Bioelectromagnetics 22:7^18 (2001)

Cows,Ground Surface Potentialsand Earth Resistivity

C. Polk*DepartmentofElectrical&ComputerEngineering,UniversityofRhode Island,Kingston,RI

The `̀ stray voltage'' problem on dairy farms is discussed briefly. By reference to publishedliterature it is shown that a `̀ step voltage'' (SV), i.e., a potential difference between front and hindhooves of a dairy cow, much less than the often quoted threshold value of 0.5 V, when applied forlong periods of time, could possibly affect cow health and milk production. Values as low asapproximately 10 mV could conceivably be significant. A measurement program carried out on 19representative Minnesota dairy farms during the summer of 1997 is described. Nine farms hadabove average (HP) and 10 below average (LP) milk production. Results show that SV was 4.2times higher on the LP than HP. However, only three farms had SV greater than 9 mV, and low milkproduction on these farms could possibly be due to absence of recommended vaccinations ratherthan high SV. Soil resistivity r measured in the farm fields was 3.4 times larger on the LP than onHP. The possible origin of SV in relation to electric distribution systems within and to farms isdiscussed. Relations between SV and r are analyzed. Conditions are specified under which SV inthe barn must be related to r measured in the field, rather than the r of the concrete floor of thebarn. It is suggested that laboratory research is necessary to establish the significance for cow healthand milk production of long term exposure to low SV levels. Bioelectromagnetics 22:7±18,2001. ß 2001 Wiley-Liss, Inc.

Key words: stray voltage; step voltage; farm electricity; earth currents; soil resistivity

BACKGROUNDöTHE ``STRAYVOLTAGE'' PROBLEM

At least since l961 it has occasionally beenreported that small electric potential differences,accidentally encountered by dairy cows, can interferewith milk production [Lefcourt, 1991]. It is nowknown that some dairy cows can detect a 60 Hz voltageas small as 0.5 V when it is applied between muzzleand hooves, and they will visibly react to it withsudden head movement [Reinemann et al., 1988].Reports on economic losses, presumably caused byelectric currents in the earth associated with electricitydistribution [TERF, 1984], led to a study sponsored bythe Minnesota Public Utilities Commission [Andersonet al., 1996]. Complaints by some dairy farmers hadsuggested that cow health and production problemswere somehow associated with electricity distribution,but not necessarily manifested by well-recognized`̀ stray voltage,'' that is, above 0.5 V between cowcontact points. A program of measurements, includingmany electrical parameters which could conceivablyaffect dairy animals, was therefore conducted onselected dairy farms in the summer of 1997 [Staehleet al., 1998].

DESIGN OF THE MINNESOTA FIELD STUDY

A premise of the study was that most health andproduction problems ascribed to contact with elec-tricity could be caused by many other environmentalconditions (e.g., water quality). It was also thought thatin the very complex dairy farm environment anyelectrical effects on animal health could be in¯uencedby nonelectrical variables (e.g., feed composition)which by themselves are important for animal health.A large number of nonelectrical conditions (e.g., stallsize and cleanliness, vaccination history) that arerecognized by veterinarians to affect cow health andmilk production was, therefore, measured in additionto electrical parameters. The latter included amplitudeof magnetic ®elds in the animal environment, electricalresistivity of the soil, 60 Hz sinusoidal steady state andhigher frequency transient ground surface voltages

ß2001Wiley-Liss, Inc.

ÐÐÐÐÐÐ*Correspondence to: Charles Polk, Department of Electrical andComputer Engineering, Kelley Hall, 4 East Alumni Avenue,University of Rhode Island, Kingston, RI 02881.E-mail: polk@ele.uri.edu

Received 25 January 1999; Final revision received 2 February 2000

at different locations, and voltages between system`̀ neutral'' wires and earth, as described below.

One hypothesis, in particular, which motivatedselection of measurements was that continuous, longterm exposure of animals to currents much smallerthan the l mA through a (typical minimum) cow-bodyand contact resistance of 500 O, caused by a potentialdifference of 0.5 V, may eventually cause adversephysiological effects. The bases for this hypothesis arethe following: (1) Electrically conductive connectionto a cow of a 10 mV potential difference would give abody current of (10ÿ2/500)� 20 mA. In one leg ofapproximately 10� 10 cm cross-section, one half ofthis current would correspond to a current density of1 mA/m2. (2) Measurement on phantom models of ahuman [Kaune and Forsythe, 1985] and calculations[Dawson et al., 1997] showed that current densities ofthis order of magnitude can be produced in anelectrically grounded erect human by a 60 Hz verti-cally oriented 10 kV/m electric ®eld. (3) Cows areabout as tall as the average human, but as a con-sequence of their different shapes, the maximumcurrent densities in cows induced by the same verticalelectric ®eld are not likely to be more than half of thoseinduced in humans [Kaune and Forsythe, 1988]. (4)Exposure of cows under laboratory conditions to10 kV/m, 60 Hz electric ®elds has shown physiologicaleffects, some not adverse to health [Burchard et al.,1996] and others that are potentially adverse [Burchardet al., 1998, 1999]. (5) Since exposure of cows to anelectric ®eld of 10 kV/m will produce internal currentsweaker than those caused by a 10 mV step voltage(SV) between front and rear hooves, similar or morepronounced effects are a likely consequence of suchSV exposure. Therefore, the possible relation of SV onthe order of 10 mV to health or production problemscannot be excluded and should be investigated.

In the Burchard et al. [1996, 1998, 1999] ex-periments, 60 Hz horizontal magnetic ®elds of 30 mTwere also present. This confuses the comparison withconductive exposure via SV, because the magnetic®elds induce additional currents and may also have`̀ direct'' physiological effects not related to current[Walleczek, 1995]. Although a 60 Hz horizontal 30 mTmagnetic ®eld would produce average current densi-ties of only about 0.1 mA/m2 in a human [Dawson andStuchly, 1998], larger values are to be expected in acow due to its larger cross-section.

Selection of the test farms was based on an earlier(1996) mail survey, followed by telephone interviewsof dairy operators in Minnesota and Wisconsin who arelisted in the database that is maintained by theMinnesota Agricultural Statistics Service of the U.S.Department of Agriculture. This survey was conducted

by the Minnesota Agricultural Statistical Services andreached a random sample of 2500 dairy operators,1250 from each state's database. At the time of thesurvey, there were about 10400 dairy operations inMinnesota and 25000 in Wisconsin. Thirty percent(752) of the mail survey questionnaires were com-pleted and returned [Staehle et al., 1998]. For themeasurements program in Minnesota, nine `̀ high pro-ducing'' and ten `̀ low producing'' farms were thenselected. They were, respectively, in the top and lowest10 percent of milk production (herd average of lbsmilk/cow/day) and ranged in size from 30 to 125 dairycows, which is representative of Minnesota dairyoperations. Seventeen farms had stanchion and/or tiestalls and two were parlor facilities, corresponding tothe 9:1 proportion of such farm characteristics evi-denced from the mail survey. The production averagein the high producing farms (HP) in the sample was67.2 lb/cow/day and 45.9 lb/cow/day in the low pro-ducing farms (LP).

Employing Student t-statistics difference wassigni®cant (P � 0:0006). This statistic is of interest incomparison with other parameters that were consid-ered in the initial selection of test farms. In view oflarge standard deviations, these other variables turnedout to be less signi®cant: Average milk somatic cellcount (SCC) was 319000 in the (HP) vs. 413000 in the(LP) and corresponded to P � 0:0994; bacteria count,which had an average of 9000 in the (HP), vs. 28000 inthe (LP), corresponded to P � 0:0896. The highlysigni®cant difference in average milk productionbetween (HP) and (LP) maximized the possibility ofidentifying variables in environment and `̀ manage-ment'' (e.g., feed composition) that affect milk yield.

PROCEDURES FOR MEASUREMENT OFSTEP VOLTAGE, SECONDARYNEUTRAL-TO-EARTH VOLTAGE,AND SOIL RESISTIVITY

Since the analysis in this paper will be particu-larly concerned with results obtained for SV and soilresistivity, the measurement procedures that wereemployed for these quantities need to be described.

Step Voltages

Step voltages (SV) in the stanchion or tie stallfarms were monitored continuously for a 12-hourperiod in one test stall. The stall was selected by ®rstestablishing (with a clip-on ammeter) the presence ofground current on the water line or other metallicstructure to which the barn neutral bus was grounded.On the assumption that the stall nearest to this bondwould have the largest cow-contact voltages, it was

8 Polk

selected for measurements [Hendrickson and Patoch,1998a,b]. The physical arrangements and equivalentcircuit for this measurement are illustrated by Figure 1.For SV measurements, connection to the stall ¯oorwas made after removal of packed bedding by using6.25� 6.25� 0.8 cm square aluminum blocks (B) withterminal screws, simulating hooves. Front and rear

hoof blocks were positioned approximately alongthe centerline of the stall and separated by 1.5 m.Electrical connection to the ¯oor was enhanced using7� 7 cm cotton squares (C) kept wet with a saturatedsaltwater solution using a wick (veterinary umbilicaltie) and salt water reservoir. The front and rear hoofblocks were spanned with a wood beam, which was

Fig. 1. Measurementofstepvoltage (SV). (a) Physicalarrangement: Terminalsa,bareconnectedtodifferent values of R1 for measurement of source resistance Rs. Source of the earth current isnot known, but the source resistance necessarily includes the contact resistance betweenmetalcontact blocks B and the floor through saturated cotton squares C. For details see text. For 12 hcontinuous recording of SV terminals a, b are connected to a 500O resistoranda high impedancevoltmeter (output storedincomputermemory). (b) Schematicrepresentationofearthcurrent paths(multiple sourcesreplacedbyasinglesource). (c) Theveninequivalent circuit of (b) withaddedloadresistor R1.

Cows,Ground Surface Potentials and Earth Resistivity 9

depressed at the center by using a jack post to the barnceiling. In barns that used rubber mats in the stalls,measurements were made with the mats in place.

The source resistance Rs was measured near thestart and end of each 12 h measurement period andcalculated by the expression Rs � R1��V0=V1� ÿ 1�where V0 is the open circuit voltage and V1 is thevoltage across the load resistor R1. An average sourceresistance was determined using three values ofR1 � 500, 1000, and 1500 O. Source resistancesranged from 256 O to more than 20 kO [Hendricksonand Patoch, 1998a]. Beginning and ending compar-isons of source resistance indicated adequate control ofsource resistance changes due to variable contactwetness and pressure. Simulating the impedance of acow between front and rear hooves, the low frequency(essentially 60 Hz) SV during the recording period wasmeasured across a 500 O resistor. Although averageand peak values of this voltage were recorded, theaverage value for the one hour of lowest electricity use,V-lu, will be examined in our discussion, since it andsoil resistivity was the electrical quantities mostsigni®cantly related to milk production (Table 1 andFigure 2).

Secondary Neutral-to-Earth Voltage

Secondary neutral-to-earth voltage (Vne) wasmeasured between the neutral bus at the barn panel anda reference ground rod located more than 100 m fromany ground connection of the farm electrical systemor the supply line [Hendrickson and Patoch, 1998a].Average values for each farm during `̀ 1-hour lowelectric use'' are shown in Table 2 and Figure 5.

Soil resistivity

Soil resistivity (r) was measured using acommercial (`̀ Vibroground'') 4-electrode `̀ Wennerarray'' [Grant and West, 1965] with a spacing of 5feet (� 1.524 m) between adjacent electrodes. Thus,the current (outermost) electrodes were 15 feet apartand the potential (innermost) electrodes were spaced 5feet. Since measurements were taken only with thissingle electrode spacing (a� 5 ft), the calculated rvalue is an apparent resistivity that assumes an earthwhich is electrically homogeneous, both laterally andin depth. Assuming a two layer earth with a top layer ofresistivity r1 bounded at the depth h by an in®nite layerof resistivity r2, it can be shown [Grant and West,

TABLE 1. Discrimination Between LP and HP Herds: Correlation with Milk/Cow/Day

LP herds HP herds Correlation coef®cientRisk Factor (Avg.) (Avg.) P valuea (r) P value

Use of mats in stalls (17 stanchion 0 of 9 5 of 8 0.0048 Not done Not doneand tie stall barns only)

Net energy in feed stuffs (percentage) 31.6 36.9 0.0059 0.635 0.0047Cow vaccination score (13 types 3.1 5.9 0.0109 0.722 0.0005

of vaccinations possible)Comfort score±cowsb 3.1 2.1 0.0134 ÿ0.772 0.0002Maximum AC voltage between 0.63 0.25 0.0334 0.175 0.4869

milk line and cow hoofsStall length (inches) 64.0 73.7 0.0446 0.452 0.1209Dry matter intake (pounds/cow/day) 44.3 48.8 0.0490 0.564 0.0147Soil resistivity in barnyard (ohm-m) 89.604 29.62 0.0506 ÿ0.233 0.3381Comfort scoreÐcalves 3.3 2.4 0.0543 ÿ0.219 0.3832Soil resistivity in the ®eld (Ohm-m) 97.264 28.30 0.0670 ÿ0.474 0.0406Average step voltage, 0.0070 0.00167 0.0727 ÿ0.471 0.0418

low electrical use (volt)Comfort scoreÐheifers 1.2 2.4 0.0778 ÿ0.348 0.1714Magnetic ®eld at the cow's back 0.26 1.24 0.0779 0.299 0.2437

during milking (milligauss)Average AC volts between milk 0.0662 0.0282 0.0832 ÿ0.195 0.4380

line and cow hoofs, low electricity use

Reproduced with permission from Staehle et al. [1998]Data is ordered from the lowest P value for the comparison of averages to the highest P value. Nineteen herds were included for all herdparameters except those indicated. LP, low milk production herds (45.9 lb/cow/day average); HP, high producing herds (67.2 lb/cow/dayaverage).aP value calculations were based on a two-sample t-test for all variables except for use of mats in stalls, for which a chi square test forindependent variables was employed.bCow comfort ratings were performed by the veterinarian on the research team using the following scoring system: 1� clean, dry,well-bedded; good ventilation. 3� adequate cleanliness, mostly dry, with some stale air. 5� dirty, wet, with little or no bedding andstagnant air.

10 Polk

1965] that r� r1 if (a/h) < 0.3. For the 5-footelectrode spacing used, this would require a depthh> 16 ft. However, from data given by Grant and West(their Figure 14-5), it can also be shown that for a morelikely farm situation of h� a� 5 ft, the ratio of the

apparent r, recorded in the ®eld study, to r1 is given by0.65< (r/r1) < 1.5 if (1/2)r1< r2<1. This r wasmeasured `̀ in the ®eld'' between 90 and 400 m fromthe barn, as well as in the barnyard. The ®eld valuesshowed signi®cant correlation with milk production

Fig. 2. Milkpercowperday (m/c/d)vs.V-lu:SVaverageduringlowusehour.ThePearsoncorrelationcoefficient r and its level of significance P on this and the other scatter plots (Figures 3, 5, 6) wereevaluated as in Mould [1989] pp.175 1̂77: P is the probability that there is no linear associationbetweentheabscissaandordinatevalues.All19 test farmsare included.

TABLE 2. Data for Each Test Farm

Farm m/c/d r V-lu Vne NEFidenti®cation lbs O-m Volt Volt % CVS CC

A 53.92 36.768 0.001 0.077 29.65 5 2B 74.64 28.918 0.001 0.084 38.94 5 1.5C* 66.5 25.086 0.005 0.818 36.95 6 3D 66.7 8.618 0.008 0.629 36.62 5 2.333E* 78.64 22.6 0 0.547 40.98 7 2F 31.34 19.916 0.002 0.412 27.13 5 4G 49.91 170.438 0.009 0.547 n 0 3H 25.67 36.002 0.002 0.165 28.28 0 4I* 69.14 19.152 0.001 0.132 39.17 7 2.67J 55.71 185.756 0.004 0.738 32.11 5 2.5K 46.08 141.71 0.014 1.328 33.38 0 4L 53.25 21.258 0.002 0.251 36.39 5 2.33M* 63.54 35.81 0.001 0.358 37.41 5 2.67N* 67.43 48.26 0.002 0.813 35.47 5 2O 51.91 11.3 0.001 0.228 25.80 5 2P 60 16.854 0.002 0.372 37.03 5 2.33Q 27.85 321.724 0.027 0.795 32.87 0 nP1 72.63 21.256 0.002 36.55 8 1P2 50.64 55.918 0.001 32.08 6 3.67

Abbreviations: m/c/d�milk per cow per day; V-lu� step voltage during low electricity use; Vne� neutral to earth voltage during lowelectricity use; NEF� net energy in feed stuffs, CVS� cow vaccination score (13 best, 0 worst); CC�Cow comfort score (1 best, 5worst). n� no data.*Farm using rubber mats in stalls. Farms P1 and P2 are `̀ parlor farms.''

Cows,Ground Surface Potentials and Earth Resistivity 11

(Table 1 and Figure 3) and will be considered in moredetail in the analysis below.

RESULTS OF THE FIELD STUDY

The large amount of data gathered by the ®eldstudy was subjected to statistical analysis by Dr. WillMarsh of the Department of Clinical and PopulationSciences at the College of Veterinary Medicine,University of Minnesota. The most salient results ofthis analysis are summarized in Table 1, which isreproduced from Staehle et al. [1998]. It indicatesthose variables, which exhibited the most signi®cantdiscrimination (lowest P-values) between HP and LP.The P value calculations were based on a two-samplet-test for all variables except for use of mats in stalls,for which a chi square test for independent variableswas employed. Cow comfort ratings were assigned bythe veterinarian on the ®eld study team, R. Schell,DVM, using a scoring system ranging from 1� clean,dry, well-bedded, good ventilation to 5� dirty, wet,with little or no bedding and stagnant air. Data onthe table are ordered from lowest P value for thecomparison of averages to highest P value. Nineteenherds are included for all variables except for the use ofmats in stalls, which is not applicable to the two farmswith parlor facilities. Table 1 also gives the correlationcoef®cient r between each variable and milk/cow/day(m/c/d) and its P-value, which depends on the scatterabout the assumed linear relation to m/c/d asexplained, for example, in Mould [1989].

Table 1 shows that many variables, normallyconsidered by veterinarians in the dairy industry, are

strongly correlated with milk production. Particularlynotable are net energy in feed stuffs, comfort scores,and vaccination history. However, Table 1 also showsthat average SV during the one-hour low electricity useperiod on the farms (V-lu) and soil resistivity in the®eld (rF� r) are signi®cantly, but negatively corre-lated with m/c/d. This relation is further con®rmed bythe fact that use of mats in stalls, which provideselectrical insulation, indicated highly signi®cant dis-crimination between (LP) and (HP). Figure 2 showsconsiderable scatter of m/c/d when SV is less than0.01 V, but a linear relation between m/c/d and SVabove that value. In view of the hypothesis discussedabove that V-lu� 10 mV is necessary for a possibleeffect on cow physiology, it is of interest to note thatwhen one considers only V-lu values above 9 mV inFigure 2, the correlation coef®cient between m/c/d andV-lu becomes 0.994. However, in view of the smallnumber (3) of farms over 9 mV, the P-value becomes0.069. SVs of 3 mVor less that were measured on 15 ofthe 19 farms have apparently no relation to m/c/d.Figures 2 and 3 and Table 2 show that for the three LPfarms where SV during low electricity use (V-lu) was9 mV or larger, the value of m/c/d decreased nearlylinearly with soil resistivity.

We were intrigued by the fact that both V-lu andrF indicate trends in the same direction, particularlysince `̀ intuitive'' examination would possibly suggestthat high r should lead to small earth currents andtherefore to low SV, opposite to what was observed(Table 1 and scatter plots of Figures 2 and 3). Closerexamination, however, will show that the observedrelation is what one should expect due to the

Fig. 3. Scatterplotofm/c/dvs. soilresistivity in field r.All19 test farmsare included.

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characteristics of electrical distribution to and on farmsand the construction of dairy barns.

CHARACTERISTICS OF RURAL ELECTRICITYDISTRIBUTION IN THE U.S.

To relate the observations to the electricitydistribution system, it is necessary to indicate someof its characteristics. The usual electrical connectionsto farms are illustrated by Figure 4. The primary, highvoltage side (7.2 kV line to ground in Minnesota) isusually a single phase line that can be as short as 100feet or as long as several miles. It originates on one ofthe phases of a 3-phase Y-connected system. Thegrounded neutral conductor of the single-phase line isbonded to the neutral of the more or less distant 3-phase line, which comes from a substation. At thetransformer, which is usually located on a pole at theentrance to the farm, the high voltage is stepped downto 240 V. The center of the low voltage winding (aswell as the transformer casing) is grounded; 120 Vloads on the farm are connected to one or the otherhalf of the secondary side, preferably (but rarely inpractice) in such a way that loads are `̀ balanced''resulting in zero net current through the central`̀ neutral'' wire. Heavy machinery is normally con-nected directly across the 240 V supply.

If the 120 V farm loads are not equallydistributed among the two 120 V circuits, substantialcurrent may ¯ow in the neutral wire. Since it has ®niteresistances (RN), different points along its length willbe at different potential. Generally, the distributionpanels at each building entrance on the farm areseparately grounded as indicated by P1 and P2 inFigure 4. If current ¯ows in the neutral wire withresistances RN, points P1, P2, and PT (the transformer

ground) will be at different potentials. This will causecurrent ¯ow through the earth or preferentially throughthe grounded metal structures (e.g., water pipes) whichexist in almost all barns. Sometimes metal housings ofequipment, which should always be grounded, are alsoelectrically connected to the neutral wire (a codeviolation!) and thus provide additional ground con-nections at still different potentials. Most of theundesirable ground current on the farm will ¯ow onelectrically connected metal structures and will causepotential differences, for example, between a metalwater trough and soil. However, if points A and B inFigure 4 (for example, panels at the farm home andin the barn) are at different potentials, some currentwill also ¯ow through the soil. The magnitude of thatcurrent will depend on ground resistivity, on thepotential difference along the neutral wire, andparticularly on the resistance of the various groundconnections.

In addition to the on-farm sources of earthcurrent, off-farm sources are also possible. These areof at least two types: those related to the primary feedline, which is grounded on the primary side of thetransformer in Figure 4 and those that are completely,or at least partially, independent of the farm electricalsupply. Considering ®rst the sources related to theindividual farm supply, we note that the primaryneutral is grounded at least every 400 m along thedistribution line and sometimes more frequently. Sincethe neutral wire on the primary side may be ofrelatively small size, a substantial fraction of theneutral current may ¯ow in the soil. In a survey of 48utility distribution systems in Minnesota [Hendricksonet al., 1995] mean earth currents for different utilitiesvaried between 0.14 A and 25.74 A, with an average of4.46 A for all utilities. If the exceptionally high valueof 25.74 A for one utility is excluded, the average forthe remaining systems is 3.98 A.

For safety reasons, for example to avoid ®re orother damage by excessive current ¯ow in case of anaccidental short circuit or lightning strike, the primaryand secondary neutral conductors at the transformerare normally rigidly connected. This will, however,cause return current of the primary feed to ¯owthrough the secondary neutral and over groundconnected metal structures on the farm, both undernormal operation and even if the farm circuit isdisconnected at the main switch. It also makes thecombination of primary and secondary grounds aterminal for any possible earth current circuit whoseother terminal may be the ground connection of adistant transmission line or other source. Sincepotential differences due to the current ¯owing throughthe conductive path between primary and secondary

Fig. 4. Typicalconnectionofsinglephaselinetoa farm.Pole trans-formerandpossible isolatingdevice�- are shown.

Cows,Ground Surface Potentials and Earth Resistivity 13

have been found to cause undesirable `̀ stray voltage''problems, isolation devices, as indicated in Figure 4,are used in some installations. These ground isolationdevices are normally open, but to provide safety, forexample during a lightning strike, they close when apreset threshold voltage between line and farm groundis exceeded. Several different types are in use and theirfrequency characteristics vary, so that while all devicesprovide isolation at 60 Hz under normal conditions,some provide no isolation at any time for higherfrequencies, and therefore for transients [Jenkins et al.,1995].

Since all ground rod or other ground connectionshave ®nite resistance and since any earth current willplace the earth at some non-zero value of potential (seeAppendix), any measured neutral-to-earth voltage Vne

will indicate earth currents. On farms without iso-lators, these currents could originate on the primaryside and be due to the earth return current on the utilityline leading to the farm. Measured values of groundrod resistance vary between a few and several hundredOhms, with an average of about 50 O; the values areweakly correlated (r� 0.64) with soil resistivity[Hendrickson et al., 1995].

We consider next the possible off-farm sourcesof earth current that are not directly related to thedistribution line to the particular farm. It is apparentthat the multiple ground connections on the farm (atone or several different potential levels) can provide aterminal for an earth `̀ circuit'' whose other terminalmay be the different earth potential due to some distanttransmission or distribution line or other source, suchas a distant current-carrying water or oil pipe line.Approximating such a distant source and a localground rod as a two-point source-sink system, we notefrom Eqn. A-(8) in the Appendix that even a current of1 mA from a distant source will cause a ground surfacepotential difference of 24 mV across 1.5 m when thelocal ground rod is at a distance of 2 m and r is400 Om. Although a completely rigorous analysis ofearth currents due to transmission or distribution lineswould have to include magnetic ®eld induction effects[Meliopoulos, 1988; Olsen, 1996], they would give notmore than very minor corrections to surface potentialswhen only very short segments (< 400 m) of 60 Hzdistribution lines between grounding points areconsidered.

ANALYSIS OF MEASURED ELECTRICALVARIABLES

In the survey summarized in Tables 1 and 2 andFigures 2 and 3, the correlation of milk production(m/c/d) with step voltage V-lu, as well as with earth

resistivity r, was signi®cant. However, as indicated inTable 2, ®ve of the test farms used rubber mats in stalls.Since these mats provided substantial, but unknownresistance between concrete ¯oors and the measure-ment points, the V-lu data from these farms are notuseful for any analysis designed to establish possiblerelations to earth currents. Two additional farms were`̀ parlor farms'' where animals may move rather freelyto different locations in the barn or may spend mosttime outside. These seven farms, six with V-lu� 2 mVand one with V-lu� 5 mV, were therefore excludedfrom analysis exploring relations between the differentelectrical variables. For the remaining twelve farmsthe step voltage during low electricity use, V-lu iscompared with the neutral to earth voltage, Vne inFigure 5, and with soil resistivity r in Figure 6. Whilethe scatter plot of Figure 5 suggests a possible linearrelation between V-lu and Vne, the correlation coef®-cient is only 0.693, compared with r� 0.850 forcorrelation between V-lu and r in Figure 6. Thesuggested association within each variable pair is r2

[Sheskin, 1997] or, respectively, 48% and 72%. (Moreprecisely, r2 represents the proportion of variances inone variable that can be accounted for by variance inthe other variable). It is apparent that neutral-to-earthvoltage, measured at the distribution panel in the barnis not as strongly correlated with V-lu as is soilresistivity measured in the ®eld. We were at ®rstsurprised to ®nd the strong V-lu to r correlation, sinceresistivity of the concrete barn ¯oor is likely to bedifferent than resistivity measured in the ®eld (it wasnot possible to drive electrodes for a Wenner array intothe barn ¯oors). However, it is shown in the Appendix(Eqn. A-4) that for the usual barn ¯oor constructionÐless than 8 inches (� 20 cm) of concrete and crushedrockÐthe surface potential depends on the resistivity

Fig. 5. Scatter plot of neutral-to-earth voltage V-ne vs. step vol-tageV-lu.Twoparlor farmsandfive farmswithrubbermatsin stallsareexcluded.

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of the underlying earth, which is likely to be the sameas that measured in the ®eld.

Both Figures 5 and 6, as well as Figures 2 and 3,indicate considerable clustering of points below V-luvalues of 2 mV. Examination of Table 2 shows thatseven (78%) of the nine HP farms with m/c/d> 60 lbhave V-lu� 2 mV and the other two (D and C) haveV-lu� 8mV. Also 70% (7 out of 10) of the LP haveV-lu� 4 mV, but 30% of the LP have V-lu� 9 mV.Thus, while most farms (16 out of 19 or 84%) in thesample had V-lu� 8 mV, the highest V-lu (� 9 mV)were only found among the LP. The farm withthe highest V-lu (� 27 mV) also had the highest r(� 322 Om).

CONCLUSIONS

1. As expected, many different environmental condi-tions that are completely unrelated to the electricaldistribution system can and do affect milk produc-tion on dairy farms. Nevertheless, in the investi-gated sample of 19 dairy farms, the step voltageduring low electricity use on the farm V-lu was 4.2times higher on average in the 10 below-averageproducing farms (LP) than in the nine farms (HP)with above average milk production.

2. The Minnesota ®eld study did not ®nd `̀ crediblescienti®c evidence to verify the speci®c claim thatcurrents in the earth or associated electricalparameters . . . are causes of poor health and milk

production in dairy cows'' [Staehle et al., 1998], butneither did it ®nd any evidence that currents in theearth from on- or off-farm sources are not the sourceof the small step voltages which were measured orthat these SVs cannot affect cow health.

3. The three farms with V-lu> _9 mV contributedsigni®cantly to the difference in m/c/d between LPand HP. If they were to be excluded, the differencein averages of m/c/d between LP and HP would besmaller (19.3 instead of 21.3) (compare Table 2 andFigure 2). All three were among the 10 LP farmsselected at random from the 10% of Minnesotadairy farms with the lowest milk production.

4. The inverse relation between V-lu> 9 mVand m/c/dshown in Figure 2 involves the farms identi®ed asG, K, and Q in Table 2. Examination of Table 2shows that net energy in feed stuffs (NEF) isrelatively high for farms K and Q (35.2% averagecompared with 31.6% for all LP farms) and thus isunlikely to contribute to low m/c/d. However, theinverse relation between V-lu> 9 mV and m/c/dcould be accidental, because all three farms havezero (the lowest possible) cow vaccination score(CVS) and two (G and K) have also poor cowcomfort scores (3.5 averageÐworse than the 3.1value for all LP farms). The only other farm (H)in the sample with CVS� 0 has also exceptionallylow m/c/d despite small V-lu (� 0.002 V). Thepossibility that V-lu> 9 mV may contribute to lowm/c/d can nevertheless not be excluded, particularly

Fig. 6. Scatterplot of soilresistivity in field rvs. stepvoltageV-lu.

Cows,Ground Surface Potentials and Earth Resistivity 15

since neither CVS nor CC can explain the lineardecrease of m/c/d with increasing V-lu among farmsG, K, and Q (Figure 2).

5. When farms using electrically insulating rubbermats in stalls, as well as two `̀ parlor farms'' withrelatively freely moving animals are excludedfrom the sample, the weak, but statistically signi-®cant correlations between milk production andeither step voltage (r�ÿ0.471) or soil resistivityr (r�ÿ0.476) suggested by Figures 2 and 3, appearas a strong correlation (r� 0.850) between V-lu andr for the remaining 12 farms (Figure 6).

6. Step voltage (V-lu) is also correlated (r� 0.693)with the voltage measured between secondaryneutral and ground (Vne) as shown in Figure 5,but not as strongly as with r. A perfect linearrelation between V-lu and Vne could only beexpected if the conducting paths between thesecondary neutral and various grounding points inthe barn were identical in all farms; this is clearlynot the case. A perfect linear relation between V-luand r could only be expectedÐassuming a singlesource-to-sink pathÐif the ratio of current to thesquare of the distance to the nearest grounding pointwere identical for all farms (Eqn. A-8).

7. The amplitude of earth currents near primarydistribution lines appears to depend primarily onneutral return current, the size of neutral wires, andresistance as well as location of electrical system-to-earth connections. With a predetermined levelof earth current, one can then expect a strongcorrelation between step voltages and soil resistiv-ity (compare Eqn. A-8).

8. At present it is not known whether and how thelong-term exposure to step voltages above 9 mVcan affect health and/or milk production of dairycows. This can only be established by laboratoryexperiments where major variables known to affectanimal health can be controlled.

9. In view of the results discussed above, it presentlyappears to be desirable to measure soil resistivitywhen a dairy farmer reports possible electricity-related cow health and production problems that arenot explainable by other variables (e.g., absence ofvaccinations). A very detailed investigation of theon- and off-farm electrical distribution systems isthen indicated if r of the uppermost earrth layer (aswas measured for the present report) is larger thanabout 150 Om.

ACKNOWLEDGMENT

The author is indebted to Mr. Riley Hendrickson,who performed the electrical measurements in the ®eld

study and with whom this paper was discussed in greatdetail. Also acknowledged are the many contributionsto the design of the Minnesota ®eld study by theauthor's other colleagues as `̀ Science Advisors'' to theMinnesota Public Utilities Commission: L.E. Ander-son, H.E. Dziuk, A. Furo, D. Hird, A.R. Liboff, J.L.Richardson, R.W. Staehle, and L.E. Stetson and by theliaison with the PUC and PUC Research DirectorPatricia Hoben. Credit is also due to R.C. Hendrick-son's colleagues on the team that performed themeasurements during the summer of 1997, J. W.Patoch, R. Schell DVM and W. Bickner, as well as toDr. Will Marsh who did the statistical analysis of thedata shown in Table 1 and Figures 2 and 3. The authoralone is responsible for the analysis presented here andthe conclusions drawn.

REFERENCES

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Burchard JF, Nguyen DH, Richard L, Block E. 1996. Biologicaleffects of electric and magnetic ®elds on productivity ofdairy cows. J Dairy Sci 79:1549±1554.

Burchard JF, Nguyen DH, Richard L, Young SN, Heyes MP, BlockE. 1998. Effects of electromagnetic ®elds on the levels ofbiogenic amine metabolites, quindinic acid and b-endorphinin the cerebrospinal ¯uid of dairy cows. Neurochem Res23:1527±1531.

Burchard JF, Nguyen DH, Block E. 1999. Macro- and traceelement concentrations in blood plasma and cerebrospinal¯uid of dairy cows exposed to electric and magnetic ®elds.Bioelectromagnetics 20:358±364.

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Dawson TW, Caputa C, Stuchly MA. 1997. High-resolution organdosimetry for human exposure to low-frequency electric®elds. IEEE Trans Power Delivery 13:366±373.

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Hendrickson RC, Michaud M, Bierbaum A. 1995. Survey todetermine the age and condition of electric distributionfacilities in minnesota. Report 1: Analysis of overheaddistribution feeder testing data. St. Paul, MN: MinnesotaPublic Utilities Commission.

Hendrickson R. 1997. On-farm research pilot ®eld studyÐelectrical measurements presentation for the science advi-sors to the Minnesota Public Utilities Commission,December 15, 1997. St. Paul MN: Minnesota P.U.C.

Hendrickson RC, Patoch JW. 1998a. Electric environment on17 dairy farms. ASAE, 2950 Niles Rd., St. Joseph, MI49085-9659: Proc 1998 ASAE Annual InternationalMeeting.

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Hendrickson RC, Patoch JW. 1998b. AC earth current on dairyfarms. ASAE paper no 983002. ASAE, 2950 Niles Rd., St.Joseph, MI 49085-9659: Proc 1998 Annual InternationalMeeting.

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APPENDIX

Surface Potential Difference BetweenTwo Grounded Electrodes: Relation toEarth Current and Earth Resistivities

The problem is illustrated by Figure 7 and theanalysis is based on Smythe [1989]. Current I isinjected into a two-layer earth by a pair of electrodes,separated by a distance 2b. The midpoint between theelectrodes is located at x� 0. The y-coordinate(positive, out of the plane of the paper) is perpendi-

cular to the straight line between the electrodes, andthe z-coordinate is the vertical distance into the soil,measured from the surface. The earth resistivities arer1 for 0 � z < a and r2 for z � a. Smythe [1989]showed that the potential at the surface V � VS isgiven by

VS � r1I

2p

�10

1ÿ beÿ2ka

1� beÿ2kaJ0�kÿ�dk A-�1�

where ÿ� radial distance from either electrode in thex-y plane,

b � r1 ÿ r2

r1 � r2

A-�2�

and

k2 � 1d2Z

Zdz2: A-�3�

Z is the z-dependent part of the solution of Laplace'sequation in cylindrical coordinates V�R�Z, where Ris a solution of Bessel's equation and � a sum oftrigonometric functions. The value of the separationconstant k follows from the boundary conditions of thepresent problem: continuity of V at z� 0 and z� a,V� 0 at z�1, continuity of z-directed current density(1/r)(dV/dz) at z � a and (dV/dz)� 0 at z � 0. Fordetails see Smythe [1989, pp. 157, 180, 189, 192, and263].

If the thickness of the layer near the surface isvery small compared with the distance b or if b� 1, VS

becomes practically only a function of r2 rather than ofr1 and r2. If ka! 0 as k!1, it follows from A-(1)and A-(2) that

VS � I

2pr1

r2

r1

�10

J0 kÿ� �dk � Ir2

2pÿ: A-�4�

Fig. 7. Twolayerearthwithelectrodesat x � � b.

Cows,Ground Surface Potentials and Earth Resistivity 17

This result can also be obtained by a series expansionof the integral in A-(1) in powers of b.

To indicate the validity of A-(4) for the problemof measurements of VS over a concrete ¯oor, i.e., toshow that VS will depend on the conductivity r2 ofthe substrate (which is essentially the conductivitymeasured `̀ in the ®eld''), we consider the followingexample: distance from the source or sink of currentÿ � 10 m, thickness of concrete and underlying gravel(if any) a � 0:2 m. If the resistivity of the concrete¯oor (which is usually porous and contains somewater) r1� 2r2, where r2 is the conductivity in the®eld (a � 0), b� (1/3) and the error in VS resultingfrom using A-(4) rather than A-(1) is not more than4%.

For electrodes at y � 0, x � b and y � 0, x � ÿb

ÿ� � xÿ b� �2�y2h i1=2

ÿÿ � x� b� �2�y2h i1=2

:

A-�5�

Superposition of potentials due to electrodes at ÿ� andÿÿ de®ned by A-(5) and now assuming a uniform earthconductivity r � r1 � r2, as for the measurement of

`̀ conductivity in the ®eld,'' we obtain from A-(4) andA-(5)

VS � rI

2pxÿ b� �2�y2

h iÿ1=2

ÿ x� b� �2�y2h iÿ1=2

� �:

A-�6�

This expression is the basis for evaluation of r by theWenner array where 2b � 3s and VS is measured aty � 0 and x � ��s=2�. The potential difference �VW

between the points at x � �s=2� and x � ÿ�s=2� is then

�VW � rI

2ps: A-�7�

Evaluating the open circuit voltage �VOC between twopoints separated by a distance x1 near one of the sourceor sink electrodes at x � �bÿ d�, where d� b and�x1=2� � d, one ®nds

�VOC � rIx1

2pq2: A-�8�

18 Polk