Design of an Optical Oscillograph for the Investigation of Lightning Phenomena Citation Wolfe, Karl Morgan (1932) Design of an Optical Oscillograph for the Investigation of Lightning Phenomena. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/s7rp-jr31. https://resolver.caltech.edu/CaltechTHESIS:09132024-214202659 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): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 1 January 1932 Record Number: CaltechTHESIS:09132024-214202659 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:09132024-214202659 DOI: 10.7907/s7rp-jr31 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16727 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 17 Sep 2024 16:35 Last Modified: 17 Sep 2024 17:38 Thesis Files PDF - Final Version See Usage Policy. 15MB Repository Staff Only: item control page

DESIGN OF AN OPTICAL OSCILLOGRAPH FOR THE INVESTIGATION OF LIGHTNING PHENOMENA Thesis by K. M. Wolfe In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1932 SUBJECT OUTLINE I. Lightning Problems and Characteristics . • .. • • • • • .. • • ... II. The Optical Oseillograph Page l .......................... . (a) Use for Investigation of Lightning••··•••·•••• 2 (~} Principles of Operation·•••••••••••••••••••••• 3 Design of the Instrument ............................. .. IV. (a) General Considerations ..••... .• •..••.•••,••••••. 6 (b) Rotating Mirror•••••·••••••·•••••••••••••••••• ? (c) Fery Prism •••••••••••••••••••••••••••••••••••• 14 (d) Camera Box 18 (e) Coil for CS2 Cell••••••••••••••••••••••••••••• 19 Time Lag in the System .... •·....................... . (a} Time for Operation of the cs 2 Cell•·•••·•••••• 21 (b) Time for Explosion of a Wire at the Light Source 21 v. The Completed Instrument . VI. Results of Laboratory Tests. VII. Method of Operation .................. . ................ . Three pictures ·•••••••• 22 Eleven Oscillograms .• 24 (a) For Laboratory Work ••••••••••·••••••••••••••• 30 (b) For Lightning Measurements ••••••••••••·••••••• 31 (e) For Measuring Speed of Rotating Mirror•••••••• 32 (d) For Calibration of the Instrument for Current. 32 (e ) For Cara of the Instrurnent •••••••·•••••••••••• 33 VIII. Suggested Work for Perfecting this Ins trument .... Page 33 Bibliography ..•.. ~ ....•.... -• . . ......... ~. . . . . . . . . 34 Addenda .. Temperature Rise in a Wire Heated by I2R Loss 35 DRAWINGS #l - He xagonal Rotating Mirror # 2 - Mounting for Fery Prism #3 - Camera Box # 4 - Optical Bench #5 - Motor Mounting Calibration Curve for Mirr or; Watts Input to Motor by Speed in r.p.m. 1 I. Lightning Problems Although long recognized as an electrical phenomenon, Lightning continues to present many problems in the fields of Science and Engineering. Perhaps, of most immediate i~portance are those problems concerned with the protection of transmission lines and electrical apparatus, of explosives and oil storage reservoirs, against Lightning . With these problems in mind it is t hen evident that first of all the phenomena of Lightning must, themselves, be clearly understood; some of thes e being, the generation and separation of cloud charges, the mechanism of breakdown, the factors determining the path which the stroke will follow, and the electrical characteristics of the stroke, i.e., the maximum current, steepness of wave front, quantity of electricity discharged and durat i on of current flow. A current- time oscillogr am of the current in a stroke to ground, s hould give these latter undetermined electrical chara ct e ristics of the flash, and it is with these phenomena that this research problem is chiefly conearned. Lightning Characteristics The best authorities estimate the current in a Lightning flash to vary from 5,000 to 100,000 amperes, and the quantity of electricity to vary from a small fraction of a coulomb to 100 coulombs. C. T. R. 1 Wilson estimates the average quantity discharged in a flash to be 20 coulombs. It is generally believed that the current does not oscillate but is damped out at the end of the first half cycle; also that the wave is a flat-topped wave with a very steep wave front, being of the order of a micro-second. 2 II (a). The Optical Oscillograph While looking about for some optical scheme for measuring the current in a Lightning flash, for some scheme wh ich would not be attended by the difficulties to be encountered with the Cathode-Ray Oscillograph, an _article 2 was noted, describing an "Optical Oscillo- graph," which had been used for measuring condenser discharges. Further investigation indicated t hat this instrument would be most useful for Lightning investi gation. Some of its advant~€e s are as follows:1. It has been used to record currents of 15,000 amperes, and within a range of frequencies up to 200,000 cycles. The upper limit with respect to frequency is de tennined by the light which can be gotten through the system and is for the most part a rmtter of cost and design. 2. As the impulse can be used to furnish the necessary light, the apparatus can be made operative at the right instant of time to record the transient or impulse wave. A small gap is placed in series with t he electrical circuit, at the li ght source of the instrument, so t hat t he i mpulse must form an arc here instantaneously with the flow of current. 3. Such an instrument is comparatively cheap, can be ruggedly designed for use in the field, re quires little auxiliary apparatus and can be put in operati on and left for hours at a time in anticipation of a li ghtning flash. It is not, at least, in its present state of development, suitable for measure~ents of small currents, as a s trong magnetic field is necessary to produce the magneto-optic effect; nor is it suitable for measurements of voltage. 3 Principles of Operation 2 II (b). ~ It'lsulo ted Rod, Tower or S\iip's Most . Fig. 1. F G N-1 Q. N-2. l.:2 \ Schematic Diagram Showing Apparatus an d Method of Connecting Tower Circuit about cs 2 Cell and through Gap to Ground. G = L-1 = S1 = N-1 = Gap ac r oss which impulse forms an arc. Converging lens. 4-3/8" focal length, 2" diameter. Stop to keep extraneous li ght out of the system. l" nicol prism. Q, = Plate of Crystal Quartz C = CS2 cell N-2 = - cm. long, 3 5 cm. diamet er . - 2-1/2" long, l" diamet er. l " nicol prism. Adjustable slit, adjustable both horizontally and vertica lly. L-2 = F Converg ing lens. 2" diameter, 9-1/2"' focal length. = Fery Prism. __ 8" Foaal length Camera Lens, located on rnountir:g in Camera Box. 4 M = B = Camera Box. E = Rotating Hexagonal Mirror. Electric motor for driving mrrror. A rod or tower would be insula ted from ground with a set of compression insula tors for approximately 100,000 V. A net of wires soldered to the rod above the insulators connects to a 0000 copper cable. This cable makes one turn about the cs 2 and t h en connects to one terminal of the small gap placed at the focus of converging lens (L-1). The other t ermin al of th is gap connects solidly to ground. When the tower is struck an arc form5 across the small gap giving the necessary light at the correct instant of ti me. A v ery finely dravm wire of iron, lead or tungsten may be used to short the gap, which wire will explode, instantaneously with the arrival of t he impulse, thus providing a good li ght source. Lens #1 renders the li ght coming from the gap plane parallel and nicol prism #1 in turn, produces "plane" polarized light. The Q,uart z plate, a piece of crystal quartz, cut perpendicularly to the Optic axis, produces rotary dispersion, i.e., rotates the plane of polarization of each wave length according to the equation, B1 Form. (1). ? where 1 is length of plate, A and Bare constants, A the wave length of light and e the angle of rotation. The ma gnetic field produced by current flowing in the coil about the cs 2 cell rotates the planes of polarization of the li ght passing through the cell accordi ng to the same law as that for quartz. 5 Form. (2) 9' = A.' + magnetic field. This rotation, small compared to t hat of the quartz , H being here the strength of the plate, follows t he variations of t he electric current, practically 3 instantaneously , adding to or subtracting from that produced by the quartz plate. Nicol prism #2 cuts out all those wave lengths, of which the planes of polarization lie in its crossed posit i on. The light now appears app:t'oxima tely white to the eye, but certain· colors are absent and a linear spectrum woul d show dark bands or li nes as indicated in Fig. 2. I I ~ I I ~ I I I I ~ I I I I I I I I ~ I I I I I I I I 11WI A Fig. 2. These dark lines move back and forth through the spectrum in unison with the current flowing through the coil about the cs 2 cell. They are not uniformly displaced in the spectrum, however, and the displacement of any one is not a linear function of the current. In the equation 9' = A' let 9 = + B'H ,:z Form. ( 2). n 1T, n being any whole number. Solving B'H Form. ( 3 ) . n 1T - A' which g ives t he wave length of the dark bands in a linear spectru..T!l_ as in Fig. 2 . 6 A Fery prism produces dispersion according to the equation Form. ( 4). Substituting for A2 , Form. (3), D =A"+ B"'(n ~ - A) Form. (5). which shows that ·the dark bands will be uniformly displaced in a spectrum formed by a Fery prism, and the displacement of these dark bands will be a linear function of the current. A true current-time oscillogram of the current is now obtained by reflecting the beam of light from the Fery prism onto a rotating mirror from which it is again reflected coming to a focus on a film as indicated in Fig. 1. III. (a). Design General Considerations On account of the losses in the Optical System and by reason of the high fre quency or steep wave front currents to be measured there is need for a maximum of light through the system. The size of the nicol prisms fixes a limit to this maximum. A very strong magnetic field is necessary to produce the magnetooptic effect. Lightning currents are thought to lbe irn,~ense, from 5,000 to 100,000 amperes, so a very few turns, perhaps even a fraction of one turn, may be sufficient for the coil about the CS2 cell. The wave front of a lightning discharge is of the order of a micro-second; therefore, if this wave front is to be measured accurately the spectrum must move over the film with a velocity of at least 1/16" '/ per micro-second or l,OOO,OOO = 66,700"/second. 16 Now as seen from Fig. 3, E>eaM e= 2.'3 cle = 'I- 4ft ctt ,H the light beam moves over the film with just twice the velocity of the radian drawn perpendicular to t he mirror face, -therefore, the necessary speed of the radian at the film is Fig. 3. about 33,000"/second. Assu_ming the perpendicular radian drawn from the face of the mirror to the film to be 10" in length, r.p.s. = 33,000 2 i( X 10 = 525 .. r.p.m.= 31,500, the required speed of the mirror. III. (b). Rotating Mirror There was first to be determined the necessary speed in r.p. m., t he nu.'Ilber of faces, the length and width of faces, the most suitable bearings and the best material for t he mirror. As shown above, the speed required of the mirror is approximately 30,000 r. p .m. By making the radian from mirror to film longer the r. p. m. could be reduced, but in this case the width of the fac es, or what amounts to the same thing , the diameter of the mirror would need to be increas ed, as may be seen from Fig. 4. 8 Fery Pri!>m Fig. 4. Difficulties in polishing and balancing, as well as cost, mount rapidly with t he mirror diameter. As a fur ther limitation, it was both diff icult and expensive to make a Fery prism with focal lengt h longer than 40". If at the prism the beam of light is 3" in diameter and from there focuse d at a distance of 40" and if the mirror is placed 10" from t he focus (as s hown in Fig . 4), t hen the beam will be 3/4 11 in diamet er at the mj_rror. Fi g . 5 shows that the l ight Film beam must be of minimum possible t hickness at the mi r ror t hat t e intensity of the light refl e cted and focused on the Retlec.t ed Liqht Be for thi5 Position o-f film may be a maximum t hroughout the range of s wing of the r eflect ed be am . 1"'cident Li'lht Bea.m . Ji"! 1g ' . 5. I n consi derati on g of these limitations a general compromise was made us i ng the following dimensi ons:- See Drawing #1, Length of radian from mirror face to film .................. Nol of fac es ............................ Mirror speed in r.p.m. 10" approx. = 30,000 = 6 Dia. of circumscri bed circle for Hex.mirror~ Width of face ........................... Length of mirror = ........................ 2-1/ 4 11 1-1/8" 1-1/2 11 A narrow beam of light incident to a face of a hexagonal mirror is re f lected within a 120° arc as t he mirror rotates, a 90° arc for an octagonal mirror and 180° arc for a square mirror. The 180° swing requires an excessively long film, the octagonal mirror is quite difficult to make and its fac es a r e narrow, hence the hexagonal mirror was chosen as the more desirable. In order to raise the "critical speed" of t he mirror and shaft well a bove 30,000 r.p.m. the distance between bearings (see Drawing #1) was made as short as possible. Besides, it is best that the spec- trum be not too long, as the i ntensity of the light in the spectrum diminishes di r ectly as its length is increased, One inch was taken as a maximum length for the spectrum and t he mirror was made 1-1/2" in length. 10 Material for Mirror Requirements:- (a). High re f lecting power - preferably not less than 70%. (b). A non-rusting, non-corrosive material. (c). Of a high and definite te nsile strength. (d ). Not too hard or brittle to wo rk by ordinary mea ns. A mirror made of glass and silver-pl a t ed can be ma de considerably cheaper than one made of steel or other me tal. The tensile strength of glass is, however, an uncerta in quantity varying fro m 2,000 to 10,000 lbs. per s q. in .. Severe stre s ses may be set up by temperature changes and it is known that high spe e d rotating glass mirrors may fly to pieces very u~expectedl y . Silver ha s a hi gh reflecting power in t he vi s ible range but poor i n t he vi ol e t and ultra-vi ol et, - besi des tarnishes to some extent. The magnalium alloys have good reflecting power for a short ti me but are entirely unsuited on account of their tendency to fracture and crumble. Stellite is too hard and brittle to turn on a l athe. Nitralloy, a steel alloy which can be cas e hardened to a very high degr ee of hardness, was s elected as t he rr:a. teri al for the mirro r . It is practically non-corr osive and has a very hi gh tensile strength; its maximum reflecting power is unknown. It was planned to polish the faces as well as possible, after case-hardening . In case the r eflecting power was then f ound to be insufficient the faces could be pl ated with a thin layer of chromium by evaporation, (.0002" to .0004" in thickness). Chromium is known to have a r eflecting power of 70% (approx .) an d to be 11 non-corrosive. The work spent in polishing the steel would not be wasted, for, to polish chromium plating satisfactorily, it is necessary that the original surface be first brought to an optical finish and that the chromium be deposited in a very thin layer. Centrifugal Forces Acting on Mirror Material - Nitralloy Steel - Tensile Strength 120,000 lbs./sq. in. Weight - 600 lbs.fem.ft.= .348 lbs./cu.in. Diameter= 2-1/4 11 • R.p.m. = 30,000 r. p • s . = 500 . Velocity at surface= 3540"/second. 2 Centrifugal force= mV = • 348 x 35402 = 10,000 lbs./sq.in. r 32.2 X 12 X 1.125 Chromium plating is not affected by t his stress. Critical Speed of Rotating Mirror 4 In designing a device such as this high speed rotating mirror, it is most essential that the "critical speed'' be far above or far below the operating speed. The critical speed, in its most simole form, is that speed at which the bending moment produced by the centrifugal forces, which arise in turn, from the deflection caused by the weight of the rotating member, is just balanced by the restraining forces of the rotating member, this being with perfect dynamic balance in other respects. It corresponds to the natural period of vibration of the rotating member. Unbalancing, aside from that due to deflecti on under load, lowers the critical speed. 12 The calculation of criti cal speed is at best only a fair estimate, as is evident from the following assumptions. 9= acc.elerotio\'\ Lowest critical speed= of qravity. V\ Z: Inii Yn 2 1 m1 , m2 , ~=rotor masses. I I Yl, Y2, Yn = corresponding I defl ections. ' For a single concentrated l oad at the cent er of a --, beam support ed at both eno.s, w Bear-inq Cettter. ---~ c.v- - \/ ym(l"t. Form.{6). Fig. 6 shows the rotat i ng member and Fig.? an equivalent shaft and load, assumi ng, ri 9 .6. entire weight concentrated at cent er, shaft supported P ~EHec.tive Loa, at bearings (not fixed ) and .. 1'; 2= !/4" diameter of shaft as 9/16 " . I, These assumptions may - - be considered safe as the '°1,1) ~ q, ~ t P/2 Fig. be arings are, in fact, P/2. I ?• pa rtially fixed and the 13 shaft diameter is much greater than 9/16" throughout a large portion of its length; both factors tend to increase t he stiffness and to raise the critical speed. Wt./cu.in. = .35# . Wt. of rotating member= P P = .35-ir(l 2 X il + ( ~ ) 2 X i2:. 2 32 4 = 1.76# I= ~oment of inertia of shaft cross-section, about a center axis = 4 ~ = .0491 X .563 4 = .00495 in.4. Ym.ax. =max.deflection of shaft under load P Ymax. = Pl 3 48 EI 2.75 3 48 X 30 X 106 X .00495 l.?6 = r.p.m. = 8640 21T X V 32.2 x 12 5.16 X 10- 6 = = 5.16 X 10- 9.64 X 103 6 It = 8640 rad./sec. x 60 = 82,500 = lowest critical speed. A previous design gave a critical speed of 30,000 r.p.m. In the final design the length "l" of shaft was :rmde as short as possible and the diameter increased considerably with the result that the critical speed was raised to 82 ,500 r.p.m .. Bearings For many applications of light loading and high speeds, ball bearings are often ~ore desirable than bronze bea rings in tha t they do not wear so rapidly and are freer from frictional losses and lubrication difficulties. 14 Bearings specially selected at the factory for small tolerances, and of a separable type were employed; norma l speed being 10,000 r.p.m. with a maximum load of 48# . The separable type is most satisfactory as the end pressure may be adjusted for most quiet opera tion while running (see Drawing #1.) A wringing fit was made for the ball race on the shaft, it being .0002" tight while the housing was made.0002" large for t he stationary ring. A shri nk fit of any kind would deform the ball race and ring and cause chattering so the ball races were fastened ti gh tly to the shaft by nuts (see Drawing #1.) The base was made extremely heavy to help eliminate vibrations and deformati ons of any sort. III ( c). :Wery Prism5 . The Fery prism produces the spectrum and focuses it onto the film. Furt he r, as explained under "Principles of Operation", it produces to dispersion according/the law: making the dispa.cement of the dark bands in the spectrum a linear function of the current in the surge. As stated above the focal distance ( see Fig. 4.) should not be great er than 40". The spectrum should not exceed l " in length; the shorter the spectrum the greater the intensity of light at the film while on the othe r hand it is desira t l e to make the spectrum long so as to give a larger and more sensitive scale of current. 15 The dimensions of the rotating mirror being now fixed, in no case will the light beam leaving the Fery prism be greater than 3" in diameter. The diameter of the Fery prism was accordingly taken as 4 " . The following calculation illustrates the method of design:Size of glass blo_ck - 4-1/2" x 4-1/2 11 x 1-1/4". Kind of glass - Boro-silicate - BSC-7. Indices of Refraction Nd l.5151 F 7065 C 6563 d 5875 e 5461 4861 g 4359 b-C C-d d-e e-F F-g g-h .00143 .00246 .00191 .00365 .00433 .00359 b '.l. = Ile = 1.5151 - h 4047 3700 .00246 = 1.51264 - - 1.52499 Ilg= = 1 .52858. The wave lengths which may here be considered useful for photographic purposes range from = 6563 to = 3700 (approx.). A prism of maximu.m thickness and maximum angler is cut from the glass block. ~ ----------'--~~T /: 4'' 4-1/i Fig. 8. .1 ~I Dimension "A" must not be cut down to a fine edge {Fig. 8) else the prism would be easily broken. The faces of the prism are, in fact, spherical, but a plane triangle may be used for calculating the length of spectrum, without error. First solve for the angle (i1), Fig. 9, of minimum dispersi on, using an index of refraction ng, (for a wave length midway in the s pectrum). Then angle OC. = 90°. For n~. sin i1 = Ilg sin r1 Si 1vered = 1.52499 X . 2676 11 = .40815 i1 = 24° 5' 49. 4". For nc· sin i1 = nc sin r2 = 1.51264 sin r2 = . 40815 sin r2 = . 26983 r2 = 15° 39' 15.4". / sin i2 = nc sin r3 = .40168 i 2 = 23° 41' 2" . For llh. sin il = Ilh sin r4 = .40815 . . r4 = 15° 29' 11. 9' '0'2 = r1 1 - r4 = 2' 25.7" 17 sin i3 = nh sin r5 = .41024 i3 = 24° 13' 10.75". f> = i3 - i2 = 32' 8.75" = .5357° t"- = length of spectrtlm ( A = C to allowing 50% for nh ~ = h) = • 5357 X 'Tr 180 X 36" = .337" - n3700' t,t- = .505" The leng th 5 of the spectrum is a constant for any position of the slit on the circle "B" Fi g. 11. In the above calculation }A, was too s hor t. A block of Light Flint glass, 6" x 6" x l-l/21t · in the rough , was procured and having an index of refracti on, ng = 1.61 approx. One quarter inch in thick- ness was allowed for roughing out the Fig. to. blank and dimension "A" Fi g . 10 was made 3/16". This blank was laid out to scale and an a rc of a circle 36" rad. drawn t hrough points Ir (a) and ( b ) Fi g . 11, with center ~ u J at "x". .... 0 "p", and radius of 18" was ~ r awn tangent to th e prism f a ce. ~ a:: B trial another arc, cent er at 11 0 Fig. 11. Circle "B" with cent er " was dravm t hrough points 18 .( c) and ( d). Angle " r " was measured and t he angle "i" of minimum dis per- sion calculated. The length of spectrum - 6500 to - 3700) was about 7/8", which was satisfactory. It is a property of the Fery prism that, if a diverging beam, from a slit or other source loca ted on the tangent circle "B", is projected into t he prism, it will produce a s pectrum and focus it at some point on t h is circle "B". If the slit is placed at "z••, giving the angle •• 1 11 of minimum dispersion, the spectrum will be focused in the vicinity of "z". In t his device it is necessary to separate the pos ition of slit a nd spectrum, on the circle ••B" , to some such positions as "n" and i• o" respectivel y . A Fe r y prism is subje ct to astigmatism. To correct for t his the back of the prism was not silvered , a mi r ror •~" with the sa,ne radius of curva- ture as t he back of the prism, being mount ed behi.nd 1the prism with a d justing screws for t h ree positions (Drawing #2.) One position of t h is mirror may always be found ~h ich wil l corre ct the astigmatism present in the spectrum. Camera Box III (d). Drawing #3 shows the main features in the desi gn of the ca,ne ra box . The distance from mirror to film was t aken as 10" ± It is to be noted that the curve a. "A" , Fi g . 12, is not a circle. Fig. 12. 19 The li gh t beam must focus at the film throughout the length of the film, which means that the distance from "a" to ttb" plus tha t from "bu to "c" equals a constant, ab + """to = k, f~r all positions of the rotating mirror. The curve "A" was accordingly plotted and a templet made to locate the position of the film. Both the Camera Box and Optica l Bench were made light-t tght throughout. A ca~era bellows di r ects the li ght from the Fery prism onto the rotating mirror (see Drawings #3 and #4 .) By this means the camera box may be moved in or out or rotated with respect to the Fery prism, as may be re quire d . (See Fig. 11. ) III ( e). Coil for CS2 Cell From that which is known of the nature of li ghtni ng it is plain that the inductance of the coil a1:out the cs 2 cell must be a minimum, else the stroke may side flash to ground, not nassing through the coil. An opposing limitati on is that a very strong magnetic field is necessary to produce the magneto-optic effect. From an inspection of an oscillogram of a condenser discharbe, taken at the Mount Wilson Observatory, it was noted that approximately 3000 amperes flowing in a coil of one turn and 1-1/2" in diame ter would be needed to produce a perceptible shift in the dark bands of the spectrum. Using one turn, the current scale as formed by the spectrum would range from 3000 ± to 150,000 ± amperes. The current scale may be widened, in the design of the .B'ery prism, to give a greater deflection for a given current. There is, however, a limit to this, for as has been shown, one of the chief problems in recording hi gh frequency oscillati ons is that of getting sufficient light t hrough the 20 system. The intensity of the light varies inversely with the length of the spectrum. The use of one turn for t he coil is based on the estimated values of lightning currents, which may be far from correct. Inductance of Coil Wire - 0000 copper cable + dia. = .46" 47ra (log -Sar - 2) El. & Mag . - Jeans - p.445 . r = . 23" = .575 cm. a = rad. of coil = 3/4" = 1.91 cm. L = 7ra (-7 + 4 log 8 X 1.91 = 36.6 abhenries. .575 9 X 10= 36,6 henries. L It is not believed that the inductance of a coil of one turn is sufficient to alter the wave shape of the current appreciably, for assume i = 10 5 amps., Energy= l2 Li 2 = l2 x 36.6 x 10-9 x 1010 = 183 watt sec., an amount, insignificant compared to that of any lightning stroke to ground. The voltage appearing across the top of th e coil for a current of 50,000 amperes, and wave fro~t equal to that of a fre quency of 10 6 cycles/sec. = 50,000 x 2rr x 10 6 x 36.6 x 10-9 = 11,500 volts. The coil should be insulated on the top, where the t wo ends cross, with a piece of 1/4" micarta. IV. (a). Time Lag in the System The ti ~e required for t he magneto-optic effect (Far aday effect) to take place in the CS2 cell is entirely negligible compared to ti me 21 intervals of the order of a micro-second. The action of this cell involves the partial rotation o~ polarization of the molecules of the carbonbisulphide, which are under the influence of the magnetic field. A test by Bichat and Blondlot 3 showed that this effect is practically instantaneous. {b). In measuring real lightning currents the light developed at the light source should be sufficient without the use of a fine wire. No appreciable time delay could then enter in, as the ti~ for the breakdown of a short gap is of the order of 10-8 seconds or less as shown by measurements of Dunnington 6 at Berkeley, Calif ornia. A wire of some metal such as tungsten or platinum, when exploded gives a light far more intense than that produced by the same current in a discharge through air. For measuring condenser discharges in the labora- tory, it is c )nvenient, therefore, to,~lace a fine ( 1 or 2 mils) wire of tungsten at the light source. If this wire is too large or the gap too short, considerable time lag may be introduced into the system. Experience shows that a 2 mil tungsten wire, 3/4 of an inch long will cause no measurable tj_me lag when the time scale is 1/16 inch per micro-second. A metal of higher resistance and lower melting point will, of course, explode in tess time than one of tungsten. A further improvement in focusing of the optical system might make the use of a fine wire a t the light source unnecessary. A fair estimate of the time required for the wire to explode may be had by plotting a temperature-time curve for the point at the center of the wire from the equation derived in the addenda to this report. lack of The accura t e data regarding coefficients of heat conduction, resistance, etc., at high temperatures, limits the use of such an equation. 22 v. THE COMPLETED INSTRUMENT Following the design outlined above the Optical Oscillograph was built and tested. Figure 13 below shows the instrument completed and assembled. Fi g . 13. The Assembled Instrument Figure 14 shows t he Camera Box and Rota ting .U rror in more detail. The top part of the Camera Box is light, tight and remova ble; it holds the film which ~ust be loa ded in a dark room. (3\ ~ (1) Film holder. (2) Shutter. ( 3) Camera Box. ( 4) Rote.ting ~irror . Fi g . 14. Camera Box, Dismounted . Figure 15 sh ows the Optical Bench a nd various parts placed in operating positions. Fig. 15. Optical Bench. .-- 23. G is the gap in which is placed the fine tungsten wire. M is a plane mirror placed close behind the gap. L1, is a 2" diameter, 4-3/8" focal length lens. s1 , is a stop which limits the light beam to a si ze which the Nicol prisms can handle and keeps extraneous light out of the system. N1, is a one inch Nicol prism. Q , is a crystal quartz plate, 2" in dia. Either of the two plates pro- vided, one 2 cm. the other 5 cm. long may be used here. C., is the carbon bisulphide cell with coil in place. N2, is the second Nicol prism. Lz, is a 2 diameter, 9-1/2" focal length lens. 11 S2, is a double slit on which lens L 2 is focused. F, is the Fery prism. A camera bellows connects t he camera box to the housing over the Optical Bench; this provides much flexibility in focusing the Fery prism. However, it is necessary that both camera box and optical bench be placed on a sol id plane table so that the li ght beam from the Fery prism enters the ca~era box at exactly the correct elevation. After testing, it was found advisable to make several changes in the instrument. The camera box and bellows were set at a different angle with respe ct to the optical bench to reduce disto~tion in the focusing of the Fery prism. An 8" focal length camera lens* was placed in the front end, position "x", Fi g . 1., of the camera box and directly in the path of the light beam from the Fery prism. Here also was placed a 2" diameter 5" focal length double con- cave lens, the effect of which was to increase the effective focal length of the camera lens to about 15". The advantage of this system is that the magni- fication of the Fery prism, which was large was much reduced, making possicle much sharper focusing of the spectru.~ on the film. *The camera lens was borrowed. 24 There would be no advantage in using this addition al camera lens in t he meas uri ng of very large currents, such as lightning; as t he re with t he large amount of light available even a large broad specturm would most likely come out clean and sharp. RESULTS OF LABORATORY TESTS VI. The circuit used for testing in the laboratory is tha t given in Fig. 16. I<. G1 C1 1.10 V. o.c . C G 1dl Figure 16. G is the gap at the light source of t he instrument across which the fine tungsten wire is stretched . C is t he coil wound about the carbo n bisulphide cell. C1 is a 1.75 micro-farad con denser wh ich can be char ged to about 25,000 volts. G1 is a gap or switch which breaks down when the conden ser becomes fully cha rge d. R is a resistance of about 100,000 ohms (a water tube) placed in t he circuit to limit the chargi ng current of the condenser to prevent burni ng out the Kenotron rectifier tube K. The circuit C1G1CG must be made of a large low resistance conductor in order that a large current may flow. Following are a number of current-t i me oscillograms t aken under t he condit ions specified. It is to be noted that in these oscillograms any one single li ght or da r k band of the group may be use d. The ti me axis is a horizontal line drawn through the cente r of th e single li ght or dark band under cons ideration, and the current axis, a vertical line. 25 .µ s:: Ill I- I,, :::, u ,o Figure 17 . 0scillogram taken on ordinary roll film . Speed of rotating mirror Scale of time axis - - - 16,000 r . p .m. 16 ,000) x 2 x ( 2x 10") x ~ z 33,500"/ second 60 = . 0335"/ micro-second= 1/32"/ micro - second, approx. Radius of light beam is 10" in all cases . Number of turns on CS2 cell 8. The camera lens mentioned on page 23 was not used . Frequency of damped oscillation - 38,500 cycles approx. A method for calibrating the instrument for current is included in Part VII of this report . Figure 18. Figure 18 is an oscillogram taken under the same conditions as that in Figure 17, except that it was taken on super-sensitive panchromatic film, which gives a wider spectrum. 26 Figure 19. Oscillogram taken on ordinary roll film. Speed of rotating mirror - 20,000 r.p.m . Scale of tiI!l9 axis - - - - . 0418"/ micro-second. Number of turns on cs 2 cell T - - 4. Frequency of damped oscillations T The camera lens was not used. 89,000 cycles. An adjustment of the Fery prism and of the camera box, different from that used for Figures 17 and 18, was employed. This would necessitate a separate calcibration for the current scale. Length of quartz plate - - - 5 cm. Figure 20-a. Figure 20-b. Figure 20-a Figure 29b. Speed of mirror - - 24,000 r.p.m. 20,000 r.p.m. Scale of time axis .05"/micro.sec . . 0418"/micro-sec. No . of turns on cs 2 cell 4 Length of quartz plate 5 cm. in both cases. 12 All other data for Figures 20-a and 20-b same as for Figure 19. As seen from Figure 20-b, the scale of the current axis depends on the number of turns in the coil about the cs 2 cell. All the above oscillograms are the result of early attempts to operate the instrument and are not the best that can be obtained with it . 27 Tin,e in - Mlcro-sec.ol'\ ds o I w w ~ ~ ~ Figure 21. M Oscillogram taken on super-sensitive panchroll'litic film. Speed of rotating mirror - 16,000 r.p.m. Scale of time axis .0335"/micro-second. Number of turns on CS2 cell 8. Length of quartz plate ---- 2 om. Frequency of damped oscillations 45,000 cycles. The camera lens mentioned on page 23 was used, being placed in the location marked "x'' of Figure 1. Timeih Mic.ro - secol'\ds, Figure 22 . Oscillogram taken on super-sensitive panchromatic film. Speed of rotating mirror - 10,000 r.p.m. Scale of time axis .021"/ micro -second . Other data same as for Figure 21. 28 Time i n Mic.ro - seconds - Figure 23. For the sake of economy four discharges were recorded on each loading of film in t he camera box . Thus occasionally the oscillograms overlapped as in Figure 23, above. The surge recorded ontbe left in Figure 23 is the same in all details as that one in Figure 21 . characteristics of the one on the right are listed below . Oscillogram taken on super-sens itive panchromatic film. Speed of rotating mirror - 25,000 r.p.m. Saale of time axis - - - - .053" / micro-second. Other data are the same as for Figure 21 . Figure 24. In the oscillogram of Figure 24, the quartz plated used was 5 cm. long. All other data are the same as t hose under Figure 21. The 29 ~ to 25a. :, V Figure 25. Oscillogram taken on super-sensitive panchromatic film. Speed of rotating mirror - - - 29,000 r.p.m. Scale of time axis T 'S T .061" / micro-second. Number of turns on cs - 2 cell 8. ' Length of quartz plate 5 cm. Frequency of damped oscillations 45,000 cycles. The camera lens was used. The oscillogram in the left of Figure 25 fell on the end of the film in the camera box, as explained in the Figure at the bottom of pa ge 8 . The light beam from the mirror was divided into two sections, recording an oscillogram at each end of the film. Hence, note the dimness of the record, Figure 25a. In this test the slit s 2 was opened to 1/32" square, about four times the size used in previous tests. This explains the brightness of the record 25b even though the time scale was quite large. The data for Figure 26 are just the same as for Figure 25. Figure 26 . The 30 details of this oecillogram are spoiled by the ove r lapping of a second surge; however, it is a good record of a surge virtually dampe d out. Tne camera lens used in these later tests was too small to accommodate the entire beam conve r g ing from the Fery prism. Part of the beam hit the holder of the lens, which explains t he dimness of the lJwer half of the spectr~~ (oscillogram) of Figure 26. To measure t he current accurately in thes e oscillograms it is first necessary to calibrate the instrument for the particular combinati on used, the combination of quartz plate, coil for t he cs 2 cell, and position of the camera box with respect to the optical bench. A fine lin e is then ca r eful ly drawn for the time a xis and the oscillogram observed under a microscope having finely graduated rulings in the field of vision. The rotating mirror was driven at 33,000 r.p.m. for 30 minutes to test its r eliability at t his speed. METHOD OF OPERATION VII. (a) For Laboratory Work. Pla ce l ens 11 at exactly 4-3/8 " from the tungs ten wire placed in the gap G and lens L2 at exactly 9-1/2" f r om the slit 82• Remove the mirror block M (Fi g . 15), place a strong point source of li ght s uch as an electric a rc in front of the system (if an electric arc is us ed, it is necessa ry to keep the electrodes adjusted to asingle point source as near as possible); remove the cover to the mirror of the Fe r y prism, also the s hutt er and lid to the camera box; open t he vertical slit of s 2 wide and place an old piece of strip film in th e film holder of the camera bo x . Now adjust the position of t he Fery prism and of t he came ra box until the spectrum reflected from the rotating mirror falls upon the strip film; turn Nicol prism H2 until the lines in the spectrum are clear a nd easily discernible. If the lines in the spectrtL~ are not parallel to the camera box, turn t he quartz plate~ ei ther 31 backward or forward a little. Rotate the rotating mirror slightly by hand and observe the spectri.nn as it travels from one end of the film holder to the other. If the spectru..~ fades out toward one end of the film holder it is owing to the fact that the bea~ from the Fery prism is not falling upon the rotating mirror at the right angle; this can be corrected by adjus ting the screws on the back of the Fery prism mirror and the lever on the top of the Fery prism itself. in both directions. Stop down the slit s 2 to 1/32" to 1/64" By moving t he camera box, adjust its position relative to t he optical bench so that the spectr1.un focuses exactly on the position of the film in the film holder. Locate the point source of light as nearl y as possible on the center line of t he optical system and dire ctly behind the fine wire in the gap G. Adjust the holder of the gap G until the i~age of the fine wire falls exactly and undistorted on the slit s2 . If a piece of white paper is placed about 6" beyond t he slit s 2 the image of the fine wire may be easily seen when properly lined up. Set all a d justments tightly, replace t he mirror block M behind the g~p G, and replace t he covers to the optical bench. holder in a dark room and place in the camera box. Load the film Before setting off the condenser discharge, being the mirror up to the desired speed and remove the shutter from the film holder. A camera lens located as explained on pa ge ?3 will greatly increase the sharpnes s of ~ocus of t he spectrum. The diameter of such a lens must be sufficient to handle the light beam from the Fery prism, about 1-1/2". (b ). It is not expected that the leads provided on the optical bench would be used when measuring li ghtning currents. The instrument would be placed in a nearly vertical position and all co nductors made as short and direct as possible. The motor used at present will not drive the mirror above 20,000 r.p.m. continuously wi thou:t. O;Werhea ting• 32 (c). For Measurement of Mirror Speed. The diagra~ of Figure 27 illustrates the method by wh ich the speed of Out ut -+------hl~llt--------t-Out- Wesft!rn Electric Osei I \atol" ,. ,, ♦ 0 put - 111 -: , . . f - - - - - - ~ put Ampli{ier. Go1vanoV1i'leter. O·S0,000 Cy c: 1e~ Rot<1ti n, Mirror. Figure 27. Lamp . the mirror was measured and a calibration curve obtained. By coupling the amplified impulses of the photo-cell to the output of the Western Electric oscillator, as shown above, a beat frequency equal to the difference of the fre Quenctes of the two circuits was produced. The natural mechan i cal frequency of the needle of the galvanometer was about 30 cycles. ·.'hen the beat frequency came in the neighborhood of this frequency, 1 the needle would flutter, and as more careful adjustment of the W.E. oscillator brought the beat frequency lower and lower, the needle would oscillate slowly to and fro, and when the needle ce ased to move, t he fre quency of the i mpulses to the photo-cell must of course have be en t he same as that of the osci l lator. As each face of the mirror gave rise to a si ngle impulse in the pho to-cell and each impuls e corresponded t o a single cycle in the output of the a~plifier, (as the impulses were uni-directional), the speed of the mirror in r. p .m. was equal to, = 60 x frequency of oscillator = 10 x frequency of oscillator 6 A calibra tion curve was plotted between r.p.m. and watts input to the motor, driving the rotating mirror, wh ich is included in this report. {d). To Calibrat e the Instrument for Current. A sugge stion for doing t his is to connect the coil of the CS2 cell in the low side of a spot-welding transformer of large current rating, as for example, 4000 or 5000 amperes for a small time interval. Use an ordinary 33. electric lamp for the light source and rotate the mirror by hand. The r.m.s. value of the current may be determined by measuring the current in the primary if one also knows the ordinary design data of the transformer. An oscillogram of a few cycles t aken in this manner may be used to determine the current scale of oscillograms of condenser discharges. Care of the Instrument ( e). The several parts of this instrument are mostly high quality optical goods and re quire much care in handling. ing the lens and prisms. scratched or chipped. Soft cotton may be used for clean- The Nicol prisms are soft and brittle, thus easily The rotati ng mirror, which is made of a steel alloy, s hould not be exposed to dampness or fumes. The cover to the mirror of the Fery prism should be kept in place when the prism is not in use. optical surfaces s hould be cleaned before taking an oscillogra.m. All The ball bearings to t he rotating mirror should be oiled with about two drops of a very li ght oil, such as typewriter oil, for every half hour of operation. Do not put so much oil in the bearings that it is thrown out onto the mirror. It will be found necessary occasionally to clean the commutator of the motor. VIII. SUGGESTED WORK FOR COMPLETING AND PERFECTING THIS I NSTRU1VIENT It is believed that an optical system having t wo slits would make possible much sharper focusing of the spectrum a nd g ive a current scale which could be more accurately rea d. Slit s 2 would be a vertical slit only; the other slit would be placed at the focus of the Fery prism and be a horizontal one. Between t his slit and the rotating mirror would be placed the camera lens as mentioned above. The instrument should be calibrated for current either by the method outlined above, or by some other suitable method. 34 BIBLIOGRAPHY 1. C. T. R. Wilson - Phil. Trans. Royal Soc. , London, A-221 - ?3 - 115, 1920. 2. "An Optical Oscillograph" - Sinclair Smith - Astro-Physiai Jour., Sept., 1928. 3. Physical Optics - Wood - Speed of Magne tic Rotation, Pa f, e 500. 4. Elasticity - Timoshenko & Lessells. Stress Analysis in Electrical Rotating Machinery --M. Stone - .A.PM - 50 - 16. {Publication of the A.S.M.E.). 5. As tro-Physieal Journal, Vol. 34, p. 79, 1911. 6. Dunnington, Physical Review, Oct. 15, 1931. 35. Addenda . Temperature Rise in a Wire Owing to I~ Loss A metal wire connects t wo me t al plates as shown in the fi gure and forms part of an electrica.l circuit. The problem is to find the e quat i on for temperature of the wire; t his e quati on to hold for the following assumptio ns and conditions. T T i l(½Q,'. ' -x: =- .Q;2- ton ~tan t A--------, ~urre~t Su~ We will assu.rne, 1. t hat the plates are kept at a constant tempe r - ature T. c ~ f y ent i~ the r1ec.1Y'1t1>.1 Ci1'C \,\.\-\ • 2. That tao voJ.tage E of tbo eatie1'y remains constant. 3. That t he expressi on for resistance per unit length of the wire is r = r 0 (1 + « V), where d... is the coefficient of increase in resistance with unit increase in tempera ture. 4. That the heat loss by radiation and conduction to the medium surround ing the wire is proporti onal to the 1st power of the tempera ture rise of the wire above t he surrounding med ium. Let the following symbols represent the quantities designated: V = temperature at a point x of the ~ire and at a time t, r = resi s tance per unit length of wire in ohms per cm. 0 h = coefficient of hea t conduction for the wire in cnl/cm2/c/sec. = cal cm. oc. cm2 sec . . p = coefficient of heat for the wire = cal/gm ./ c = 0 p = density of the wire = gm cm3 cal gm. oc. l = length of wire in cm. a = cross-sectional area of the wire in cm2. T = temperature of end plates and of surround i ng medium and is constant calories e = constant of emissivity= cmZx degrees Crise in t emp . above surrounding med.x se <f = perimeter of wire in cm. r 0 = resistance of wire at temperature T. A = ecr - Q.( ha B= ~± e T O" q = heat generated per unit length of wire ha 2 per second t =J cal :::: joules = i r cm . x sec 4.185 x cm 4.185 cm. k = p .P h a= .239 1 2 r 0 cal cm. sec. Boundary Conditions From symmetry it is evident tha t t he center of the wire will always be a point of maximum temperature; this gives condition 1. follows from the assumptions made. which gives condition 3. Condition 2 After an i nfinite time t he tempera ture of the wire will have arrived at a steady sta te; t h is means then that which is condition 4a. = O, The switch is thrown at the ti ~e t oY ot • 0 Condition 4b follows from the solution for the steady sta te, given below in e quation (8). = 0 at X = ~/2 1. at x = 0 and at x = i 2. 3. 4a. 4b. at all times. at all times. V = T at t = 0 for all values of x. oV = 0 when t = Q0 for all values of x. ~ oV ax = a value to be determined from the e quation for the steady st a te heat flow; see e Quation 8 below. 57 e The heat generated in a action of the wire between x and = q dx cal /sec. xi dx is = heat flow out of sectiol The total heat flow at xis in the negative direction and= -ha~ cal/sec.= The total heat flow at x~dx is in the negative direction and cal/sec. = heat flow into section d?f . As heat is being generated in the wire it is clear that more heat must flow out at x than flows in at x~dx. Heat storage in section dx - ~ yd x ~t - §> ap - = Q. cal/sec. Heat lost by radiation and convection in section dx = elV -T) o' dx ,,, cal/sec. :tfow,heat storage in section dx equals the heat flo w into the section plus ;jhe heat generated in the section ,minus the heat lost by radiation and convection second. 1 per and minus the heat flow out of the section. This is expressed in the following equation. apysY- q - e ~ v - T ) er • 'ut To be effective the small tungsten :tri.re at the light source must explode in a small fraction of a micro-second or less. Actually, we know that during this time the current of the condenser discharge is increasing ~ery rapidly. The simplifying aasuuption will be mRde that the current constant. ha ~ 2 . ~ t 1 ~ <:J...V J - e O' tV-TJ • ot = 6'-Y 6. '8-P ~ t>.,_V ;f ot o'I ()~.,_ = - y ea'-ece i h. a. B . ~ ± e~T "' a. remains 38 The equation for the steady state is, 7. 2 d V' - AV'= - B. , the complementary solution of which is dx 2 ,/A'- 1. + P cosh ffe. X, and the particular solution is V1 = J sinh B A The complete solution for the steady state is, therefore, 8. V' = B + J sinh ,{A•'Y. + P cosh A -{A.~-1.. , where J and P are constants. When t equals to infinity the equation for V, the solution of equa tion 6 must reduce to the steady state solution, 8, above. If we make the assumption that, .t<'i,l'!'anf'n.t 9. V = u e- (+ ~ + V' , whe re u may be a function of both t and x, also, and substitute this into equation 6, an e quation in u results, the solution of which is well known. 2 ou 10. = The equation in u is, ou k 2> x2 a t Let u = XT, where X = f(x) only and T = f(t) only. This substituted into 10 gives the two equations below, 11 and 12. 'l. T ~::kx. u T. If we divide this through by XT the vari'o x2 ot ables will be completely separated. lOa. 2 l Oa. X -1 -o-... - = X k T ox 2 o T -,,-• Ot is equal to the same constant. ll. 1 Let us put, and X 12. Two such functions can only be equal if each 1 d T T d t = - m2 k The solutions of 11 and 12 are well known and are respectively, X = Em cos mx _ m2t T = Cm e -y- + Fm sin mx, 39 The most general form in which to write the solution for 00 m2t 13. u = e- ""'1r (Em cos mx + Em sin mx) u is then, I,. 'h\" 0 Substituting this value of u in equation 9. we obtain the gene ral solution for VAt { V = e - f( 14. (Ero sin mx + Fm cos mx)1 + B + J sinh -{A: i+ A + P co sh VA! X We will now apply the boundary conditions to the above equation and determine the constants Em, Fm, m, P, and J. Applying condition 2, that V =Tat all times at x = 0 and x = f , we see that the coefficients of e- ~ must vanish for both cases. Fm = 0 ctnp if we put Therefore, , sin mx will equal O when x m=Il'1T T X = 0 X = T = B A + p i.e. ;e, T = AB Therefore, 16. J = (T 15. - -AB 1 sinh Applying condition 3 that at t = O, V = T for all x, to 14, we obtain, oO 17. I Em sin nx T = h,:;1 + B A + J si nh l/A· x + P cash VA°"• x. Substituting for J and p in the above, we arrive at the result, 18. 1 Em sin mx = (T - !) • [ 1 - coshyA· x V\ 11 note;lll\=7 · h =1 1 - coshff~ . sinh'\f'A"•x.l s inh 1n. 'A_:fl --1 Treating the left hand member as a Fourier series, we obtain the following value of 19. R lil = .§. (T - I Em, B A ( 1 - cos n '1T) A m(m2 + A ) ) where m = n1T Q 40 The complete solution for V now becomes, sin .!L2L x + 20. ( + Lcosh VA· x + 1 - cosh sinh -fi:·~ VA·~ Conditions 1 and 4 were used to check the above result. 41 SUMMARY OF RESULTS OF RESEARCH WORK The Optical Oscillograph was designed and built for the particular purpose of measuring lightning currents,but so far there ha s not been an opportunity to talce it into the field and try it on actual lightning discharges. It wa s,however tested in the laboratory, obtaining oscillograms such as those included in this report. ~n the osillograms a time scale of 1/16" per micro-secomwas easily secured; with a 1/2 h.p. ~otor to drive the mirror at a higher speed it would not be at all difficult to get a time scale of 1/8" per micro-second. Th~is evidence concerning lightning to indicate that this time scale is suffic ient to give good definition of any ordinary lightning surge oscillogram~ The current scale is not entirely satiafactory for measuring condenser discharges because the amplitude of the curves is so small. Knowing, though, that the charge of an average lightning discharge may be from 50 to- 500 times that of the condenser used in the laboratory tests,one would expect tbii.t oscillogre.ms of lightning currents ½~uld show a much wider deflection along tre current axis. (The average charge of a lightning discharge is about 20 coulombs while the charge of the condenser u sed in the laboratory tests never e xce13ded . 1 coul o,:ib). In measuring lightning currents the difficult problem will be to get the lightning to str ike a particular rod or tower. This means that to get result s within a reasonable length of time the instrument used must be set up on some mountain pealc infested with numerous thunderstorms,and most likely in some isolated region.This oscillograph is admirably adapted for such a task due to its portability, its ease of operation and the certainity with which a surge is recorded.