Rectangular Wires as substitutes for the MAA and a Torquing Auxiliary in the Begg treatment -An Experimental study Authors:
Tejashri Pradhan, MDS Associate Professor Department of Orthodontics and Dentofaci al Orthoped ics, Tatyasa heb Kore Dental College and Resea rch Centre, New Pargaon - 4161 37 Maharashtra, Indi a e-mail:
[email protected] Phone: 9960511 444
Vijay Jayade, MDS Former Professor and HOD, Department of Orthodontics and Dentofacial Orthopedics SD.M. Coll ege of Dental Sciences, Dharwad, Presently Professor Emeritus, Sibar Institute of Dental Sciences, Guntur, Andhra Pradesh, Indi a
Objectives
1. To measure and compare the torquing action of different rectangular wires with those of the MAA and a four spur auxiliary. 2. To select or recommend ideal rectangular wires for different torque requirements in the Begg technique.
Materials and Methods
An experimental set up consisting of an upper typodont with ivorine teeth was employed. It was fitted with the Begg brackets. Rectangular wire sectionals in 0.016"x 0.022", 0.017" x 0.025", 0.018" x 0.025" and 019" x 0.025" sizes and made of Stainless Steel, Braided Stainless Steel, Superelastic NiTi, Braided NiTi, Copper NiTi, a -Titanium and B- Titanium were tested. The MAA and the four spur torquing auxiliary were made in 0.009" supreme grade and 0.012" premium plus grade wires respectively. Torquing forces generated by the above wi res inserted in the ribbon mode and the auxiliaries were accurately measured using a dial gauge and components of an electric circuit. Force comparisons were drawn to find out if forces generated by any\of the rectangular sectionals were comparable with those generated by the MAA and the four spur torquing auxiliar.
Results
1. Forces were higher when rectangular wires were engaged first rather than piggyback. 2. Torquing effects of braided NiTi sectionals in 0.025" x 0.Q17" size engaged before the basewire are comparable with the MAA. 3. Torquing effects of braided stainless steel sectional in 0.025" x 0.017" size and Superelastic Niti sectional in 0.025" x 0.017" size engaged before the base wire are comparable to those of the four spur auxiliary.
Conclusion
Appropriate rectangular sectionals can be effectively substituted for the MAA or the four spur torquing auxiliary.
KeyWords
Controlled tipping, torque, Rectangular sectionals, MAA and four spur auxiliary.
INTRODUCTION
a decline now, it is still practiced by many orthodontists in Indi a and in some other countries.
Th e li ght wire tec hniqu e was introduced to the profession by Dr. P. R. Begg in 1954. It soon beca me immensely popular beca use of some original ideas, especia ll y the appli ca tion of light forces. Although on
However, the present day Begg practi ce differs from the traditional Beggl as it aims to overcome many of the drawbacks of the latter. One such major difference
7
MATERIALS AND METHODS
relates to bio-mechanica l considerati ons. The Classica l Bcgg treatment consisted of uncontrolled tipping during the firs t two stages and root movements in the third stage. One the other hand, the current emphas is is on contro lled tipping in the initi al stages, since it makes the overa ll treatment more efficient mechanics-w ise and also minimizes possibi lity of root resorption.
The stud y was ca rri ed out at th e Departm ent of O rth odonti cs, S.D .M . Co ll ege of Dental Sc iences, Dharwad. It consisted of an experimental compari son of d ifferent rectangular w ires w ith the M AA and torqui ng auxiliary. A pilot study was undertaken, w hich indica ted that it is possi ble to use for root movements a rectangular w ire bent in the form of an arc in the edgewi se mode (a long the narrow di mension) but engaged in the ribbon mode.
Mol len hauer's2 aligning auxi liary (popu larl y ca lled as th c "MAA") has been incorporated in the modern refi ned Begg practi ce for cont rol led labi o- lingual tipping of the anteriors during the fi rst and second stages of trea tment. MAA, besi des aligni ng, also exert s ultra light torquing and uprighting forces on the anterior tceth. The gentl e torquing effect does not appreci ably deepen the bi te nor tax th e ancho rage. Thi s is accomplished by usi ng a stiff base w ire in the 0.0 18" prem iu m plus grade, in combinati on w ith very gentle roo t movi ng forces from the MAA made in ultra light 0.009" supreme grade wi re.
Materials I) The rectangular wi res tested w ere (Fi g 1)
Idea llabio-l ingual incli nations of the teeth at the fini sh of appliance therapy are very important for obtaining stable results. The Begg torquing auxiliary (usuall y having four spurs, sometimes two spurs) used in the III stage provides opt imum fo rce to improve the ax ial inclination of the anteri or teeth . The des ired max ill ary and ma ndi bu lar incisor inclin ati ons, th ro ugh their interincisa l angle, not only increase the posttreatment stabi lity but also enhance dental and facia l esthetics. However, the time and skill involved in fa bri ca ti ng the torquing auxiliari es or the M AA puts off many operators from employing them, thu s affecti ng the quality of their treatmen t results.
Figure 1 : Armamentarium
a) 0.0 16" x 0.022" and 0.017" x 0.025" Stai nless Steel h) 0.016" x 0.022", 0.01 7" x 0.025", 0.018" x 0.025" and 0.019"x 0.025" Brai ded Stain less Steel
Therefore it was fe lt that there was a need to expl ore substi tute components which could be ei ther obtained preformed or fa bricated easily, and w hi ch would serve, equall y efficiently, the sa me purpose as of a torquing auxi liary or the MAA.
c) 0.01 6" x 0.022", 0.01 7" x 0.025", 0.018" x 0.025" and 0.0 19"x 0.025" Super elastic N iti
A recta ngular w ire bent along its narrow dimension (i.c. in the edgewise mode) in the form of an arc of a circle but engaged in ri bbon mode in Begg brackets acts like a torquing auxiliary. Usi ng modern wi res such as NiTi, Cu NiTi, rectangul ar braided stai nless steel, rectangular braided NiTi w ire etc, it should be possible to develop torqu ing forces ranging from ultra light to ligh t range, to establish equ iva lence between certain rectangu lar w ires on o ne hand and the MAA and torquing auxiliary on the other. This study was designed to eva luate the torq uing acti on of different rectangular wires and help in selecting the appropriate rectangular w irc fo r a given cl in ica l situati on.
f)
d) 0. 01 7" x 0.025" Brai ded Ni ti e) 0.01 7" x 0.025" and 0.0 19"x 0.025" Copper Niti (35°C) 0.018" x 0.022" a- Titanium
g) 0.01 7" x 0.025" and 0.0 19"x 0.025" B- Tita ni um (A ll the above were tested in ribbo n mode, although the dimensions mentioned are in the edgew ise mode, since it is the way they are commonly designated) h) 0.022" x 0.018" N iTi Torque Bar (TP Lab3) II) The MAA was made of 0.009" supreme wi re and the torquin g auxi liary was made of 0.012" premium plus w ire (A.J. Wi lcock Co. Australi a).
8
1;"",,-
=---= -----= --=-.=:: Methodology
on th e labia l aspect. This pl ate had small vertical projection s extending ap ica lly in the area of incisors. Each of the four in c isor roots also ca rri ed copper conducting pl ates fitted at th e level of the verti ca l projections. One end of an electri ca l wire was soldered to the labi al conduct ing plate, and its other end was connected to a battery cell. Another w ire connected from the battery cell to a bulb formed one part of the circuit .Each of the conducting points on the four incisor roots also had pieces of electri ca l w ires soldered on th em. Th e other end s of th ese wires co uld be indi v iduall y connected (depending on the tooth on which force measurement was made) to an electri ca l w ire. The other end of this wire was connected to the bulb, thus completi ng the other part of the circuit (Fig 4). All the way through the experiment, the two
The methodology was adopted from M.Hammond and W .P.Rock's4 method. The basis of this experim ent was an upper typodont (Fig 2) in which ivorine teeth were
Figure 2 : Typodont fixed. The roots of the six anterior teeth were allowed free antero-posteri or movement by trimming the lab ial and lingual wa ll s of the acrylic sockets. Begg brackets were fi xed to the teeth. Roots of the anterior teeth were built up with acryli c and screws were inserted in the api ca l area. The teeth were aligned to idea l arch form so as to ensure that th e brac kets were co rr ectly positioned. A 0.020" premium wire was used for making the base arch wi re. The test jaw was mounted on a wooden fr ame. A dial ga uge was fixed to a metal post fitted on the same base (Fig 3).
Figure 4 : Electrical Circuit conductin g points were maintained in a constant position. Rectangular sectionals were cut from anterior part of preform ed lower archw ires (in the di fferent sizes and made from different material s as mentioned above) with the curvatures maintained at the original preformed arc. These were engaged in the brackets in two different ways (as described below) and force measurements were taken. A. At the beginning, the rectangular sectional wire that was being tested was engaged in the Begg brackets, and th e base w ire was fixed pi ggyback over the rectangular wire (Fig 5). The two wires were tied into
Figure 3 : Experimental set-up The indicator arm of the gauge was suspended verti ca lly so that forces from the hori zontal movement of the root ap ices could be read on the dial gauge. Electrica l Ci rcuit A thin copper conducting plate of 3mm width extending over the six anteri or teeth, was fi xed over the acrylic
Figure 5 : Rectangular wire bent in edge wise mode but engaged in ribbon mode torque. 9
the bracket with a ligature wi re. Thi s allowed lingual root torque to fully mani fest itself (Fig 6). At this point,
..• :" j
-~ ~."
1-~"
.l ..
'. ,-_.,,*, , 4h.~~. "t
~
,
Figure B : Thread pulled from torqued to pre torqued postion completing the circuit, and the reading taken.
Figure 6 : Rectangular wire engaged before the base wire, and palatal root allowed to manifest. a thread was tied between the screw at the api ca l area of one of the four incisors and the dial gauge arm (with di al gauge at zero position as seen in Fig 7) . The thread
Thus the forces were measured at the root apex. The readings for different rectangular w ires were directl y compared with those of MAA (Fig 9), four spur auxiliary (fig 10) and TP Niti Torque Bar.
Figure 9 : Mollenhauer's Aligning Auxiliary IMAAJ . Figure 7 : Thread tied at the root apex, and Dial gauge maintained in '0' position.
,
was pulled away from the lingually inclined position till the contact occurred at the two conducting points and the light glowed (Fig 8). The pulling force required for the light to glow was read at this juncture. An average of three readings was taken . The procedure was repeated for all four incisors, employi ng various rectangular secti onals
".
j , .. t ••-.
~J ~,~,
_.'
~. f '''l. ;.~ ..~ ..
.t,.\".!A HI,t .....'-....a..... •
B. For all the rectangular sectionals, another set of readi ngs was taken by engaging them piggyback over the main wire. The MAA, torquing auxi liary and the torque bar were always engaged piggyback over the base wire.
Figure 10 : Four spur auxiliary.
10
RESULTS Table No. I : Forces generated in grams by the rectangul ar wi res engaged before the base w ire
R. LATERAL
R. CENTRAL
L. CENTRAL
L. LATERAL
ROOT
ROOT
ROOT
ROOT
0.022"x 0.0 16"
18
20 .5
19.5
18
0.025"x 0.01 7"
20
26
25.5
20
0.022"x 0.016"
11.5
14
14
11 .5
0.025"x 0.01 7"
14.5
16.5
16
13.5
0.025"x 0.018"
15
18
18
15
0.025"x 0.01 9"
16
19.5
20
16
O.022"x 0.01 6"
11
14
14
11
0.025"x 0.01 7"
12.5
16
16
12.5
0.025"x 0.0 18"
14
18.5
18
14
0.025"x 0.01 9"
16.5
20
19.5
16.5
10.5
12.5
12
10
0.025"x 0.01 7"
12.5
16
16.5
12.5
0.025"x 0.019"
15.5
18.5
18
15.5
16
17.5
18
15.5
0.025"x 0.01 7"
12.5
15.5
15
12.5
0.025"x 0.01 9"
15.3
19
20
16
DIAMETER OFTHEWIRE Stai nless Stee l
Braided Stai nless Stee l
N iTi
Braided Niti 0.025"x 0.01 7" Cu-N iTi
a - Titanium 0.025"x 0.018"
& - Titanium
N.B. The force va lues equivalent to those of MAA are pri nted in bo ld font, and to those of four spur torquing auxiliary are underlined .
11
Table No. II. forces generated in grams by rectangular wires engaged piggy back and also the MAA, torquing auxiliary and the torque bar. R. LATERAL
R. CENTRAL
l. CENTRAL
l. LATERAL
ROOT
ROOT
ROOT
ROOT
16.5
20
18.5
21
19 21.5
16 18
11
12.5 13.5
12 14
11.5
11 .5 12.5 14
15 17
15
11 .5 12
17.5
14
9.5 10.5 11 .5
12 13.5 15.5
12.5 13 15.5
10 10.5
0.025"x 0.Q19" Braided Niti
13
17
16.5
11 .5 12 .5
0.025"x 0.017" Cu- NiTi 0.025"x 0.017"
7.5
10
10
7.5
11
12.5
13
11.5
0.025"x 0.019"
13
16.5
16
13
0.025"x 0.018" Titanium
13.5
15
16
13.5
0.025"x 0.0 17"
11
13
12.5
11
0.025"x 0.0 19"
11.5
Four spur 0.012" P +
14.5
14 16.5
13 17.5
12 15
MAA 0.009" Sup Torque Bar 0.022"xO.018"
11 11.5
13 14
12.5 13
11 12
DIAMETER Of THE WIRE Sta inless Steel 0.022"x 0.016" 0.025"x 0.Q17" Braidcd Stain less Steel 0.022"x 0.016" 0.025"x 0.017" 0.025"x 0.0 18" 0.025"x 0.019" NiTi 0.022"x 0.016" 0.025"x 0.017" 0.025"x 0.018"
a - Titanium
P-
..
N.B The force values equivalent to those of MAA are prmted m bold font, and to those of fo ur spur torqumg auxiliary are underlin ed.
DISCUSSION
Th e fo ur spur auxili ary for lingual root torqu e in third stage, w hich is common ly used at present, is the one made in 0.012"premium plus wi re. Although the forces produ ced by this auxi l ia ry are low, th e moments generated by them are adequate. Thi s is because the moment arm is much greater in a torquing auxiliary than in a rectangular arch wi re twisted for torq uing effect, as was pointed o ut by Nikolai' (Diagram 1).
M echanism of root movement and controlled tipping in the Begg technique Dr Juli e Ann Staggers' rightly pointed o ut th at uncontrolled tipping fo llowed by root movement is not an efficient method of retraction. As already mentioned, the emphasis of refin ed Begg is on con tro lled tipping followed by root movement. She also raised a doubt whether the MlF ratio of approx imately 12 :1, required for roo t movements, could be obtai ned in the Begg tcchnique. The expla nation provided below wi ll show how the required MlF ratios both for root movement and controlled tipping are obtai ned in the refi ned Begg.
When the moment produced by the torquing auxi liary acts in conjunction w ith light CI II elastics, the MlF ratio is close to the requ ired 12 :1 mm for controlled root movement in the lingua l direction. 12
~, ~ .., .'
,.,. ' .
,....w·J.1·~
c
B
A
Diagram 1
Diagram 2
The Class II elastic fo rce, acting alone on the upper anterior teeth, would ca use their uncontrolled tipping in crown lingual root labia l fashion (as in Diagram 2A). The intrusive force in the archwire would resist this tipping by providing a cou nter-moment (Diagram 26). The co upl e generated by the MAA augments thi s counter-moment (Diagram 2C). Depending on the ratio of combined counter-mom ents to the magnitude of CI II force, a M/ F ratio of about 8 :1 as required for co ntro ll ed tipping could be provided . To obta in satisfactory M/ F ratio in II stage, MAA sho uld be cont inued till the end of the II stage. Thi s prevents undesirable uncontrolled lab ial tipping of incisor roots, and therefore shortens the III stage.
F2
02
01
Diagram 3 The lever system represented by a torquing auxiliary
Rationale for testing various wires As shown in the above diagram 3 by Hammond and Rock4, there is defin ite proportional ity between the force exerted at the crow n level b y any torquing element and the force experienced at the root apex level, w hich is expressed as
We thought of testing w ires of different dimensions and different physical properti es based on composi ti o n, as we had to select wires w hi ch would generate forces comparable to tho se of two mec hani sms namely, 1) Lighter forces exerted by the MAA, and 2) Stronger fo rces equivalent to that of a torquing auxiliary
FXD=FXD Since it was not poss ible to directly measu re the forces forming the couple that generated from rectangul ar wi re-b racket relati o nship at th e c row n leve l, we dec ided to measure the forces experienced at the roots apex level required for pulling the root s from their full y torqu ed positio n to the pretorqued posi tion .Thi s was done for all rectangul ar w ires, as also for the MAA made of 0 .009" supreme w ire and the four spu r torquing aux iliary made in 0.012"premium plu s w ire. Thus a direct comparison was possibl e.
Methodology The method used in this study was aimed at measuring the forces exerted by torquing elements at the root apex . The present study differed somewhat from the original study of Hammond and Rock' as well as an ea rli er st ud y co ndu cted by Dr Anuradha Sooda' in o ur Depart ment on different designs of torqu ing aux iliari es, w herein the forces were measured at the bracket level. As the moment arm of the torqu ing spur is suffi ciently long, it is possible to lift the spur and measure the force at the spu r tip. On the other hand, the moment arm in the case of rectan gul ar wire, is too short to lift si milar to a torquing spur. Th erefore, we made a sli ght mod ifi ca tion from the previous studies, based on the analysis provid ed by Hammond and Rock', for measuring forces exerted by torquing elements at the root apex.
Forces measured were a combination of the actual force experienced at the root apex plus the force required to overcome friction between the root and the mesia l and distal aspect of the socket wa lls. A formula was devised to estimate these two forces as close to the actual va lues as possibl e. The derivation of the formul a is explained in the appendix.
13
Interpretation of the Results
spur auxil ia ry (0.01 2"premium plus ) as seen in the tables I & II.
1) The amo unt of fo rce produced increased progressively from a sma ller cross-section of the wire to that of a higher cross section, as wou ld be expected.
d) Forces produced by rectangular stain less steel wi res were 10und to be much higher than the forces exerted by the four spur torquing auxi liary.
2) Forces produced are always more when rectangular wi res are engaged first rather than piggyback. (D iag 4 ). This could be beca us e a portion of th e rectangu lar wire projects beyond the bracket slot w hen it is engaged piggyback, as show n in diagram no. 4.
e) Forces produced by the braided N iTi and Super elasti c Niti were consta nt over time.
SUMMARY AND CONCLUSIONS The forces exerted by certain sectional rectangular wires (which had a curvature along the narrow dimension i.e. in an edgewise mode; but were engaged in the ribbon model were compared to those from the MAA and the four spur torquing auxiliary o n the same experimental set up . The results were as follows: Forces produced by stainless steel wires were found to be the highest followed by braided stain less steel, super elasti c Niti, a-tita nium, Cu NiTi, and Btitanium.
'-v _ Diagram 4 Rectangular wire engaged before and engaged piggyback 2
Forces produced are always slightly higher when rectangular w ires are engaged first rather than piggyback.
3
Forces generated by 0.02S"x 0.017" braided NiTi engaged before the base wire are comparable with those from MAA (0.009" supreme)
31 The magnitude of force varied from material to material. Highest forces were produced by Stainless Steel and the least forces were produced by the braided Niti wires. 4) Compa rison of the va lues of rectangular wi res and the MAA or th e four sp ur aux ili ary o n the experim ental set up
4 Forces generated by 0.02S"x 0.01 7"braided stainless steel and 0.02S"x 0.o17"Super elastic Niti, engaged before the base w ire are comparab le with the four spur auxiliary (0.01 2"premium pl us)
a) The forces generated by 0.02S"x 0.01 7" braided NiTi engaged before the base wi re and 0.02S"x 0.017" braided stain less steel, 0.02S"x 0.017"atita nium and 0.02S"x 0.017" Cu-NiTi engaged piggyback are comparable w ith the MAA (0.009" supreme).
Hence, the 0.025" x 0.017"braided NiTi wi re ("Turbo" w ire of Mis Ormco) is efficient in bringing about contro lled tipping in the initial stages and 0.025" x 0.017" braided stainless steel is a usefu l substitute for the four spur torquing auxiliary in the third stage of Begg mechanics.
b) The wi res which generate higher forces than the MAA but lesser forces than the four spur auxiliary are 0.022" x 0.0 16" braided stai nless steel and 0.022" x 0.016" super elastic Niti engaged before the base wire; as also 0.02S"x 0.018" braided stain less steel and 0.02S"x 0.018" super elastic N iTi engaged piggyback over the base wi re. Th ese cou ld be used as braking mechanis m during the second stage.
REFERENCES 1. Begg P R, Kesling P C. Begg Orthodontic theory and technique. 2nd ed.Phiiadelphia: W.B. Saunders Company 197 1.p130-139. 2. M ollenhauer B. An aligning auxiliary for ribbon arch brackets: rectangular boxes from ultra fi ne high tensile wires. Aust Orthod J 1990; 11 :219-226.
cl Forces generated by 0.02S"x 0.01 7" braided stai nless steel, 0.02S"x 0.017" Super elastic Niti, 0.022"x 0.018" a-titani um and 0.02S"x 0.017" Cu-N iti engaged before the base w ire and 0.02S"x 0.019" Super elasti c Niti , 0.02S"x 0.019" braided stain less steel and 0.02S"x 0.0 19" Cu- NiTi and 0.02S"x 0.019" B- titanium engaged piggyback are comparable w ith the four
3. T P Orthodontics Catalog. 1990: Product no. 343101,95. 4. H ammond M , Rock W P. Forces produced by auxiliary torqu ing springs in Begg techn ique. Br J Orthod 199 1; 18 : 219-223. 14
F2
5. Staggers lui ie and German e Nicholas. Clini cal considerations in the use of retra ction mechani cs. Clin Orthod 199 1; XXV: 364-369 6. Nikolai R I. Bioengi neering analysis of orthodontic mechanics.2 nd ed. Phil adelphia : Lea & Febiger. 1985.307-308.
D2
7. Sooda Anuradh a. Evalu ation of forces in all three pl anes produced by torquing auxiliaries of various d es i gn s m ad e from differ e nt di am e te r w ires.Dissertati on submitted to Karnatak University, 1997; 5-7 and 20.
DI
Diagram 6 Th e lever system represented by torquing auxiliary
APPENDIX
F x O=F x O
Th e M/F rat io for co ntroll ed tipping should be approx imately liz of th at for root movement. Since the class II elastics used in differen t stages usuall y rem ain th e same throughout the treatment, it wou ld mean that th e moment produced by the MAA (MM) in the initial stages should be approx imatel y one half in magnitude of the moment produced by th e torquing auxiliary (MT) in th e third stage. As th e moment arm (box height in th e MAA and torquing spur length) is kept at Smm for both, thi s would further mean that the forces measured fo r the MAA (FM) should be approximately one half th e forces measured for the torquing auxiliary (FT) as deducted below : M
"'I
,
2
If we term th e force m easured at th e apex as A and the fri ctional resistance as R,
F = A - R. 2
Further 01 in both th e experimental setups is 5 mm and 02 is approximately 1Smm. Substituting th ese va lues, the derivation is as follows:
oI x F, = 0 2 x (A - R). SXF ,
Therefore ~ = A-R,
Therefore
O ,X F, 0 = A-R 2
Therefo re R =A - 1/3 F
= F x 0 and M = F x 0 M
T
T
A (i .e. observed force at the apex noted in our study) for four spur auxi liary is 17 gms and th e sa me for MAA is 13gms.
o
is sa me .i.e. 5mm in both the cases . Since M should be liz of M , F must be liz of F . " T
M
T
F1 (i.e. force measured for th e Smm of moment arm of th e torquing auxiliary or th e MAA in th e previous study) for the torquing auxiliary was 30 gms and for the MAA was 15 gms.
Such a relationship was observed in an earlier study . 7 carn ed o ut by Dr. Anuradha Sooda . In th e present stud y such a rel ationship was not observed. (The force meas ured for th e torquing auxiliary on th e central incisor is approx imately 17gms,while that from MAA on the same tooth is 13gms as can be seen from Table no 1I ). The difference in th e two studies is expla ined below:
Substituti ng th ese va lues, R for four spur auxi li ary = 17 - 3013 = 7 gms and R for MAA is 13-15/3 = 8 gms Thus, the fri ction al res istan ce obtained in both the situations is nearly th e same, and it is approximately 7 to 8 gm s. Thus, it ca n be seen th at th e method of measuring the forces at th e apex is va l idated, although th e force magnitudes noti ced in our experim ent are app arently at va ri ance from the earli e r meth od.
The force noted at the apex is a combinati on of th e force experienced from th e torquing element plus th e fri ctional resistance created by th e contact of th e roo t aga inst th e wa ll of acry li C socket. In th e previous experiments, force for lifting the spurs away from the tooth surface was directl y measured. Therefore fri cti on did not play any appreciable role.
Hence, th e present study was undert aken to find out experimenta lly which rectangula r wires (composition wise as well as size-wise) would have capabiliti es comparable to th e MAA or th e four spur torq uing aux iliary.
The apparent discrepancy is resolved using the equ ation gi ven by Hammond and Rock', whic h is furth er elaborated as under:
15
