William p. Harrison Jr.

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Howard Johnson > 1! "a#er: $The "ermanent Magnet Motor$

The Permanent Magnet Motor

%y Howard R. Johnson and &i''iam ". Harrison( Jr.

Reprint of 1979 PaperNow posted for the first time on the Internet

Table of Contentslin!s to "ontent below#

• )o*er "age

• +. +ntroductory ,emar-s %y Howard Johnson/ ##. 10!

• ++. Theoretica' na'ysis &i''iam ". Harrison( Jr./ ##. 201!

o 1. +ntroduction . . . #. 2

o 3. The ttracti*e 4heet . . . #.

o 5transcri%ed to here6

o 7. The ,e#u'si*e 4heet . . . #. 17

o 8. The 4inusoida' Mode' . . . #. 18

• ,e9erences . . . #. 12

'' content is now #osted and transcri%ed. Ju'y 1( 37.

Note$+n origina' co#y( a'' 9igures came at the end as an a##endi;. Here they areinserted within the te;t where the transcri#tion has %een com#'ete. "ages and

Figures not yet transcri%ed are inc'uded at the end o9 the transcri#tion. "agenum%ering on origina' was added 'ater( and is o99 a 'itt'e. +t has %een correctedhere. "a#er scanned %y Doug'as Mann. Transcri#tion %y 4ter'ing D. ''an. Comment$

Johnson had wor!ing model before Harrison "omposed

mathemati"al model 00 Doug'as Mann

00 )o*er "age 00

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The Permanent Magnet Motor

b%

Howard R. Johnson

and

&i''iam ". Harrison( Jr.

Engineering Fundamenta's Di*ision


3/20

00 "age 3 00

%est magnetic materia's + cou'd 9ind in com%ination with an interstitia' materia' that was

high'y diamagnetic to 9orce the e'ectron s#in to stay in #'ace.

The =.4. Na*y 'ater made such a com#ound using %ismouth 5%ismuth6 and good magneticmateria's( %ut the interna' coerci*e 9orces were so great that this strong magnet wou'd 9a''

a#art i9 not encased in g'ass. +t was a'so e;#ensi*e.

4o + -e#t chec-ing magnetic materia's whi'e + wor-ed on designs that + thought shou'd %e

im#'emented. +t was a uiet( sometimes 'one'y o% o*er the years( 9or + didnCt share my #'ans

with my associates. My se'90im#osed security wou'd not #ermit it( and + -new o9 9ew #eo#'e

who wou'd %e interested anyway.

+n the 9i9ties( as ceramic magnets %ecame %etter and harder( and 'ong09ie'd meta' magnets

a##eared on the scene( + %egan to 9reee some designs and to ha*e magnets custom made to 9it

them.

+t was a%out this time that + mentioned the 9act that ust as + %e'ie*ed e'ectron s#ins made

#ermanent magnets( + a'so %e'ie*ed that they were res#onsi%'e 9or the A ang'es in thestructure o9 snow9'a-es gi*ing the si;0s#o-ed whee'( the si;0sided s#o-es( etc. The dean o9

the schoo' where + was teaching said( $May%e so$ and as- me i9 + -new that snow9'a-es were

mentioned in the i%'e as %eing im#ortant. + to'd him( $No( + didnCt -now that($ %ut + 'oo-ed it

u#. +t said: $Hast thou entered into the treasures o9 the snow? r hast thou seen the treasures

o9 the hai'? &hich + ha*e reser*ed against the time o9 trou%'e( against the day o9 %att'e and

war.$

My comment was( $&e''( may%e this is more im#ortant than + thought.$ 4o + went ahead

and wor-ed on it another ten years.

00 "age 7 00

+ went to the @i%rary o9 )ongress and 'oo-ed u# snow9'a-es. + 9ound a wonder9u' %oo-

there %y Dr. ent'ey o9 New Ham#shire. He has s#end many years ma-ing these studies( and

he had 'earned a 'ot( as we'' as turning out one o9 the wor'dCs most %eauti9u' %oo-s. He had

9ound that snow9'a-es ha*e gas #oc-ets oriented on A ang'es and that the gas has a higher

#ercentage o9 o;ygen than air. ThatCs one reason why snow water rusts so we''. This higher

concentration o9 o;ygen a'so interested me %ecause o;ygen is more attracted to a magnetic

9ie'd than other gases.

Fina''y( using the %est ceramic magnets + cou'd 9ind and the %est meta' magnets( + wor-ed

out a scheme 9or a 'inear motor. The stator wou'd %e 'aid out as i9 it were unwound 9rom

around a motor. The #arts o9 the armature wou'd ride ust a%o*e the stator and ha*e the same %e*e'ed angu'ar orientations + ha*e ust mentioned.

Dies were made 9or the cur*ed armature magnets( and an order was #'aced 9or these sha#es(

des#ite the o%ections o9 magnet manu9acturers who said it was a %ad design. They didnCt

-now what it was 9or( %ut they were sure it was a %ad design. They wanted to ma-e horseshoe

magnets. They e*en %egged me to content myse'9 with ha'9 an order. + did not agree 00 and

once again you ha*e that 'itt'e matter o9 9aithI 9aith to try to im#'ement a new theoryI 9aith to

s#end your own 'imited 9unds when you ha*e a a 9ami'y and other 9inancia' res#onsi%i'ities

staring you in the 9aceI 9aith to %uc- the recognied authorities and manu9acturers in the 9ie'dI

9aith to %e'ie*e that your wor- is good and that some day( des#ite a'' the haards( you wi''

a##'y 9or and recei*e #atent rights in your own country and #erha#s throughout the rest o9 the

wor'dI and 9ina''y( 9aith that you can resist %eing smashed into dust %y industria' giants andor

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%eing ro%%ed %y others who -now on'y how to stea'.

00 "age 8 00

e'ie*e it or not( my 9irst motor assem%'y showed a%out two #ounds o9 thrust. The 'itt'etoy car on which + 9astened the armature magnets 9or su##ort ran in %oth directions o*er the

stator( showing that the 9ocusing and timing o9 the interactions was not too %ad.

This was the 9irst 'ight at the end o9 a rather dar- tunne' + had %een tra*e'ing 9or many

years. + %reathed a rea' sign o9 re'ie9 as my young son #'ayed with this $new toy($ and was

a%'e to o#erate it as easi'y as + cou'd.

9ter much testing o9 'inear and circu'ar designs( and 'oo-ing 9or an attorney 9or years

suited to securing a #atent on the new theoretica' wor-( + was 'ed to Dun-an eaman o9

eaman B eamon in Jac-son( Michigan. +t too- some time to #re#are the #atent. The

attorney %ui't some mode's himse'9 to chec- certain #arameters. Fina''y( we entered the case

in the #atent o99ice e;#ecting a 'ot o9 o##osition. &e were correct. &e got it. ut again( 9aith

sa*ed the day as we %att'ed 9or many years to gain a rather com#'ete *ictory. Now the wor- reuires di99erent -inds o9 9aith: 9aith in those who ha*e ta-en cut 'icenses

and who wi'' 'icenseI 9aith to continue the research to re#'ace scarce materia's in the magnetsI

and 9aith that this wor- wi'' continue to #rogress and that it wi'' e*entua''y 9u'9i'' its goa'.

For a num%er o9 reasons( the #ermanent magnet motor has not recei*ed much

consideration. +n 9act( nothing too radica' has %een done since Faraday too- some *ery crude

materia's and showed the wor'd that it was #ossi%'e to ma-e a motor. This wor- o9 his 'arge'y

in9'uenced the thin-ing o9 )'er- Ma;we'' and others who 9o''owed.

Today( the two greatest o%stac'es to using a #ermanent magnet motor

00 "age K 00

are( 9irst( the %e'ie9 that it *io'ates the conser*ation o9 energy 'awI and( second'y( that the

magnetic 9ie'ds o9 attraction and re#u'sion decrease according to the in*erse suare 'aw then

the air ga# is increased.

+n 9act( %oth contentions are uite wrong %ecause they are %ased on wrong considerations.

The #ermanent magnet is a 'ong time energy source. This has %een shown 9or many years

in the rating o9 magnets as high or 'ow energy sources 9or many a##'ications o*er 'ong usage.

'ouds#ea-er com#osed entire'y o9 e'ectromagnets wou'd %e unrea' in sie and energy

consum#tion. Yet( des#ite e;am#'es o9 this ty#e( many hesitate to a##'y the same #rinci#'es

to motors and e;tend them e*en 9urther %y using #ermanent magnets 9or %oth the stator and

armature. The e'ements o9 a'' e'ectric and #ermanent magnet motors are simi'ar. 9ie'd im%a'ance

must %e created( the 9ie'ds must %e 9ocused and timed( and magnetic 'ea-age must %e

contro''ed.

+n the wound motor( %rushes and contact rings gi*e the timing( the sie and sha#e o9 the

wound 9ie'ds and #o'es gi*es the 9ocusing( and the motor case and -ind o9 iron used he'# to

'imit the 'ea-age.

+n our #ermanent magnet motors the timing is %ui't into the motors %y the sie( sha#e( and

s#acing o9 the magnets in the stator and armature. The 9ocusing is contro''ed %y the sha#e o9

the magnets( #o'e 'ength( and the width o9 the air ga#. This air ga#( through which magnets

o##ose and attract each other( is a rare #henomenon. =sua''y when a magnetic air ga# is

increased( the 9ie'd decreases in*erse'y as the suare. &hen the air ga# o9 the #ermanent magnet motor is increased( a curious %ut de9inite change

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ta-es #'ace. There is a 'arge decrease in the reading at south #o'e o9 the armature and an

increase in the

00 "age A 00

reading at the north #o'e. Thus( a Ha''0e99ect sensing #ro%e wi'' gi*e a higher gauss reading at

the north #o'e and a decreasing count at the south #o'e. This he'#s e;#'ain why the thrust is

%etter with a 'arger air ga# than a sma''er one. The attracting 9ie'd is minimied and wi'' not

#roduce a 'oc-ing 9orce( whi'e the re#u'sion o9 the crescent magnet is great enough to

generate a thrust *ector com#onent that wi'' dri*e the armature.

s + tried to e;#'ain in the #atent( + %e'ie*e that the #ermanent magnet is the 9irst room

tem#erature su#er conductor. +n 9act( + %e'ie*e that su#er conductors are sim#'y 'arge wound

magnets. The current in a su#er conductor is not initiated %y a strong em9( such as a %attery(

%ut is instead actua''y induced into e;istence %y a magnetic 9ie'd. Then( in order to determine

how much current may %e 9'owing in the su#er conductor coi'( we measure its magnetic 9ie'd.

This a##ears to %e something 'i-e going out the door and coming %ac- in the window. nother rather uniue 9eature o9 su#er conductors is the 9act that their magnetic 'ines o9

9orce e;#erience a change in direction. No 'onger do these 'ines 9'ow at right ang'es to the

conductor( %ut they now e;ist #ara''e' to the conductor. Theoretica''y( the hea*y conductor

currents e;ist in the 9ine 9i'aments o9 nio%ium within each sma'' wire o9 nio%ium tin 9rom

which such su#er conductors are made. +snCt it interesting that the 9iner the wire the 'ess the

resistance unti' e*entua''y there is no resistance at a''?

00 "age ! 00

++. THE,ET+)@ N@Y4+4 5%y &i''iam ". Harrison( Jr.6

1. +ntroduction

Des#ite the 9act that the 'inear *ersion o9 the #ermanent magnet motor Johnson( 1!/ may

a##ear conce#tua''y sim#'e see Fig. 1/( the com#'e; interactions o9 the 9ie'ds a'one #'ace it in

a c'ass with other uite so#histicated moti*e systems.

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Figure 1. Partial front and plan views of a linear model of the Howard Johnsonpermanent magnet motor.

Many parameters play an important part in making possible the successful designof a permanent magnet motor. A number of these variables relate directly to thegeometry of the system and its components. Mathematical models for both thelinear and circular versions of Mr. Johnson's motors are presently under

development, and include such controllable parameters as stator-to-armature airgap, stator element air gap spacing, armature pole length, stator magnetdimensions, magnet material variations, magnetic permeability and geometry ofbacking metals, and multiple armature couplings, to mention only a few.However, much of the early work involved uit simple mathematicalinvestigations, and even at this level some remarkable revelations resulted. Also,as often is true with simple models, considerable insight into the mechanismsthat might prove predominant was gained. !herefore, it is our intention to sharewith you some of those early analytical investigations and "ndings. #ven though $oulomb's %aw, embodying the inverse suare relationship as itdoes, may yet prove suspect, it nevertheless provides an e&ceedingly simple yetviable form upon which to base an elementary model of the linear version of thepermanent magnet motor. escribing the interaction between two magnetic


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monopoles, $oulomb's %aw in vector form is recalled as

1/

00 "age 2 00

where M and MC are the #o'e strengths #ositi*e i9 north( negati*e i9 south/( u 5mu6 is the

#ermea%i'ity o9 the medium in which the #o'es are 'ocated( r is the straight0'ine se#aration

distance %etween the two #o'es( and 9 5with 'ine o*er to#6 is the *ector o9 9orce see Fig. 3/

acting at each #o'e #ositi*e in magnitude 9or re#u'sion and negati*e 9or attraction/.

Figure 2. Coulomb's Law

The *ector nature o9 E. 1/( the 9act that 9Cs 'ine o9 action is co'inear with the straight0'ine

distance r %etween #o'es( its su#er#osition #ro#erties when a##'ied to mu'ti#'e #o'es( and its

restriction to static systems 9i;es in s#ace are a'' we'' -nown conditions on E. 1/. &e wi''

use the su#er#osition #ro#erty o9 E. 1/ to e;tend its a##'ication to a s#atia' domain

containing many more #o'es than the two shown in Fig. 3. Howe*er( E. 1/ wi'' 9irst %e

reso'*ed into sca'ar com#onents so that ana'ytica' e;#ressiors 5sic6 can %e more easi'y

de*e'o#ed.

ur ana'ysis wi'' %e two0dimensiona' and co#'anar( restricted to the *ertica' ;0y #'ane. +t

shou'd %e noted that the horionta' stator $trac-$ o9 H.,. JohnsonCs 'inear mode' com#rises a

#'ura'ity o9 9'at magnets( rectangu'ar in cross section( each ha*ing an as#ect ratio 'ength0to0thic-ness ratio/ o9 1A. This high *a'ue contri%utes to the two0dimensiona' nature o9 the mode'

and he'#s to minimie and e99ects in the direction. Thus there is some usti9ication 9or a

two0dimensiona' ana'ysis( at 'east in the case o9 the 'inear mode' we are considering here.

s shown in Fig. 7( we consider 9irst a north #o'e o9 strength M 'ocated at coordinates E

5e#si'on6( n 5nu6/ with a second north #o'e o9 strength MC( 'ocated on the ;0a;is at ;(/.

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Figure 3. Positional locations of two opposing north monopoles in x-y space.

Force 9( acting on the mono#o'e at E(n/( when reso'*ed into its horionta' and *ertica'

com#onents yie'ds( res#ecti*e'y(

00 "age --

3/

and

7/

3. The ttracti*e 4heet

To i''ustrate some o9 the assum#tions and e;tensions o9 )ou'om%Cs @aw that wi'' %e made(

the sim#'e e;am#'e o9 a magnetic sheet 'ying a'ong the ;0a;is wi'' %e considered 9irst seeFig. 8/.

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Figure 4. patial orientation of thin! magneti"ed sheet having high aspect ratio andwith south face up.

The sheet( o9 9inite 'ength @( is a #ermanent magnet magnetied across its y0direction

thic-ness and ha*ing high as#ect ration to e'iminate 0direction edge e99ects/. The south0#o'e

9ace wi'' %e oriented u#( with north 9acing downward on the underside o9 the sheet.

=nderside e99ects wi'' %e ignored as though the sheet re#resented a continuous distri%ution o9

on'y south mono#o'es a'ong the ;0a;is. To incor#orate such distri%utions into E. 1/ we

re#'ace MC with the di99erentia' dMC and introduce the 9unction ;/ so that

dMC L ;/ d;. 8/

!hen the magnitude of the total force vector, ( )with line over top*, acting on anisolated north monopole of strength M situated somewhere within the upper halfof the &-y plane, becomes

K/

00 "age 1 00

where & )chi* is the ratio &+%. Assuming that the magnetic density along thesheet can be represented by the southern constant - )beta/*, and neglectingend e0ects at & 1 2 and & 1 %, #uation 3/ reduces to

A/



10/20

where

!/

the strength #arameter MC ha*ing %een determined %y integrating E. 8/ o*er the sheet 'ength

@( and # 5rho6 is the ratio r@.

+9 the north mono#o'e is #'aced direct'y a%o*e the center o9 the sheet( at coordinate

E5e#si'on6( n5eta6/( with E5e#si'on6 L @3 and the *ertica' air0ga# se#aration distance n eta/

ta-en as ar%itrary( the symmetrica' distri%ution o9 incrementa' 9orce *ectors acting at E(n/

wi'' a##ear as shown in Fig. K.

Figure 5. #orth monopole symmetrically above the center of a magneti"ed! attractingsheet.

Note that a shi9t o9 the north mono#o'e to the 'e9t resu'ts in a 9orce im%a'ance which tends to

#u'' the #o'e %ac- to the right( as shown in Fig. A.

Figure 6. $orce imbalance acting on a north monopole above a magneti"ed sheettending to restore the pole to sheet center.

4o considering now only the &-component of ()line over top*, similar to #uation


11/20

5/ we write

2/

where 6 and 7 are the dimensionless ratios

/

and

1/

00 "age 11 00

(or any "&ed position 6,7/ of the north monopole in the upper half plane, #. 8/can be integrated to give

11/

This ratio is shown in Fig. ! as a continuous 9unction o9 'ocations with Y treated

#arametrica''y.

Figure 7. %-direction distribution of the %-components of attractive force exerted on a

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north monopole by a thin! magneti"ed sheet.

!he 7 1 9 curve represents the "eld in:uence on the north monopole situated ata constant air-gap separation n)eta* 1 %/ uite some vertical distance above the

sheet; whereas at 7 1 2.9 the monopole is located much closer to the & a&is.n order to trace some tra?ectories through this "eld, we now observe that they-component of force ()line above* will be

13/

This 9unction is show in Fig. 2 with a Y *a'ue o9 .3.

59igure 2 is omitted un'ess it is the 'ast( un'a%e'ed 9igure/6

>n dimensionless form the euations of motion for tra?ectory paths of themonopole above the sheet in planar 6 - 7 space become

17/

and

18/

where

00 "age 13 --

1K/

1A/

and

1!/

+n these e;#ressions t is rea' time and T is sim#'y a time constant chosen ar%itrari'y. s

#re*ious'y noted on #age ( @ is the 'ength o9 the sheetI whereas( g is the gra*itationa'

acce'eration constant and & is the downward weight 9orce o9 the mo*ing mono#o'e a%o*e thesheet. For the magnetic 9orce terms T5Gamma6/mag and TY/magwe su%stitute direct'y Es.

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11/ and 13/( res#ecti*e'y.

4e*era' o9 the traectories resu'ting 9rom the integration o9 Es. 17/ and 18/ are shown in

Fig. .

Figure 9. &raectories of a north monopole in an attractive field generated by the thin!magneti"ed sheet lying in the %-interval (-).

They a'' e;hi%it the e;#ected %eha*ior. s a'ready im#'ied in the discussion o9 Fig. !( the

9unction T5Gamma6/mag

gi*en %y E. 11/ has a sta%'e #oint o9 eui'i%rium at L 13 andthere9ore dri*es the 9ree09a''ing mono#o'e towards sheet center( regard'ess o9 the initia' dro#0

#oint 'ocation. The 9unction TY/mag 9rom E. 13/ is eua''y #ersuasi*e in #u''ing the

mono#o'e down towards the sheet itse'9( and mani9ests that attraction uite #er*asi*e'y

through the integration o9 E. 18/( e*en when the G term may %e omitted as it was in the

traectories o9 Fig. /. ctua''y( the com#uter integration #rocedure wi'' not carry the

mono#o'e a'' the way to sur9ace contact with the sheet at Y L %ecause o9 the in9inite

condition which e;ists there as re9'ected %y E. 13/. Thus( tai'ings o9 these traectories Fig.

/ ha*e %een com#'eted %y manua''y o*err iding the #'otter.

00 "age 17 00

s we wou'd antici#ate in wor-ing with this ty#e o9 centr a' 9ie'd( where in E. 8 is a

sim#'e constant( the 9ie'd is conser*ati*e with cur' o9 F5'ine o*er to#6 *anishing. 'so( the

re*erse symmetry o9 T/mag a%out L 13( as seen in Fig. !( con9irms that the energy integra'

9or this 9unction wi'' *anish within any a##ro#riate 'imit #airs o9 .

7. The ,e#u'si*e 4heet

y su%stituting 5%eta6 9or in E. 8/( the sheet o9 'ength @ 'ying a'ong the ;0a;is

%ecomes re#u'si*e( with its northern 9ace directed u#ward( o##osing the north mono#'e a%o*e

it at 'ocation E5;i6(n5eta6/. 9 course the sign in E. A/ %ecomes #ositi*e and the 9unctions

T/mag and TY/mag re*erse their %eha*ior according'y( as i''ustrated in Fig. 1.

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Figure 10. %-direction distributions of *r %+mag and *r ,+mag for the repulsive field of a thin!magneti"ed sheet acting on a moving north monopole.

gain T/mag wi'' ha*e an eui'i%rium #oint at L 13( %ut now it is desta%i'iing. s a

conseuence( resu'ting traectories 9or the north mono#o'e are much more interesting in this

case than they were with the attracti*e sheet. 4e*era' #aths are shown in Fig. 11 with

di99erent *a'ues used 9or the &F ratio in E. 1!/.

Figure 11. &raectories of a north monopole in a repulsive field generated by a thin!magneti"ed sheet lying in the %-interval (-).

"arameter G was inc'uded( and in each e;am#'e the traectories commenced at .( .3/ with

ero initia' *e'ocity.

The attracti*e and re#u'si*e sheet resu'ts are easi'y demonstrated since $ru%%eried$

9'e;i%'e sheet magnets are commercia''y a*ai'a%'e( such as those so'd %y the "ermag

)or#oration o9 Jamaica( New Yor-. +t may a'so %e interesting to note that with s'ight

modi9ications this 9irst sim#'e ana'ytica' sheet mode' can %e used to gain some insight into

o#eration o9 the so0ca''ed $magnetic &an-e'$ motor re#orted on %y 4cott 1!/.


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00 "age 18 00

8. The 4inusoida' Mode'

The 9irst #a#er Harrison( 1!/ re'ating( indirect'y( to any mathematica' ana'ysis o9 the #ermanent magnet motor ado#ted a cosine 9unction Fig. 13/ to simu'ate the distri%ution o9

in9'uence #arameter MC generated %y the 9'at stator trac- o9 Mr. JohnsonCs 'inear mode'.

Figure 12. Pole strength influence factor! '! as a cosine function of linear displacement distance! x.

n e;#erimenta''y determined distri%ution( shown in Fig. 17( was o%tained %y mo*ing a

Ha''0e99ect #ro%e courtesy o9 F. &. e''( +ncor#orated( o9 r'ando( F'orida/ o*er the stator

trac- o9 one o9 Mr. JohnsonCs ear'y 'inear mode's ha*ing se*en 9'at ceramic magnet e'ements.

Figure 13. xperimentally determined magnetic flux density! /! along a linear model



16/20


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Figure 14. 0scillatory path of a north monopole restrained to %-direction motion over a three-element linear stator assembly.

s Mr. Johnson has %rought out( the 9ocusing armature magnet o9 his 'inear mode' wi'' start at

either end o9 the stator trac- sim#'y %y insuring that the north end o9 this %i#o'ed crescent is

'eading the south see Fig. 1/. 4o( in Fig. 18( we are showing the 0direction motion 9rom

right to 'e9t instead o9 9rom 'e9t to right as in our #re*ious e;am#'es. 'so( %y sim#'y rotating

the 9igure c'oc-wise through ninety degrees( it %ecomes easy to 9o''ow the %eha*ior o9

dimension'ess *e'ocity(


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Figure 15. Continuous path of a north monopole restrained to %-direction motionshown traversing a linear stator assembly comprised of seven permanent magnet

elements.

+t was 9ound that through sma'' *ariations in ; # in E. 3/( as the mono#o'e ad*anced a'ong

its traectory #ath 9rom one #osition to another( su99icient contro' o*er the mo*ing #o'e

cou'd %e e;ercised to carry it o*er the 9u'' 'ength o9 the stator and %eyond.

5c'ic- 9or en'argement6

Figure ?? - Plot of tables in maga"ine article *computer dynamic measurement+ 1seenote regarding 'mystery' figure2

00 "age 1! 00

,EFE,EN)E4

• Harrison( &i''iam ".( Jr.( $ 4o'ution 9or the #tima' Ga# o9 a Mono#o'e E'ement

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Mo*ing in a 4inusoida''y Distri%uted Magnetic Fie'd$( #a#er #resented to the

Engineering 4ection(


20/20

to the techno'ogy( and 7/ the grou# has the a%i'ity to ma-e a success o9 the endea*or.

All truth passes through three stages: First, it is ridiculed;

eco!d, it is "iole!tl# opposed; a!d $hird, it is accepted as sel%&e"ide!t.

-- Arthur Schopenhauer (1788-1860)

'(he! #ou)re o!e step aheado% the cro*d #ou)re a ge!ius.(he! #ou)re t*o steps ahead,#ou)re a crac+pot.'

-- Rabbi Shlomo Riskin, (Feb.18)

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William p. Harrison Jr.

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