SR-4 STRAIN GAGE INSTRUMENTATIONFOR POWER MEASUREMENT

by

Gerald C. ZoerbAgricultural Engineering Department, South Dakota State College, Brookings, S.D.

During the past ten years, the SR-4electrical resistance strain gage hasbecome an extremely important device in the research and developmentfields of Agricultural Engineering.With suitable instrumentation theSR-4 strain gage may be used toaccurately measure physical variablessuch as force, pressure, torque, vibration, and displacement in addition toits fundamental use in strain measurement. When the SR-4 strain gage isused to measure a variable such astorque, the device is called a transducer. A transducer is defined as anelectromechanical device which converts a physical quantity being measured (temperature, pressure, torque,etc.) to a proportional electrical output.

In testing agricultural machinery,power measurement using SR-4 straingages is simply the aplication of atransducer to measure a force or a

torque. Knowing the appropriatespeed, these variables may be readily converted to horsepower. Whereconsiderable testing is to be done,however, an electronic integrator asdescribed by Avery and Yoerger (2)would be desirable. In torque measurement for example, the integratoroutput is in terms of horsepower, theproduct of the average torque andaverage rpm for that test.

Detailed discussions of the application of SR-4 strain gages to farmmachinery design and development,have been reported by Burrough (5),Jensen (8), Lauderdale (9), andSchoenleber (13). The primary purpose of this paper is to discuss SR-4strain gage instrumentation from thestandpoint of basic circuits used andthe determination of circuit parameters. As an application, an SR-4 drawbar dynamometer is described.

STRAIN GAGE PRINCIPLE

The bonded wire resistance strain

gage consists of a grid or pattern ofsmall diameter wire (0.001") cemented with specific adhesives to the partor member being tested. The changein surface dimensions of the member

under load causes a similar changein the length and cross section of the

gage wire, with a resultant change inelectrical resistance of the gage. If themember is in tension the gage resistance increases. The opposite effectoccurs for a compressive load. Theamount of the change in resistance inrelation to the change in length is ameasure of strain sensitivity and isdefined as the gage facter:

G=AR/R-r AL/L [1]

where G=gage factor

AR and AL=changes in resistanceand length respectively.

R=initial resistance of the gage

L=initial length of wire.

In the above equation AL/L is bydefinition, the unit strain, microinch/inch, and will be designated bythe letter "e" in this paper. For proper use of SR-4 strain gages, it is apparent that the material to which thegage is cemented must not be strainedbeyond the elastic limit.

A few statements regarding SR-4strain gage types and characteristicsare necessary for background. A complete discussion is given by Perry andLissner (10) and by Schoenleber (13).SR-4 strain gages are classified by filament material and by mounting materials. Type A gages are made fromadvance wire (45% nickel and 55%copper) and have a gage factor ofaround 2.0 and a resistance of 120ohms. Type C gages made from iso-elastic wire (36% nickel, 8% crom-ium, 0.5% molybdenum, remainderiron), have a gage factor of about 3.5and a resistance of about 500 ohms.A high gage factor is desirable sinceit increases the output and thereforedecreases the amount of amplificationrequired. There is a linear relationship between unit change in resistance and unit change in strain for theadvance and isoelastic gage wires. Theisoelastic gage is much more temperature-sensitive than the advance gage;however, with either type the effect oftemperature on changing gage resistance may be cancelled out in aWheatstone bridge circuit. Straingages are available in gage lengthsfrom 1/16 to 6 in. Information per

28

taining to gage selection for variousapplications may be obtained fromthe Baldwin-Lima Hamilton Corporation who manufacture all SR-4 strain

gages in the United States.

To use the bonded strain gage as atransducer, it is necessary to measurethe change in resistance which occursin the gage when the member to whichit is attached is placed under load. Fora 120 ohm gage having a gage factorof 2.0, and subjected to a stress of1000 psi, the change in resistance ARis given by equation [I].

AR=e G R=33 x icr6x 2.0 x 120=0.008 ohm. Strain e=S/E where Eis the modulus of elasticity for steel,taken as 30 x 10° psi. To accuratelymeasure this small change in resistance, a Wheatstone bridge circuitmust be used.

BALANCED WHEATSTONE

BRIDGE CIRCUIT FOR STATIC

STRAIN MEASUREMENT

At Balance:

I] R2 = I2 R4

1 ~ ^ 3

Figure I. Wheatstone Bridge Circuit - Balanced

The circuit shown in Fig. 1 is anexample of the null balance methodof strain measurement. Ri is an activegage, R2 is a "dummy" or unstrainedgage to provide temperature compensation, R3 and R* are precession wirewound resistors to complete the bridgecircuit. At balance the potentials atN and P are equal and thus no current flows in the galvanometer.

An increase or decrease in strain inthe member to which Ri is attached,will cause an unbalance in the circuit.The bridge is re-balanced by adjustment of R3. The adjustment ofR3 may be incorporated into a dialwhich is calibrated in micro-inches ofstrain. The difference in the initialand final strain readings gives theamount of strain suffered by the straingage. This strain can be convertedinto force or torque units in a transducer application. Fig. 1 representsthe elementary principle of the nullbalanced Wheatstone bridge althoughcircuits of commercial instrumentsare much more elaborate (10).

UNBALANCED WHEATSTONEBRIDGE FOR STATIC STRAIN

MEASUREMENT

Although the null balance Wheatstone bridge circuit has greater accuracy than the deflectional or unbalanced Wheatstone bridge, it has otherdisadvantages. The principal objection to the null balance circuit isthat it must be rebalanced after loading or for each degree of loading.With the unbalanced Wheatstonebridge circuit, the galvanometerdeflection is a measure of thestrain or load applied and no nullbalancing or computation is requiredfor each reading. At balance or zerostrain the meter reading is zero at midscale; movement to the right can indicate tension while movement to theleft indicates compression. Anotheradvantage of the deflectional or unbalanced bridge circuit is that it canindicate the magnitude (and sign) ofslow variations in strain with timewhich cannot be shown on the nullindicator. With the null balance circuit there is only one position wherethe meter needle indicates the correctvalue, namely at null balance.

It is often impossible to purchaseexpensive strain gage equipment.Clyde (6) and Jensen (8) have shownhow inexpensive strain gage transducers can be constructed using anunbalanced Wheatstone bridge circuit. The following analysis is presented as a guide to the design of astrain gage transducer circuit. Theprincipal considerations in selectionof the parameters are bridge supplyvoltage, bridge output voltage, andgalvanometer or meter current.

Fig. 2 shows a Wheatstone bridgewith four active gages. The bridge input voltage is limited by the powerlevel at which the strain gage canbe operated without danger of electri-

UNBALANCED WHEATSTONE

BRIDGE CIRCUIT

ANO

EQUIVALENT CIRCUIT

N

RT *5"^r-oX Ro

fV"V/™*P

#R9

Figure 2. Unbalanced Wheatstone Bridge Circuit andEquivalent Circuit.

cal overheating. This level is determined by the thermal conductivity ofthe test member. Aronson and Nelson(1) quote values of one-fourth wattfor small metal members up to onewatt for large steel and aluminummembers. For 120 ohm gages this allows a current of 45 to 90 ma throughthe gage. The allowable bridge voltage (Fig. 2) is E= L (R, -f R,), neglecting the very small current thatflows in the galvanometer when thebridge is unbalanced. Assuming anallowable current of 50 ma, the bridgesupply voltage would be 12 volts.

The formula for bridge output voltage is obtained by the use of Thev-enin's theorem which may be statedas follows: Any network with two accessible terminals may be replaced byan emf acting in series with an impedance; the emf is that between the terminals when they are unconnectedexternally, and the impedance is thatpresented by the network to the terminals, when all sources of emf inthe network are replaced by their internal impedances. Applied to Fig.2, Thevenin's theorem states that theentire bridge circuit may be replacedby an emf, Eo and an impedance Roreacting in series as shown in theequivalent circuit, Fig. 2 (c). Theemf, Eo, is the open circuit voltageacross the two accessible points NP.The impedance, Ro is that seen bythe galvanometer or amplifying device looking into the bridge circuitfrom the two points.

The first step is to find the differences in potential between N and Pwith switch S open. With four activegages, if Ri is strained in tension R4will also be in tension, while R2 andRa will be in compression. Assumingthe magnitude of the tensile and compressive strains to be equal, gages Riand R» will increase in resistance byAR while R2 and R3 will decrease anequal amount. The voltage at N interms of the bridge voltage and gageresistance is given by:

29

/R,

Vn=E (-R7R.+AR+AR+R, - AR

/Ri+aR \\—£RT )= E

)

since Ri=zR». Similarly the voltage atP:

Vf=K (I'"- )The expression for the output voltage,Eo may be written as:

Eo=Vn-V/3

/Rt+AR _(R3-AR) \\ 2Ri 2R. /Kl

And since Ri=Ra, Eo=EaR

~RT[3]

From equation [1],aR/Ri=G e, whichwhen substituted in equation [3] yieldsEo=E G e [4]If the number of active gages is lessthan four, the output is reduced proportionately. Equtation [4] shows theimportance of using as a high abridge supply voltage as possible andthe value of a high gage factor.

The use of four active gages as inthe bridge circuit of Fig. 2 providesmaximum output for a given gagetype and in addition has automatictemperature compensation. Examination of equation [2] shows that an apparent increase in strain due to atemperature rise, will be cancelled outin the adjacent bridge arms. As indicated in Fig. 2 (b), the battery isassumed to have negligible resistance,which is permissable for most bridges.The circuit impedance Ro, with Eremoved is found by:

Ro= (R'+RQ JR-+R0Ri+Rs+Ra+R*

Since Ri=R2=R3=rR4, equationreduces to: Ro=Ri

5

6

The equivalent circuit of Fig. 2 (c)can be used to calculate the galvanometer current Ig:

Ig —Eo E G e

Ro+Rg Ro+Rg [7]

A general expression for current inthe microammeter or galvanometerfor a given strain is:

Ig=G E N e

4 (R+Rg) [8]

where N=the number of active gagesin the bridge and R=bridge arm resistance (R=Ro for a bridge havingall arms of equal resistance)

Since the voltage drop across theindicating meter Eg =Ig Rg, it followsfrom equation [7] that

Eg=EoRg

R„-}-Rg P.

The factor Rg/ (Ro-f-Rg) gives the reduction in output voltage from theopen circuited to the loaded condition. If the bridge output is fed to apotentiometer circuit which may beconsidered as having infinite resistance, equation ([9] shows that Egis essentially equal to Eo.

A variable resistance is usuallyplaced in series with the battery sothat the bridge voltage may be maintained at a constant value. This vari

able resistance also allows for some

adjustment of bridge output voltageso that convenient scale deflections

can be obtained during the calibration process. Equations using Kirch-hoff's laws become quite involved butby the Thevenin method the calculations for Eo and Ig are only slightlylonger.

c (/>.

WHEATSTONE BRIDGE WITH RESISTANCE

Figure 3.

THE BATTERY CIRCUIT.

From Fig. 3 the bridge resistanceRb, is given by:

(R.+R-) (R.+RQ— Rt+R^-I-Ra-I-R,

Note the difference between Rb andRo; although for a four arm straingage bridge, the numerical value isthe same. The net supply voltage isE, =E—IbRa where lb is the currentfrom the battery and lb = E

Rb+RT

Substituting this value for lb inthe above equation and simplifyinggives:

Rb + Ra l J

The value Et is used as the voltageimpressed on the bridge (instead ofE) to compute Eo of the Thevenincircuit using equation [2]. The impedance Ro may be found by employinga delta to wye transformation of threeof the resistances followed by paralleland series combinations (14). However, for small unbalances, such as encountered in a strain gage bridge, Ramay be ignored and Ro, the resistancefrom N to P, computed as (Ri-f-R«)in parallel with (Ra-f-R.) as before.

CALIBRATION

The most common method of calibration used in the Wheatstone bridgecircuit is to shunt a relatively largeresistor into one leg of the bridge.This operation causes the bridge tobe unbalanced and can be considered as an artificial or simulated strain.

When the resistor Rp is shunted inparallel with Ri (Fig. 3) the equivalent resistance between points A andB is R. The change in resistance.

&R=Ri-R=Rr-Ri Rprt+tr;

Rr

Rt+Rp

rm

ARFrom equation [1], e= •^—rr

Substituting the value for AR in equation [11], gives:

e=Ri

G (R.+Rp)[12]

Equation [12] gives the magnitude ofthe simulated strain produced whenshunting Rp with Ri which causes aresistance change between A and B ofAR. The bridge unbalance with fouractive gages will be four times as greatfor a given actual strain, e, so equation [12] must be divided by the number of active arms, N:

[13]Rt

GN (R.+Rp)

To extend the calibation range ofthe transducer, more than one resistor can be shunted with Ri. The required magnitude of this resistor foran expected strain can be calculatedfrom equation [12].

By making Rp equal to 100,000ohms the value of Ri+Rp is essentially 105 ohms, so equation [13] may bewritten:

e=:R,x 10-5

GxN

The rheostat Ra, (Fig. 3) may beadjusted slightly so that the meter or

30

chart indication will read directly inthe transducer units, such as ounds offorce.

APPLICATION OF BRIDGE

THEORY TO A STRAIN GAGE

DRAWBAR DYNAMOMETER

In the fall of 1958, tests were conducted at South Dakota State Collegeto determine the effect, if any, ofspraying deep rooted legumes such asalfalfa, on the subsequent draft requirements in plowing. There hasbeen considerable farmer speculationthat chemical treatment of the alfalfa

plant would destroy or decay thetough roots and thereby sufficientlyreduce the energy requirements forplowing to more than pay for thechemical application. A strain gagedynamometer similar to the one described by Clyde (6) was designed*for use in these tests. With a maxi

mum pull of 5000 pounds, the strainat midspan of the beams where thegages are located, is lOOOpin/in, whichcorresponds to an outer fiber stress of30,000 lb. per in2. Common SAE 1020steel was used.

It was desirable for these tests tohave a record of the draft as the plowmoved across sprayed and check plots.Fig. 4 shows how the Varian recorderwas connected into the circuit used

by Clyde. The instrumentation isshown in Fig. 5. The O-20 microam-

PHYSICAL AND ELECTRICAL LOCATIONS Of, SR-4 STRAIN GAGESFOR DRAWBAR DYNAMOMETER

Figure 4. Physical and electrical locations of SR-4strain gages for drawbar dynamometer.

meter housed in the control box 3,was used to indicate pull for classlaboratory demonstrations when itwas not necessary to use a recorder.The control box and the dynamometer provided an indicating dynamometer at a total cost of approximatelysixty dollars. For recording it wasnecessary to use the inverter 2, to supply 60 cycle 110 volt power to runthe Varian recorder, 5. The old plowseat shown in Fig. 5, allowed a second tractor rider, who could markthe chart as each plot was traversed.

*The dynamometer was designed andconstructed by Mr. Donald Hamann,South Dakota State College, as partialcredit for a course in instrumentation.

As an example of the bridge theoryoutlined above, the following calculations are made for the strain gagedynamometer circuit using the recorder:

R,=R.=Ra=R4=120 ohms(SR-4, type A-5 gages)

The G-10 Varian recorder lias arange of 0-10 millivolts. For the maximum pull expected the bridge outputvoltage should be 10 mv. Using equation [4], the bridge supply voltage iscalculated as:

Eo

Gxe

0.010

:2.TJx().001=5.0 volts

Using a variable resistor of 0-1000ohms for Ra and a six volt battery,provided a means of obtaining a con-slant bridge supply Et, of fivevolts. With the maximum of six volts

applied to the bridge (Ra set at zero),the gage wattage is only 0.075 watts.

The three 25K resistors in Fig 4(a) are used to obtain initial bridgebalance, and to provide a dampeningeffect when the microammeter is

used in the circuit.

By equation [13], the simulatedstrain is:

R, 120

Figure 5. Instrumentation for Alfalfa Plowing Test!I. Tractor BjHery; 2. nverter (6V DC—110 VAC);3. Control Bjx; 4. Strain gage; 5. Recorder

SR-4 TORQUOMETERSStrain gage torquemeters have been

designed to measure torque in machine shafts anil have been described byBurrough, Jensen and others (4) (5).(8) (11) (12) (13). Inmost cases thesetorquometers transmitted signals fromthe rotating shaft to stationary contacts by copper disks rotating in amercury pool. Commercial units employ slip rings. The circuit principles

for a strain gage torquometer aremuch the same as those outlined forthe drawbar dynamometer. The gagesare cemented to the shaft at angles of15 degrees to its axis, thus placingtwo gages in tension and two in compression. Preliminary calculationsshould be made to determine thebridge output expected. Usually thebridge output is amplified and recorded with a commercial oscillograph.

DYNAMIC STRAIN MEASURE

MENT (INDICATING)

Dynamic strain means a considerable variation in strain during a shortinterval. For dynamic measurements,circuits more complex than those described for static measurement, arerequired. It is unlikely that the average engineer will design his own instrumentation as may be done forstatic strain indication. Furthermorelittle knowledge of instrumentation isrequired for operation of commercialunits. It is desirable, however, fromthe standpoint of instrument selectionto consider the types and characteristics of some typical circuits. The basicWheatstone bridge and potentiometercircuits are used in measuring dynamic strains. The table below is asummary of four circuits used to indicate strain on an oscilloscope.

BASIC WHEATSTONE BRIDGE CIRCUIT AND ASSOCIATED

INSTRUMENTATION FOR SENSING DYNAMIC STRAIN

Bridge Supply Coupling and/or Amplification Strain Measurements Indicated on Oscilloscope

Condenser-coupled, audio-frequency amplifier.

Direct coupled, D.C. amplifier

Chopper and audio-frequencyamplifier

L"GxN(R-fRp) 2x4 (120-|-36,000)= 415p.in/in.

From equation [4], this is an outputvoltage of:

Eo=E G e=5x2x415xl0-i=4.15mv.

The rheostat, Ra, was adjusted togive this value on the Varian chart,i.e., the pen was set at 41.5 lines. Astain of 415^in/in is equivalent to astress of 12,450 lb. per in2. (E = 30xl0"lb/in2). This bending stress substituted into the flexure formula for thedynamometer beams correspond to apull of 2010 pounds. Calibration ina testing machine checked the calculated values closely. As a convenientscale calibration, the rheostat Ra, wasadjusted to give 4mv (40 chart lines)when the testing machine load was2000 pounds. Thus the number 61chart lines multiplied by 50 yieldedpull in pounds. With the above setting for Ra, the 36K resistor shuntedwith Ri produced a chart deflectionof 38.5 lines. During the field tests, aperiodic calibration or check wasmade by shunting the 36K resistorwith Re and adjusting Ra to give38.5 lines on the chart.

Results of the draft requirementsfor plowing sprayed and unsprayedalfalfa have been reported by Ham-ann and Zoerb (7).

1 D.C.

2 D.C.

3 D.C.

Dynamic only

Static and dynamic

Static and dynamic

Static and dynamic4 A.C. Audio-Ire

quency oscillator Audio-frequency amplifier

static; and dynamic; strain

recording

For static strain recording a self-balancing Wheatstone bridge used inconjunction with a potentiometer circuit is often used. The unbalanced

signals up to 100 cps., the basic sys-an imposed strain is amplified andused to drive a motor which rebalan

ces the circuit. The balancing motor isconnected mechanically to a recording pen. For measurement of dynamicsignals u pto 100 cps., the basic system used is to amplify the bridge out

31

put which in turn drives a galvanometer having a pen directly attachedto it. Most recorders used in strain

gage work can be classified either as agalvanometer type or a self-balancingpotentiometer recorder (3). The galvanometer type may be direct writingor may use the light beam technique.Some direct writing recorders have afrequency response of up to 1000 cps.Frequency response of 5000 cps. arepossible with the light beam type using light sensitive chart paper and asensitive galvanometer. For dynamicvariations above the frequency response of the galvanometer recorder,the oscilloscope must be used. Tech-

niques have been developed to photograph high frequency strain signalswith an oscilloscope camera operatingon the Polaroid Land principle.

Selection of strain gage amplifyingand recording equipment require theconsideration of the following factors:

1.—The type of strain to be measured(static or dynamic) and therefore thefrequency response required. For thepotentiometer type the full scale balancing time is important; the shorterthe better.

2.—The sensitivity of the instrument in mv. per chart line and themeasurement range.

3.—The number of chart speedsavailable and the type of markingwhether ink or inkless.

4.—Single or multiple channel.

5—Input and output impedance sothat components may be electricallycompatible.

6.—The availability of the equipment and its cost.

Most of these factors are includedin the instruments specifications.

SUMMARY

Transducer applications of the SR-4bonded electrical resistance straingage have become an important toolin machinery design and testing. TheWheatstone bridge is the basic circuitused for static and dynamic strainmeasurement. An analysis is made ofthe unbalanced Wheatstone bridgecircuit as applied to an SR-4 straingage drawbar dynamometer. Instrumentation for dynamic measurementis discussed briefly.

REFERENCES CITED

l.Aronson, M. H. and Nelson, R.C.Strain Gage Instrumentation, Instruments Publishing Company,Pittsburgh 12, Pa., 1958.

2. Avery, B. W. and Yoerger, R.R. Adata integrator for use with astrain gage recorder. ASAE Transactions, Vol. 1, No. 1, pp 36-37,1958.

3. Aronson, M.H. Introduction toRecorders, Part I. Instruments andAutomation, Vol. 31, No. 5, pp830-835, 1958.

Recorder Survey, Part II. Instruments and Automation, Vol. 31,No. 8, pp 1360-1365, 1958.

4. Bigsby, F.W. Power requirementsof a combine cylinder when threshing solid and hollow stemmedvarieties of wheat. Paper presentedat 51st Annual ASAE Meeting,Santa Barbara, California. June

23-25, 1958.

5. Burrough, D.E. Power and TorqueDistribution in Farm MachineDrive Shafts. Agricultural Engineering, Vol. 34, No. 6, pp 382-384,386, 1953.

6. Clyde, A.W. Drawbar dynamometerusing strain gages. AgriculturalEngineering, Vol. 36, No. 8, pp521-522, 1955.

7. Hamann, D.D. & Zoerb, G.C. Theeffect of chemical weed spray onalfalfa root decay and subsequentdraft requirements for plowing.Paper presented at the wintermeeting, American Society of Agricultural Engineers, Chicago, 111.,Dec. 15-18, 1959.

8. Jensen, J.K. Experimental StressAnalysis, Agricultural Engineering,Vol. 35, No. 9, pp 625-629, 634,1954.

9. Lauderdale, G. Use of strain gagesin agriculture. Paper presentedat the North Atlantic SectionMeeting of the ASAE, Aug. 29,1957 in Newark, Delaware.

10. Perry, C.C. and Lissner, H.R. TheStrain Gage Primer, McGraw-HillCo., New York, 1955.

11. Reece, C.K. Investigation and design of a torquometer using SR-4strain gages, unpublished master'sthesis, Kansas State College, 1957.

12. Richardson, R.D. and Filby, D.E.A tractor pulley torquemeter employing electrical resistance straingages. Journal of Agricultural Engineering Research. Vol. 4, No. 1,pp 16-23, 1959.

32

13. Schoenlaber, L.H. Strain gages andstress coat in machinery design.Agricultural Engineering, Vol. 36,No. 5, pp 309-317, 323. 1955.

14. Stout, M.B. Basic Electrical Measurements, Prentice-Hall, Inc., NewYork, 1950.

Continued from page 19

LIST OF REFERENCES:

1. DILL, H. W. Jr., Use of the Comparison Method in AgriculturalAir Photo Interpretation. Photo-grammetric Engineering, Vol.XXV, No. 1, March, 1959.

2. HOCKENSMITH, R. D., andSTEEL, J. G., Recent Trends inthe Use of Land CapabilityClassifications. U.S. Departmentof Agriculture, Washington, D.C.

3. MOLLARD, J. D., SulphateMapping From Aeral Photographs. Proceedings of the Western Regional Meeting of theCement and Concrete ResearchGroup, October 26th and 27th,1954. National Research Coun

cil of Canada.

4. PHILPOTTS, L. E., The Use ofAerial Photo in the Change ofLand Use in Southwestern Saskatchewan. Canada Departmentof Agriculture, Ottawa, Ontario,August, 1957.

5. STICKLING, W. and BLACK-WELL, S. R., Drainage Area asa Hydrologic Factor on theGlaciated Canadian Prairies.Prairie Farm Rehabilitation Administration, Regina, Saskatchewan. Presented to the eleventhGeneral Assembly I.U.G.G., Toronto, Ontario, September, 1957.

ACKNOWLEDGEMENT

The writer wishes to acknowledgethe assistance of several members ofP.F.R.A. who read the manuscriptand made worthwhile suggestions, inparticular, Mr. D. H. Pollock. Photographs were processed by the Photographic Section of P.F.R.A. Figure1 is from a paper by W. Stickling andS. R. Blackwell, entitled, "DrainageArea as a Hydrologic Factor on theGlaciated Canadian Prairies".