US2563840A - Spherical triangle calculator - Google Patents

Description

` Aug. 14; 1951 R. J. HUNDHAUSEN 5 3 SPHERICAL TRIANGLE CALCULATOR Filed Sept. 2, 1947 2 Sheets-Sheet 2 3 In Van/or.

Patented Aug. 14, 1951 SPHERICAL TRIANGLE CALCULATOR Robert J. Hundhausen, Brentwood, Mo.

Application September 2, 1947, Serial No. 771,746

3 claims.v (CI. 33-1) (Granted under the act of March 3, 1883, as

amended April 30, 1928; 370 O. G. 757) The invention described herein may be manu factured and used by or for the Governmentof the United States for governmental purposes with out the payment to me of any roya-lty thereon in accordance with the provisions of the act of April 30, 1928 (Ch. 460, 45 Stat. L. 467).

My invention relates to spherical triangle calculators and particularly to one which accurately `visualizes problems and enables an operator to accurately visualize his problem and, without resorting to mathemati-cal calculations, to solve numerous spherical angle problems, including both right angle and oblique spherical triangles, as Well as to solve numerous astronomical, geological; and mining problems. v

In the accompanying` drawings:

Figure 1 is a perspective view of my device.

Figure 2 is a plan view.

Figure 3 is an enlarged section, looking outwardly from the center of the frame.

Figure 4 is an enlarged detail on the line 4-4 of Figure 3.

In these drawings: p

A base II rigidly supports four columns '2, Which in turn rigidly hold a Separable frame '3 (Figures land 2). The frame '3 is divided on the diametrical plane '3st, the two halves being coupled by four screws 39 and two coupling plates l3b. The frame '3 (Figures 3 and l) is provided with an upper circular groove i l of T-shape sec- 6 tion and a similar lower circular groove 15 also -of T-shape. The frame l is graduated adjacent to a central aperture and is also provided with an upper internal groove 'B for a graduated ring l '1. The frame '3 is provided with a second internal groove :a for a second graduated ring '9. These rings l" and 9 correspond to those for the upper and lower motions of a surveyor's transit. Upon the ringll (Figure 4) there are rigidly secured two supporting bearing blocks 28, each 'having a lateral semi-circular groove 2' for com- 'panion arcuate lugs 22 of blocks 23 which are *rigidly secured to a semi-Circular plate 24 at op- ,which is rigidly attached a graduateduuadrant 29 which is terminally pivoted to said smaller arcuate seal-e member 25 by a pin 30.

The above described elements of my device which are mounted above a plane midway of the frame '3 are duplicated .below said horizontal plane; the ring '9 supporting companion bearing blocks 3' (Figure 4) which are engaged by companion lugs 32 of blocks 33 to which blocks is rigidly attached a second semi-circular plate 34 having a marginal slot 35. The arcuate extent of the blocks 23 and 33 is ninety degrees minus the thickness of the plates 24 and 34, respectiv-ely. A second arcuate scale member 36 is also graduated for ninety degrees and is frictionally engaged by the sides of said slot 35 and is rigidly attached to the ring '9. A second graduated quadrant 31 is mounted on a slide corresponding to slide 28 which slide is supported in the downwardly open circular slot '5 and is pivoted to the scale member 36 by a pin 38. Referring to Fig ures l and 2, it is apparent that by moving the quadrants 29 and 3" to the same side of the separable ring '3, the opposite side of the ring '3 may be removed by unscrewing two screws 39 and one screw 39a, therebymaking possible the disassembling of my device whenever necessary.

My device provides a means for mechanically solving problems involving three dimensions and may be easily adjusted for an infinite combination of variables. The answers to problems may be read directly on my device, for example, to obtain data for plotting geologie maps, for use in the fields of mathematics, astronomy, surveying, mining and the like.

Among other problems which may 'be solved with my device are:

1. In mining; determining the pitch and bearing of the line of intersection of two planes (veins, faults, etc.)

2. The apparent dip of a plane c-ut by a geological section. r

3. The strike and dip of a plane; given the bearings and dip angles of two ncn-parallel lines.

4. The solution of any right spherical triangle; knowing any two parts in addition to the right angle.

5. The dihedral engle between any two planes.

6. The solution of oblique spherical triangles knowing three of the principal parts.

The solution of a solar problem is simply a particular problem in the solution of a spherical triangle after the usual corrections are made on account of latitude and altitude.

There are suitable graduations on the margins of each of the movable parts as well as on that of ble therein, a second pair of arcuate bearings mounted on said second ring at diametrically opposite points, a second semi-Circular plate provided with a circumferential slot and fastened to said arcuate bearings with an axis of rotation midway between and parallel with the planes of said internal grooves, a second slide provided With an interlocking extension mounted in the lower of said circular grooves, a second graduated quadrant rigidly supported by said second slide in a plane perpendicular to the plane of said annular frame, a second graduated arcuate scale member rigidly supported by and perpendicular to said rin and passing through said marginal slot in said semi-circular plate, and a second pin pivotally Connecting said graduated quadrant and said second arcuate scale member whereby said upper and lower calculating portions which are mounted on a common annular frame provide a means for solving problems involving spherical triangles having* points and lines of intersection lying on any part of a spherical surface.

ROBERT J. HUNDHAUSEN.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS

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