DE589682C - Calculating device based on nomography - Google Patents

Description

Computing device based on nomography is based on a nomographic basis and aims to simplify the mechanical evaluation and coupled nomograms in such a way that also double equations with two unknowns ground nomographically solvable *.

According to Fig. I, the mathematical basis for the simplest special case is, namely explained on the basis of nomograms with only straight parallel scales.

The three scales u, v and w, in connection with the straight reading line z, represent a nomogram of the simplest kind for which the general function a = 9P (dic, x " y) (i) applies. If of the four quantities a, dic, x1 and y are any three; e.g. the first three are known, the fourth can be determined arithmetically or graphically or nomographically.In the present case, the value d1c would be the position of the three scales, x1 the End point El and known through a the end point A , and one finds the unknown value of y on the y-scale, represented as a line whose end point G is marked by the connecting line z1 of the two known end points El and A. After the (hypothetical) Example in Fig. I, at x1- o.8 with a. = 2io, the searched value y is found at y = 75.

But if two quantities are unknown in equation i, for example x1 and y, the problem is unsolvable. In technology, such equations with two unknowns often appear in the double form a - 99, (dl ° = x, y) (2 a) b = T2 (m / nI x, y) (2b) Each of the two equations 2 a and 2 b can be represented by a nomogram of the type explained, each is, taken by itself, unsolvable - but both can be combined in the following way: Equation ?, A is given by the nomogram 2i, v, w with -i, equation 2b represented by the other nomogram u, v, w with z2. In both equations, x and y are unknown, so that (apart from the position of the scales to each other) only the endpoints A and B are known, but not Ei, G and E2. Now you choose any point G and draw the straight lines z1 - GA and z2 # - GB. If the selected point G were the correct one, the same value for x would have to be displayed for El as for E2, since the same x occurs in both equations 2a and 2b. Otherwise one chooses a different point G, draws the rays GA and GB etc. again and tries until the point G is found at which El and E2 are at the same scale values at the same time. This case is shown in Fig. I. Here (with a - 2io and b - 55,000) the quantity you are looking for is x = 0.8 and the value you are looking for is y = 75.

Solution method described above "applies in general, also for nomograms with converging or curved scales or reading lines.

The present computing device eliminates the cumbersome trial and error when executing the above solution (see Fig. 2 and 3). Here the scales are designed as slideways g with the scale numbering pushed out to the side. The scales ü and ui, which are designed differently for special reasons, will be discussed in more detail below. The slides A, G and B can be moved and clamped in the slideways g. Reading noses N attached to the side of the slides enable the exact position identification. The two pointers Z1 and Z2, which meet in a joint on the slide G and are also rotatably supported there, rest on the slides A and B, freely rotatable and slidable. At their outer ends, the pointers bear the reading lines r, which indicate the reading points E1 and E2 in the scales it and 2i.

The solution to the above problem with two unknowns proceeds as follows with the help of this device: The sliders A and B are set with the help of the reading lugs N to the given endpoints of the distance value a (scale v) and the distance value b (scale v ') , clamps it tight and now pushes slide G along the w-scale. Here, the pointers Z1 and Z2 rotate and move on the rotatable upper parts of the sliders A and B, and the reading lines r, and r2 slide accordingly over the scales u and zi . At the moment when the same value appears at Ei (scale u) as at E2 (scale u '), one pauses. The solution has been found. You read off the value for x at Ei (or at E2) and the value for y at G.

In the example of Figs. 2 and 3, the scales u and ü are designed as variable scales in a manner known per se, in that a numbered set of curves h, 1, under a line (wire p1 in frame P, stretched or scratched on the glass pane P2 Line p2) is movably arranged. The apparent points of intersection of the line p with the group l below form the scale points of the scale it and u '. The numbering of the relevant curves counts as numbering of the points on the scale. By moving the family of curves, the position of the intersection points and thus the scale division changes, so that to a certain extent a new scale takes the place of the previous one. Since even the smallest shift in the curves causes a corresponding change in the scale, such a family of curves visually represents a (theoretically infinite) number of scales on the smallest surface. The curves are shifted by shifting the surface on which the curves are recorded (sheet of paper, movable carriage, rotating rollers, infinite belts, etc.). Depending on the conditions of the task to be solved, the displacement can be necessary along or across or along and across to the scale axis p, independently or inevitably depending on the movement of the articulated slide G and can be provided accordingly. In the simple example of Figs. 2 and 3 - the curves of the scales it and zt 'are recorded on rollers W, which are rotated independently of G and only transversely to p, while their longitudinal displaceability only serves to replace the rollers. The setting scale e in conjunction with mark f is used to identify the position of the rollers and thus at the same time to identify the set scale.

By using such variable scales, the range of solvable tasks is greatly expanded. It can hereby z. B. also tasks of the following kind can be solved: # a 7-`- ('i (dc, e, x, y) (3 a) b - p. =. (m? ia, e, x, y) (3b) Given a, b, , y. Wanted x and e. Solution: Find the sliders A, G and B at the points that correspond to the given values a, y and b. The pointers Z are therefore immovable, but the end points E1 and E2 still point to different values x. Well, you turn both reels, but in such a way that every moment e1 - e2. This shifts the curves below Ei and E2. At the moment when they become x == x2, one pauses. One finds the desired values x - x1 (- x2), e-el (-e2).

If instead of the slideways g bars or rails are arranged as girders the sliders A, G and B, on which the sliders also move iznd can be clamped like in the tracks g, so you can move these rods on the device frame that supports them and thereby their relative position, so the ratios d [c and inlyt vary at will or the scales also at an angle place. The same displaceability can be found for the scales u and u 'and for provide the rollers W or the plates P or both. This becomes the area of application the number of solvable tasks continues to increase.

Claims (1)

PATENT CLAIMS: r. Reclining device on a nomographic basis, characterized, that to solve two equations with two Unknown .two nomograms are coupled in the following way: Two rulers are articulated so that the hinge point is only along a scale can move, and guided by a tab, each along a further scale is displaceable and lockable. There are also at least a fourth and There is a fifth scale on which, together with the first scales, the reading of the searched sizes takes place. Device according to claim i, characterized in that some or all of the scales can be arranged to be movable (displaceable). 3. Device according to claims 1 and 2, characterized in that such scales are also used which can be changed in a manner known per se by shifting a family of curves are.