US2390374A - Trunnion tilt corrector apparatus - Google Patents

Trunnion tilt corrector apparatus Download PDF

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US2390374A
US2390374A US201949A US20194938A US2390374A US 2390374 A US2390374 A US 2390374A US 201949 A US201949 A US 201949A US 20194938 A US20194938 A US 20194938A US 2390374 A US2390374 A US 2390374A
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shaft
elevation
gun
generating
cos
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William B Jordan
Frithiof V Johnson
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General Electric Co
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General Electric Co
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    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F41WEAPONS
    • F41GWEAPON SIGHTS; AIMING
    • F41G3/00Aiming or laying means
    • F41G3/10Aiming or laying means with means for compensating for canting of the trunnions

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  • This invention relates to the control of guns and the like, more particularly to the control of guns on swaying foundations, such as on a rolling ship, and it has for its object the provision of improved apparatus for directing guns whereby corrections are applied to the guns compensating for the inclination of the trunnions of the guns due to the roll of the ship, or other foundation on which the guns are mounted.
  • the calculated adjustments of range to be applied to the gun in elevation and of deflection to be applied to the gun in train are based on the assumption that the ad-- justments will be applied to the gun in true vertical and horizontal planes; that is, it is assumed that the trunnions of the gun about which the gun is elevated lie in a true horizontal plane, and that they are mounted so that the gun is adjusted in train on a true vertical axis.
  • the gun is usually mounted with its trunnions parallel with the deck of the ship on which the gun is carried, and thus, it is adjustable in elevation on an axis which is parallel to the deck and in train in an axis which is perpendicular to the deck.
  • This invention contemplates the provision of improved apparatus whereby the roll or inclination of the ship or other support on which the gun is mounted about the line of sight of a target is continuously introduced as a correction so that the calculated elevation and train adjustments, based on the assumption that the gun is to be adjusted in true vertical and horizontal planes, are continuously modified in accordance with the inclination of the ship so as to direct the adjustment of the gun to cause it to assume continuously the position in space that it would occupy when adjusted with reference to the true vertical and horizontal.
  • the line of sight will be a horizontal line from the deck to the target.
  • suitable apparatus comprising means for utilizing the calculated values of elevation and deflection corrections, and also utilizing continuously the angle of cross roll of the ship about the line of sight so as to modify the calculated values of elevation and deflection and regenerate them continuously as corrections which can be applied directly to the gun in elevation and train to cause it to assume the proper position in space with reference to the true vertical and horizontal.
  • FIG. 1 is a diagrammatic representation of trunnion tilt corrector apparatus arranged in accordance with this invention
  • Fig. 2 is a diagrammatic representation illustrating the'trunnion tilt problem which is solved by the apparatus of Fig. 1.
  • this invention has been shown in one form as applied to apparatus intended to correct for the trunnion tilt of a gun mounted on shipboard.
  • the range correction which will be called elevation correction hereinafter, is a function of the range of the target, velocity and direction of the wind, speeds and directions of ship and target, etc, as calculated, and is an angular adjustment to be applied to the gun in a vertical ,plane.
  • the train correction which will be called deflection correction, is calculated from the velocity and direction of the wind. drift, speed, direction of ship and target, etc., as calculated, and is an angular adjustment to be applied to the gun in a horizontal plane.
  • the gun mounted on shipboard is adjusted in elevation on its trunnions in a plane which is perpendicular to the deck and in a train plane which is at right angles to the elevation plane. It is clear, therefore, that when the ship is rolling so that the gun support inclines from the horizontal, the gun is not rotated in true vertical and horizontal planes respectively, but in planes at angles to these planes, the magnitude of the angles depending on the inclination of the ship.
  • the deck is not in a true Fig. 1.
  • the point P on the surface of a sphere is representative of the direction in which the gun should be directed.
  • This point P has an elevation value E and a deflection value D referred to axes a and b representative of the true horizontal and true vertical respectively.
  • E and D are the calculated adjustments to be applied to the gun in elevation and train, respectively.
  • the axes a and b are rotated through the angle 1 to the positions a and b. This is the condition when the deck of the ship rolls about the line of sight to a target through the angle 7, known as the angle of cross roll.
  • the angle 7 is the angle from the horizontal that the deck tilts around the line of sight, which line of sight, as pointed out previously, is the horizontal line between the sight and the target when the deck is at even keel. It will be apparent that when the axes are so rtated through the angle 7 if the point P is to retain the same position in space that it had before, the coordinates E and D respectively become the coordinates Ec and Dc respectively. It is the values of the corrected coordinates Ec and Do that are desired.
  • the exact formulae for the solution of this problem are the trigonometric equations:
  • Sin E Sin E Cos 'yCOS E Sin 7 Sin D Sin E Sin Cos E Cos 7 Sin D Cos E Cos D Equations 1 and 2 are derived as follows: Referring to Fig. 2, from well-known spherical trigonometrical formula applied to the spherical triangle pMN,
  • Cos o -E0 Cos (90E) Cos Sin (90-E) Sin 7 Cos (90 -1)) This equation may be written as its equivalent:
  • Equations 3 and 4 are empirical equations, and approximately solve the problem illustrated in Fig. 2.
  • the range or elevation E may vary from the limit 0 to 40"
  • the deflection D may vary between 6 and +6
  • the angle of cross roll 'y may be between -20 and +20
  • the maximum errors that have been encountered with these equations are 7 minutes in elevation, and 33 minutes in deflection.
  • K1, K2, K3 and K4 are IS fi 1 and 1 respectively. Should the ranges of the problem be varied as to elevation, deflection and cross roll, or as to One or more of these factors, these values should be varied accordingly to control the error within easonable limits.
  • f(E) empirically determined, is roughly a linear function of E, and expressed by the following equation:
  • this value may be and preferably should be varied if the limits of the problem vary, so as to correct the maximum errors.
  • the value f(E) is generated in the mechanism [3.
  • the mechanism I3 comprises a cam I4 having a spiral-like, cam groove l5 in which a follower pin I6 operate-s.
  • the follower pin 16 controls the movement of a slide rack I! with which a gear l8 cooperates.
  • Th cam M is provided on its periphery with a gear l9 which is driven by a spur gear 20. This gear in turn is driven by a shaft 2
  • the cam groove I5 is so arranged that it operates the rack H to generate in the movement of the gear l8 th value f(E) as expressed by Equation No. 5.
  • the gear l8 drives a shaft 23 which is connected to the input of a differential 24 by a gear 24a, the other input of which is directly connected with the shaft I0 introducing the value of E as calculated.
  • the constant K1 is introduced into the mechanism by properly proportioning the number of teeth on the gear 24a to the number of teeth on the dif- E35. tiff-55b" use.
  • the screw 28 is turned ated radially by means of a gear Plate 55 which in t adjust the position of th pin 21 by a member turn is operated by means of the shaft ll operat- 29 which drives a bevel gear 30 secured to the member and which gear meshes with a bevel gear 3
  • the member 29 is rotated by means of a spur gear 3 la which meshes with gear teeth 29a on the periphery of the member, as shown.
  • the gear 3Ia is driven by a shaft 32 which introduces flE).
  • the shaft 32 as shown, is driven from a. shaft 33 through bevel gears 34, and the shaft 33 in turn is driven from the shaft 23 by means of bevel gears 35 and a differential 36, the function of which will be described in greater detail hereinafter.
  • the screw 28 is mounted on a gear member 31 by means of a block 31a attached to the member 31, and, as shown, projects through the gear members 29 and 38.
  • the gear member 31 is mounted for free relative rotation with reference to the member 29, and on the same axis as the member 29.
  • the member 3! has gear teeth 38 on its periphery.
  • This member 31 is driven by a gear 39 mounted on a shaft 48 which is connected through bevel gears 41 with a shaft 42 which in turn is connected with the cross level shaft l2 through bevel gears 43.
  • the gear 39 introduces the factor K2.
  • the factor K27 therefore, is introduced by the shaft 48 which rotates the gear 3'! in accordance with this value, and therefore, superimposes upon the radial movement of the pin 21 an angular movement which is proportional to the value K27.
  • the resultant movement of the pin 21 is imparted to slides 44 and 45 fixed at right angles to each other, and intersecting each other at the pin 21.
  • the slide 44 is arranged to move only in a horizontal direction and the slide 45 is arranged to move only in a vertical direction.
  • the movement of the pin radially in accordance with the value ,f(E) and angularly in accordance with the value K27 imparts to the slides 44 and 45 respectively such motions that they generate the values ,f(E) Sin K2 and ICE) Cos K27, respectively.
  • the horizontal motion of the slide 44 drives a shaft 46.
  • the slide 44 is provided with a gear rack 41 which meshes with a gear 48 mounted on the shaft 46.
  • the vertical motion of the rack 45 is imparted to a shaft 49 by means of a rack 50 on the slide and a gear 5
  • the motions of the shafts 49 and 46 are utilized to generate the corrected adjustments EC and Do, as will be described in greater detail hereinafter.
  • the purpose of the differential 36 will now be understood. It will be observed that when the shaft 42 is operated to rotate the member 31 and ing through a differential device 51, a shaft 58 and a gear 59 meshing with gear plate 56.
  • the gear 56 operates the screw 55 through bevel gears 60.
  • the pin 54 is operated angularly in accordance with the angle of cross roll 7 by means of a gear 6
  • the gear 62 is arranged to introduce the factor K4.
  • the motion of the pin 54 is imparted to slides 65 and 66 arranged at right angles to each other and intersecting each other at the pin, as shown.
  • the slide 65 can have only vertical motion and the slide 66 can have only horizontal motion.
  • the mechanism 53 is such that the motion imparted .to the slide 65 is the value D Sin K47, and the movement of the slide 66 generates D Cos K47.
  • the motion of the slide 65 is imparted to a shaft 61 through a gear rack 68 mounted on the slide and meshing with a gear 69 on the shaft 61.
  • the shaft 6! drives a shaft I0 through the bevel gears H.
  • the motion of the slide 66 is imparted to a rack H mounted on it and this motion of the rack is imparted to a shaft 12 by means of a gear 13 mounted 0n the shaft and meshing with the rack.
  • the differential device 51 functions as does the differential 36, that is, to compensate for the radial movement that would b imparted to the pin 54 by the interaction of the gears 60 when gear 6
  • K1 is introduced into the mechanism by properly proportioning the number of teeth on the gear 15a to the number of teeth on the differential input gear driven thereby, and this constant is multiplied by f(E) in the differential.
  • K1J(E) Cos K27 is added to the input of the shaft 25 in the differential 14 to generate the value EK1f(E)+K1f(E) Cos K27 so that this resultant is generated by the output shaft 1'! of the differential 14.
  • the value D Sin K47 generated in the shaft 10 is subtracted from this value generated in the shaft 11 in a 5 differential 18 to generate in the output shaft 19 the screw 28 as a unit, the shaft 32 for the moof the difi ti l the following Value; ment may be considered fixed; therefore, when the member 31 is rotated to introduce K27, motion E"K1f(E)+K1f(E) COS KZY-K3 D Sm K47 w uld be imparted to th s r w 28 t move the p the factor K2 being introduced in the differential 21 radially by the interaction of the gearing 30 7o 18.
  • the above value is the same as the value exand 3
  • the differential 36 introduces the rotapressed in Equation3: tion of the shaft 42 into the calculating device 26 E K K D K to unwind, so to speak, the rotation imparted to KW Cos 27) 3 m 47 the screw 28 due to this interaction of the gears Whlch 15 30 and 3
  • Equation 4 is added in the differential 80 to the output of shaft 46, which is ,f(E) Sin K27, to generate in the output shaft 8
  • the apparatus of this invention may also be used in other applications where it is desired to maintain the position of a point in space fixed on the surface of a sphere even though the original axes of the point are inclined.
  • a trunnion tilt corrector mechanism for a gun mounted on a swaying foundation mechanism for generating a corrected adjustment to be applied to said gun in deflection comprising, a
  • first input shaft and a second input shaft for introducing ascertained values to be applied in elevation and deflection respectively
  • a third input shaft for introducing the angle of cross roll of the mount around the line of sight of a target
  • means operated responsively to said first input shaft for generating a predetermined function of elevation means operated responsively to said last-named means and said third input shaft for generating a product of said function of elevation and a predetermined trigonometric function of said angle of cross roll
  • a second resolver operated responsively to said second and third input shafts for generating a predetermined product of said ascertained deflection and a predetermined trigonometric function of the angle of cross roll
  • a fourth shaft operated by said first and second resolvers so that its movement generates said corrected deflection adjustment as the sum of the products of said function of elevation and predetermined trigonometric function of the angle of cross roll and of the ascertained value of deflection and predetermined trigonometric function of the angle of cross roll.
  • mechanism for generating a corrected adjustment to be applied to said gun in elevation comprising. a first input shaft and a second input shaft for introducing ascertained values to be applied in elevation and deflection respectively, a third input shaft for introducing the angle of cross roll of the mount around the line of sight of a target, means operated responsively to said first input shaft for generating a predetermined function of elevation,
  • a resolving mechanism operated responsively to said last-named means and said third input shaft for generating a product of said function of elevation and a predetermined trigonometric function of said angle of cross roll
  • a fourth shaft operated responsively to said first input shaft and said means for generating said predetermined function of elevation so that the movement of said fourth shaft generates the difference between said ascertained value of elevation and said function of elevation
  • a second resolver operated responsively to said second and third input shafts for generating a predetermined product of said ascertained deflection and a predetermined trigonometric function of the angle of cross roll
  • a fifth shaft operated responsively to said first resolver and said fourth shaft so that its movement generates the summation of the difference of ascertained elevation and said function of elevation and the product of said function of elevation and predetermined trigonometric function of said angle of cross roll generated in said first resolver
  • a sixth shaft operated responsively to said second resolver and said fifth shaft so that its movement generates the difference between the value generated in said fifth shaft and
  • mechanism for generating corrected elevation adjustments to be applied to said gun comprising three input shafts, the first to introduce th ascertained value of the elevation adjustment to be applied to said gun, the second to introduce the ascertained value of the deflection adjustment to be applied to said gun, and the third to introduce the angle of cross roll of the mount around the line of sight of a target, a resolver operated responsively to said second and third shafts for deriving the product of ascertained deflection and a predetermined function of the angle of cross roll, first means operated by said first shaft for deriving a predetermined function of ascertained value of elevation, second means operated by said first means and said first shaft for generating the difference between ascertained elevation and said predetermined function of ascertained value of elevation, a second resolver operated by said first means and said third shaft for deriving the product of said function of ascertained value of elevation and a predetermined function of the angle of cross roll,
  • mechanism for generating a corrected adjustment to be applied to said gun in elevation comprising, a first input shaft and a second input shaft for introducing ascertained values to be applied in elevation and deflection respectively, a third input shaft for introducing the angle of cross roll of the mount around the line of sight of a target, means operated responsively to said first input shaft for generating a predetermined function of elevation, a resolving mechanism operated responsively to said last-named means and said third input shaft for generating a product of said function of elevation and a predetermined function of said angle of cross roll, a fourth shaft, means operating said fourth shaft responsively to said first input shaft and said means for generating said function of elevation so that the movement of said fourth shaft generates the difference between said ascertained value of elevation and said function of elevation, a second resolving mechanism operated responsively to said second and third input shafts for generating a predetermined product of said ascertained def
  • mechanism for generating a corrected adjustment to be applied to said gun in elevation Ec comprising first, second and third shafts for introducing respectively ascertained values of elevation E, deflection D, and the angle of cross roll 7 of said ship about the line of sight of a target, a cam operated by said first shaft and a follower operated by said cam, said cam and follower constructed and arranged so that the movement of said follower generates a predetermined function of the ascertained eleva tion value f(E), first generating means operated responsively both to said movement of said follower and to the operation of said third shaft in introducing the ascertained angle of cross roll y constructed and arranged to generate the product (E) Cos Kzy, second generating means operated responsively both to said second and third shafts in introducing respectively the ascertained values of deflection D and angle of cross roll 7 constructed and arranged to generate the product D Sin Kw, a fourth shaft, means operating said fourth shaft responsive
  • first, second and third shafts for introducing respectively ascertained values of elevation E, and deflection D, and the angle of cross roll 7 of said ship about the line of sight of a target, a cam operated by said first shaft and a follower operated by the cam so that its movement generates a predetermined function of the calculated elevation value ,f(E) first generating means operated responsively to said follower and said third shaft for generating the bearsh doom product ,1 (E) Sin y, second generating means operated responsively to said second and third shafts for generating the product D Cos Y and means operated by said first and second generating means for generating the summation: j(E) Sin y-l-D Cos y.
  • mechanism for generating corrected adjustments to be applied to said gun in elevation E and deflection D comprising first, second and third shafts for introducing respectively ascertained values of elevation E, the deflection D and the angle of cross roll y of said ship about the line of sight of a target, first means operated responsively to the operation of said first shaft for generating a predetermined function of the ascertained elevation value of f(E), means operated responsively to the'operation of said first means and said third shaft for generating products of f(E) and predetermined functions of y and further means operated responsively to said second and third shafts for generating products of D and predetermined functions of y, means operably connected to said first shaft, said first means, and to said means for generating said products so as to be operated thereby to generate corrected values of elevation in terms both of said products of f(E) and D and said predetermined functions of y, and also in terms of said ascertained values of j
  • mechanism for generating corrected adjustments to be applied to said gun in elevation Ec and deflection Dc comprising first and second shafts for introducing ascertained values of elevation E and deflection D measured with reference to the true vertical and horizontal, a third shaft for introducing the angle of cross roll y of said ship about the line of sight of a target, a calculating mechanism having a, pin mounted for circular movement about a fixed axis and for radial movement with reference to said axis, a pair of mutually perpendicular slides mounted for movement at right angles to each other and intersecting each other at said pin where the pin is connected to them for operating them, a second calculating mechanism similar to the first, a cam operated by said first shaft and a follower operated by the cam to generate a predetermined function of the elevation value ;f(E), means connecting the pin of the first mechanism with said follower so that the pin is moved radially in accordance with the movement of said follower, means connecting said second shaft with said second
  • mechanism for generating corrected adjustments to -be applied to said gun in elevation E and deflection Dc comprising first, second and third shafts for introducing respectively ascertained values of elevation E, and deflection D, and the angle of cross roll 7 of said ship about the line of sight to a target, a cam operated by said first shaft and a follower operated by the cam to generate a determined function of the calculated elevation value I (E) having approximately the following value:
  • first generating means operated responsively to said follower and said third shaft for generating the products flE) Cos 21 7 and second generating means operated responsively to said second and third shafts for generating the products D sin y and D cos y, and means operated responsively to said first shaft, said cam follower in generating said value f(E) and said first and second generating means constructed and arranged to utilize said ascertained values of elevation E introduced by said first shaft, said value f(E) generated by said cam follower, and said products f 'E) Sin f(E) Cos generating means to generate the corrected adjustrnent in elevation Ec to be applied to said gun, and means operated responsively to said first and second generating means constructed and arranged to utilize said products j(E) sin y and D cos 7 generated by said first and second generating means to generate the corrected adjustment in deflection Do to be applied to said gun.
  • mechanism for generating a corrected adjustment to be applied to said gun in deflection comprising, a first input shaft and a second input shaft for introducing ascertained values to be applied in elevation and deflection respectively, a third input shaft for introducing the angle of cross roll of the mount around the line of sight of a target.

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Description

Zita-4U! OR 2,390,374 N x Dec. 4, 1945. w. B. JORDAN ET AL 2,390,374
TRUNNIOILgI IQI' ,CORRECTOR APPARATUS Filed April 14, 1958 I8 27 *fi In ventors:
William B. Jordan, Frithiof V. Johnson,
10 X7 6AM '5 Tm Attovns-zy.
Patented Dec. 4, 1945 UNITED OUtu u" I STATES PATENT OFFICE TRUNNION TILT coannc'roa APPARATUS Application April 14, 1938, Serial No. 201,949
1*!) Claims.
This invention relates to the control of guns and the like, more particularly to the control of guns on swaying foundations, such as on a rolling ship, and it has for its object the provision of improved apparatus for directing guns whereby corrections are applied to the guns compensating for the inclination of the trunnions of the guns due to the roll of the ship, or other foundation on which the guns are mounted.
In the directing of guns, the calculated adjustments of range to be applied to the gun in elevation and of deflection to be applied to the gun in train are based on the assumption that the ad-- justments will be applied to the gun in true vertical and horizontal planes; that is, it is assumed that the trunnions of the gun about which the gun is elevated lie in a true horizontal plane, and that they are mounted so that the gun is adjusted in train on a true vertical axis. The gun, however, is usually mounted with its trunnions parallel with the deck of the ship on which the gun is carried, and thus, it is adjustable in elevation on an axis which is parallel to the deck and in train in an axis which is perpendicular to the deck. Therefore, it is only when the ship is on even keel that the gun is adjusted on train and elevation axes which are truly vertical and horizontal. Consequently, it is only when the ship is on even keel that the calculated corrections for train and deflection are properly applied to the gun.
This invention contemplates the provision of improved apparatus whereby the roll or inclination of the ship or other support on which the gun is mounted about the line of sight of a target is continuously introduced as a correction so that the calculated elevation and train adjustments, based on the assumption that the gun is to be adjusted in true vertical and horizontal planes, are continuously modified in accordance with the inclination of the ship so as to direct the adjustment of the gun to cause it to assume continuously the position in space that it would occupy when adjusted with reference to the true vertical and horizontal. It is to be understood that when the deck of the ship is horizontal, the line of sight will be a horizontal line from the deck to the target. As the ship rolls and pitches, there is an inclination or rolling of the deck about this horizontal line as an axis. It is this roll or inclination of the deck which the apparatus of this invention is intended to compensate for.
In accordance with this invention, suitable apparatus is provided comprising means for utilizing the calculated values of elevation and deflection corrections, and also utilizing continuously the angle of cross roll of the ship about the line of sight so as to modify the calculated values of elevation and deflection and regenerate them continuously as corrections which can be applied directly to the gun in elevation and train to cause it to assume the proper position in space with reference to the true vertical and horizontal.
For a more complete understanding of this invention, reference should be had to the accompanying drawing in which Fig. 1 is a diagrammatic representation of trunnion tilt corrector apparatus arranged in accordance with this invention; and Fig. 2 is a diagrammatic representation illustrating the'trunnion tilt problem which is solved by the apparatus of Fig. 1.
Referring to the drawing, this invention has been shown in one form as applied to apparatus intended to correct for the trunnion tilt of a gun mounted on shipboard.
It will be understood that in directing a gun on a target, the range correction, which will be called elevation correction hereinafter, is a function of the range of the target, velocity and direction of the wind, speeds and directions of ship and target, etc, as calculated, and is an angular adjustment to be applied to the gun in a vertical ,plane. The train correction, which will be called deflection correction, is calculated from the velocity and direction of the wind. drift, speed, direction of ship and target, etc., as calculated, and is an angular adjustment to be applied to the gun in a horizontal plane. As pointed out previously, the gun mounted on shipboard is adjusted in elevation on its trunnions in a plane which is perpendicular to the deck and in a train plane which is at right angles to the elevation plane. It is clear, therefore, that when the ship is rolling so that the gun support inclines from the horizontal, the gun is not rotated in true vertical and horizontal planes respectively, but in planes at angles to these planes, the magnitude of the angles depending on the inclination of the ship.
It is a function of the apparatus of this invention to utilize the calculated adjustments in elevation and deflection to be applied to the gun, and modify them continuously in accordance with the angle of cross roll of the ship about the line of sight to the target; and to regenerate the values in elevation and deflection that must be applied to the gun to cause it to be directed in the proper direction. It is to be understood that it is assumed in this application that when the ship is on even keel its deck will be truly horizontal. In
practice, it may be that the deck is not in a true Fig. 1. Let it be assumed that the point P on the surface of a sphere is representative of the direction in which the gun should be directed. This point P has an elevation value E and a deflection value D referred to axes a and b representative of the true horizontal and true vertical respectively. It will be understood that the values E and D are the calculated adjustments to be applied to the gun in elevation and train, respectively. Now let it be assumed that the axes a and b are rotated through the angle 1 to the positions a and b. This is the condition when the deck of the ship rolls about the line of sight to a target through the angle 7, known as the angle of cross roll. The angle 7 is the angle from the horizontal that the deck tilts around the line of sight, which line of sight, as pointed out previously, is the horizontal line between the sight and the target when the deck is at even keel. It will be apparent that when the axes are so rtated through the angle 7 if the point P is to retain the same position in space that it had before, the coordinates E and D respectively become the coordinates Ec and Dc respectively. It is the values of the corrected coordinates Ec and Do that are desired. The exact formulae for the solution of this problem are the trigonometric equations:
(1) Sin E =Sin E Cos 'yCOS E Sin 7 Sin D Sin E Sin Cos E Cos 7 Sin D Cos E Cos D Equations 1 and 2 are derived as follows: Referring to Fig. 2, from well-known spherical trigonometrical formula applied to the spherical triangle pMN,
Cos pN=Cos pM Cos MN+ Sin pM Sin MN Cos angle pMN 2 Tan D= and since pN=90Ec 10M =90-E MN =1,
and
Angle pMN=90+D the above equation may be written as follows:
Cos o -E0) =Cos (90E) Cos Sin (90-E) Sin 7 Cos (90 -1)) This equation may be written as its equivalent:
Sin Ee=Sin E Cos 'yC0s E Sin 7 Sin D r which is Equation 1.
Again referring to spherical triangle pMN, from well-known spherical trigonomical formula:
Sin angle pMN Cot angle MNp =Sin 'y Cot pMCos 'y Cos angle pMN Sin (90+D) Cot (90Dc) =Sin 'y Cot (90E) COS 7 C05 (90+D) which may be written as its equivalent:
Cos D Tan Dc=Sin '7 Tan E+Cos 7 Sin D which may be written as its equivalent:
Tan Tan E Sin Cos '7 Sin D Cos D Multiply numerator and denominator by Cos E, then Sin E Sin 7+ Cos E Cos 7 Sin D Tan Cos E Cos D which is the aforesaid Equation 2.
The mechanism arranged in accordance with this invention does not solve these precise equations, but solves the problem by means of the approximate equations as follows:
(3) Ec=EK1f(E) (1COS K27) K3D Sin Kry (4) Dc=f(E) Sin Kzy-i-D COS Kr'y In these formulae K1, K2, K2 and K4 are constants, and ICE!) is a function of the coordinate E, as will be explained in greater detail hereinafter.
Equations 3 and 4 are empirical equations, and approximately solve the problem illustrated in Fig. 2. In a specific problem where the range or elevation E may vary from the limit 0 to 40", where the deflection D may vary between 6 and +6, and where the angle of cross roll 'y may be between -20 and +20, the maximum errors that have been encountered with these equations are 7 minutes in elevation, and 33 minutes in deflection.
In this specific problem, the empirically determined values of K1, K2, K3 and K4 are IS fi 1 and 1 respectively. Should the ranges of the problem be varied as to elevation, deflection and cross roll, or as to One or more of these factors, these values should be varied accordingly to control the error within easonable limits. The value f(E), empirically determined, is roughly a linear function of E, and expressed by the following equation:
1 92 Sin 3.6E
19 n tan mm Here again, this value may be and preferably should be varied if the limits of the problem vary, so as to correct the maximum errors.
Referring more specifically to Fig. 1, it will be understood that the calculated or ascertained values of elevation E and of deflection D are introduced into the mechanism by means of shafts I0 and H, and that the angle of cross roll is introduced into the mechanism by the shaft I2. It will be understood that these values E, D and y will be generated by any suitable auxiliary mechanisms which form no part of this invention.
The value f(E) is generated in the mechanism [3. The mechanism I3 comprises a cam I4 having a spiral-like, cam groove l5 in which a follower pin I6 operate-s. The follower pin 16 controls the movement of a slide rack I! with which a gear l8 cooperates. Th cam M, as shown, is provided on its periphery with a gear l9 which is driven by a spur gear 20. This gear in turn is driven by a shaft 2| that is driven by the shaft [0 through bevel gears 22. The cam groove I5 is so arranged that it operates the rack H to generate in the movement of the gear l8 th value f(E) as expressed by Equation No. 5. The gear l8 drives a shaft 23 which is connected to the input of a differential 24 by a gear 24a, the other input of which is directly connected with the shaft I0 introducing the value of E as calculated. The constant K1 is introduced into the mechanism by properly proportioning the number of teeth on the gear 24a to the number of teeth on the dif- E35. tiff-55b" use.
ferential input gear driven thereby, and this constant is multiplied by f(E) in the differential. Also in the differential 24, the value K1,f(E) is subtracted from E so that the output shaft 25 of dially on the screw 28 is not affected by the rotation of the member 31.
The motion of the shaft l I which introduces the calculated value of deflection D and the shaft the differential generates the value EK1f(E). 5 42 which measures the ascertained value of the A resolving mechanism 26 generates the values angle of Cross r0 7 also oper e r lv n e h- ,f(E) Cos K27 and (E) Sin K27. This mechanism anism 53 which is similar to the mechanism 26. comprises a pin 21 which is mounted for radial Here the p n 54 mounted on the screw 55 is opermovement on a screw 28. The screw 28 is turned ated radially by means of a gear Plate 55 which in t adjust the position of th pin 21 by a member turn is operated by means of the shaft ll operat- 29 which drives a bevel gear 30 secured to the member and which gear meshes with a bevel gear 3| attached to the screw. The member 29 is rotated by means of a spur gear 3 la which meshes with gear teeth 29a on the periphery of the member, as shown. The gear 3Ia is driven by a shaft 32 which introduces flE). The shaft 32, as shown, is driven from a. shaft 33 through bevel gears 34, and the shaft 33 in turn is driven from the shaft 23 by means of bevel gears 35 and a differential 36, the function of which will be described in greater detail hereinafter.
The screw 28 is mounted on a gear member 31 by means of a block 31a attached to the member 31, and, as shown, projects through the gear members 29 and 38. The gear member 31 is mounted for free relative rotation with reference to the member 29, and on the same axis as the member 29. The member 3! has gear teeth 38 on its periphery. This member 31 is driven by a gear 39 mounted on a shaft 48 which is connected through bevel gears 41 with a shaft 42 which in turn is connected with the cross level shaft l2 through bevel gears 43. The gear 39 introduces the factor K2. The factor K27, therefore, is introduced by the shaft 48 which rotates the gear 3'! in accordance with this value, and therefore, superimposes upon the radial movement of the pin 21 an angular movement which is proportional to the value K27.
The resultant movement of the pin 21 is imparted to slides 44 and 45 fixed at right angles to each other, and intersecting each other at the pin 21. The slide 44 is arranged to move only in a horizontal direction and the slide 45 is arranged to move only in a vertical direction.
The movement of the pin radially in accordance with the value ,f(E) and angularly in accordance with the value K27 imparts to the slides 44 and 45 respectively such motions that they generate the values ,f(E) Sin K2 and ICE) Cos K27, respectively. The horizontal motion of the slide 44 drives a shaft 46. For this. purpose, the slide 44 is provided with a gear rack 41 which meshes with a gear 48 mounted on the shaft 46. The vertical motion of the rack 45 is imparted to a shaft 49 by means of a rack 50 on the slide and a gear 5| on the shaft. The motions of the shafts 49 and 46 are utilized to generate the corrected adjustments EC and Do, as will be described in greater detail hereinafter.
The purpose of the differential 36 will now be understood. It will be observed that when the shaft 42 is operated to rotate the member 31 and ing through a differential device 51, a shaft 58 and a gear 59 meshing with gear plate 56. The gear 56, as shown, operates the screw 55 through bevel gears 60. The pin 54 is operated angularly in accordance with the angle of cross roll 7 by means of a gear 6| which supports the screw and is driven by a gear 62 that in turn is driven by a shaft 63. The gear 62 is arranged to introduce the factor K4.
The motion of the pin 54 is imparted to slides 65 and 66 arranged at right angles to each other and intersecting each other at the pin, as shown. The slide 65 can have only vertical motion and the slide 66 can have only horizontal motion. The mechanism 53 is such that the motion imparted .to the slide 65 is the value D Sin K47, and the movement of the slide 66 generates D Cos K47. The motion of the slide 65 is imparted to a shaft 61 through a gear rack 68 mounted on the slide and meshing with a gear 69 on the shaft 61. The shaft 6! drives a shaft I0 through the bevel gears H. The motion of the slide 66 is imparted to a rack H mounted on it and this motion of the rack is imparted to a shaft 12 by means of a gear 13 mounted 0n the shaft and meshing with the rack.
The differential device 51 functions as does the differential 36, that is, to compensate for the radial movement that would b imparted to the pin 54 by the interaction of the gears 60 when gear 6| is adjusted.
The motions of these two shafts l0 and 12 are also utilized to generate the values Ec and Do. That of the former is combined with the motion of the shaft 25 to produce the value E0. The shaft 25, as pointed out previously, generates the value EK1f(E), and this valu is introduced by the shaft 25 into a differential device 14; also feeding into this differential device 14 is the shaft 15 which is driven from the shaft 49 by bevel gears 16 to generate the value J(E) Cos K27. 1A5 shown, the shaft '15 is connected to an input gear of the differential 14 by means of a gear 1512. Here the constant K1 is introduced into the mechanism by properly proportioning the number of teeth on the gear 15a to the number of teeth on the differential input gear driven thereby, and this constant is multiplied by f(E) in the differential. The value K1J(E) Cos K27 is added to the input of the shaft 25 in the differential 14 to generate the value EK1f(E)+K1f(E) Cos K27 so that this resultant is generated by the output shaft 1'! of the differential 14. The value D Sin K47 generated in the shaft 10 is subtracted from this value generated in the shaft 11 in a 5 differential 18 to generate in the output shaft 19 the screw 28 as a unit, the shaft 32 for the moof the difi ti l the following Value; ment may be considered fixed; therefore, when the member 31 is rotated to introduce K27, motion E"K1f(E)+K1f(E) COS KZY-K3 D Sm K47 w uld be imparted to th s r w 28 t move the p the factor K2 being introduced in the differential 21 radially by the interaction of the gearing 30 7o 18. The above value is the same as the value exand 3|. The differential 36 introduces the rotapressed in Equation3: tion of the shaft 42 into the calculating device 26 E K K D K to unwind, so to speak, the rotation imparted to KW Cos 27) 3 m 47 the screw 28 due to this interaction of the gears Whlch 15 30 and 3| so that the position of the pin 2'! ra- The output of shaft 12, which is D Cos K47,
is added in the differential 80 to the output of shaft 46, which is ,f(E) Sin K27, to generate in the output shaft 8| of the differential the summation f(E) Sin K27+D Cos K47, which, as pointed out above, is the value of corrected deflection Dc as expressed in Equation 4.
In the operation of the apparatus, it will be understood that the values of E and D will be fed into the apparatus by means of the shafts l and H as they are calculated, and that the angle of cross roll y will be continuousl introduced into the mechanism by means of the shaft l2. The apparatus continuously regenerates these values in the manner previously described to generate the corrected adjustments to be applied to the gun, EC and Dc, the shafts l9 and 8! generating these values, respectively. The values generated in these shafts may be used in any suitable manner to direct the gun, such as to operate suitable gun indicating mechanism (not shown).
It will be understood that the apparatus of this invention may also be used in other applications where it is desired to maintain the position of a point in space fixed on the surface of a sphere even though the original axes of the point are inclined.
While we have shown a particular embodiment of our invention, it will be understood, of course, that we do not wish to be limited thereto since many modifications may be made, and we, therefore, contemplate by the appended claims to cover any such modifications as fall within the true spirit and scope of our invention.
What we claim as new and desire to secure by Letters Patent of the United States is:
1. In a trunnion tilt corrector mechanism for a gun mounted on a swaying foundation, mechanism for generating a corrected adjustment to be applied to said gun in deflection comprising, a
first input shaft and a second input shaft for introducing ascertained values to be applied in elevation and deflection respectively, a third input shaft for introducing the angle of cross roll of the mount around the line of sight of a target, means operated responsively to said first input shaft for generating a predetermined function of elevation, a resolving mechanism operated responsively to said last-named means and said third input shaft for generating a product of said function of elevation and a predetermined trigonometric function of said angle of cross roll, a second resolver operated responsively to said second and third input shafts for generating a predetermined product of said ascertained deflection and a predetermined trigonometric function of the angle of cross roll, and a fourth shaft operated by said first and second resolvers so that its movement generates said corrected deflection adjustment as the sum of the products of said function of elevation and predetermined trigonometric function of the angle of cross roll and of the ascertained value of deflection and predetermined trigonometric function of the angle of cross roll.
2. In a trunnion tilt corrector mechanism for a gun mounted on a swaying foundation, mechanism for generating a corrected adjustment to be applied to said gun in elevation comprising. a first input shaft and a second input shaft for introducing ascertained values to be applied in elevation and deflection respectively, a third input shaft for introducing the angle of cross roll of the mount around the line of sight of a target, means operated responsively to said first input shaft for generating a predetermined function of elevation,
a resolving mechanism operated responsively to said last-named means and said third input shaft for generating a product of said function of elevation and a predetermined trigonometric function of said angle of cross roll, a fourth shaft operated responsively to said first input shaft and said means for generating said predetermined function of elevation so that the movement of said fourth shaft generates the difference between said ascertained value of elevation and said function of elevation, a second resolver operated responsively to said second and third input shafts for generating a predetermined product of said ascertained deflection and a predetermined trigonometric function of the angle of cross roll, a fifth shaft operated responsively to said first resolver and said fourth shaft so that its movement generates the summation of the difference of ascertained elevation and said function of elevation and the product of said function of elevation and predetermined trigonometric function of said angle of cross roll generated in said first resolver, and a sixth shaft operated responsively to said second resolver and said fifth shaft so that its movement generates the difference between the value generated in said fifth shaft and the product of ascertained deflection and predetermined trigonometric function of the angle of cross r011 generated in said second resolver.
3. In a trunnion tilt corrector mechanism for a gun mounted on a swaying foundation, mechanism for generating corrected elevation adjustments to be applied to said gun comprising three input shafts, the first to introduce th ascertained value of the elevation adjustment to be applied to said gun, the second to introduce the ascertained value of the deflection adjustment to be applied to said gun, and the third to introduce the angle of cross roll of the mount around the line of sight of a target, a resolver operated responsively to said second and third shafts for deriving the product of ascertained deflection and a predetermined function of the angle of cross roll, first means operated by said first shaft for deriving a predetermined function of ascertained value of elevation, second means operated by said first means and said first shaft for generating the difference between ascertained elevation and said predetermined function of ascertained value of elevation, a second resolver operated by said first means and said third shaft for deriving the product of said function of ascertained value of elevation and a predetermined function of the angle of cross roll, third means operated by said second resolver and said second means for adding the values generated thereby, and fourth means operated by said first resolver and said third means for subtracting said product generated in said first resolver from the value derived in said third means to generate the corrected elevation adjustment.
4. In a trunnion tilt corrector mechanism for a gun mounted on a swaying foundation, mechanism for generating a corrected adjustment to be applied to said gun in elevation comprising, a first input shaft and a second input shaft for introducing ascertained values to be applied in elevation and deflection respectively, a third input shaft for introducing the angle of cross roll of the mount around the line of sight of a target, means operated responsively to said first input shaft for generating a predetermined function of elevation, a resolving mechanism operated responsively to said last-named means and said third input shaft for generating a product of said function of elevation and a predetermined function of said angle of cross roll, a fourth shaft, means operating said fourth shaft responsively to said first input shaft and said means for generating said function of elevation so that the movement of said fourth shaft generates the difference between said ascertained value of elevation and said function of elevation, a second resolving mechanism operated responsively to said second and third input shafts for generating a predetermined product of said ascertained deflection and a predetermined function of the angle of cross roll, a fifth shaft, means operating said fifth shaft responsively to said first resolving mechanism and said fourth shaft so that the movement of said fifth shaft generates the summation of the difference of ascertained elevation and said function of elevation and the product of said function of elevation and predetermined function of said angle of cross roll generated in said first resolving mechanism, a sixth shaft, and means operating said sixth shaft responsively to said second resolving mechanism and said fifth shaft so that the movement of said sixth shaft generates the difference between the value generated in said fifth shaft and the product of ascertained deflection and predetermined function of the angle of cross roll generated in said second resolving mechanism.
5. In a trunnion tilt corrector mechanism for a gun mounted on a ship, mechanism for generating a corrected adjustment to be applied to said gun in elevation Ec comprising first, second and third shafts for introducing respectively ascertained values of elevation E, deflection D, and the angle of cross roll 7 of said ship about the line of sight of a target, a cam operated by said first shaft and a follower operated by said cam, said cam and follower constructed and arranged so that the movement of said follower generates a predetermined function of the ascertained eleva tion value f(E), first generating means operated responsively both to said movement of said follower and to the operation of said third shaft in introducing the ascertained angle of cross roll y constructed and arranged to generate the product (E) Cos Kzy, second generating means operated responsively both to said second and third shafts in introducing respectively the ascertained values of deflection D and angle of cross roll 7 constructed and arranged to generate the product D Sin Kw, a fourth shaft, means operating said fourth shaft responsively both to the operation of said first shaft and said follower so that the movement of said fourth shaft generates the difference Ef(E), means operated by said fourth shaft and said first generating means for generating the summation: [E-f(E) ]+[]'(E) Cos Kzy], and means operated by said last-named means and also operated by said second generating means for generating the difference:
6. In a trunnion tilt corrector mechanism for a gun mounted on a ship, first, second and third shafts for introducing respectively ascertained values of elevation E, and deflection D, and the angle of cross roll 7 of said ship about the line of sight of a target, a cam operated by said first shaft and a follower operated by the cam so that its movement generates a predetermined function of the calculated elevation value ,f(E) first generating means operated responsively to said follower and said third shaft for generating the bearsh doom product ,1 (E) Sin y, second generating means operated responsively to said second and third shafts for generating the product D Cos Y and means operated by said first and second generating means for generating the summation: j(E) Sin y-l-D Cos y.
7. In a trunnion tilt corrector mechanism for a gun mounted on a ship, mechanism for generating corrected adjustments to be applied to said gun in elevation E and deflection D comprising first, second and third shafts for introducing respectively ascertained values of elevation E, the deflection D and the angle of cross roll y of said ship about the line of sight of a target, first means operated responsively to the operation of said first shaft for generating a predetermined function of the ascertained elevation value of f(E), means operated responsively to the'operation of said first means and said third shaft for generating products of f(E) and predetermined functions of y and further means operated responsively to said second and third shafts for generating products of D and predetermined functions of y, means operably connected to said first shaft, said first means, and to said means for generating said products so as to be operated thereby to generate corrected values of elevation in terms both of said products of f(E) and D and said predetermined functions of y, and also in terms of said ascertained values of j(E) and of E, and means operably connected to said means for generating said products so as to be operated thereby to generate corrected values of deflection in terms both of said products f(E) and D and said predetermined functions of y.
8. In gun directing mechanism for a gun mounted on a ship, mechanism for generating corrected adjustments to be applied to said gun in elevation Ec and deflection Dc comprising first and second shafts for introducing ascertained values of elevation E and deflection D measured with reference to the true vertical and horizontal, a third shaft for introducing the angle of cross roll y of said ship about the line of sight of a target, a calculating mechanism having a, pin mounted for circular movement about a fixed axis and for radial movement with reference to said axis, a pair of mutually perpendicular slides mounted for movement at right angles to each other and intersecting each other at said pin where the pin is connected to them for operating them, a second calculating mechanism similar to the first, a cam operated by said first shaft and a follower operated by the cam to generate a predetermined function of the elevation value ;f(E), means connecting the pin of the first mechanism with said follower so that the pin is moved radially in accordance with the movement of said follower, means connecting said second shaft with said second pin so that it is moved radially in accordance with the calculated value D, means connecting both of said pins with said third shaft so that they are rotated about their axes in accordance with the angle of cross roll y of the ship about the line of sight to a target, the slides of the first calculating mechanism thereby measuring the products (E) sin Kzy and J(E) cos Kay and those of the second the products D sin Kw and D cos Km, and means operated by said first shaft in introducing said ascertained values of elevation E, said cam follower in generating said value f(E) and also by the slides of said calculating mechanisms in generating the products HE) cos y and D sin y for generating the corrected value of elevation E0 to be applied. to said gun, and means operated responsively to said slides of said calculating mechanisms in generating the products I (E) sin y and D cos y for generating the corrected value of defiection Do to be applied to said gun.
9. In a trunnion tilt corrector mechanism for a gun mounted on a ship, mechanism for generating corrected adjustments to -be applied to said gun in elevation E and deflection Dc comprising first, second and third shafts for introducing respectively ascertained values of elevation E, and deflection D, and the angle of cross roll 7 of said ship about the line of sight to a target, a cam operated by said first shaft and a follower operated by the cam to generate a determined function of the calculated elevation value I (E) having approximately the following value:
first generating means operated responsively to said follower and said third shaft for generating the products flE) Cos 21 7 and second generating means operated responsively to said second and third shafts for generating the products D sin y and D cos y, and means operated responsively to said first shaft, said cam follower in generating said value f(E) and said first and second generating means constructed and arranged to utilize said ascertained values of elevation E introduced by said first shaft, said value f(E) generated by said cam follower, and said products f 'E) Sin f(E) Cos generating means to generate the corrected adjustrnent in elevation Ec to be applied to said gun, and means operated responsively to said first and second generating means constructed and arranged to utilize said products j(E) sin y and D cos 7 generated by said first and second generating means to generate the corrected adjustment in deflection Do to be applied to said gun.
10. In a trunnion tilt corrector mechanism for a gun mounted on a swaying foundation, mechanism for generating a corrected adjustment to be applied to said gun in deflection comprising, a first input shaft and a second input shaft for introducing ascertained values to be applied in elevation and deflection respectively, a third input shaft for introducing the angle of cross roll of the mount around the line of sight of a target. means operated responsively to said first input shaft for generating a predetermined function of elevation, a resolving mechanism operated responsively to said last-named means and said third input shaft for generating a product of said function of elevation and a predetermined function of said angle of cross roll, a second resolving mechanism operated responsively to said second and third input shafts for generating a predetermined product of said ascertained deflection and a predetermined function of the angle of cross roll, a fourth shaft, and connection means between said fourth shaft and said first and second resolvers so that said fourth shaft is moved to generate said corrected deflection adjustment as the sum of the products of said function of elevation and predetermined function of the angle of cross roll generated in said first resolving mechanism and of the ascertained value of deflection and predetermined function of the angle of cross roll generated in said second resolving mechanism.
WILLIAM B. JORDAN. FRITHIOF V. JOHNSON.
US201949A 1938-04-14 1938-04-14 Trunnion tilt corrector apparatus Expired - Lifetime US2390374A (en)

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2428870A (en) * 1944-04-15 1947-10-14 Ford Instr Co Inc Computing gun sight
US2824693A (en) * 1946-01-05 1958-02-25 Hubert M James Computers for stabilization systems
US2993644A (en) * 1958-03-27 1961-07-25 Resnick Bernard Altitude computer

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2428870A (en) * 1944-04-15 1947-10-14 Ford Instr Co Inc Computing gun sight
US2824693A (en) * 1946-01-05 1958-02-25 Hubert M James Computers for stabilization systems
US2993644A (en) * 1958-03-27 1961-07-25 Resnick Bernard Altitude computer

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