US3437268A - Mathematical averaging apparatus - Google Patents

Description

April 8, 1969 R. s. WHITE MATHEMATICAL AVERAGING APPARATUS Filed June 26, 1967 INVENTOR. ROY S. WHITE IHlSm United States Patent O 3,437,268 MATHEMATICAL AVERAGING APPARATUS Roy S. White, Rte. 1, Cleveland, N.C. 27013 Filed June 26, 1967, Ser. No. 648,887 Int. ci. Guam 1/12 U.S. Cl. 235-61 8 Claims ABSTRACT F THE DISCLOSURE This invention relates to devices for performing mathematical operations and more particularly to an apparatus utilizing volume-ratio principles by which the average of several numbers may be quickly obtained through varying the volume of one container proportionally by the use of one or more volume segments with respect to the constant volume of a second container.

Background, brief summary and objectives of the invention Numerous clerical and teaching tasks require repetitive averaging of a `quantity of numbers to obtain information useful in daily business and school activities. IFor example, in the course of the school year, a high school teacher must add approximately twelve thousand quantities and perform some two thousand seven hundred divisions in averaging grades of students. This obviously demands a great deal of time for monitoring student progress which time could be more productively spent in direct instructional periods. While a number of devices are available for obtaining grade averages such as that disclosed in U.S. Patent No. 1,023,961, none of the devices known utilizes a hydraulic circuit in accomplishing the averaging operation. Most of the devices are comprised of a number of graduated scales positioned in a side-by-side relationship so that an average number may be read directly or interpolated from a number of input quantities.

The division step which must be performed in obtaining the average value of a group of quantities is accomplished in the present invention as the result of the speciiic dimensional ratios between cross-sectional areas of an accumulator tube, a force-tube and a number of volume segments which can be inserted in the accumulating tube to make volume adjustments. The cross-sectional area of one volume segment is equal to the internal cross-sectional area of the force-tube, and the internal cross-sectional area of the accumulator tube is equal in the preferred embodiment to ten times the internal cross-sectional area of the force-tube. Thus the volume segments are used to reduce the effective internal cross-sectional area of the accumulator tube, and the addition of one such segment produces a ratio of 9:1 between the elfecti've internal cross-sectional area of the accumulator tube and the internal cross-sectional area of the force-tube. The positioning of additional volume segments 'within the accumulator tube changes the ratio to 8:1 when adding two volume segments, 7:1 when adding three segments; 6:1 when adding four, and so on.

The addition operation which is initially required in obtaining the average value of a group of quantities is accomplished by introducing volumes of fluid corresponding to the individual quantities in the group to be averaged into the accumulator tube. Thus where X1, X2,

3,437,268 Patented Apr. 8, 1969 X3 Xn are quantities in a group of n quantities for which the average is to be found, the equation governing the equation being valid provided in the embodiment shown that X is equal to or greater than 50.

With the foregoing in mind, it is therefore an object of the present invention to provide an apparatus for performing averaging computations utilizing a hydraulic circuit in accomplishing this operation.

Another object of the present invention is to provide a practical machine for use by school teachers and instructors in averaging grades and the like.

A further object of the present invention is to provide an apparatus of the type described which may be made of a size and capacity sucient to verify a known mathematical formula for an infinite number of quantities to be averaged.

Yet still another object of the present invention is to provide an apparatus of the type described which has a minimum of moving mechanical parts and is thus simple in construction, reliable in operation and economical to manufacture.

Many of the other objects and attendant advantages of the present invention will become more obvious from the following detailed description ta-ken in conjunction with the drawings in which like characters of reference designate like parts.

Figure description lFIG. l is a perspective view of the preferred embodiment of the present invention showing the force-tube and adjacently positioned accumulator tube, both tubes aligned with respect to a graduated scale placed therebetween.

FIG. 2 is a plan view of the preferred embodiment of the averaging apparatus shown in FIG. 1 illustrating the placement of eight volume segments within the accumulator tube to adjust the volume cross-sectional area ratio between the accumulator tube and the force-tube.

FIG. 3 is a perspective View of a single volume segment, one or more of which are used to adjust the volume ration of the accumulator tube with respect to the force-tube consistent with the number of quantities to be averaged.

FIG. 4 is a side elevational sectional view of a preferred embodiment of a grade averaging apparatus as illustrated in FIG. 1 showing the hydraulic connections between the force-tube and the accumulator tube and the air relief valving in the force-tube plunger.

Detailed description of the invention Referring now to the drawings and particularly to FIG. 4, a reservoir |10 designed to accommodate a supply of lluid is encapsulated by a generally cylindrical body portion 12 closed at the top and bottom by appropriately designed caps 14 and 16, the top cap 14 containing an air vent 17 to provide free fluid ow within the reservoir and related components by pressure equalization. An accumulator tube generally designated 18 is positioned on the top cap 14 and communicates with the reservoir 10` by means of an orice 20 having an extended lip 22 extending into the accumulator tube chamber 24. A plunger 26 extends longitudinally within chamber 24 of accumulator tube 18 and is elevated to some degree above the top 28 of the accumulator tube for manual manipulation. The plunger has a stopper portion 30 which, when positioned within lip 22, seals orifice 20I to prevent the fiow of fluid from within the accumulator tube chamber 24 back to reservoir 10` unless the plunger 26 is removed.

A second orifice 32 provides a connection from the chamber 24 of accumulator tube 18 to the accumulator tube check valve shell generally designated 34. Check valve shell 34 includes a ball valve seat 36 containing a third orifice 38, the orifice being controlled by a ball valve 40 normally seated therein.

A ver-tical force-tube shown generally as 42 is integral with and extends upwardly through top cap 14 from reservoir 10, the tube having a lower portion 44 extending substantially within the reservoir. The tube lower portion 44 has a ball seat 46 containing another orifice 48 which allows fluid communication between the forcetube 42 and the reservoir. A ball valve 50` controls the opening of this orifice by operating as subsequently described.

The lower portion 44 of force-tube 42 is connected to the check valve shell 34 by a passageway 52 which will permit fluid flow therethrough during the averaging operation also to be described subsequently.

A hollow plunger 54 telescopes within force-tube 42 in a snugly lslidable manner so that fiuid flow may be induced into or from the tube during the averaging operation. Additionally, an indicator 56 is secured to and extends from plunger 54 downwardly so as to directly indicate readings of quantities to be averaged. Plunger 54 has a bore S extending throughout its length but which is restricted in size at the lower portion 57 to form a ball seat 61 having another orifice 63. A ball valve 65 and shiftable weight S11 control the opening by operating in a manner to be subsequently described.

A connecting web 58 spans the force-tube 42 and the accumulator tube 18 and holds a graduated scale placed thereon for use by the operator in averaging a given number of quantities on the present invention.

The operation of the present invention is initiated by filling the reservoir with a liquid preferably containing some coloring ingredient to make it readily visible when positioned within the accumulator tube and the forcetube. Plunger 54 is then depressed to its lowest position and then raised to some intermediate position. When the plunger is raised, atmospheric pressure forces the liquid to raise the ball valve 50 from its seat 46 and enter the space formerly occupied by the plunger 54. As there is usually an air pocket between the liquid and the plunger 54, this pocket must be removed before the device can be operated with accuracy. Removal is accomplished by placing the top 55 of the other plunger 26 against ball so as to retain that ball on its seat 36, and then urging plunger `54 downwardly. The pressure of the trapped air between the plunger 54 and the liquid in the force-tube 42 causes the ball 65 and the movable weight 51 positioned atop the ball to rise from its seat 61 within the bore 55 of plunger 54, and the trapped air then escapes through the top 59 of the bore 5S of force-tube 42. The weight 51, which has a diameter sufficiently small to allow air passage along its sides within bore 55 of tube 42 retains the ball valve 65 on seat 61 during subsequent opera-tions.

After releasing the ball valve 40 and replacing plunger 26 in orifice 20, the plunger 54 is depressed, the ball valve remains over orifice 48 and the liquid is forced through the connecting passageway or cross-over tube 52 to the accumulator tube check valve shell 34 where it raises ball valve 40 from orifice 38 and enters the accumulator tube 18 through orifice 32. The fuid remains in the accumulator tube until the sealer 30 is withdrawn from opening 20 which then allows the fiuid in the accumulator to return to the reservoir 10.

The divisional operation which must be performed in finding the average value of a group of quantities is accomplished because of the specific dimensional ratios between the cross-sectional areas of the accumulator tube 18 and the force-tube 42 and the volume segments, one of which is shown in FIG. 3 and designated 60. The crosssectional area of a volume segment `60 is equal to the internal cross-sectional area of the force-tube 42, and the internal cross-sectional area of the accumulator tube 118 is equal, in the preferred embodiment shown, to ten times the internal cross-sectional area of the force-tube 42. The volume segments 60 are used to reduce the effective internal cross-sectional area of the accumulator tube, and that addition of one such segment to the accumulator tube produces a ratio of 9:1 between the effective internal cross-sectional area of the accumulator tube and the internal cross-sectional area of the force-tube. The addition of subsequent segments to the accumulator tube produces a diminishing ratio of 8:1 if two segments are added, 7:1 if three segments are added, 6:1 if four segments are added, and so on. In averaging a group of ten quantities, no volume segments are used, but when less than ten quantities are to be averaged, the number of volume segments to be used can be determined by use of the formula S=lO-N, where S is the number of volume segments to be used and N is the number of quantities in the group to be averaged.

The operation of addition, which also must be performed in finding the average value of a group of quantities, is accomplished by causing quantities of liquid which represent the values of each of the original quantities in the group to be averaged to accumulate inthe accumulator tube. The quotients `are produced by the action of the ratio between the effective internal areas of the accumulator tube and the force-tube as explained above.

The average value of a group of numerical quantities is found by filling the reservoir with liquid and the correct number of volume segments determined by the number of quantities to abe averaged. The plunger 54 is then depressed to its lowest position and subsequently raised to ydraw in liquid until the sealing ring 62 (in the event an indicator 56 is not used) registers with the quantity mark on the graduated scale 58 representing one of the group numbers to be averaged. The plunger is then depressed until the sealing ring 62 aligns with the 50 mark on the graduated scale. The plunger 54 is then again raised until the ring registers with the graduated scale mark which indicates the value of the second quantity in the group after which it is again depressed until the sealing ring registers with the lowest graduated mark on the sca-le or, as indicated above in this embodiment, the 50 graduation scale. The procedure is then repeated for each quantity in the group of quantities to be averaged. The liquid level in the accumulator tube then indicates the average on the graduated scale 58.

As is `apparent from the above description, it is possible to find the average of n quantities while using the present invention by raising and depressing the plunger 54 n times after which the computed average may be read from the graduated scale line which coincides with the liquid level in the accumulator tube 18. The capacity of a grade averaging 4device such as is disclosed herein can be varied by providing the accumulator tube and force-tube with larger or smaller diameters and constructing volume segments of larger or smaller graduations if necessary. Since the manual addition and subsequent manual division required in averaging a given number of quantities is eliminated, and since little mental activity is required t0 operate the embodiment of the invention herein set forth, teachers, instructors `and the like can average grades or numbers in approximately one-quarter of the time required for manual averaging with considerably less mental fatigue.

Obviously, many modifications and variations may be made in the construction and arrangement of the accumulator tube, the force-tube, the graduated scale, and the interconnecting hydraulic passage connecting the two, as Well as the other phases of the present inventive concept in light of the above teachings without departing from the real spirit and purpose of this invention. Such modifications of parts as well as the use of equivalents to those herein illustrated and described are reasonably included and contemplated.

I claim:

1. A device for computing the average value of Ia number of quantities comprising: a fluid supply; first fluid container means; second fluid container means operatively connected to said first means; means for measuring the fluid quantity in said iirst and second container means; means for inducing fluid representing a quantity to be averaged into said first container means and from said first container means into said second container means; and means for varying the volume of said second uid container means according to a predetermined relationship where- Iby a number of quantities represented by fluid volume may be averaged and the average value of the quantities indicated by the measuring means according to the fiuid contained in the second fluid container means.

2. A device as claimed in claim 1 further comprising: a reservoir for retaining said fluid supply operatively c011- nected with said first and second iluid container means.

3. A device as claimed in claim 1, said measuring means including a graduated scale positioned to indicate uid level in said rst and second container means.

4. A ,device as claimed in claim 2, said inducing means including a piston mounted in said first container means operable to draW a Huid quantity from said reservoir into said first container means and force the fluid quantity into said second container means.

5. A device as claimed in claim 2, said varying means including insert means for varying the effective volume of said second container means.

6. A device as claimed in claim 2, said iirst iluid container means including a vertical force-tube.

7. A device as claimed in claim 2, said second Huid container means including a vertical accumulator tube.

S. A device as claimed in claim 2, said measuring means including a graduated scale positioned to indicate Huid level in said first and second container means, said inducing means including a piston mounted in said rst container means operable to draw a uid quantity from said reservoir into said first container means and force the uid quantity into said second container means, said varying means including insert means for varying the effective volume of said second container means, said first fluid container means including a vertical force-tube, and said second fiuid container means including a vertical accumulator tube.

References Cited UNITED STATES PATENTS 3,217,545 11/ 1965 Kreisman 73-400 RICHARD B. WILKINSON, Primary Examiner. L. R. FRANKLIN, Assistant Examiner.

U.S. Cl. X.R. 23S- 200

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