US2066884A - Mechanisms for the calculation of functions with several variables - Google Patents

Description

Jan. 5, 1937. I J. HAQRLAS 0 ,884

MECHfSNISM FOR THE CALCULATION OF FUNCTIONS WITH SEVERAL VARIABLES Filed April 11, 1936 4 Sheets-Sheet l Z --mmnnnnnmllvmmmnnmm-Q) j Attorneys Jan. 5, 1937. HARLAS 2,066,884

MECHANISM FOR THE CALCULATION OF FUNCTIONS WITH SEVERAL VARIABLES Filed April 11, 1936 4 Sheets-Sheet 2 fi a.

INVENTOR JIRI HARLAS,

ATTORNEYS Jan. 5, 1937. J. HARLAS 2,066,834

MECHANISM FOR THE CALCULATION OF FUNCTIONS WITH SEVERAL VARIABLES Filed April 11, 1936 4 Sheets-Sheet 5 Y INVENTOR JIR! HARLAS mww I AT 70m 5Y5 Jan. 5, 1937. J. HARLAS 2,066,884

MECHANISM FOR THE CALCULATION OF FUNCTIONS WITH SEVERAL VARIABLES Filed April 11, 1956 4 Sheets-Shet 4 my. a.

INVENTOR JIR! HARLAS ATTOR N 5Y5 UNITED STATESPATENT oFncE micnmsius FOR THE cnwum'rron or mc'nons wrrn saw-mar. vnnnmms Jii'i Hal-lac, Prague, Cmechoslovakia application April 11, 1936, Serial No. 1am in Clechoslovakia September}, 1932 3 Claims. (Cl. 235-81) My invention relates to improvements in mechanisms for the calculation of functions with several variables, more particularly for military purposes, for instance, for anti-aircraft service, being a continuation in part of the applications flied May 3, 1933 under Serial Number 669,087 and December 4, 1934 under Serial Number 755,997, Mechanisms for the calculation of functions .with several variables.

The object ofmy invention is to replace a system of curves hitherto used together with three variables, by a single moving curve applied mechanically and shifted by a combined movement as a function of one of the given variables.

- Another object is to provide such a device which is simple and easily handled and used.

A further object is to have a device of this character wherein the operation is fundamentally based upon the movements and positions of a swingably mounted curvilinear member.

Other objects and advantages will appear more fully hereinafter as the specification proceeds.

The nature of the invention is graphically explained with reference to the drawings, in which Figure 1 shows diagrammatically the problems arising when it is attempted to train a gun at, or

to locate a movable target such as an airplane.

Figure 2 shows one of the mechanisms hitherto used forthis purpose, now serving as a basic from which to flgure herein.

Figures 3, 4 and 5 show diagrammatically the method of calculation used according to my invention.

Figure 6 shows a plan elevation, Figure 7 .a cross-section and Figure 8 a perspective view of a device made according to the invention.

The device as illustrated serves for quick mechanical ascertaining of the so called reduced distances p, necessary in commanding anti-aircraft search lights, i. e. the actual distance of the airplane under observation having regard to the necessary correction of the acoustic aberration (paralaxis). This reduced distance is a component for further calculations which however do not come into consideration in this connec-- tion. v

The device will first be explainedtheoretically in its application for ascertaining the so called reduced distance necessary for directing or aiming anti-aircraft guns and search lights. The value of p is given by the equation I c-k 1+zsin a. 5 wherein c is the speed of sound (333 metres per second) k is reduction constant, selected for the device,

an is the acoustic site or angle, and

Z is a variable given by the equation 10 wherein 0 is dead time of operation, ascertained by actual test, and

y is the altitude in metres of the airplane under observation.

We convert this function into the form of a polar diagram as shown in Figure 3 of the drawings where the curves represent the difierent values of Z.

The value Z although theoretically a variable, is however in practice a constant. For a certain trained team of soldiers and for a certain given mechanism the dead time of operation can be assumed as a constant, and an airplane, intent on bombing or photographing, files as a rule in an altitude which does not vary perceptibly or suddenly, so that 1/ is also a constant.

One finds from a study of this system'of curves that the different curves can be replaced by a single curvewhich may be called moving curvewhich passes constantly through the point a and which makes the two movements:

1. Rotation about the point a,

2. Translation through the point a so that its path coincides with the path of the different curves Z of the diagram.

The two movements of the. moving curve are merely the functions of Z.

P Consequently it is unnecessary to trace the Z system of curves. It suflices to have the moving curve passing through the point a and to move it as a function of Z to-the necessary positions.

When utilizing this moving curve there is no necessity for interpolation; it is sumcient to follow up the moving curve by an index to obtain the value of p in the form of a translation with reference to the starting point 0.

' The device embodying myinvention comprises 50 a curvilinear member I of metal or the like, having a slot which represents the moving curve. Member I is guided by means of a pulley 2 which is journaled by means of member 43 on the frame 41 so that it can both oscillate round said pulley and slide upon said slot, and is hinged at b by means of a pin 4 to a lever 5 which is journaled at m in bearings 6. Worm-wheel I5 is fixed to the other end of the lever 5 and meshes with a worm l6 disposed on the spindle II. the latter carrying a second worm I8 which meshes with a worm-wheel I connected with a disc I by means of spindle 9, joumaled in bearings 24. Spindle I1 is provided with a hand-wheel l8 and is journaled in bearings I9 and 20. On the face of the disc 8 are marked a group of curves I to VI, representing the difierent values of the dead time of operation from second to second. Adjacent to the face of the disc 8 are disposed two indicators Ill and I2 placed on a nut 2| adapted to be moved by means of a screw 22 which is provided with a knob II and journaled in bearings 23.

In the slot of the curvilinear member I a pulley 25 glides which is journaled on the member 28 which in turn is slidably guided in a guiding arm I4 rotatable about point 0.

The angle formed by the line 011 and the longitudinal axis (line 00) of the guiding arm I4 correspond to the angle E... while the distance 00 gives the value p which can be read on the scale provided on said arm in which case the mechanisms further referred to are superfluous.

According to the mode of execution illustrated and described however this value p is commuted into a corresponding angle in order to be transferred to further mechanisms by means of the following auxiliary device which does not form an integral part of the invention but is described only in order to facilitate comprehension of the operation of the device.

Arm 26 is provided with a toothed rack 21 which meshes with a pinion 28 connected by means of the spindle 29 with a bevel gear 30 and thereby with the shaft 3I of the planetary wheels 32 of a differential gear. Angle E. is transmitted doubled from shaft 33 by toothed wheels 34 and 35 to one of the wheels 36 of the differential gear. Wheel 35 is connected with bevel wheel 31 which meshes with bevel wheel 38 of doubled radius; bevel wheel 38 is turned therefore in angle of a, and as it is connected by means of the hollow shaft 39 with the guiding arm I4, this angle e. is transferred to the latter. If the wheel 28 and the planetary wheels of the differential gear turn through an angle of and the wheel 36 through an angle of 2a, the wheel 40 and the shaft 4| will turn through an angle of p.

until the curve, for instance, I which corresponds to the given dead time of operation 0, intersects point In. If shaft 33 is turned through angle Ea, shaft 4| is simultaneously turned through the angle.

k.c 1+z sin where I Curves I to VI are plotted in the following manner:

Various values of Z correspond to various angles a, p, 'y, a as indicated in Fig. 4. Value Z, however, depends on the value of 0 and 1/, as indicated by the equation Scale 1/ is marked on the radius P on the disc I, as well as angles 2a, 25, 2- and 2a with regard to the same radius P. Curve I for the value o=1 is obtained by inserting the different values of 1! into the equation Thus, for example, the intersection of curve I with line Z=0.133 has a distance from the center with line Z=0.333 the distance ,cisely known.

What I claim is:

1. A device for calculating functions with several variables, comprising a curvilinear member having a slot, a pulley engaging in said slot, a link member hingedly connected to one end of said curvilinear member, a rotatable disc which carries on the face thereof a plurality of curves indicating diflerent values of the dead time of operation from second to second, gearing operatively connecting said disc with said link member, a nut carrying two indicators and a scale indicating the height of the object to be followed. which scale is disposed adjacent to the face of said disc, a screw serving to move said nut along said scale, and an arm provided with a scale and swingable over said curvilinear member.

2. A device for calculating functions with several variables, comprising a curvilinear member having a slot, apulley engaging in said slot, a link member hingedly connected to one end of said curvilinear member, a rotatable disc which carries on the face thereof a plurality of curves in-v dicating different values of the dead time of operation from second to second, gearing operatively connecting said disc with said link member, a nut carrying two indicators and a scale indicating the height of the object to be followed, which scale is disposed adjacent to the face of said disc, a screwserving to move said nut along said scale, a swingable arm provided with a scale and consisting of two telescopic parts, and a pulley Journaled on the outer part of said am and engaging in the slot of said culvilinear member.

3. A device for calculating functions with several variables; comprising a curvilinear member having aslot,apulleyengaginginsaidslot,a16

aoeaasa 3 link member hingediy connected to one end of said curvilinear member, a rotatable discwhich carries on the face thereof a plurality of curves indicating different values of the dead time of operation from second to second, gearing operatlvely connecting said disc with said link memher, a nut carrying two indicators and a scale indicating the height of the object to be followed, which scale is disposed adjacent to the face oi. said disc, a screw serving to move said nut along said scale, a swingable arm consisting 01' two telescoping parts, a pulley journaled on the outer part of said arm and engaging in the slot of said curvilinear member, and means for commuting the changing distance between the axis of rotation of said arm and the axis or said pulley into a corresponding angular value.

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