US2431696A

US2431696A - Relay desing calculator

Info

Publication number: US2431696A
Application number: US550843A
Authority: US
Inventors: Keister William
Original assignee: Bell Telephone Laboratories Inc
Current assignee: AT&T Corp
Priority date: 1944-08-23
Filing date: 1944-08-23
Publication date: 1947-12-02
Anticipated expiration: 1964-12-02

Description

Dfli. 2, 1947. w, KEISTER 2,431,696

RELAY DESIGN CALCULATOR Filed Aug. 25, 1944 s Sheets-Sheet 1 I I I I;

BRIDGE! (GALV- m WIRE SIZE RES/SHNCES FILLEO ENAMEL FILLED S ILK SPOOL IVOUND ENAMEL [06' ONE FOR EACH P3 TYPE WIFE 2/0 rrP: 0F

WIRE J POINT -4GANG SWITCH rm: s/zz s v Tl/Rm am-4m:

TURNS PER LAYER MYERS 204 i 'u 3 k I08 I I07 i k as :2], m l/s M /09.9 (L) V 09 43 44} I09Al 109 44 mac E 205 INS/DE oum-rm LENGTH RESISMNCES RES/572N655 INVENTOR W. KE/S TE/P BY A TTORNEV Dec. 2, 1947. WKEISTER 2,431,696

RELAY DESIGN CALCULATOR Filed Aug. 23, 1944 3 Sheets-Sheet 3 PROTECTIVE 0N Res/sun t 44] 7- MAX. 0.

ALSL

' MIN/i, cu. 5L

U I n "P: f 506 ETC.

i INVENTOR M. KE/STER 1 B @a M A TTORNE Y Patented Dec. 2, 1 947 RELAY DESIGN CALCULATOR William Keis ter, Short Hills, N. J., assignor to Bell Telephone Laboratories, Incorporated, New York, N. Y., a corporation of New York Application August 23, 1944, Serial No. 550,843

11 Claims. (Cl. 235-61) mination necessitates considerable calculation because the data and formulae cannot be of a positive nature and the proper winding must be obtained by balancing the various factors involved.

Similarly the operating time of the relay can be calculated directly when the design of the relay and the circuit conditions are known, but when a relay is to be designed to operate in a given time, large numbers of calculations may be required before a design is arrived at which will satisfy all of the requirements.

In accordance with the present invention, means is provided for making the mathematical calculations necessary for relay winding design by electrical means. More specifically, a multiple Wheatstone bridge is provided whereby the bridge when balanced in connection with given quantities will indicate the corresponding values of the remaining variables required for the design of that relay winding. .In the multiple Wheatstone bridge formingthe subject-matter of this invention at least two of the legs are varied simultaneously in a plurality of the individual bridges. According to oneform of the invention, the circuits are so arranged that the same galvanometer may serve a plurality of individual bridges.

These and other features of the invention will be more clearly understood from a consideration of the following description read in connection wifh the drawings in which:

Fig. 1 shows the basic relationship between the physical quantities employed in designing relay windings;

Fig. 2 shows the practical circuits employed in suchabridge; while,

Fig. 3. shows a typical panel board for such a bridge;

Fig. 4 shows a theoretical multiple bridge for determining the time of operation of relays; and

Fig. 5 shows a practical circuit employed in a bridge of the type of Fig. 4.

structurally, the design of a relay winding involves the size of the space in which the winding is to be located and the size of the wire. These functions in turn involve the diameter of the core, the length of the core on which the; wire is to be wound and the depth of the Winding as well as the gauge and insulation of the wire itself, which determines the number of turns and number of layers which may be placed in the space available. Electrically, the voltage and current being used and the resistivity of the wire must be considered; I

The principal formulae used in the calculations necessary for relay winding design are as follows:

where L=length of coil in inches B=effective breadth of one wire.

The number of layers which may be wound in a given space may be expressed by the equation i where h=depth of coil space C=efiective depth of one wire filler.

The number of turns which may be used may be expressed by the equation I including insulating Calculations relating to resistance To obtain resistance when the number of turns, gauge of wire and dimensions of winding space are given:

From the formulas set-forth at page 504 of the Standard Handbook for Electrical Engineers, seventh edition, the total resistance of a relay Winding may be stated where =ohms per unit length of the wire, and f=length of a mean turn in inches.

where d: diameter of the core.

From Equation 3 the value of h may be derived as where K=B C=efiective V cross section 'of one turn of wire.

Hence Equation 3a may be written A bulge factor do is sometimes used to allow for-the 'fact that the first layer of 'the'coil may :not fit snugly against-the.core and has the effect or increasing the apparent core'diameter. Therefore,

Total resistance R is in accordancecwith the equation where the resistivity factor A which may be determined from one of the following equations:

When the resistance, number of turns and coil dimensions'are-given I R *N(h+d+ d. When the desired-voltage, ampereturn-s and "coil dimensions are given ..E Nl (h+d+a (6) where E=voltage I=current in amperes.

When the resistance and coil dimensions are given The general theory on which'is based the use of the Wheatstone bridge for solving mathematical equations maybe set forth as follows:

The balance condition for an zordinaliy Whe tstone bridge-is represented by theequations ,4 where R1, R2, R3 and R4 are the values of the resistances in the four arms of the bridge. If a mathematical equation can be put in the form of either Equations 8a or 812 it can be solved by means of a bridge. It is only necessary to choose scale factors and calibrate the various resistances to represent corresponding variables. Then any setting of the resistances which balances the bridge gives concurrent-values of the variables.

The *scalefactor isa constant which relates ohms resistance in the bridge to units of the corresponding variable in the mathematical equa- --tion. Forexample, if the resistance R1 represents a variable'X and it is determined that 10 ohms lshallrepresentmneunit of X we have where Rl-iS in ohms.

This may be expressed R1= X (9b) Here ,u is the scale factor of X and in this example ,u=10.

Scaleiac'torsareot two'types, Inkonecase the scale factor is an arbitraryconstantchosen to give. reasonable values of resistance-or to-- obtain satisfactory balance over a given range of variables. In the othercase it is-necessaryto hold one or more members of the bridge at a-fixed value in order'to make the bridge Equation 8 conform to a given mathematical formula. This scalefactor depends on the value chosen-for the fixed resistance.

For scale factorsof the first type consider a mathematical equation of the iorm It is obvious'tha't' the validity' o'j this equation is not affected by the introduction of arbitrary constants n1, #2, #3 and #4 in any of the following ways,

or, in genera mm X "mm Z ='R3=n2,c':i .R4.=7 ,142#4Z *I-Iere, ,ul g'is the scale'factor or W," 1 i4 the scale factor ofX, etc., and Ri R4 are inunits of resistance (ohms).

The second "type of scale factor has a value depending onsomefixe'd resistance'in the bridge. For example,- considerimplemultiplication,

introducing la .con.st' mt, this may be elven the form of the bridge equations (.8).

5 Type one scale factors may now be introduced in any of several ways as discussed above. For example:

HaX u K 1 Z MY m Referring to (8a), [.LSKI corresponds to R3 and by choosing an appropriate fixed value Rx for this resistance the value of K1 can be determined as follows:

where Rx is expressed in units of resistance. Now, substituting in (110) Comparing this with (812) In a particular example suppose that X has values between 0.1 and 0.5 and Y has values between 20 and 100 and it is desired to represent X and Y with resistances Varying from 1000 to 5000 ohms.

If 1000 ohms is to represent a value of 0.1 for X, then Likewise 1 00 H4=gF= 50 Choosing a resistance of 2500 ohms as appropriate for Rx, then (11c) gives,

(10,000X) (50 Y) (W (10.000X) (50 Y) (200Z) (2500) Comparing this with (8b) and taking the unit of resistance as one ohm.

R1=10,000X ohms R4=50Y ohms R2=200Z ohms Rs=2500 ohms The values for the bridge for solving (11), XY=Z then may be tabulated as follows:

Calibra- Scale Range of Range of Reslstame variable Factor 1 Variable Resistance Ohms X 10, 000 001 0. 1-0. 5 1, 000-5, 000 Y 50 02 20-100 1, 000-5, 000 Z 200 O05 2-50 40040, 000 2500 ohms Fixed Resistance An equation which includes addition in conjunction with multiplication can be solved by connecting two variable resistances in series" in one or more arms of the bridge. a formula such as may be handled by introducing a constant, K1; asin (11),

For example,

Further scale factors may be introduced and both Y and Z will have the same scale factors.

Quadratic equations such as may be solved by using two resistances calibrated in terms of a: and coupled together to be controlled by the same set of knobs. Equation 13 must first be put in the form of (8), thus Scale factors may now be introduced #11 3 l zl s i Now, choose an appropriate fixed resistance RK and set [LB/13K 1=RK, then,

=fit. 1 mm Hence,

mm K mi -mus #2H4( (13b) where c=d+dc=inside diameter of coil in inches including bulge allowance.

From Equation 3 it is apparent that the depth, h, of the winding in inches is given by,

R=AN (14) So that (14) becomes,

R=AN(h+c) (16) This is of the form (8a) and may be solved by means of a bridge.

The value of it can be determined by a second independent bridge because formula (15) can be expressed as If the two h and two N resistances of (15a) and (16a) are mechanically coupled, a dual bridge results as shown schematically in Fig. 1 and, since the resistance representing are dependent on wire size they may also be mechanically coupled.

A form wound coil is wound to even layers and in specifications of such coils it is usual to give the turns per layer 711, and the number of layers, These calculations may be made by modifications of bridge 2 as follows:

The equation of bridge 2 is,

Values of m and 122 may be obtained from the following equations:

h e (17) with resistance replacing K and in replacing with C replacing K, vii r'eplacing'N and L replaced by a fixed resistance which may be designated in.

Acircuit for the dual bridge of Fig. 1 is shown in Fig. 2 and the arrangement of the control dials is shown in Fig. 3, the same reference characters being used in Figs. 1 and 2. The resistances which represent the values of N, R, m, m, h, L and c are in the form of decade resistances for convenience in reading the setting. The dials which control the resistances, representing N and h, vary two sets of resistances simultaneously, while the resistances which represent 1 "A" uv: max and C are varied simultaneously by a single dial. Since the effective size of the wire has a different range for different types of insulation, aswitch 21s is provided which may be set in any one of three positions to render a difierent set of resistances available in accordance with the insulation to be used; A switch 203 is used to include one of the resistances MA to IMF in a circuit depending on the inside diameter of the coil to be designed. While it would be possible to use the variable resistance IMA for all calculations, certain core sizes recur so frequently as to make it' convenient to use fixed resistances for their values. Similarly, a number of fixed resistances lEiiA2 to IU9A4 are used to correspond to the length of the most common types of relays with a variable resistance HJSAI for unusual types, the switch 264 servin to include the desired resistance.

Key 289 when operated supplies battery to the circuits through resistance 29!. Key 215 is used to include either the average or the maximum value of the resistance corresponding to K in the circuit. When key 2l'5 is normal, the average value of K is employed while with key 2l5 operated the maximumvalue of K is employed. Key 262- is a three-way key. When in its normal position it serves to place bridge 2 in condition to solve the fundamental equation of the bridge,

that is, Equation 14. With key 202 moved to the left it arranges the circuit to'solve the equation involving turns per layer (111) that is Equation 1'7 and with key 202 moved to the right the bridge is arranged to solve Equation 18 which involves the number of layers (112); It is customary with certain types of relays to allow one-fifth layer for possible variation and key ZES is used to make this allowance when required; V

The solution of a winding'problem bythe use of the dual bridge of Fig. 2 requires that both bridges be balanced. In most cases this is not difiicult since several of the variables are known and these values can be set and only the remaining dial need be manipulated to obtain a balance. For convenience in adjusting the bridges, tables 353i and 382 located on the face of the panel show the adjustments which will tend to bring the bridge into balance when the deflections of the galvanometers are to the right or the left of zero.

A typical problem will indicate the manner in which the bridge may be used. Assume first that it is desired to know the resistance of the coil which will result from the use of a given number of turns of wire of a given size in a coil of known dimensions. None of the keys 29G, 2|5 or 265 is operated.

Switches

203 and 204 are set on the proper dimensions of coils, switch 219 is set on the type of wire, for example, in the position shown, which corresponds to filled enamel wire, and the switch 303 is positioned to the proper gauge thereby simultaneously adjusting resistances lElZA of the bridge I and resistances IliSAl, iiifiAZ and liifiA3 which belong to the bridge 2. Dials 326 to 323 are then operated to positions indicating the desired'number of turns resulting in the simultaneous adjustment of resistance ID!) of bridge I and resistance I68 of bridge 2. Key 28! is then operated to supply battery to the bridges and the dials 35B, 35I and 352, corre sponding to depth of coil, are adjusted until bridge 2 is balanced, atwhich time Equation 15a will be satisfied. Thereafter dials am to 3ft, corresponding to resistance, are adjusted until bridge I is balanced. The values of the resistance may then be read from the corresponding dials. If, after the solution has been obtained as above, it is desired to find the number of layers necessary to produce the desired winding, the dial and switches are left in the positions obtained and key 2:32 is thrown to its right-hand position. In this position it will be apparent that resistance Hi7 is substituted for resistance I88 and resistance I 98A3 for resistance IOGAI, while the fixed resistance 39C (111) is substituted for the variable resistance IEJSAI. Adjustment of the dials 34!), SM, 342, corresponding to (m), until-bridgeZ is balanced will indicate the number of layers by the positions assumed by the dials. On the other hand if it is desired to know the number of turns per layer, key 262 is thrown to the left substituting resistance 393 (m) for one of the resistances 1519A (L) and resistance IQS AS (C) for resistance IBGA! (Kav). Adjustment of dials 33$; 33!, and 332, corresponding to (721), until bridge 2 is balanced will give an indication of the number of turns per layer under the conditions set up.

A form of the multiple Wheatstone bridge which may be used in determining the time of operation of relays is shown in Figs. 4 and 5. A large mum-- ber of variables must be considered in determining the operating time of a relay. The determination of the operating time is fairly simple When the relay design and .circuit conditions are known but the designo'ff a relay to operate in a given time is diflicult because of this large number of variables. For example, if only the spring load and the circuit voltage are known, a relay may be designed to meet a given operating time requirement by assuming a resistance and determining the corresponding number of turns but this may result in a relay which is impossible to obtain in a standard relay structure. Other resistance values must then be tried until a practical relay is found or it is determined that it is impossible to meet a given time requirement. With the multiple bridge of Figs. 4 and 5 many of the individual calculations are made simultaneously and automatically so that trials may be made quickly and the complete range of possible coils explored to obtain the most satisfactory ones in a reasonable length of time.

The fundamental equations employed in the determination of relay operating time have been derived in the Journal of the Institute of Electrical Engineers, volume 66, No. 376, April 1928, are as follows:

where t=operating time of the relay T=time constant of the relay coil T1=time constant of core structure including Equations 19, 20 and 21 may be combined into I These equations may be restated as the following bridge type equations i may be derived from T and N by means of Equation 26; the value of the ratio of i/I may be determined from the quantities E, R and i by means of Equation 25; the ratio T/Ki may be derived from N and R by means of Equation 24 and the value of T derived from that ratio by means of Equation 27. Equation 23 combines the results secured from the other four equations to obtain the operating time t. These five equations are applied to the five bridges A, B, C, D and E forming the multiple bridge of Fig. 4.

The arrangement shown in Fig. 4 requires five

galvanometers

454, 424, 434, 444 and 454. It would, of course, be possible to use a single galvanometer with a switch to connect it into any one of the bridges, in which case the bridges would be balanced one at at ime. A more satisfactory arrangement is that shown in Fig. 5 which employs two

galvanometers

503 and 504 permitting two bridges to be balanced simultaneously.

The use of

galvanometers

503 and 504 is controlled by a three-position switch 502. When this switch is normal the galvanometers are associated with bridges A and C, galvanometer 503 being connected over contact I2 of key 502 to the junction between resistances 4i 0 and 4! 2 representing the quantities E and R and over contact l0 of key 502 to the junction between resistances 4H and 4 l 3 representing the quantities '& zandtween resistances 42| and 423 representing the quantities uT and N, respectively, and over contacts l5 and 0 of key 502 to the junction between

resistances

420 and 422 representing the quantities i and Rh, respectively. When the right-hand springs of key 502 are operated,

galvanometers

503 and 504 are connected in bridges D and E,'galvanometer 503 being connected over contact 9 of key 502 to the junction between resistances 43| and 433 representing the quantities T+T1 and t and over contact I l of key 502 to the junction between

resistances

430 and 432 representing the quantities R, and log,

galvanometer 504 being connected over contact [4 of key 502 to the junction between

resistances

441 and 443 representing the quantities and over contact [6 of key 502 to the junction between

resistances

440 and 442 representing the quantities T and K1, respectively.

As in the multiple bridge of Fig. 2, a switch 505 is provided for selecting the value of T1 corresponding to the size of core and a switch 506 for selecting the value of K1 corresponding to the various types of relays. Where the quantity such as R, i, T, etc., appears in more than one bridge, the two values are adjusted simultaneously by a and R l 1 common control dial. However, it is to be noted that thefunctions of the resistances shown as

resistances

423 and 452 in Fig. .4 are performed .by a single resistance in the circuit of Fig. and likewisethe functions of the resistances shown as resistances MI and 450 in Fig. 4, areperformed by a single resistance of Fig. 5. Resistances Rb, Rd and Re are fixed resistances representing the value of the numeral l in bridges B, D and E in Fi 4.

The general operating procedure would be as follows: In the usual problem the values of N, R, E and i are known and the value of t is desired. In addition the values of K1 and T1 are determined by the type of relay under consideration. The resistances representing the known quantities are set, after which key 500 is operated to supply battery to the bridges. With key 502 normal the resistance 4l3 representing the quantity in bridge E, and resistance 450 representing the quantit log,

1 is adjusted to balance the bridge C by means of galvanometer 504, thereby fixing the value of this resistance for use in bridge D. Key 502 is now thrown to the right and resistance 440 representing the quantity T is adjusted to balance bridge D by means of galvanometer 504 at the same time setting resistance 43! in bridge E. Bridge E is then balanced, using galvanometer 583, by adjusting resistance 433 to arrive at the value of t which gives the operating time.

Where the operate adjustment of the relay under consideration is known in terms of ocT rather than 2', the value of i is determined by means of bridge B. The left-hand'contacts of key 502 are operated and the known values of aT and N set by the adjustment of'resistances 42! and. 423. Bridge B is then balanced, using galvanometer .584, by adjusting resistance 420150 arrive at the value of z, and set its value in bridge A, after which the calculations proceed 'asabove described.

When insufiicient variables are known, such as designing a relay to meet given time requirements, arbitrary values are assumed for the required variables and the remaining values determined, trials being made until a satisfactory relation is attained or until it is found that the requirement cannot be met with standard r elay structures.

All of the variables with the exception of the quantities I %and log, 1.

are represented by. decade resistances such as indicated for the multiple bridge of Fig. 3-but these two arms will be special slide wire resistances. The

arm is a linear resistance having the slide directly coupled to the dialon the panel which is calibrated to correspond. The resistance used for the quantity is wound on a fiat strip, the contour of which is mathematically determined to conform to that quantity and the slide of Which is mechanically coupled with the slide on the resistance representing the quantity ing resistances calibrated to represent certain of said variables, one of the variables represented in each bridge being also represented in another one of said bridges, each bridge indicating a known relationship between the included variables when balanced, means for simultaneously adjusting all resistances representing the same variable, means for adjusting the remaining resistances to balance said bridges, and means for individualizing said galvanometers to said bridges to indicate when balances are reached.

2. A compound Wheatstone bridge for making calculations involving more than four variables, comprising five bridges, two galvanometers, each of said bridges comprising resistances calibrated to represent certain of said variables, one of the variables represented in each bridge being also represented in another one of said bridges, each bridge indicating a known relationship between the included variables when balanced, means for simultaneously adjusting all resistances repr senting the same variable, means for adjusting the remaining resistances to balance said bridges and means for individualizing said galvanometers to said bridges in pairs to indicate when balance are reached.

3. A compound Wheatstone bridge for making calculations involving more than four variables comprising five bridges, each composed of resistances calibrated to represent certain of said variables, at least two of the variables represented by arms of each of said bridges appearing as arms of another one of said bridges, each bridge indicating a known relationship between the included variables when balanced, means for simultaneously adjusting all resistances representing the same variables, means for adjusting the remaining resistances to balance said bridges, two galvanometers, and meansfor individualizing said galvanometers to said bridges to permit the successive balancing of said bridges.

4. A compound Wheatstone bridge for designing relay windings comprising one bridge com-. posed of variable resistances calibrated to represent the number of turns, total resistance, the reciprocal of the resistivity factor and the diameter of the core plus the depth of the coil and a second bridge composed of variable resistances calibrated to represent the depth of the coil, the effective cross-section of a turn of wire, the numaesrooe' 1,3 ber of turns and the length of the coil, means for simultaneously adjusting the value of the two resistances representing the number of turns, of

the two resistances .representing the depth of the coil and of the two resistances representing the reciprocal of the resistivityand the efiective crosssection, means for individually adjusting the remaining resistances and a galvanometer for each bridge to indicate when a .balance has been reached.

5. A compound Wheatstone bridge for designing relay windings comprising one bridge composed of variable resistances calibrated to represent the numberof turns, the total resistance, the reciprocal of the resistivity factor and the diameter of the core plus the depth of the coil and a second bridge composed of variable resistances calibrated to represent the depth of the coil, the efiective cross-section of aturn of wire, the numberof turnsand the length of the coil, means for simultaneously adjusting the values of the two resistances representing the number of turns, of the two resistances representing the depth of the coil and of the two resistances representing the reciprocal .of the resistivity and the effective cross-section, means for individually adjusting the remaining resistances, a galvanometer for each bridge to indicate when a balance has been reached, and means for adapting said second bridge to express relaydesign in terms of layers of wire comprising a variable resistance calibrated to represent the number of layers, a variable resistance calibrated to represent the depth of one layer, a fixed resistance and switching means for simultaneously Substituting saidlast three resistances for the resistances representing the m r of ur s t e .ClQSs-section of one wire and the length of the core respectively.

6. A compound Wheatstone bridge for designing relay windings comprising one bridge composed of variable resistances calibrated to represent the number of turns, the total resistance,

the reoiprocal of the resistivity factor and the diameter of the core plus the depth of the coil and a second bridge composed of variable resistances calibrated to represent the depth of the coil, the efiective cross-section of a turn of wire, the number of turns and the length of the coil, means for simultaneuosly adjusting the values of the two resistances representing the number of turns, of the two resistances representing the depth of the coil and of the two resistances representing the reciprocal of the resistivity and the effective cross-section, means for individually adjusting the remaining resistances, a galvanometer for each bridge to indicate when a balance has been reached, and means for adapting said second bridge to express relay design in terms of layers of wire comprising a variable resistance calibrated to represent the number of layers, a variable resistance calibrated to represent the depth of one layer, a fixed resistance and switching means for simultaneously substituting said last three resistances for the resistances representing the number of turns, the cross-section of one wire and the length of the core respectively, said resistance representing the number of layers being adjustable independently of said first bridge,

7. A compound Wheatstone bridge for designing relay windings comprising one bridge composed of variable resistances calibrated to represent the number of turns, the total resistance, the reciprocal of the resistivity factor and the diameter of the core plus the depth of the coil and a 14 second bridge composed of variable resistances calibrated torepresent the depth of the coil, the effective cross-section of a turn of wire, the number of turns and the length of the coil, means for simultaneously adjusting the values of the two resistances representing the number of turns, of the two resistances representing the depth of the coil and of the two resistances representing the reciprocal of the resistivity and the effective cross-section, means for individually adjusting the remaining resistances, a galvanometer for each bridge to indicate when a balance has been reached, and means for adapting said second bridge to express relay design in terms of turns per layer, comprising a variable resistance calibrated .to represent the number of turns in one layer, a variable resistance calibrated to repre,

sent the depth of one layer and switching means.

for simultaneously substituting said last two resistances ,for the resistance representing the number ofturns and the resistance representing the crossesection of .one wire respectively.

8. A compound Wheatstone bridge for designing relay windings comprising one bridge composed of variable resistances calibrated to represent the ,number of turns, the total resistance, the reciprocal of the resistivity factor and the diameter ,of the core plus the depth of .the coil and a second bridge composed of variable resistances calibrated to represent the depth of the coil, the effective cross-section ofa turnof wire, the number of turns and the length of the coil, means for simultaneously adjusting'the values of the two resistances representing the number of turns, of the two resistances representing .the depth of the coil and of the two resistances representingthe reciprocal of the resistivity and the effective cross-section, means for individually adjusting the remaining resistances, a galvanometer for each bridge to indicate when a balance has been reached, and means for adapting said secondbridge to express relay design in terms of turns per layer, comprising a variable resistance calibrated to represent the number of turns in one layer, a variable resistance calibrated to represent the depth of one layer and switching means for simultaneously substituting said last two resistances for the resistance representing the number of turns and the resistance representing the cross-section of one wire respectively, said resistance representing the number of turns in one layer being adjustable independently of said first bridge.

9. A compound Wheatstone bridge for designing relay windings comprising one bridge having as arms variable resistances calibrated to represent the number of turns, the total resistance, the reciprocal of the resistivity factor and th diameter of the core plus the depth of the coil and a second bridge having as arms variable resistances calibrated to represent the depth of the coil, the average effective cross-section of a turn of wire, the number of turns and the length of the coil, means for simultaneously adjusting the values of the two resistances representing the number of turns, of the two resistances representing the depth of the coil and of the two resistances representing the reciprocal of the resistivity and the average efiective cross-section, means for individually adjusting the remaining resistances, a galvanometer for each bridge to indicate when a balance has been reached, a resistance representing the maximum efiective cross-section of a wire and a resistance representing the depth of one layer of turns, the means for adjusting the resistances representing the average efiective' cross-section ofa wire being efiective to adjust said last two resistances, switching means for substituting either one of said last two resistances for said resistance representing the average effective cross-section, means for correspondingly adjusting an adjacent arm of said bridge, said bridge when balanced indicating the relay design in terms of the substituted quantities.

10. A compound Wheatstone bridge for designing relay windings comprising one bridge having as arms variable resistances calibrated to represent th number of turns, the total resistance, the reciprocal of the resistivity factor and the diameter of the core plus the depth of the coil and a second bridge having as arms variable resistances calibrated to represent the depth of the coil, the efiective cross-section of a turn of wire, the number of turns and the length of the coil, means for simultaneously adjusting the values of the two resistances representing the number of turns, of the two resistances representing the depth of the coil and of the two resistances representing the reciprocal of the resistivity and the efiective cross-section, means for individually adjusting the remaining resistances, a galvanometer for each bridge to indicate when a balance has'been reached, said resistance representing the effective cross-section of a turn of wire comprising a plurality of individual variable resist ances each corresponding to a different type of insulation and means for rendering one of said individual resistances efiective.

11. A compound Wheatstone bridge for designing relay windings comprising one bridge having as arms variable resistances calibrated to represent the number of turns, the total resistance, th reciprocal of the resistivity factor and the diameter of the core plus the depth of the coil and a second bridge having as arms variable resistances calibrated to represent th depth of the coil, the

average effective cross-section of a turn of wire,-

the number of turns and the length of the coil, means for simultaneously adjusting the values of the two resistances representing the number of 16 turns, of the two resistances representing the depth of the coil and of the two resistances representing the reciprocal of the resistivity and the efiective cross-section, means for individually adjusting the remaining resistances and a galvan'ometer for each bridge to indicate when a balance has been reached, resistances representing the maximum eifective cross-section of a wire and resistances representing the depth of one layer of turns, the means for adjusting the resistance representing the average effective crosssection of a wire being effective to also adjust said last two resistances, switching means for substituting either one of said last two resistances for said resistance representing the average effective cross-section and correspondingly adjusting an adjacent arm of the bridge, said resistances representing the average eifective cross-section of wire, the maximum effective cross-section of wire, the depth of one layer and the reciprocal of the resistivity factor, each comprising a plurality of individual variable resistances arranged in sets corresponding to different types of insulation and means for rendering any one of said sets of individual resistances efiective, said bridge when balanced indicating the relay design in terms of the substituted quantities.

WILLIAM KEISTER.

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

UNITED STATES PATENTS Number Name Date 1,493,586 Wood May 13, 1924 2,349,860 Hainer May 30, 1944 2,040,086 Goodwillie May 12, 1936 2,271,508 Gordon Jan. 27, 1942 2,123,142 McMaster July 5, 1938 2,114,330 Borden Apr. 19, 1938 1,893,009 Ward Jan. 3, 1933 2,087,667 Hedin July 20, 1937 2,07Q,668 Lundry Feb. 16, 1937 1,681,047 Porter Aug. 14, 1928 2,206,715 Burat July 2, 1940