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  • 8/2/2019 Validity of Measurement of Lld by Tape Method

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    1990; 70:150-157.PHYS THER.RothsteinPaul Beattie, Kale Isaacson, Dan L Riddle and Jules MDifferences Obtained by Use of a Tape MeasureValidity of Derived Measurements of Leg-Length

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    Tests and MeasurementsInjuries and Conditions: L ower Extremity

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    Validity of Derived Measurements of Leg-LengthDifferences Obtained by Use of a Tape Measure

    Key Words: Lower extremity, general; Musculoskeletal system; Radiography; Testsand measurements, unctional.

    Determining the dzference in the length of a n individual's legs is often a n impor-tant component of a musculoskeIetal emmination. Although measurements areeasily obtuined with a tape measure, the valdity of these measurements is notknown. 7 3 e p u q a e of this study was to emmine the validity of determinations of

    Leg-length diffe ren ces (LLDs) ar e of LLD that is clinically sign ifica ntthought to contribute to the occur- remains controversial. Subotnick hasrence o r severity of many clinical rep orte d that a df ier en ce of as littlesyndromes.l.2Among these cond itions as 3 mm is significant,"J wh ereasare sc0liosis,3~4 ow back pain,+' sa- Anderson has stated that a differencecroiliac painF.9 an d a variety of ru n- of less than 19 mm is acceptable.12ning injuries.lOJ1 How ever, the deg ree Summaries of various authors' opin -

    Paul Bea ttieKale lsaacsonDan L RiddleJules M Rothstein

    P B eattie, kIS, PT, is Instructor, Division of Physical Therapy, Departm ent of Orth oped ics, School ofMedicm e, University of New Mexico, Alb uque rque , NM 87131 (USA).

    leg-length dzferences (LLDsj obtained by use of a specified tape measure method(TMM). Leg-length dz$eences using the TMM and a radiographic technique weredetermimd for 10 subjects who were candidates or clinical leg-length measure-ments and for 9 healthy control subjects. Validi41 f the TMM measurements was

    determined by messing the degree of agreement between TMM-obtained LLDs andthose obtained by the radiographic method. Validity estimates as determined byinh-acluss cowelation coeficients (ICG) were ,770 or patients, ,359 or healthysubjects, and ,683 or all subjects. W e n he means of the two values obtained byuse of the TMM were compared with the radiographic measurements, the ICCsw e 85;? or the patient group, ,637 or the healthy subjecrs, and ,793 or all sub-jects. Thk study suggests that TMM-derived LLD measurements are tlalid indicatorsof leg-length inequality and that the estimates of validity are improtled by usingthe average of two determinations rather than a single determination. [Beattk P,Isaaaon f( Riddle DL, et al: Validity of derived measurements of leg-length d z m -ences obtained by use of a tape measure. Phys Ther 70:150-157, 19901

    K Isaacson, PT, is Staff Physical Therapist, Sports Physical Therapy and Rehabilitation, 2607 Wyo-ming, Albuquerqu e, NM 87112. At the time this study was cond ucted , he was a stude nt in th e Divi-sion of Physical Therapy, University of New Mexico.

    D Riddle, hlS, PT, is Assistant Professor, Department of Physical Therapy, School of Allied HealthProfessions, Medical College of Virginia, Virginia Commonwealth University,PO Box 224, MCV Sta-tion, Richmond, VA 23298

    J Rothstein, PhD, PT, is Associate Professor, Department of Physical Therapy, School of AlliedHealth Prof'essions, Medical College of Virginia, Virginia Commonwealth University.

    Thir article was s~rbtnitted pril 12 , 1989; was with the authon fot. evision for 11 week; and wasaccepted N~ vemb er , 1989.

    ions regarding clinically significantLLDs ar e sho wn in Table 1. The opin-ion of what constitutes a "significantLLD" appears to be diagnosis specific.For ex amp le, Subotnick considers adifference of 3 mm significant enoughto warrant a shoe lift for the treatmentof running-related injuries.10 Gilessuggests that an LLD of greater than9 mm could cause enou gh of achange in the angle of the lumbarfacet joints to contribute to the devel-opment of back pain.13 Papaioannouet a1 report that an LLD of greaterthan 22 mm causes significant com-pensa tory scoliosis.3

    The association of LLD with manyclinical syndromes has m ade determi-

    nation of LLDs an important pan ofmusculoskeletal examinations. There

    Physical 'TherapyNolume 70, Number 3lMarch 1990 1 5 0 113

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    Table 1 . Leg-Length ~ ~ e r e n c e s LLDs) Considered Clinically SigniJicant

    LLD(mm) Comment

    According to Subotnick,lo LLD of 3 mm or greater can causeinjury to runners.

    According to Friberg,s LLD of 5 mm or greater leads to biome-chanical compensations in the spine.

    According to Brody,ll LLD of 6 mm or greater can cause inju-ries to runners.

    According to Corrigan and Maitland,' LLD of less than 7 mmrarely causes symptoms.

    According to Giles,l3 LLD of 9 mm or greater causes changesin the angle of lumbar facets.

    According to Cyriax,s LLD of 10 mm or greater contributes tothe development of back pain.

    According to Gibson et al,4 LLD of 15 mm or greater cancause compensatory scoliosis in the standing person.

    According to Vogel,l LLD of greater than 20 mm requireslower extremity compensation.

    According to Papaioannou et a1,3 LLD of greater than 22 rnmcauses significant scoliosis.

    According to Ingram14 LLD of greater than 40 mm oftenrequires surgical correction.

    is, however, no universally acceptedclinical method for measuring LLD.I4Determining leg lengths by taking

    measurements from radiographs andthen calculating the difference is gen-erally considered to be the most accu-rate method for determining leg-length inequality.l5-l7 Because of theircost, however, radiographs areimpractical for determining UD, andradiography exposes the subject tothe adverse effects of radiation.17Therefore, other methods ar e moreoften used clinically.

    Therapists often use simultaneouspalpation of both iliac crests of astanding subject to determine LLD.The relative heights in the frontalplane of each crest are then0bserved.8~~~~~9lthough this methodis easy to perform, intratester andintenester agreement has been shownto be lacking.15.18 A modified versionof this method requires placing nar-row blocks (block method) under theobserved shoner leg until the iliaccrest heights are le ~e l. 1~ 10~~9~2~oer-

    man and Binder-Macleod studied theusefulness of the block method on a

    sample of five subjects.20 They com-pared radiographic and block-methodmeasurements using an F test and a t

    test to determine whether the meanmeasurements obtained with bothmethods differed significantly. Tests ofdfierences such as the t test or F testdo not indicate the degree of agree-ment between repeated measure-ments. Therefore, conclusions regard-ing the degree of agreement of themeasurements taken in the Woermanand Binder-Macleod study cannot bemade.

    Friberg et a1 used the block methodto determine the presence anddegree of LLD in 21 patients with lowback pain." The authors comparedmeasurements obtained with theblock method with those obtainedfrom radiographs. They used onlydescriptive statistics to repon thedegree of agreement between radio-graphic and block-method measure-ments. The average intratester errorwhen comparing radiographic withblock-method measurements was 5.8

    mm. The authors also reported that,approximately 13% of the time, the

    block-method measurements differedfrom the radiographic measurementsin the determination of which leg wasshoner.

    Other techniques have beendescribed for the clinical measure-

    ment of LLD. Among these techniquesis the use of a measurement screen.21The use of a level with moveablearms to approximate the level of theiliac crests" or the level of the ante-rior superior iliac spines (ASISs)'3 hasalso been described. There is, how-ever, no evidence supporting thevalidity and reliability of UD measure-ments obtained by use of these meth-ods. An additional drawback to usingthese methods is that they are imprac-tical because they require instrumentsthat are not usually readily availableto physical therapists.

    A frequently described method forassessing LLD requires the use of atape measure (TMM) to determine thedistances from the ASISs to themedial malleoli.l5-l7.19.20.'P'7 Subjectsare usually measured while they arepositioned supine.

    Eichler described several potential

    sources of error when measure-ments are obtained using theTMM.'6 Differences in the circum-ferences of the two legs could con-tribute to distance differences, ascould unilateral deviations along thelong axis of the leg (eg, genu val-gum, genu varum). In addition,Eichler suggested that pelvic asym-metries and difficulty identifyingbony prominences by palpationcould contribute err or to these

    measurements.Beattie and colleagues conducted apreliminary study using an operation-ally defined TMM identical to thatused in this study to examine the reli-ability of TMM meas~r emen ts .~7 heywere attempting to eliminate errorattributable to the sources identifiedby Eichler. Two examiners obtainedrepeated measurements of UD on 50subjects, 38 of whom were patientswho were considered clinical candi-dates for leg-length measurement (eg,they complained of low back or lower

    14/151 Physical TI ~erapyNolume 0, Number 3/March 1990

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    extremity dysfunction). The authors -bserved good intrarater reliability(ICC[1,1] = .807) and fair interrater Table 2. Characteristics of Patient Group (n = 10)reliability (ICC[l I .] = ,668) whencomparing the first measurements Subject Age Height Welghtobtained by each examiner. When Number (Yr) Sex (cm) (kg) Dlagnoslsthey compared the mean values of

    paired measurements, the interrater1

    34 F 168 6 1 tibia1 plateau fracturereliability rose considerably (ICC = 2 60 F 170 68 low back pain, osteoarthritis.910). These results agree with thoseof other researchers who found that

    3 36 F 168 77 slipped epiphysis of femoralhead

    reliability of TMM-obtained measure-ments improved when the means of

    4 28 M 203 100 tibia1 dysplasia

    reoeated measurements were 5 50 M 183 86 femoral fracture6 26 M 180 95 distal tibia-fibula fracture

    7 27 M 175 70 low back pain

    Encouraged by the results of the pre- 8 28 M 193 86 low back pain, sacralizationliminary study, we conducted this 9 25 M 178 79 femoral fracturestudy to determine the validity of LLD 27 F 178 69 low back painmeasurements obtained with the TMMas compared with LLD measurementsobtained radiographically. In addition,we wanted to determine whether the -ean values of paired measurements Table 3. Characteristics of ~ o m t a l roup (n = 9)obtained by the TMM are a morevalid indicator of LLD than are singlemeasurements. Subject Age Helght WeightNumber (Y ) Se x (cm) (kg)MethodSubjects

    Ten subjects, ranging in age from 25to 60 years (X = 34.1, s = 11.2), par-ticipated in this study as the "Patient"Group. Each of these subjects had ahistory of LLD or a recent history oflower extremity, pelvic girdle, o r spi-nal dysfunction that required medicalcare. These subjects, therefore, wereconsidered candidates for the clinicalassessment of LLD. A description ofthe Patient Group appears in Table 2.

    A

    second group consisting of ninehealthy subjects, ranging in age from22 to 34 years (X = 26.5, s = 3.7),also panicipated in this study, as the"Normal" Group. None of these sub-jects had a history of known LLD orlower extremity, pelvic girdle, or spi-nal dyshriction that required medicalcare. A description of the NormalGroup appears in Table 3. These sub-jects were included because asymptom-atic individuals are often evaluated forLLD during preemployment or preath-letic screening examinations. The

    validity of measurements obtainedwith use of TMM on healthy subjects,therefore, would be of value.

    If a subject in either group wasknown to be pregnant or was latemenstruating, she was excluded fromthe study because of the potential riskof exposure to radiation. All subjectswere instructed in the risks and bene-fits of participating in this study andsigned a written consent statementapproved by the Human ResearchReview Committee of the School ofMedicine, University of New Mexico.

    Procedures

    Radiographic measurements. Our

    radiographic leg-length measurementtechnique was based on use of themini-scanogram.*8 Subjects werepositioned supine on standardradiographic tables with a large radio-opaque ruler placed under their rightlower extremity. An x-ray tube wascentered perpendicularly over thesubject's right hip, and the first x-rayfilm was exposed. The tube was thencentered over the subject's knee andfinally over the subject's ankle whilethe second and third x-ray films wereexposed (Fig. 1). The ruler was thenmoved under the subject's left lower

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    Exposure 1 Exposure 2 Exposure 3(hip) (knee) (ankle)

    track -\

    8 ) -

    7'L7

    - - 'y- e-a'

    ,,/lead-marked ruler /

    Fig. 1. Illustration of three radiographic exposures we d in mini-scanogram. X-raytube i s on moveable track that allous exposures to be obtained with tube positionedabove hip, knee, and ankle of supine subject.

    extremity, and the proc edure wasrepeated for that extremity.Alicensed, boardcertified radiologistsupervised this portion of the studyand examined all radiographs forpathology.

    The mini-scanograms when placedtogether show the hip, knee, andankle with the ruler clearly visible,which allowed for measurem ents ofleg length (Fig.2) . Leg length (U)was calculated by subtracting the

    value visible on the ruler at the supe-rior margin of the head of the femurfrom the value seen at the midportionof the joint space b etwee n th e distaltibia and the superior margin of thetalus. (For exam ple, the m arking atthe tibiotalar joint space was 101 cmand the marking at the head of femurwas 16 cm; therefore,U = 101 - 16

    = 85 cm.)

    The pre lim inaq study indicated wecould reliably measureLLD with atape measure. However, because w edid not know whether we could

    obtain reliable measurements from

    the mini-scanograms, we examinedreliability of these measurements aspart of our method. Unless thesemeasurements w ere reliable,it wouldnot be reasonable to use th e mini-scanogram measurements as criteriain a validity study.

    Interrater reliability for mea surem entsfrom the mini-scanograms was de ter-mined from the m easurements takenby two of the authors (PB andKI).

    They independently measured the leglengths an d calc ulated th e LLDs. Intra-class correlation coefficients (IC C[ l,l] )were used to estimate agreementbetween the LLD me as~ rem ent s.~ 9The ICC for the 1 9 paired mea sure-ments taken by the two observersfrom all subjects was ,993. The ICCsrevealed that the measurementsofUD obtained from the mini-scanograrns we re highly reliablebetween the two examiners. The mea-surements obtained from m ini-scanograms are commonly acceptedas valid indicators of lower extremity

    bone length.20z2eherefore, webelieve that the measurementsobtained from the mini-scanogramswe re appropriate to use as criteria toexam ine th e validity of measurementsobtained with the TMM.

    Measurements with the tape mea-sure. All TMM measurements w ereobtained by one person (PB). Duringeach measurement session, subjectswo re a pair of shorts or a hospitalgown. The subjects' lower extremitieswere expose d from the level of themidthigh to their feet. Subjects werepositioned supin e on a plinth. Theexaminer positioned the subject'slower extremities in neutral hip rota-tion as determined by observation.The examiner then placed the sub-ject's medial malleoli together so thatthey met in a plane that approximatedthe midsagittal line of the b ody. Thesubject's h ip an d knees w ere, there-fore , in a position that closely approx-imated the anatomical position.

    The examiner stood on the same sideof the plinth as the limb he was mea-suring. The examiner held a blanktape measure between the thumb andthe first finger of his hand nearest thesubject's pelvis. With the same hand,he use d his thumb to palpate the sub-ject's ASIS. One end of the tape mea-sur e was placed on the ASIS at thesite w her e the exam iner believed hecould palpate the origin of the sano-rius muscle on the inferior portion ofthe ASIS. With the hand opposite tothat holding the tape m easure on theASIS, the exam iner gradually guidedthe tape do wn the anteromedialaspect of the subject's thigh, patella,

    and lower leg until he m ade contactwith the point w here the subject'smedial malleolus sloped inferiorlyand laterally (Fig. 3). The exam inerthen held t he tape taut and lifteditaway from th e subject. Another per-son recorded the value from theopposite surface of the tape.

    The examiner then repeated the sameproced ure on the subject's oppositelower extremity. Following this proce-du re, the subject was asked to standand to move about for approximatelyon e minu te in whatever manner was

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    Fig. 2. Mini-scanogram showing radiosubject's lower limb.

    comfortable and then to return to thesupine position on the plinth. Thesame examiner then repeated theentire procedure to obtain a secondpair of mt:asurements.

    Data Analysis

    The LLD was calculated by subtractingthe right leg-length measurementfrom the left leg-length measurement.

    -opaque markings on ruler placed under

    A positive value, therefore, indicatedthat the left leg wa5 longer than theright leg. A negative value indicatedthat the right leg was longer than theleft leg.

    We used the ICC (formula 1,l) oexamine the degree of agreement formeasurements taken in this study.29This form of the ICC is typically usedwhen random pairs of testers take

    repeated measurements. We did notuse random pairs of testers to takemeasurements in this study. However,this ICC formula does not excludeerror attributable to the testers,whereas other forms of the ICC dofactor out error attributable to different

    examiners. Based on our clinical expe-rience, dltferent clinicians may mea-sure LLD in the same patient; there-fore, differences between examinersmay be a potential source of error. Byusing this formula (1, l) for calculationof the ICC, we did not exclude errorattributable to the testers. We believethis version of the statistic provides themost clinically meaningful estimate ofthe amount of error associated withLLD measurements.

    The ICC was used to estimate agree-ment between LLD measurementsobtained with the mini-scanogramsand the TMM. Although the absolutevalues of the leg lengths obtainedusing the two techniques would bedser en t, the calculated (derived)LLDs would be in agreement if theTMM measurements were valid fordetermining the LLD.

    The criterion-referenced validity of

    measurements obtained with the TMMwas calculated in tw o ways. The firstmeasurements of LLD using the TMMwere compared with the measure-ments of LLD calculated from themini-scanograms. The means of thepaired measurements of LLD obtainedby using the TMM were also com-pared with the measurements of LLDobtained from the mini-scanograms.Separate ICCs were calculated for thePatient Group, the Normal Group,

    and the pooled data from bothgroups.

    Results

    The values calculated for LLD frommeasurements obtained by the TMMand by the mini-scanogram methodare presented in Table 4. The ICCvalues obtained by comparing the firstmeasurements of LLD obtained by theTMM with the measurements of LLDobtained using the mini-scanogrammethod were ,770 for the PatientGroup, .359 for the Normal Group,

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    and .683 for the entire sample(Tab. 5). The ICC values obtained bycomparing the mean values of twomeasurements of LLD obtained by theTMM with the measurements of LLDobtained using the mini-scanogramwe re ,852 for the Patient Gr oup, ,637

    for the Normal Gr oup , and ,793 forall subjects (Tab. 5 ).

    Discussion

    Validity of Tape Measure MethodValues of Leg-Length Difference

    In all cases, the sec ond measurementsobtained using the TMM demon-strated considerably greater ag ree-ment with the values from the mini-scanogram than did the first TMMmeasurements. For ex amp le, the ICCfor the first TMM m eas ure me nts ofthe Normal Group subjects comparedwith the mini-scanogram measure-ments was ,359, wher eas the ICC forthe second TMM me asurem ents com-pared with the mini-scanogram mea-surem ents was ,786 (Tab.5). The rea-son for the difference in validitycoefficients between the first and sec-on d m easurements is unclear. Thebest validity estimate (ICC = ,852) for

    the Patient Gro up, however, wasobtained by use of the mean of theTMM measurements.

    The finding that the mean of twomeasurements of LLD obtained withthe TMM was the most valid m easuresho uld have been anticipated becausepreviously we demo nstrated that reli-ability of these meas urem ents wasenhanced by use of mean values.2'Validity is dep en de nt o n reliability;

    therefore, clinicians are advised to usethe mean of two TMM-obtained LLDmeasurements.

    The TMM is an indirect method formeasuring leg length and then deter-mining LLD. The starting point ofmeasurement from theASIS allowsiilclusion of a portion of the bonypelvis Factors such as bony asymm e-try of the pelvis o r pelvic obliquity,which may no t actually caus e an LLD,could influence the m easurementsobtained by using theTMM. Asymme-

    medial malleolusI

    blank tape measure

    Fig. 3. Illmtration of tape measure method.for obtaining leg-length measurementsof supine subject. Both legs are placed as closelv as possihle to the anatomical position.Leg-length difference is calculated ly subtracting length of left 1eg.from length of rightleg. (ASIS = anterior superior iliac spine.)-

    able 4. ~eg-Length jifferences

    Calculated fromCalculated by Use of TMMa (cm) Mlnl-scanograms (cm)

    Subject First SecondNumberb Measurement Measurement W s

    "TMM = tape measure nletllod.

    "~u bje cts through 10 were the Patient Grou p, subjects 11 through 19 we re the Normal Group.

    tries in the surface contours of the cantly alter the position of the tape,thigh, knee, an d lower leg (eg, asym- leading to me aw rem en ts that would

    metries caused by swelling, muscular not reflect leg length.atrophy, or obesity) could also signifi-

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    -able 5 . Intraclass Correlatiom? for Comparisons of Leg-Length D e e n c eAlemurements Obtained by Use of Tape Measure Method ( T M M ) an d by Use ofMini-scnnogrnnlsGroup

    Flrst TMM Second TMM Mean of TMMMeasurement Measurement Measurements

    Patient (n := 10) ,770 ,803 ,852

    Normal (n = 9) ,359 ,786 ,637

    All subjects (N = 19) ,683 ,790 ,793

    "Intraclass c orrelation co eficie nts we re calculated using equation 1 ,l of Shrout and FIeiss.j9

    'The results of the preliminary studyan d of this study ind icate that LLDmeasurernents obtained by use of aTMM a re relatively valid wh en th e

    means of paired measurements areused. These measurem ents, however,like all mea surements, have a de gre eof error associated with them. Inusing me:a ure me nts in the clinicalsetting, this error must b e considered.The erro r associated with the mea-surements can only be m eaningfulwhen clinicians consider the magni-tude of LI,D that they believe warrantstreatment.

    Clinicians should know whether theyare able to correctly dete rmine whichleg is shorter in patients requiringassessm ent of LLD. Exa min ation ofour data suggests that the e rro r asso-ciated with LLD m eas ure me nts maybe highly consequential when smallLLDs are noted. When TMM-derivedmeasurementsof LLD were 5 mm orless, the examiner err ed in the de ter-mination of which leg was the shortero n four ou t of nine subjects. Thiserro r was determ ined by use of thedata from the radiographic m easure-ments. When TMM-derived me asure-ments of LLD were greater than5mm, the examiner never m ade anerror when determining which legwas shorter. Based on these data,therapists should be cautious whenmaking cllinical decisions based onTMM -obtained LLD m eas ure m ent s of5 mm or less.

    The TMM provides data relative to

    LLD in th e su pi ne subject. Thes e datad o not define the deg ree of functional

    impairment created by the LLD. Ourvalidity study sho wed relatively stro ngagreement with a criterion measure(measurements obtained by use of

    the mini-scanograms); w e d id not vali-date any other inferential use o f theTMM measurements.O ur results indi-cate that measurements of LLDobtain ed using the TMM a ppea r torepresent th e same anatomical rela-tionships that can be documented byuse of the mini-scanograms. Becausewe examined LLDs with both theTMM method and our radiographicmethod in supin e subjects, w e cannotbe sure that our measurements reflectfunctional LLD me asurem ents. Forexamp le, this method do es not assessstructural o r biomechanical asymme-tries of the foot and ankle that couldcreate an LLD during such activities asstanding, walking, and running.

    We suggest that in addition to usingTMM me asurem ents, clinicians evalu-ate th e effect of LLD o n patien ts byanalyzing specific functional activities(eg , walking, running, stair climbing).Th eref ore , although th e TMM m ay beconsidered to provide valid m easure-ments of LLD on patients, our datarepresent only a portion of the infor-mation necessary to m ake appropriateclinical decisions.

    The generalizability of ou r con clu-sions has som e limitations. The sam -ple size was small. Perhaps mostimportantly, the examiner (PB) hasused the TMM technique on manyoccasions during the p reparation for

    this study and in previous studies. Theskill of the examiner in our study may

    not be representative of many clini-cians w ho may use this techniqueinfrequently. We believe, however,based o n the preliminary study, thatclinicians can de rive fairly reliableLLD measurements by using the TMMdefined in this article. Future research

    can help clinicians by examining thereliability an d validity ofLiD measure-ments obtained on a larger samplewith a larger num ber of therapistsobtaining the m easurements. In addi-tion, studies exa mining inferentialuses of TMM-derived measurem entswould be helpful.

    The measurements obtained with theTMM appear to be valid for assessingLLDs in patients when the mean oftwo m easurements is used. Measure-ments are less valid when healthysubjects are measured. Given the indi-rect nature of this technique and theunresolved issue of what constitutes aclinically sign ificant LLD, w e believ ethat clinicians should not d epe ndsolely on TMM m easure me nts forclinical decisions.

    Acknowledgments

    We thank Jam es R Stevenson , MD, andGloria Gilreath, KT, for their assis-tance with the radiographic part ofthe study a nd B arbara Arnstadt for herassistance in p reparin g this manu-script. We would also like to expressour appreciation to the late FredRutan, MS , PT, for his assistance withthis study.

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    1990; 70:150-157.PHYS THER.RothsteinPaul Beattie, Kale Isaacson, Dan L Riddle and Jules MDifferences Obtained by Use of a Tape MeasureValidity of Derived Measurements of Leg-Length

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