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CERN-PS/ JilA-fllGNH/21

Jan,, 27th 1954

MEMO ON . THE ACCUR.A.CY 'l'O BE OBTAINED ~'RON 'lW.!; SURVEYING SYSTE:M FOR LINING..,UP THE MAGNE'i' UNI'l'S o

1) Radial tolere,x1oe on the ma~t unit~..?...

, . In all the calbulations made on the closed orbit deviation it has been

assumed tha.t the equ:Llibr:i.uri1 orbi f. ins:i.de the · uni ts can be aligned to the pe~ect

circie within ± Oo5 mmso There are .two tolerances involved in this alignment;

one is the mechanical tolerance Leo the' accuracy with :wmeh the units can be

set down arrou.nd the perfect circle v the other is the acc::.uxaoy with whlch the equi­

librium orbit can be measured inside ea.ch magnet unit . We will, assume that the

overall tolerance is divided equally between these ~wo sorts of error Leo- the units

are set down within ± 0.25 mms of a perfect circle. and the equ.i.librium orbit position ·

is known to within ! Oo25 nuns with respe~t to the ma&net uni to

The calculations assumed that the equilibrium orbitr inside each ·magnet

unit (length about 5 metres) was perfect inside the ·unit and -that at the end of each '

unit the eqt.iilibri um orbit was within :!.: o-o 5 mms of the perfect circle ,. Applying

now the assumption about splittin,g the tolerance equally between mechanical and

magnetic eITors we ha.ve that each unit is assumed to be perfect in i tseJ.f and that

the ends of each u.nit are : within ! Oo25 mms of the perfect circle o

One obviou~ but unpractical way of ·achieving this tolerance would be

to take a geodectic surveying tape and measure the ends of each unit from the centre

of the machine . Such tapes have an accuracy of l part j,n 106

at best or 1 in 105 at

the very worst,, The radius of the machine is 70 metre·a so the end$ of the sectors

can be set to 0,07 mms at best or 0.7 mrus at the worst" Tak.~n..s an average tape + therefore it seems quite possible to set the ends of each unit to - Oo25 mm~ by

this process. However there are about 100 such un:i.ts and this meuns 200 length

measlll:'ements which would take far too ·long"

The pi-oblem is therefore t-o · firJ.d a rapid way of eri..suring the above tolerances"

One suggested method is to set ~p accurate marker stations near the final position

of the ped'ect circle~ these stations being measured from the centre of the machine

either by tapes or using high grade theodolites and tria.nguJ.ationo The magnet uni ts

are then ·measured with respect to these marker stations rather than. the centre of the

machi:r:.e o Al though the number of setting operations are roughly the same all measure­

ments are done inside the ring building from ·~he ~rker stations once thes9 str;rtionsi

which can be small in number~ have been measured from the centre of· the ma.chineo 't'his

.method o:f setting up has the advantage that in case of the units becoming misalignedr

due· to · some now unlmown cause, after the initial ..setting up another survey can be taken

witho~t refering. to the machine centreo

Calculations show that it is not nece.ssary that .the lUli ts lie on a

perfe'ct circle but a perfect ellipse would be just· ~suitable' provided the major and ,

minor axis are not different by more than, say, two or three. centin.iet~es. Furthermore

the ellipse need not be qUite an ellipse bq.t can have smooth irregularities or bumps

provided the bumps are not too big or too locaL The depth of the bump orr putting '

it another way~ the maximum deviation of the periphery from the perfect circle ·(or

elli~se) depends on th~ bump length in the following aI_>proximate fashion; if' we

assume thc..t the bump is .a smooth sinusoidal excrescence,.

Length of b.ump Circumference

t 1/8

1/16

Peak deviation of bump from.perfect circle

2 ems 1

4 ems

fems

t ems

One conclusion tha.:t can be drawn from the calculations is that the

settins up of the marker stations· need not be very accurate perhaps only to acout

t ems p1Jviding there are oniy a few marker stations and that there is a very

accurate ~ethod for lining up the \lllita·~ith respect to the marker stations,. For

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instance if we imagine four m,_"irker stations 1 one at each 90° lino,then they can be

in error by terns with very little ef'.fect on the closed orbito But it is essential

that the units lie on a sm?oth cU.rv~. going through these four marker stations (or

fixed distance from th~~) and all bumps near 1/8 to 1/16 circumference long should

be avoided" Since the four marker stations are not jn visual sight of each other

due to the narrowness of the ring bUil!ling1, it will be necessary to set up sub- ·

marker stations, perhaps eight in number, within the ring buil.ding very a~curately measured from the four originai marke! statiOnso It should be pc)ssible to ~et up

the units from this total of twelve .marker stations. Whatever method ia used ' to

set up the sub-marker stations from the main marker stations must re~ult in the

sub-marker stations not being more than 1 to 2 mms away from the smoothes~ Clll'Ve

·that can be drawn through the four main marker stations.; And whatever method is - I -

evo1ved to set up the uni~a must result in _the end.a of the units not being more + .

than - Oo25 mms away from · the smoot.h.est curve that can be drawn between all marker

statieinso

2) ·· Vertical tolerance on the magnet unitso

All that has been said above about th~ radial' tolerances applies

equally well to the vertical setting up of th~ units with the difference that no

length measurements have to ·be taken ,; to the centre of the ma.chine, only height

measurements¢ Thus we set up the four marker stations to within t ems of a true

planeo The sub-marker stations are then set up from the main marker stations to

within l to 2 mms of the smoothest surfac~ that can be ~ed through the four + marker stations. Finally the units are levelled to within - 0.?5 mms of the smoothes~

slll;'face tpat can be arranged between all marker stationso

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.. JoBo 1 Adams

Geneva 27th Jano 19540