

0.015 99420. 15273. 1392. -0.607 0.003 -67.89 0.66 232.06 81.01 0.

0.020 102861. 16259. 1469. -0.942 0.008 -66.11 1.08 403.99 87.94 0.

0.025 103394. 16565. 1295. -1.266 0.014 -63.38 1.52 556.98 89.65 0.

0.030 102480. 16765. 1271. -1.575 0.023 -60.32 1.97 650.63 90.44 0.

0.035 100192. 16696. 1210. -1.869 0.034 -57.00 2.42 706.83 89.11 0.

0.040 96669. 16465. 1230. -2.145 0.047 -53.53 2.86 681.91 86.53 0.

0.045 92842. 16072. 1142. -2.404 0.062 -50.19 3.28 654.75 82.69 0.

0.050 88775. 15769. 1223. -2.647 0.080 -46.99 3.69 625.89 79.50 0.

0.055 85602 15493 1146. -2.874 0.099 -43 .78 4 .07 644 .33 76.42 0.

0.060 85492. 15966. 1162. -3.085 0.120 -40.56 4.46 645.80 78.58 0.

0.065 84375. 16124. 1045. -3.280 0.144 -37.34 4.86 639.96 78.35 0.

0.070 82219. 16217. 1075. -3.459 0.169 -34.17 5.25 626.79 77.58 0.

0.075 81975. 16885. 1195. -3.622 0.196 -31.06 5.64 629.06 80.61 0.

-i 0.

0.080 83684: 18023. 1202. -3.769 0.225 -27.86 6.05 647.75 86.36 o 005814 185. 11.-3.900 0.257 -24.61 6.49 650.33 88.05 0.

rra 0.090 79907. 18913. 1154. -4.015 0.290 -21.39 6.93 634.50 86.68 0.

Colo 0.095 74138. 18531. 1093. -4.114 0.326 -18.29 7.35 599.61 80.26 0.

0.100 30691. 15996. 9056. -4.199 0.364 -15.65 7.69 278.01 67.47 0.

0.105 9117 279 1739 -4 .276 0.402 -15 .24 7 .49 66.32 -32.60 0.

0.110 9153. 288. 1693. -4.351 0.439 -14.91 7.33 66.61 -32.74 0.

0.115 9187. 297. 1648. -4.425 0.475 -14.58 7.17 66.89 -32.88 0.

0.120 9222. 306. 1604. -4.497 0.510 -14.24 7.00 67.16 -33.02 0.

0.125 9255. 315. 1562. -4.567 0.545 -13.91 6.84 67.42 -33.14 0.

0.130 9287. 323. 1520. -4.636 0.579 -13.57 6.67 67.68 -33.27 0.

0.135 9318. 332, 1480. -4.703 0.612 -13.23 6.50 67.93 -33.39 0.

0.140 9348. 340. 1441. -4.768 0.644 -12.89 6.34 68.18 -33.51 0.

0.145 9378. 348. 1403. -4.832 0.675 -12.55 6.17 68.41 -33.63 0.

TABLE 00

C

El 0.150 0.155 0.160 0.165 0.170 0.175 0.180 0.185 0.190 0.195 0.200 0.205 0.210 0.215 0.220 0.225 0,230 0. 2 3 5 0.240 0.245 0.250 0.255 0.260 0.265 0.270 0.275 0.280 0.285 0.290 0.295 0.300 0.305 0.310 0.315 0.320 9405.

9433.

9459.

9484.

9509.

9530.

9554.

9574.

9594.

9613.

9630.

9647.

9659.

9674.

9684.

9694.

9701 9705.

9710.

9706.

9706.

9697.

9685.

9669 9639.

9614 9572.

9516.

9457.

9377 9280.

9188.

9096.

9025.

8995.

355.

362.

370.

377 384.

255.

261.

267.

274.

280.

286.

292.

299.

305.

310.

317.

324.

331.

338.

347.

354.

364.

374 385 402.

415.

434.

458.

481.

513.

551.

585.

619.

645.

656.

1366.

1330.

1296.

1263.

1231 1097 1067 1039.

1013.

987.

964.

9 4 1.

921 901 883.

867 853.

840.

829.

824 816.

814.

814.

818.

831 8 4 2 863.

894 926 973.

1031.

1085.

1141 1184.

1202.

-4.894 -4.954 -5.012 -5.069 -5.124 -5.177 -5.229 -5.278 -5.326 -5.372 -5.416 -5.459 -5.499 -5.538 -5.575 -5.611 -5.644 -5.675 -5 .705 -5.733 -5.759 -5.783 -5.806 -5.826 -5.845 -5 .862 -5.377 -5 .891 -5.902 -5.912 -5.920 -5.926 -5.931 -5.933 -5.934 0.705 0.735 0.764 0.792 0.819 0.845 0.870 0.895 0.918 0.941 0.962 0.983 1.003 1.022 1 .041 1.058 1.074 1.090 1 .104 1 .118 1 .131 1 .143 1 .154 1 .164 1 .173 1 .182 1 .189 1 .196 1.201 1 .206 1 .210 1 .213 1 .215 1.217 1 .217 -12.20 -11.86 -11.52 -11.17 -10.82 -10.47 -10.11 -9.75 -9.39 -9.03 -8.67 -8.31 -7.95 -7.58 -7.22 -6.86 -6.49 -6.13 -5.76 -5.40 -5.03 -4 .67 -4.30 -3.94 -3.57 -3.21 -2.85 -2.49 -2.13 -1 .77 -1 .42 -1.07 -0.72 -0.37 -0.03 6.00 5.83 5.66 5.49 5 .32 5 .15 4 .97 4. 79 4 .62 4.44 4.26 4.08 3.91 3.73 3.55 3.37 3.19 3.01 2.83 2.65 2 .47 2 .29 2.11 1 .94 1 .76 1 .58 1 .40 1 .22 1 .05 0.87 0.70 0.53 0.35 0.18 0.02 68.64 -33.74 68.86 -33.85 69.07 -33.95 69.27 -34.05 69.46 -34.15 71.49 -35.14 71.67 -35.23 71.84 -35.32 71.99 -35.39 72.15 -35.47 72.29 -35.5 4 72.43 -35.60 72.53 -35.66 72.65 -35.71 72.75 -35.76 72.83 -35.80 72.90 -35.83 72.95 -35.86 73.00 -35.88 72.99 -35.88 73.01 -35.89 72.97 -35.87 72.92 -35.85 72.84 -35.81 72.65 -35.72 72.52 -35.65 72.26 -35.52 71.93 -35.36 71.57 -35.18 71.07 -34.94 70.47 -34.64 69.91 -34.37 69.34 -34.08 68.89 -33.87 68.71 -33.78 TABLE 15 (Continued) ORCOEF =14.40 Q.E. 0.00 (DEGREES) TIME RiP FTRACK F-FLOATY 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 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.

CV1)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.

ra0.095 47292 10254 3045. -3 .548 0.183 -23.94 4 .02 363.70 37 .18 0 C030.100 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. 0 ~0 TABLE 160- 14 003 ri C00 0.160 0.165 0.170 0.175 0.180 0.185 0.190 0.195 0.200 0.205 0.210 0.215 0.220 0.225 0.230 0.235 0.240 0.245 0.250 0.255 0.260 0.265 0.270 0.275 0.280 0.285 0.290 0.295 8605.

8610.

8614.

8617.

8619.

8620.

8620.

8619.

8618.

8615.

8612.

8609.

8605.

8600.

8595.

8590.

8585.

8579.

8574.

8569.

8564.

8560.

8556 8553.

8550.

8548.

8547 8546.

421 431.

442.

453.

463.

473.

483.

493.

503.

513.

521.

531.

540.

548.

556.

564.

571.

578.

584.

590.

595.

600.

604.

607 610.

599 600.

600.

1890.

1873.

1857 1843.

1830.

1818.

1807.

1797 1788 1781 1773 1767.

1762.

1757 1754.

1751.

1748 1746 1744.

1743.

1742 1742 1741 1741 1741 1730 1730.

1730, -4.459 -4 .503 -4.545 -4.586 -4.625 -4.662 -4 .697 -4 .731 -4 .764 -4 .794 -4.823 -4 .851 -4 .877 -4.901 -4 .923 -4.944 -4 .963 -4 .981 -4 .997 -5.011 -5.024 -5.035 -5.045 -5.052 -5.059 -5 .063 -5 .066 -5.067 0.492 0.514 0.534 0.554 0.573 0.592 0.609 0.626 0 .642 0.657 0.671 0.684 0.697 0.709 0.720 0.730 0.740 0.748 0.756 0.763 0.770 0.775 0.780 0.784 0.787 0.789 0.790 0.791 -8.91 -8.58 -8.26 -7.93 -7.61 -7.28 -6.95 -6.63 -6.30 -5 .97 -5.65 -5.32 -4 .99 -4 .67 -4.34 -4.01 -3.69 -3.36 -3.03 -2.71 -2 .38 -2.05 -1 .73 -1.40 -1 .08 -0.75 -0.42 -0.10 4 .38 4 .22 4.06 3.90 3.74 3.58 3.42 3.26 3.10 2.94 2.78 2.62 2.45 2.29 2.13 1.97 1 .81 1 .65 1 .49 1 .33 1 .17 1 .01 0.85 0.69 0.53 0 .37 0.21 0.05 65.03 65.11 65.16 65.21 65.26 65.30 65.33 65.35 65.36 65.37 65.38 65.38 65.37 65.37 65.35 65.33 65.32 65.30 65.28 65.26 65.24 65.22 65 .20 65 .19 65.18 65.35 65.34 65.35 -31 .97 -32.01 -32.03 -32.06 -32.08 -3?2.10 -32.11 -32.12 -32.13 -32 .14 -32.14 -32.14 -32.14 -32.13 -32 .13 -32.12 -32.11 -32.10 -32.09 -32.08 -32.07 -32.06 -32.05 -32.05 -32.04 -32 .12 -32.12 -32.12

I

TABLE 16 (Continued)

Claims (24)

1. A gu: system comprising: a recoiling cannon portion having a recoil cycle, a pre-firing orientation, and a longitudinal4 ibe axis, said recoil cycle having first and second stages; a non-recoiling carriage portion; trail ends for supporting said carriage portion; a cradle portion rotatably mounted on said carriage portion; mounting means for movably mounting said cannon portion on said cradle portion for travel during recoil along a curvilinear path having first and second stages defining a direction of recoil travel, said first stage of i said curvilinear path having a curved configuration to produce an upward4puak-=ef said cannon portion during said j first stage of recoil, and said second stage of said curvilinear path having a configuration different from that of said first stage of said curvilinear path for causing vertical deceleration of said cannon portion during said second stage of recoil; and hydropneumatic recoil system means for braking said cannon portion along saidq tube axis, said recoil system means having retardation characteristics tailored to said configurations of said first and second stages of said curvilinear path, wherein in said first stage of recoil, the destabilizing moment of recoil force about said trail ends is overcome by the stabilizing moment of the forces resulting from the curved motion of said cannon portion WO 89/06778 PCT/US89/00177 along said first stage of said curvilinear path and the static weight of said gun system, and wherein in said second stage of recoil, the recoil force is reduced to a small fraction of its value in said first stage of recoil to produce a final gentle retardation of said cannon portion.

2. The gun system of claim 1, said cannon portion having a ttbe center of mass, said first and second stages of said curvilinear path each having a radius of curvature "Rinst" at the point along said path where said cannon portion is mounted to said carriage portion, said first stage of said curvilinear path having a decreasing radius of curvature in the direction of recoil travel of said cannon portion, said cannon portion having a mass and a centrifugal force said centifugal force being of the magnitude required to generate a moment about said trail .I ends sufficient, when taken in conjunction with the moment 1of static weight of said gun system, to overcome the instantaneous destabilizing moment of recoil force about said trail ends, and saidlste center of mass of said cannon portion having an instantaneous velocity "Vinst", the radius of curvature for both said stage of said curvilinear paths being defined by the equation: M Vinst 2 Rinst F WO 89/06778 GL PCT7US89/00177

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

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

6. The gun system of claim 1, said mounting means bct Yye comprising means for maintaining saidtbe axis parallel to said initial pre-firing orientation throughout said recoil cycle.

7. A gun system comprising: a recoiling cannon portion having a recoil cycle, a pre-firing orientation, a longitudinal l-t e axis and a4ttte center of mass; a non-recoiling carriage portion; trail ends supporting said carriage portion; a cradle portion rotatably mounted on said carriage portion; A 0 VX i x WO 89/06778 PCTfUS89/00177 campath means and cam follower means associated with said campath means for movably mounting said cannon portion on said cradle portion for travel during recoil along said campath means, said campath means defining a direction of Srecoil travel and having a first, curved stage for Sdisplacing said tube center of massl upwaeds during said first stage of recoil, and a second stage having a configuration different from that of said first stage of said curvilinear path for causing vertical deceleration of said cannon portion during said second stage of recoil; and hydropneumatic recoil system means for braking said 'bcay r\ cannon portion along said tbe axis, said recoil system means having retardation characteristics tailored to said configurations of said first and second stages of said curvilinear path, wherein in said first stage of recoil, the destabilizing moment of recoil force about said trail ends is overcome by the stabilizing moment of the forces resulting from the curved motion of said cannon portion along said first stage of said curvilinear path and the static weight of said gun system, and wherein in said second stage of recoil, the recoil force is reduced to a small fraction of its value in said first stage of recoil to produce a final gentle retardation of said cannon portion.

8. The gun system of claim 7, said second stage of said curvilinear path being straight. stti wegh ofsi u ytm n weeni adscn _1 i I SWO 89/06778 said said said than i PCT/US89/00177

9. The gun system of claim 7, said second stage of curvilinear path being curved in the same direction as first stage of said curvilinear path, and the curve of second stage of said curvilinear path being shallower the curve of said first stage of said curvilinear path. The gun system of claim 7, said second stage of curvilinear path being curved in the opposite direction said first stage of said curvilinear path. 1 said from

11. The gun system of claim 7, 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 parallel left and right forward cam followers attached to said cannon portion on opposite sides of saidtutbe axis forward of saidtatze- center of mass and parallel left and right rear cam followers attached to said carre\ cannon portion on opposite sides of said tube axis rearward br re.\ of said-tabe center of mass, and said campath means comprising parallel left and right forward campaths and parallel left and right rear campaths positioned to movably engage said left and right forward and rear cam followers, respectively. j: d yr, li i 1 1 E LL WO 89/06778 PCT/US89/00177

13. The gun system of claim 7, said campath means being fixedly mounted on said cannon portion and said cam follower means being fixedly mounted on said'cradle portion.

14. The gun system of claim 7, said cannon portion having r.4tate center of mass, said first and second stages of said curvilinear path each having a radius of curvature "Rinst" at the point along said path where said cannon portion is mounted to said carriage portion, said first stage of said curvilinear path having a decreasing radius of curvature in the direction of recoil travel of said cannon portion, said cannon portion having a mass and a centrifugal force said centifugal force being of the magnitude required to generate a moment about said trail ends sufficient, when taken in conjunction with the moment of static weight of said gun system, to overcome the instantaneous destabilizing moment of recoil force about ba re-\ said trail ends, and said 4 tube center of mass of said cannon portion having an instantaneous velocity "Vinst", the radius of curvature for both said stages of said curvilinear path being defined by the equation: -A1 Rinst M Vinst 2 F WO 89/06778 70 PCT/US89/00177 The gun system of claim 7, said campath means and said cam follower means comprising means for maintaining said tubeq axis parallel to said initial pre-firing orientation throughout said recoil cycle.

16. The gun system of claim 12, said left and right forward and rear cam followers comprising, respectively, left and right forward and rear twin roller sets.

17. The gun system of claim 16, said left forward and rear twin roller sets having rectangular longitudinal cross- sections, said left forward and rear campaths having corresponding rectangular cross-sections, said right forward and rear twin roller sets having trapezoidal longitudinal cross-sections, and said right forward and rear campaths having cross-sections which are rectangular with a necked in portion.

18. The gun system of claim 12, said gun system further comprising front yoke means supporting and housing said cannon portion forward of saidAtebe center of mass for Sattaching said left and right forward cam followers to said cannon portion and rear yoke means supporting and housing u ac r e-\ said cannon portion rearward of said4etobe center of mass for attaching said left and right rear cam followers to said cannon portion. i- N Af WO 89/06778 PCT/US89/00177 71

19. The gun system of claim 13, said campath means comprising parallel left and right forward campaths attached to said cannon portion on opposite sides of said4tte axis forward of said tuea center of mass and parallel left and right rear campaths attached to said cannon portion on opposite sides of said tube axis rearward of said tube center of mass, and said cam follower means comprising parallel left and right forward cam followers and parallel left and right rear cam followers positioned to movably engage said left and right forward and rear campaths, respectively. I The gun system of claim 19, said left and right i forward and rear cam followers comprising, respectively, I left and right, forward and rear, upper and lower twin i roller sets and left and right forward and rear circular 5 housings respectively housing said left and right, forward and rear, upper and lower twin roller sets.

21. The gun system of claim 11, said gun system further comprising yoke means surrounding and housing said cannon portion for mounting said cam follower means on said cannon portion. 72 -72-

22. A method for stabilizing a gun system upon firing, the gun system comprising a non-recoiling carriage portion, trail ends supporting said carriage portion, a cradle portion rotatably mounted on said carriage portion, a recoiling cannon portion having a longitudinal barrel axis and a barrel center of mass and being movably mounted on the cradle portion for travel during recoil, and a recoil system for braking the cannon portion along the barrel axis, said method comprising the steps of: displacing the barrel center of mass, in a direction having an upward vertical component along a first curved path normal to the barrel axis as it recoils axially until the recoil velocity of the cannon portion is S* reduced to a predetermined level by the recoil system and "displacing the cannon portion along a second path configured to vertically decelerate the cannon portion as it recoils, wherein the shape of the first and second paths are i tailored to the retardation characteristics of said recoil system. S 23. The method of claim 22, wherein the step of *i displacing the cannon portion along a first curved path is carried out by displacing the cannon portion along a first curved path having a decreasing radius of curvature 1 in the direction of recoil travel. ii *I 9105G7.rshspe.003,31912cIa,72 WO 89/06778' PCT/US89/O 177

24. The method of claim 22, wherein the first and second curved paths each have a radius of curvature "Rinst" at the point along each path where the cannon portion is mounted to the carriage portion, the cannon portion has a mass and a centrifugal force the centifugal force being of the magnitude required to generate a moment about the trail ends sufficient, when taken in conjunction with the moment of static weight of the gun system, to overcome the instantaneous destabilizing moment of recoil force about the trail ends, and the center of mass of the cannon portion has an instantaneous velocity "Vinst", and wherein said displacing steps are carried out by displacing the cannon portion along the paths having a radius of curvature defined by the equation: M Vinst 2 Rinst F The method of claim 22, wherein said step of displacing the cannon portion along a second path is carried out by displacing the cannon portion along a second path which is straight.

26. The method of claim 22, wherein said step of displacing the cannon portion along a second path is carried out by displacing the cannon portion along a second path which is curved in the same direction as the first path, the *1 S> -74- curve of the second path being shallower than the curve i of the first path.

27. The method of claim 22, wherein said step of displacing the cannon portion along a second path is carried out by displacing the cannon portion along a second path which is curved in the opposite direction from the first path.

28. The method of claim 22, wherein said displacing steps are carried out with the longitudinal barrel axis of the cannon portion remaining parallel to its initial pre-firing orientation throughout its recoil cycle.

29. A gun system substantially as hereinbefore described with reference to the accompanying drawings.

30. A method of stabilizing a gun system substantially as hereinbefore described with reference to the accompanying drawings. 60O00 t DATED this 7th day of May 1991 Royal Ordnance plc. S* *By Its Patent Attorneys DAVIES COLLISON 910507,rshspe.003,31912cla,74