High Voltage Precision Measurements Citation Hobson, Jesse Edward (1935) High Voltage Precision Measurements. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/0qx0-5576. https://resolver.caltech.edu/CaltechTHESIS:10302024-204151379 Abstract No abstract. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Electrical Engineering) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Electrical Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Sorensen, Royal Wasson Thesis Committee: Unknown, Unknown Defense Date: 1 January 1935 Record Number: CaltechTHESIS:10302024-204151379 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:10302024-204151379 DOI: 10.7907/0qx0-5576 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16824 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 05 Nov 2024 19:38 Last Modified: 05 Nov 2024 19:53 Thesis Files PDF - Final Version See Usage Policy. 12MB Repository Staff Only: item control page

HIGH VOLTAGE PRECISION MEASUREMENTS Thesis by J'esse .IM.ward Hobson In Partial Ful.fillment of the Requirements for the Degree of Doetor o:f' Philosophy California Institute of T'eehnology Pasadena, California 1935 CONTENTS Pa~e Summary------------------------------------------ l Introduction ------------------------------------ 4 The Relation Between Foree and Voltage---------- 10 Test Apparatus and Test Procedure---------------- 22 l~xperimental Results -------------------------- 29 Dis cuss ion ------------ -------------------------- 37 Con cl usi ons ---------------------------------- ---- 39 Acknowledgments--------------------------------- 41 Bibliography ------------ ----------------------- 42 ILLUSTRA'l'IOHS Fig. l. Image Charges in Two Isolated Spheres, for One Sphere Grounded---------------Fig . 2. Curve Showing the Variation of the Spacing Factor with Gap Spac i ng Fig . 3. 17 Variation of Force vrH 1·1 Voltage with the 100 cm. Gap at Sparking Dist ance-------- Fig . 4. 10 19 Variation of .ltorce with Voltage for Constant Spaci ngs of the 100 cm. Gap 21 Fig . 5. Side View of tho Insulated Sphere :~1ounting 23 Fig . 6. View of the Motor and Sphere Movement Mechanism-----------------------------Fig. ? • Overhead View of the Sparkless Sphere Gap Voltmet er --------·- -------------------- Fi g . 8. 23 23 The Original Tower Mounting of the Insula ted Sphere------------------------ 24 Fig. 9. Water Hose Series Resistance------------ 24 Fig . 10. The Laboratory Assembly of the Sparkless Sphere Gap Voltmeter-------------------- 24 Fi g . 11. Force Measuring Apparatus-------------- 24 Fig . 12. Experimental Calibrati on Curve of the 100 cm. Sphere Spark Gap from ]'orce Fi g . 13. Measurements---------------------------- 36 Wave Form of the Applied Voltage-------- 32 'I'ABL].:S Table I. Calculated Images for 30 em. Gap Spacing of 100 cm. Spheres------------------------ 13 Table II. Computed Value of the Spaci ng Factor S --- 15 Table III. £xperimental Data------------------------- 30 SUMMARY i'he development of a sparkless sphere gap voltmeter as an ab s olut e s tanda rd of hi gh-voltage measur anent is described in this thesis. The forc e , due to ele ctrostatic charges, exis ting between two condu cting spher es, one of which is grounded, the oth er insulated f r om ground and maintained at a high potential, may be eas ily measur ed. From the force measurements the pot ential difference may be accurately and easily calculated from the fundamental laws of the sta tic electric fi eld. The force is a function only of t he potential differ encet t he size of t he spheres, the spacing between t hem , and. t he dielectric constant of t heir ambient medium. Using one hundred centimete1: spher es, potential differenc es up to ei 1sht hundred fifty t housand vol ts have b een measured by this method . For convenience of comparison vii th pres Ent sphere gap voltmeter curves, voltages measured by t he force method were a ppli ed to the one hundred c entimete1· s phere gap and spa r king di s t ances observed . The cu::·ve thus obtained dliffers considerahly from the A,nerican Institut e of El ectrical Engineers standa rd sparkover curve now used for one hundred centimeter spheres. The electrosta tic-forc e method for measurement of high voltages possesses s everal adva nt a ges which are not found in the ot her system.a now used. The more i mportant of these advantages are:- 2. l,. The fo r ce-voltage r elaUonship may be analytically derived from lrnovm. el ectro-static l aws; hence, provi des an absolute primary s t andard of high-volta ge meas urement. 2. The t ests showed complete freedom from erra tic r eadi ngs so often attendant with the spark gap meter. 3. No empirical correction is nec essary for the effects due to chang es in temperature, htnnidi ty, and barometric pr essure. 4. Since th ere is no electrical dischar ge associa ted with the the measurement, high frequency surges a r e not produced in/circuit at tho tirn.e of measur ement. 5. The calibration when extraneous influences are avoided depends in no way on empirical data. 6. A r esistance in s eries with t he measuring appa r a tus to li,ai t current f low is not necessa ry. ?. 'l'he erra tic and little-known phenomena occurri ng with the el ectrical breakdown of air form no pa rt of. the operation of t he met er. 8. The use of forc e measurements pe r ni t s continuous voltage applica tion and avoids the neces sity for an ope.~ing of t he t est ci r cuit at the ti me of measurement . 9. The relationship between f orce and voltage is equally applicable for direct and alt ernating current circuits. 10. The measurements are always R. M.S. or eff ective values regardless of wave form. 11. It is not required that the spheres be smooth or polished, or that they withstand electrical discharge. 12. 'l'he distu:rbing effects Lntroduced by grounded laboratory walls, floor, and ceiling ma.y be computed and are quite negligible under reasonable eondi ti ons of operation. 13. The sensitivity of t he apparatus is such t hat the maximum error of measurement should be well within one per cent. Although the apparatus a.sat present developed is essentially a laboratory type and of such form as to be used primarily for the calibration of secondary ste.ndard instruments, the fundamental pri nciple involved appears to be readily applicable to a more portable and practical i nstrument for routine test measurements. Tlle results of this research have been discussed in a technical paper, "The Spa rkless Sphere Gap Voltmeter", by Professor R. W. Sorensen, Simon Ramo, and the author of this thesis. The paper was written to be present ed before the Mid-Summer Convention of the ATUeriean Ins titute of llectrical Er;gineera at Ithaca, New York, June, 1 G35. 4. INTRODUCTION Industrial development at the elose of the nineteenth century required the transmission o.f electrical energy from convenient power sources to con·t ers of commercial activity. As energy quanti- ties and distances of transmission b ecame gr eat er, higher voltage transmission lines were found necessary for economieal and efficient operation. To build and operate these lines, engineers were forced to find new methods of design and constructi on; to develop insulating materials; and to investigate the behavior of dielectrics in order to guard against elect r ical breakdown and to limit tho corona po1l'rer loss associated with hi gh voltages. 'I'he:re was the closely related problem of protection a t:, ;ainst the de.ma;,~i ng ef'fects of lightning disturbances. The r oQuirements of such problems called f'or new methods of measuring voltage because the inBtruments in gen erdl use could not be i nsulated for the hig her- voltages. Needle gaps have been used to measu1·e quite satisft1 cto:rily potential differe nces not in excess of one hundred thousand volts by fi. nding the breakdown voltage for two co-linear needles separated in air. Above that range stray fields which are alwa;ys present in the laboratory may cause considerable deviations in mea.sure:nent. of the ueedle gap are: Other disndvantages the inconsistency of flashover; the variation of performance with changes in air density, hu,-nicli ty, and air (1,2)* pressure; and the required empirical calibration. * See Bibliography for all references. {5,4) The sphere gap was introduced by F. W. Peek, Jr., of the General Electric Cor:1pany , as an instrument of more extensive applicat i on for meas uri ng high voltages. The nashover voltage of the sph ere gap WdS found to be only slightly influenced b y hu.:ni di ty changes, and was not affected by stray fields and adjacent grounded obj e cts as much as the needle gap. By assumihg the breakdown gradient of air to be a constant value, Peek attempted to rri.a.ke a rigorous calibrati on of the sphere gap by calculat ions 01' t he :uaxi rnum field gradient. His attempts were unsuccessful because of the complicated cJ:,.uracter of the electrical breakdown of air. Hi s proposed calibration cur ves, adopted by the A-nertcan Ins titute (5) oi' hl.ectrical Engineers as standards :for hi gh voltage measurement, were consequently based on an empirical calibration or ~mall spheres by tertiary vol t-eoil :neasure7;1onts at the supply t l'ansformer. The cali b.r-ati on curvoe f or twenty-five centime ters, fifty centimeters, soventy-fi ve c 0nti:neters, and one hundred centimeters diameter spheres were obtained by extrapola tion of the empirical curves obtained for six and one-quarter centimeter and twelve and onehalf centimeter spheres. 'l'his extrapolation involved the question- able as sumption that the i n.fluence af el e ctrode size on breakdown voltage could be neglectc-.-d. This assumption,, \'Jith the empirical ealibro.t ion, made tile a ccura cy of the calibrati on curves doubtful. The i nconsistent behavior of the sphere gap, due in part to the series resistance required to li~it current flow and to damp high frequency oscillations, und the inability to duplicate measurements either with the sarne apparatus or in different laboratories are perhaps the ::nost obj ectiona ble features of the sphere spark gap. Al.though the use of t he spa rk gap has remained the standard method for measuring high potential differences, numerous other methods have been used. The bibliography of thia thesis contains references to several of those methods. 'l'h e corona voltmeter, tert- iary volt-coil, vacuum tube crest voltmet er, charging current voltmet er, electrostatic force meter, and i cmic wind voltmeter have been partially successful. Two attempts have been •"lade to develop an absolute standard of measurement. One met hod involved measuring the period of oscilla- tion of a metallic ellipsoid suspended in a uniform electrostatic (6,7) (8 ,9) field. The rotary voltmeter, a more recent development, was based on the measurement of the r ectif'ied chr,. rging current of a condens er. The latter apparatus was developed by Kirkpatrick of the Leland Stanford University. NM ther method was suitable for very high voltages because of insula tion difficulties. The development of an accurate, and preferably primary standard method of measurement has become very desirable, due to the recent int er est in insulation coordination and surge i nvestigatio n . Such i nt er est was evid enced by t he discussi ons of leading high voltage engtneers a t the Mid-Summer Convent i on of the American Institute {10,11,12,13) of Electrical .Engineers in 1934, and by the activity of the Measurements and Standards Gon'lmittee of the American Institute of Llectrical 11ngi neers for a re-cu.libra.tion of t he sphere gap. It was t ;ds inter~.st together with tho evident di s-satisfaction vi t h existing method s f01: high voltage 1;ieasure.rn{-:nt that created the desi r e for the develop;:;ient of a primary standard of measur ement, bJ which other apparatus might he ca librat ed , ana by the use of which many difficulth-, s encountered wi th the spark gap might be avoided. The following ehm':1cteris t i. cs of perf'ormance were desired:l. 'l.'lle i ,rntrument should be a primary standtl rd; thut is, it should be ca pable of culi brutian dir e ctl~r fl'',)m an analytical consideration of known i'widam0rrtal le.'.'rs of the elc,;ctrostatic and electromagr1etic field. 2. It should be readily a pplicable for mE:asuring voltages up to one mill i on vol t s and often higher. 3. The allowable error of raeasurement should be wi t h i n one per cent and should lend itself to calculatio~ . 4. The disturbances associated with the electrical breakdown of :insulation material should not be present in the measurement since those effects are u11known and uncertain. 5. Measurements should be capable of duplication. 6. Temperature, air pressure, and hu·1idity should. have no inf luence on the operation or the meter. 8. 7. There should be a minimu.~ disturbance due to stray fields. 8. The instrument should be equally applicable to the measurement of continuous, power frequency, and surge potentials. It should also operate independently of the voltage wave form. 9. Polarity and time-lag effects should be entirely absent. 10. The size, cost, and ease of op er ati.ng the instrument should be such as to make it useful in routine testing. The first, fourth, and sixth eharacterL:: tics directed this research to a consid eration of calculating the exi.sting electrostatic forc,;i as a fu.."lction of the :potential difference between electrodes of' such for,n and dimensions as to perini t accurate anulysis ~f the electrostatic fi eld. Parallel plates were first condderp,d, but there were objectionable featur es of edge influence and the necessarily l e.r ge size of plates. Adja.cc:nt spheres were chosen as being sui ta·b le for investigation since edge effe cts I ere reduced to a minimum, &,d since the pos sibil ity of a distorti m of the fiel d due to corona formation was remote. Spheres of a suitable size were avail able in the Southern California Edison Company's High Voltag e Laboratory at the California Ins titute of Technology. The force acting to r educe the gap between the spheres could be calculated as a :filnction of sphere dimensions, spacing , and the potential difference between the two spheres. This co.lcul:::1ted force is of such magnitude, varying from )Ile hundred to rour hundred grams, as to be easily and accurately measured.. The spheres were mounted and tests were under- taken to det ermine the degree to which this s-parkless sphere gap 9. voltmeter would satisfy the requirements for a precision i nstrument of hi gh voltage measurement. 10. Tilli Rll.A'l'ION BETVTEE.N FORCE MID VOLTAGE Two adjacent conducting spheres are assumed to be isolated in free space , with no disturbing electrtcal fi elds or objects near t hem ~· Sphere A, Fig. 1, is maintained at a potential V while sphere Bis at ground potential. A series of inverted i "llages may be used conveni ently for the calculation of the force acting on (1 4,15) each sphere. V•V V•O A B .q,. .::, C Figure 1. The field about a n isol a ted erph!:ire .A a t a p.: )ten ti!:11 V is that d -µe to a charge q1 = av at t he cenier of the sphere, if "a" is the radius of the sphere. Ii' a grounded sphere , B, of t he smne radius i s brought to a posit i :,n i n the vici ni ty of A wi th a di.stance "c" 11. between sphere centers, the ori ginal field will be distorted due to tlle presence of B. However, a cha rge of q2 = - ~ cu at a distance C 2 d2 = ~ from tho center of the grounded sphere B, and lying on the line of centers, will give zero potential over the surface of sph6re B in the presence of cha rge cu. 'l'hese two charges will not, however, satisfy the condition that th e surface of sphere A be an equi-potential. To satisfy this conditi on a cha rge q_3 is intro- duced 011 the line of cent ers in sphere A at a distance d 3 from the sphere cc1rter, such t:h..a t 43"" q 3 a is then the inverted image of q 2 , a.r..d the :;.-esul tant potential of sphere A due to 42 and q3 is zero, so that the total potential of sphere A is the desi r ed value V due to q1 alone. To keep B at zero potential under tho influence of qi, Q.2, and q3, the charge q3 must be imaged by a charge~ in Bat a distance of a 4 , wh ere q4 - Th'U.5 a doubly infin ite series of i :.:11c-i.t es is created in order to :naintain A at a pot cr1tial V, and B at zero pot.en~;ial. The field at any point outside the spheres is the resultant fi eld due to th0s0 charges . All oi" the i :nage charges La sphere A will have the same➔ s ign as the ori c;inal chc, r ge q1 , while t 1ose in I3 will have the opposite sign. 12. In general: a dn = C - <lu-1 The total force acting on sphere B tending to inove ·the sphere toward A is the su.rn of forces a cting on each charge in B due to all the charges in A. The force of attraction between two cha rges q 8 and qt, separated by a distance fin a medium of dielectric com,tnnt k is: F• We s hall co:nsider the spheres to be surrounded by air , hence k i s v 0ry near 1mi ty . The total force a cting on 3 may 'b e express ed as a double sum.mation overs and t, CP F• \ t:P \ L' Lz. (odd) (e'ten) Cls qt (e - d s -dt)2 Since o is always gr eater than 2a, the nth i mage charge is much smaller than the (n -l)th charge and the s eri e s repres ented by the above summaticm i s rapidly c-:> nvergen.t. The inclusion of ;11ore pairs of i mag es co ntributes rapi dly diminishing amounts to the total force. To evalua te the s eri es , it is necessary to take only as many i:nages as a re required to make certain that the total force of all neglected i mages will be l ess than t he allowable error. 13. A calculation for 100 om. spheres with a difitanee between centers of 130 cm. (30 cm. gap spacing) will illustrate the method. The first four pairs of images and the distance of each from the center of the sphere in v,hi ch it is imag ed are given in Table I. TABLE I. Calculated Images a = 50 cm., Spacing = 30 c entimeters Sphere B (potential zero) Sphere A (potential V l CU 5 Va q3 .174 Va = q5 = .0378 Va q7 = . 00833 Va = dl 0 cm. d3 = 22.6 cm. d5 = 23.4 cm. d7 23. 5 cm. = q2 = -.!3Bo Va q4 = -.086 Va q5 = -.0177 Va Q.8 = -. 00393 Va d2 = 19.2 cm. de = 23.55 cm. d4 = 23.2 cm. do= 23.45 cm. •r11e force, due to these four pairs of cht1 r ges only, is then:- F• qi q2 + + (lJ. q4 (130 - d4} 2 + Q.1 46 (130 - <16)8 g~ !l:2 ~ + (1 30- d2 - d3) (130 - d:zF + q3 q4 (130 -_ d4- d3)g q_3 + qe, (130 - d6 -d3J;:! + + + q_~ q2 ct7 42 (130-d2 -d5) 2 (130- d2 -d7} 2 q'7 q4 q4 % + (130d4 -d7)2 (130-d4 - d;f % q6 + (.130-do - d~ + q5 48 {1.30-da ._ d5~ + q6 Q.7 (130- d 0 -d7f, q7 48 (130- de -dr,'r- If Vis expressed i n statvolts, a in centimeters (a :ror this case is equal to 50 centimet ers), and 1,• in dynes, the e quation reduces to: F,.,. .137 v2 dynes. 14. In general, F • S v2 dynes where Vis expressed in stetvolts and Sis a constant depending only on the s~here radii and the distance between sphere cent ers. Then V = /"[" statvol ts if F is expressed in dynes. If Fis expressed in grams, and Vin v0lts: V • 9405 JT' volts This equation is the r elation used to calculate from force measurements the potential differences between the spheres of the sparkless sphere gap voltmeter. In the calculat ed example of Table I, with charges(?) and ( 8) , neglect ed , the value of S would be redue ed about one per c ent. Since the contribution of charg es (7) and (8) to the total force is less than half the contribut i on of charges (5) and (6), the error made by neglecting all che rges beyond (8) cannot exceed one per cent. Sir William Thomson (Lord Kelvin) in his "Papers on fil.ectro(14) statics and Magnetism", page 96, has tabliated the value of Sas a functi 0n or radius and spacing for two spheres of equal radii. The values, correct to five sign ificant fi gur es, are g iven in Table II. as a function of gap spacing in centimeters (the distance between a t jacent sphe re surfaces) for 100 cm. spheres. This table may be used directly for spheres of oth er dimensions, the only requirement being that the t wo spheres have equal radii. For TABLE II. COl\~PUTED VALUE O]' TlIE SPACI NG FACTOR S (Sir W. Thomson - "Papers on Electrostatics and Magnetism" p. 96.) Sphere Gap Setting 0 -s 00 5 1.13844 10 .52852 15 .32917 20 .23159 25 .17432 30 .13696 35 .11082 40 .091.'74 45 .07720 50 .06592 55 .05693 60 .04963 65 .04363 70 .03863 75 .03441 80 .03084 86 .02775 00 .02509 95 .02278 100 .020?5 16. example, if the radius of each sphere is equal to a centimeters, then the sphere gap spacings given in Tahle II. are multiplied by the factor ·~ . The tabulated value of Sin Table II is plotted as a function of gap spacing in .l!'igure 2. It is int eresti 1·.g to note that the value obtained for S in the example of Table I by considering only eight images is .137 as compared with .13696 from the table obta ined by considering many more image charges. The relation between force and potential dif'ference could have been obtained from energy consid erations. In t e rms of the (15} Maxwell capacity coefficients {See "hlectricity and Magnetism", Sir James Jeans, pages 92-95), the charge, ¼l, existing on sphere A when it is maintained at a potential Vi and sphere Bis maintained at a potential V2 is:- Similarly, the eharge, Q.2 ., existing on sphere B is:Q.2 • %-1 V1 + 42-2 V2 where qJ_-1 , QJ.-2 = 42-1 , and q2-2 are coefficients depending only on the dimensions of the sys tem. The coefficients are defined thus:- qi ...1 is the charge existing on sphere A when it is raised to unit potential with sphere B grounded, Q.2-2 is the cha rge existing on Sphere B when it is raised to unit potential with sphere A grounded, and ql-2 is the charge induced on sphere A when it is e;ro unded a nd sphere B is raised to unit potential. 17. 1,.20 ]J.0 lp0 .90 .so .70 s .60 G50 .40 ., \ \\ . 30 .20 '\ .10 0 10 20 ~ I'--,.__ 30 ~r--40 r--- 50 60 70 80 SPHERE GAP SPACING IN CENTIMET1RS Fig. 2. 90 100 18. In terms of the capacity coeffici ents and the potentials of the two sphf;res, the energy of the system is:- W• If c is the coordinate of' distance bet ween sphere centers, the force tend ing to i ncrease the separation of the sphe r es is:- The negative sign indicates that there is an attractive force between the spheres. If sphere Bis maintained at ground potential, the equation for force reduces to:1 2 0 9,-1 de This expression is identical to that obt&ined from the consideration of image cha rges. s - - The constant S now b E>comes:- 1 2 •rhe relation between :force and the square of the potential difference between the spheres could also have been derived by integ rating over one sphere the force scting on each element of that sphere due to the el e ctrostat ic field. The constant S of pro portlonality may be evaluated mo r e easily, however, from the forces existing between i,:nage cha rges than by either of the latt er methods. It is of course necessary that the spheres be separated by a distance greater t han that at which sparkover would occur for the 19. 400 / j 300 I 200 I 100 0 I I I I / ~ --........... "'~ V V r\ . I .luu GUU .:>U (J 400 5 00 600 ?00 KILOVOLTS 800 900 1000 1100 VARIATION OF FOPCE \'/I 'r:-I VOLTAGE WITH THE 100 cm. GAP AT SPARKING DISTANCE Fig. 3. 20. voltage to be measured. The force acting between the spheres is increased as the gap spacing is decreased for a given potential difference between the spheres; hence, the maximum force which may be obtained for a part icular potential difference is that corresponding to a gap spacing slightly larger than the critical sparkover distance. Using the spark-over distance corresponding to the insulated sphere potential of a 100 cm. sphere gap, with one sphere (16) grounded, given by ]f. W. Peek , the maximum force which may be measured between the sph0res of such a gap was calculated as a function of the potential of the insulated sphere. obtained are plotted on the curve of Fig. 3. The data thus It may be observed from this curve that the force increases with the potential differ- ence until at a voltage of about 625 kilovolts the increased gap spacing has more ef'fect in reduci ng the force than has the increased potential in increasing it. 'l'he variation of force v;i th potential difference for the 100 cm. sphere gap at constant spacings of 15 em., 30 cm. , 50 cm., 75 cm., and 100 cm. is shown on the curves of Fig. 4. Since large forces may be 1neasured with small relative error, the cur ves illustrate the importance of maintaining the gap spacing as small as sparkover will permit .. fr, 0 ~ zH o::; 0 ~ ~ 100 0 200 I 300 400 I 100 I I I 300 400 I ~I I I I 600 KILOVOLTS 500 I,Y I I 700 800 12' I I Fig. 4. I 900 1000 lr1~I I VA...'UATION OF J.l'OR CE WITH VOLTAGE FOR CONST.ANT SPACUIGS OF THE 100 cm. GAP 200 I I 1100 I I 500 . - - - - - - . - - - - r - - - - - , - - - - , - - - - - - r - - - - - - r - - - - - - - - - - - - - - - - , - - - - - - - 4 ~ . ~ 22. TEST APPARATIJS AND '.J.lEST PROCJIDURE Two polished cast-al.urninum spheres, 100 cm. in die.rnet er, were available in the High Voltage Laboratory at tile California Institute of Technology. The spheres a re mounted as s l1own in Figures 5, 6, 7, and 10 to form the sparkless sphere gap voltmeter. The right- hand sphere assembly of Figures 5 and'? is suspended from the roof of the laboratory by two suspension i n sula tor strings. of the sphere is twenty feet above the floor. The cent er An. iron pipe shank twenty fe et long supporting the sphere is adapted to slide horizontally in wooden bearings mounted on the supporting b eam. 'l'he motion is obtai ned by a screw mecha nism driven by means of an insulating rope belt from o. motor on the l aboratory floor, shown in .!fig . 6. The assembly is insulated fro :1 gromtd for more than one million volts. Fow:· ropes connected to tho supporting beam through porcelain "goose-egg" insulators are stretched horizontally to the corners of the laboratory to prevent any motion of the frame. The arTangement of th ese ropes may be seen from the photographs of Fig . 6 end Fig. 7. The d>ther s phere, fastened to an iron pipe shank fifteen :reet long , is suspended wt th the shank hori z ontal and coaxial With the shank of the insulated sphere. The suspension is made from the roof by four ropes arranged in pairs. a pair attached at either end of the shallk and forming the lett er V from the shank to the laboratory roof. The V formation ma.y be s een by a closi:: inspection of 2 3. Ji~. : 1;_ ,_,_" ~ I, 5 2 4. 0) 25. the photographs. This met hod of auspension prevents lateral motion of thr,1 sphere but permits motion in the longitudinal direction along a horizontal line through the sphere centers. 'l'he shank and sphere are grounded by- flexible connections. A light cord attached to the end of the shank of the grounded sphere passes over a ball-b earing bicycle wheel used as a pulley, and suppor t s a weight pan, shown in .Fig. 11. shank is mount ed an illuminated hair line. Near the end of the A ca thetometer tele- scope focused on this hair line is used to observe any •~otion of the gro unded sphere ass embly. A short square rod, projecting at right angles to the shank, moves between adjustable stops which are fastened to th e weighing table on the laboratory balcony and 1i'.11its (See Fig. 11) the horizontal motion. The apparatus is so sensitive that the moti .) n resulting from a weight of less than one-half gram on the pan may be easily observed with the cathetomet er. The inherent damping of the rppes prevents oscillation and makes unnecessary any special provision for added damping . In s etting up for r eadings the grounded sphere is permitted to assu.,~e its natural posi t ion due to gravity forces, and the hair line of the shank is then centered in the fi eld of vis i on of the ca thetomet er. 'l'he insulated sphere is moved very slowly t01-"ierd the grotmded one until the sphr,rea are inceontact. The position of cont act may be better obs erv ed by ~a.tching the cros s hair with the co.thetomet er than b y the usual el ectrical means o-f determining 26 .. contact. The position of a hair line carried by the shank of the movable sphere •.relative to a meter s.cale 0 11 the r:;upporti r.g beam, is noted as the reading of zero gap spacing. The insulated sphere may be moved with the motor driven mechanlsm to v ary the gap spacing from zero to 150 centimeters. Voltage is applied to the insulated sphere from the million volt trans:fonner supply through a series resistance shown in Fig. 9. T'nis resistance of' a bout two and one-half' megohms consists of water running through sixty f eet of three-quarter inch gardell hose. The water is sprayed from tho ceiling into a tub at the top of the hose, flows through the hose, and runs -from the lower end into a tank on the laboratory floor. .Pie tins are inserted in the ho.s e at eighteen inch intervnln in the upper and lovser sectims to prevent corona formntion on the rubber hose. It has been found impossible to use the rheostat for more than 850,000 volts, since fo r such higll voltages the voltage gradient along the hose,. when eparkover of the gap occurs, causes external flashover . .A longer hose of larger cror;;s section W•:J uld give the same s eries resistance but would permit the application of llii:;her voltages. The ample clearance a round the spheres is shoVJn by I!'ig ures 5, 6, and 7. Fig. 8 is a photograph sho1nng ·the insulated sphere assembly supported on a wooden tower, t:ne first construction made for test :purpos es. Fig. 10 illustrates the location of the measuring apparatus relative to the sphere gap. 27 • .After carefully leveling the grounded sphere shank; moving the insula ted sphere in to find the position of :!ero gap spacing; and after moving it out e.gain to the desired gap spacing, voltage messurcments are made . t.'l.ap distances a.re measured by noting the position of the insulated sphere shaft relative to the meter scale on the wooden beam, seen in Ir"ig. 7. 'l'he spheres a re now adjusted for the desired spacing with the hair line carried by th e grounded sphere coincident with that of t he ca thet:)meter. With thesE> adjustments :na.de voltage is applied to the insulated sphere and held constant during the test by means of the tertiary co U vol tmet E"Jr at t;li e control desk. As the vol ta;:;;e increases np to t he t est value, t he f orce acting on the g rounded sphere tends to move it toward t he other s phere, but the stops on the measuring table are ad justed so the sphere can move only a short distance, about one-fourth inch, from the rest position. With the voltage held constant and at the final value, small sho+ is put on the wei ght pan tmtil the g rounded sphere moves ba ck to the r est position, as obs erved when the hair li ne on the shank is aligned with that of' t he cathetometer. 'l'he gap spacing is now the desired value and tte weight on the pan 1s the force a c t i ng on the i rounded sphere . The shot is earefu1.J.y weighed in grams and the voltage , applied to the insulated sphere, is co.lculnted from the relation V • 9405 /. ,! s volts where the value of S corresponding to the gap spacing is taken from Table II. 28. In order to compare the voltage measurement thus obtained with that which would have been obtained with the spark gap met er using the calibrat io n curve of Peek for 100 cm. spheres, the voltage is held constant after the force measurement. The grounded sphere is clamped in the r est posit i oJ1 b y the thmnb-screw stops on the measuri ng table, and the insula ted aphere 1s slowly moved with the motor driven mechanism to decrease the gap until sparkover occurs. The sparkove:• distance is read from the meter scale on the insulated bea~ end t he corresponding voltage is obtained from Peek's curveA The latter measurement requires that air pressure , temperature. and relative hu·n.idity be known. These values are r ead from instruments on the table and the proper corre ctions are ap ;;lied to adjust the sparkover distance to that corres ponding to standard atmospheric conditions (760 mm . of mercury pres.s ure, 20° centigrade~ and 6CYfo r elative humi dity). 29. EXPERIMMiITAL RESULTS More than three hundred test measuranents of voltage~ ranging from 0 to 850,000 vol ts, have been made with the sparkless sphere gap voltmeter. It has been :found possible to reproduce under all test conditions the f orce measurement for any potential applied to the i nsulated sphere within the limit of accuracy of observing the t ertiary-winding voltmeter. In accordance with the experience of other obs e rvers and with the state.ment made in the Intr<;>duction, the sparkover distance correspond i ng to a given potential difference has been found i nconsistent. It should be remembered, however, that sparkover observations form no part of the voltage measurement with the s parklesa sphere gap voltmet er, and were made only to compare the r esults with the calibration curve of the sphere spark gap. Measurements select ed at random covering the t est range are given in Table III. The fifteen s ets of data are suf:ficient to det errnine the calibration curve of the sphere spark gap . From the data of colu.rnns A and B, the a ir density corr ection factor, O~ is calculated Imi ng the standard r elation: .392 b 273 + T where bis the barometric pressure in millimeters of mercury, recorded in column B; and Tis the temperature in degrees Centigrade, 0 1.039 65 742 742.5 66 65 1 4 .5 747 742 .5 66 65 ?43 752 747 11 13 12 12 11 13 13 12 13 13 13 4 5 6 7 8 9 10 ll 12 13 14 15 '747 747 65 65 1.023 1. 023 1.023 65 747 1.023 1.023 1.025 1. 015 1.018 1.025 1. 033 65 65 742.5 66 747 1.03 65 745 18 3 1.002 1.001 65 744 18 2 65 1.025 65 743 11 H0: . 1 oo. ~ D B C A Read- Temp Press Rel. ing mm. Hum. E F G H I J 13.6 13.6 13.6 15.8 1 3 .6 13.6 33.5 15.8 15.8 13.5 12.9 33.5 13.6 12.5 16.0 83.6 83.6 78.e 75.8 68.6 68.6 83.5 60.8 55.8 48.5 47.9 63.5 38.6 32.5 26.0 70 70 65 60 55 55 50 45 40 35 35 30 25 20.0 10.0 225 224 220 210 202 195 190 180 170 152 146 120+ 119 85 53 320 309.l 338.9 330 362.5 336.8 351 350 362 363 320 273 296 207 186 857,000 841,000 829,000 76'7,000 750,000 724,000 685,000 632,000 590,000 531,000 505,000 420 ,000 388,000 280~000 176,000 82~ 79.4 76.3 69.6 65.3 62.5 77.40 54.80 51.50 44.80 42.0 56.90 35.3 27.91 25.1 69.l 65.8 62.7 53.8 51.7 48.9 43.90 39.00 35.30 31.30 29.l 23.40 21.7 15.41 9.1 72.1 E>8 .4 65,4 55.7 53.7 50.6 45.5 40.2 36.2 31.8 29.7 24 .0 21.7 15.4 9.5 Force Distance cm. Tertiary Force Cal cula. t ed Snarkover Distance cm. Scale Distance Voltmeter (Grams) Voltage Scale Distance Distance Reading Dietenc~ Readin!? Corrected Zero Gap TABLE III. - EXP~:;LMENTAL J?,ATA g • 31. 6 recorded in column A. is used to correct the sparkover dis- tance to that of standard atmospheric conditions in this manner: The scale reading of sparkover distance recorded in colu.l!lll J, less the zero gap distance of column :E, gives the sphere gap spacing at sparkover. Tl~is value, appearing in the middle column of J, is used with Peak's curve to find the corresponding voltage. The voltage thus obtained is multiplied by the correction factor, and the sparkover distance, corresponding to the corrected voltage is again obtained from Peek's curve. 'l'he voltage recorded in column I is calculated from the relation: V = 9405/ F s where F is the force in grams from coln.mn H, and S is the spacing factor from Table II, corresponding to the gap spacing of colu..rnn F. The calculated voltag es are R.M.S., or effective, values since the force is a function of the aqua.re of the potential difference across the gap. The experimental curve of Fig. 12 has been drawn from the data of calculated voltage plotted against the corrected sparkover distance. The points on the curve sheet are plotted to show the erratic behavior of the gap at sparkover. drawn to Peak's curve has been the smne scale :for comparis on with the calibration curve for the 100 cm. sphere spark gap as obtained from force measurements. 32. The breakdown voltage or a sphere gap is dependent on the maximu.~ rather than t he effect iv e value of the applied voltage wav e. For dirGct cornpa ris -.)n with Peek 's curve, the vol tag e wave must be sinusoidal . Fi g . 13 shows two wav e forms ; the lower curve is that of t he s upply voltage at the transforraer, and t he upper curve is t he voltage wave applied to the i nsula t ed sphere . Fi g. 13., The oscillogram of output wave form was obtai ned by i ns ert i ng a wat er hose resi s tance of fiv e megohms between the i nsula ted sphere and ground with one element of a General El ectric mechanical oscillograph connected in s eries with the resistance . Another element of the oscillograph was connected across t he supp ly vol tage line to obtain the lower wave. An analysis of the voltage wave 33. applied to the spheres (the upper wave of Fi g . 13) using fifty ordinates .h as b een made. Th e effecti ve value of the wave has been found to be 99.25'fo that of a true sine wave having the smn.e crest value. '!'he dis t urbing influencesof t he e.nd woll of the laboratory and the labor atory floor on the fi eld between the spheres. have been investigated analyticall:y- by consideri ng images of the original infinite set of image char ges obtained for the case of isolated spheres. The spheres wer e i ma ged gehind the end wall and under- neath the floor in each case, a distance equal to t hat of the real spher es fro m these gr ound ed planes. Ea ch of the orig inal s eries of charges then ca used the creation of an infinite series of images to maintain the disturbing planes a t zero pot ential and the two real spheres as equipotential surf'aces. Slide- rule computations for the n eter spheres s et at 25 cm. gap s pacing , to determine the disturbing effect of grounded planes, were made, one plane 20 feet from the gap parallel to the line of the sphere centers represented the laboratory floor; and the othor 20 fe et fro;n the gap perpendicula r to the line of the sphere ccmters, represented an end wall. Since only an approximate indication of the disturbance was desired, i mage charges less t han one per cent of the original charge were neglected; and cha r ges loca ted within a f ew centimet ers of ea ch ot her were grouped in a mean position when 34. considering the forc es exer ted on t hem by charges several hundred centimeters dist anto The result of th es e calculati o ns indica ted the exror due to the assump ti on of isolated spheres to be of the ord er of 1/2 per cent. The error may he asce rtained as accurately as desi red by co nside ri ng more image cha rges. Grom.tded t est planes, six feet in diame t er, wer e plu c ed as n ea r a s possibl e to the spheres without causing sparkover from spheres to plane when a pot ential was applied to the i n sulated sphere. The c llange of force acting on t h e grounded sphere due to the presence of th e t est planes was very small. A model has been made representing to scale th e mounti ng of the spheres in the laboratory. 12.5 om. spheres were used, and planes representing the labora tory wa l ls, fl oor, a nd ceiling were set at va rying distances from tlle sphere gep . The influence of these planes was investigated by obs e rving the change in the force acting on the grounded sphere as the planes were moved into positio n while hold ing the a p plied potential : oonstant. The force, for a 7 .5 cm. spacing of t he g ap and the applied potential, was nbout 12.5 grams. The voltag e variation of the transformer supply has been such that th e chang e of force due to this va riation , during the t est, compl e tely masked the cha ng e due to the pr es ence of the g round planes. No fur t her i nv estigation s with t he model have b e en made to date,. a l though eff'orts are b e i ng J1.ad e to secure a c:mstant voltage s upply a.nd the obs erva tio ns wiJ.l be continued in the nea r fu t ure . 'rl1e disturbing eff e ct, if any, of the cond ucti ng s phe re shanks will also be tnvesti gat ed with the model. A fur ther analytical s t udy of the inf'luence of g ro u.T1d ed objects in the vicinity of t he s parkles s s phere gap voltmet er on f orce measurements will b e ma<le for each spacing of the gap when the apparatus has been permanently mounted in the laboratory. •rne inf luence is small and the computa tions necessarily t;nvolved are very tedious, so that a more comple te study is thought to be unnecessary until the apparatus has been pennanently located. ,.:. ~ H .....:1 ~ ~ ~ V ~ 10 I 20 30 '- 40 ( 60 '- ....0 ~ 50 !> H E-< 70 r 80 ( 90 l 100 C 1/ 10 ~ / ~ / 20- ~- 40 }"'C' •• - 50 Fig . 12. SPARKOVER DISTANCE IN CENTIMEI'ERS 30- v~ -~ /". ./ ». e· • ·....- -. .. . . /. . . . •/. . ~ . --- 60 --- -- -.-- 70 Expe r li.ment a Ct1rv e ---~ V ~ / P 3ek's V~ ___ ..... ....- 80 - en OJ 0 37. DISCUSSION Since the force measuring apparatus is very sensitive, and since force measurements of voltage may be reproduced at will, the scatt ering of test resul.ts shown in Fig. 12 must be due to the inconsistent behavior of the sphere gap at sparkover. The incon- sist ency is due to several factors; namely, changing atmospheric conditio ns, changing states of' ionization of th e gap, dust and moisture deposits on the sphere surff;ces, and restrict ions of ener gy available for electrical breakdown because of t he high s eries resistance needed to protect the sphere surfaces from damage. The erratic b ehavior is more ~n·onounded for the higher voltages applied to the gap , and :i.s perhaps the most effective argu'tle.."1t which may be used a gai nst the spark gap as a standard of m0asurement. If the spark gap is to remain in gen eral use a.s the measuring instrument for high voltag es, engineers ane agreed that a re-calibration is necessary; particularly for the 50 cm., 75 cm., 100 cm., and 200 em. gaps. The sparkleas sphere gap voltmeter is ~ore suitable for a calibrat ing instru.rnent than any other yet proposed. It would be nece ssa ry for only two v ery car efully constructed laboratory met ers to be used for calibrating the spark gaps ased in this country for experimental and industrial measurements, one sparkles.a sphere gap meter to be used a s a check a gainst the other. The accuracy of' measurement by the se t wo met ers could be determined to within a small fraction of 'Jne per cent. 38. It would be more desirable if the sparkless voltmeter should replace entirely the spark gap for measuring purposes. That this would be possible is evidenced by the construction and use of a (18) vol tmetcr in the Darmstadt labora:tol"J by E. Heuter which depends for its operation upon the movement of one sphere of a sphere gap a rr,ai nst the r esj_ s ting roree of a spring when voltage is applied. The development was ..,1ade simultaneously and 1 :-idependently of that made by the author and other workers in the Edison CJmpany' a Laboratory. No attempt was made by Heuter to express the r esulting force in terms of the measured voltage; consequently, his voltmeter is a secondary standard instrument. The development of. a more portable and compact voltmet er, a.sing the principle employed in the sparltless sphere gap met e r, is to be atte,n.pted during the :following months. '.l.'he meter will probably not be as accurate as the primary standard laboratory type, but will be much more satis:factory for general use than would the spark gap meter even if a re-calibration of the latter instrument were accurately made. Before the sparkle.s s sphere gap vol t ,:10t er is to be used as a precioion instrument, fur t her i nvesti gt:,tions of the influence of the sphere shanks and oth er objects disturbing the field between t he spheres should be rrede both analytically and using the test model. 39. CONCLUSIONS The theory of operation and. the laboratory tests of the spark- less sphere gap voltmeter meke evident the following advantages ot' the meter as an i nstrtm1ent for the precision measurement of' high voltages: 1. The force voltage relationship may be analytically dDrived from knovm electrostatic laws; hence, provides an absolute primary standard of high voltnge measur~nent. 2. The measuring apparatus has b een found to be of such sensitivity that the experimental error is always l ess than onehalf o:r one per cent. 3. There is complete freedom from the erra tic r e adings so often attendant with the spark gap met er. 4. The operation of the meter is in no wa~r dependent on temper ature, humidity, and baro:metrie pressure. 5. '.l.'he calibration of the met er is not dependent on empirical 6. 1{easurements are always made in t erms of t ;1e effective data. value of the applied voltag e ~~ve. ?. The relationship between force and voltage is equally applicable for dire ct and alternating vol taE.;es of any frequency. 8. The use of the sparkless gap permits cont tnuous voltage applicatton and avoids the necessity for an opening o:f the t est circuit at the time of measurement. 40. It is not required that the spheres be smooth and SJ. polished or that they Wit t1stand electrical discharge. 10. A resistance in sori es 1~1 th the measuring apparatus to limit current flot1 is not necessary. 11., ment. The method may be used for any range of' voltage measure- The only change necessary is that the size o:f the spheres used be such as to give :forces which may be readily llleasured. 12. Measurements of' voltage may be duplicated at any time. 13. The ef:fects of field distortion may be accurately ca.lcu- l a ted. 14. Polarity and time lag effects are entirely absent. 15. The instrument with some modification as to mounting is equally suitable for a l aboratory prima ry standard or for a more portable secondary standard for general use. ACl:J.'JOWLEJJG-UclJTS 'l'b.e author wishes to express his sincere appreciation for th0 encouragement, advice, and constent coope:ration given by Professor R. W. Sorensen. He is also 1ndeb·ted to Mr. Simon Ha.mo for his valuable assistance in the development and construction of the sparklcss sphl>.re gap vol.tmeter; and to Messrs. Gilbert D. McCarm, Louis T. Rader, a.'1d Jack M. Roelu-rr for their assistance in the laborntol"'J. 42. BIBLIOGRAPHY 1. Peek, F. W., Jr., Discussion, Trans. A.I. E.E. v. 32, p. 812, 1915. 2. Chubb&. Fortescue, . "Calibration of the Sphere Gap Voltmeter", Trans. A.I.E.E., v. 32, P~ 739, 1913. 3. Peek, F. W., Jr., ttThe Sphere Gap as a Means of ~!easuring High Voltage", Trans. A.I. E.1~., v. 33, p. 923, 1914. 4. Peek, F. W., Jr., .,The Sphere Gap as a Means of Measuring High Voltage", G.E. Review, v. 16, p. 286, 1913. 5. A.I.E. E. Standards No. 4, 1928. 6. Thor.l!lton, "High Voltage Precision Measurements", I.E.E. Jl. v. 69, 1931. • 7. Thornton & Thompson, "Absolute Standard of Measurement of High Electrical Pressures", I.E.L. Jl., v. 71, n. 426, 1932. 8. Kirkpatrick, P., "'11he Rotary Voltmeter 11 , A.I.:E.E •.Tl. v. 51, n. 12, 1932. 9. Kirkpatrick&. Miyoka, ".:burther Development of Rotary Voltmet e r", Rev. Scientific Instruments, v. 3, n. 8 &. v. 3, n. 1, 1932. 10. Meador, J. R., "Calibratio11 of the Sphere Gaptt, Electrical Engineering, v. 35, p. 942-8, 1934. 11. Bellaschi & McAuley, "Impulse Cali brat ton of Sphere Gaps", Electric Journal, June, 1934. 12. Bellaschi, P. L., ttT.he Measurement of High Surge Voltages", A.I.E.J!,. Tra ns., v. 52, p. 544, 1933. 13. Discussion, .Electrical Engineering . v. 35, p. 1652, 1934. 43. 14. Sir w. Thomson (Lorc1 Kelvin), "Papers on El ectrostatics and Magnetism"~ Yiacmillan Co. , 1884. 15 . Sir J. Jeans, "lle ctr i city a nd Magnetism", Cambri dge Un iversity Pres s, 192?. 16. Peek, F. W., Jr., "Dielectric .Phenomena in High Voltage F..ngineering", Third Edition, McGraw-Hill Book Co., 1929. 17. Carroll, J. S. & Cozzens, B., "Sphere-Gap and Point-Gap Arc-ove.r Voltage", Trana. A.. I. E. E., p. 1, 1929. 18. Heuter, E., "Ub er die Mes sungeffektiver Spannungswerte mittels der Kugel funk enstreeke", Eleetroteehnische Zeitsehrift, P• 833, 1934. Additional References on High Voltage Measurement 19. Hendricks, Ao B., Jr., n11h e Voltmet-er Coil in Testing Transformers", Trans. A.I. E. E., v. 35 , p. 11?, 1Ql 6 . 20 . lli.gcumbe & Ockenden, " Some Recent Advances in A . c. Measuring Instru.menta t', I. E. E. Jl. v. 65 , p. 553, 1927. 21. Sharp & Doyle, " Crest Voltmet er s" , 'l'r ans. A.I.E. E., v. 35, p. 99, 1916. 22. Chubb , L. W., "The Cres t Voltmeter", Trans. A.I.E:. A., v. 35, p. 109, ,-., 2 .:.i. \liner, D. ]'., ncrest Voltmeters and Their Chn.racteri s tics", U ec. Jour. v. 22, p. 571, 1925. 24. Work, W.R., "Not es on the Measurement of High Volta ge" , Trans. A.I.E . E., v. 35, p . 119, 1~16 . 44. 25. Ryall, L. E., "Design and Construction of a Simple Neon-tube High Tension Crest Voltmeter 0 , I.E.E. Jl., v. 69, p. 891, 1931. 26. Whitehead & Costellain, "Sphere Gap Galibr-ation", I.E. E. JL., v .• 69, P• 898, 1931. 2.7 . Davis, Bowdler, Standring, "Measure..rnent of High Voltages with Special Reference to Measurement of Peak Voltages", I .E.E. Jl., v. 68, p. 1222, 1930. 28. Peters, J. F., "The Klydonograph", Elec. World, April 19, 1924. 29. T'nornton, "The Ionic Wind Vol t,-net er and Thermo-}4ectrosta tic Relay", I. E • .E. Jl., v. 69, P• 533, 1931. 30. Crozier, B., "The Design, Construction, and Test of a Vacuum Tube Crest Vol tm.eter 1; M.S . Ji .1£. 'l'hesis, Purdue University, June, 1933. 31. "Electrostatic Voltmet ers of Hartmann and Braun", Archiv. fuer Technisches, v. 1, n. ?, 1932. 32. Starke and Schroeder, ftElectrostatic High Tension V,.il tmeter", Arch.iv. i'u.er .Electroteclmik v. 26, n. 4, 1932. 33. Plum.'ller, "High Voltage Measurements", Elec. Rev. (London} v. 107, n. 2766• 1930. 34. de la Joree, "Measurement of High Voltnges", Societe Francaise des Electriciens, Bul. v. 6, n. 62, 1927. 35. Palm, A., "High Voltage Vol tmetcrs", hlektrotechnische Zei tschrift, v. 47, n. 30-31, 1926. 45. 36. Rayner, "A Precision Form of the Kelvin :Electro.static Voltmeter", I .E. L • .Jl., v::. 59, n. 297, 1921. 37. Hobson, J. E., "An Outline for a Textbook in High Potential Measurements", M.S. Thesis~ Purdue Univ ersity, 1933.