Paper No. 2024
Index C ateg ory N o. 6
USING HELIUM TO PREDICT
THE MASS PROPERTIES OF AN OBJECT
IN THE VACUUM OF SPACE
by
Richard Boynton, President
Robert Bell, VP Engineering
Kurt Wiener, Chief Engineer
Space Electronics, Inc.
Berlin, CT 06037
For presentation at the
50th Annual Conference
of the
Society of Allied Weight Engineers, Inc.
San Diego, CA 20-23 May, 1991
Permission to publish this paper, in full or in part, with full
credit to author and Society may be obtained by request to:
S.A.W.E., Inc.
344 East "J" Street
Chula Vista, California 92010
The society is not responsible for statements or opinions in
papers or discussions at its meetings.
Richa rd Boynton is President of Space Electronics, Inc., Berlin, Connecticut, a company
he fou nd ed in 1 95 9. Sp ac e E lec tro nic s, In c. m an ufac ture s in struments to m eas ure
mom ent of ine rtia , center of gravity, and product of inertia. Mr Boynton holds a B.E.
degree in Electrical Engineering from Yale University and has completed graduate studies
in Me c h a n ical Engineering at Yale and M.I.T. He is the author of over 46 papers,
including 15 papers presented at past SAW E conferences. Mr. Boynton has been a
mem ber of SA W E for 23 ye ar s a nd is currently President of the Boston Chapter. He has
designed many of the mass properties me asuring instruments m anufactured by Space
Electronics. Als o, M r. B oy nton is th e C hie f Exe cu tive Officer of Mass Properties
En ginee ring Co rpora tion, and is a p rofession al folksinger.
Ro bert Be ll is V ice Pr es ide nt of E ng ine er ing at S pa ce Ele ctr on ics . M r. B ell rec eiv ed his
engineering education at Worchester Polytech. He has over 28 years experience in mass
properties, an d h as de sign ed nu m ero us instrum en ts and fixtures for mass properties
m eas urem ent. He is the autho r of a prev ious S AW E pa per.
Ku rt Wiener is C hie f Eng ine er of S pa ce Ele ctr on ics , Inc. M r. W ien er ho lds a B .S . in
Mechanical Engineering from M .I.T. an d a M .S . in Ind us tria l Ed uc ation fro m Cen tra l CT
Sta te College. He is a form er A sso ciate Professor of Mechanical Technology at Vermont
Technical College. His previous work includes machine and control system design, and
teaching these topics in industry. He is the author of two SAW E pape rs.
2
1. the effe ct o f air entrapped within the
test pa rt, the reb y a dd ing to th e actual
m ass o f the test part
Abstract -- How can the mass properties of
ob jects desig n e d to operate in space best be
measured in an earth based la b ?
Ma ss
properties m ea su rem en ts of lightw eig ht o bje cts
designed to operate in th e vacuum of outer
space have traditionally been made in a vacuum
ch am be r, in or de r to e limin ate the erro rs d ue to
the mass of th e air sur rou nd ing the ob ject.
V a c u u m c h a m b e r s a re e x p e n s iv e a nd
inconvenient to use.
The novel m ethod
described in this paper e liminates the effect of
the air mass without requi ri ng a vacuum
cham ber. This method works for any shape
ob ject.
2. the effe ct of the atmospheric gas
entrained on the outer surfaces of the
test part adding to the effective mass of
the test p art.
3. the effect of the damping term on the
equation of motion of a torsion
p en du lu m.
4. the deflections of the test ite m du e to
the drag forces.
Summary of Boynton's helium method
(Space Electronics is applying for a patent on
this m eth od .)
5. the buoyancy effect on CG m oment
For large lightweight objects such as decoys, the
magnitude of these errors can be considerable.
The de gre e to which entrapped and en tra ine d a ir
influence the test re su lts is a fu nction of the
shape an d s tructure o f the te st p ar t. A so lid
object will ex pe rie nc e o nly the effect of entrained
air, while a hollow cylindrical object with interior
baffles will have an erro r du e m os tly to
en trapped air. The percentage measurement
error is a function of the relative m ass of the
entrapped or en trained a ir vs the mass of the
so lid po rtion of th e te st pa rt. Smooth-surfaced,
dense objects, such as solid cylinders, will show
neglig ible difference in MO I (or POI) when
measured in a ir or vacuum. On the other hand,
large lightweight objects may show more than
15% difference in MO I when me asured in air vs
va cu um , and the buoyancy effect on sealed
lightweight ob jects can cause CG measurement
erro rs o f sev era l inch es .
1. M ea su re th e o bje ct in a n a ir en viro nm en t.
2.
M eas ure the same object in a helium
en viro nm en t. Sin ce the he lium is at a tm os ph er ic
pressure, there is no need for a thick-walled
cham be r. Ev en a th in p las tic e nc los ur e w ill
work.
3. Th e M O I of the test o bje ct in a vacuum can
t h e n b e c a lc u la t e d f r o m
the se
tw o
m ea su rem en ts, us ing the follow ing form ula :
I V = 1.2 I H - 0.2 I A
where;
I V = MO I (predicted) in a vacuum
I H = MO I measured in helium
I A = M O I m ea su re d in air
Since the mass properties instruments have an
on-line digital com puter, these calculations can
be done automa tically.
For the test ob jects we considered, the error due
to dam ping a nd d eflection w ere less than 0.1%,
and w e w ill ign or e th es e e ffe cts in the remainder
of th is pa pe r.
4. Buoyancy effects on CG unbalance mom ent
can be corrected using a similar procedure.
Introduction -- Me asu rin g the mass properties
of ob jects de sign ed to o pe rate in the vacuum of
outer sp ac e p os es pro ble m s n ot e n countered
when pe rfo rm ing sim ilar measurements on
earth-based test objects. Th ere are five prim ary
sources of error introduced to the measurement
by the air atmosphere. These are:
P roblem s associated with measuring in a
vacuum -- Yo u c an elim ina te the effect of air by
measuring the mom ent of ine rtia of a n o bje ct in
a vacuum, but this leads to a numbe r of
problems:
1. Th e o bje cts to be teste d wh ich are
mo st affected by air tend to be large.
This requ ires large va cuu m cha m bers
w hich are massive, expensive, and
3
requ ire long setup a n d ev ac ua tion tim e
for e ac h te st.
Using H elium to sim ulate low atm osph eric
pres sure -- If a 2 p sia atmosphere can be used
to obtain one of the data points, then it follows
that any other method yielding the equivalent of
2 psia can also be used. This led us to believe
that testing in a helium atmosphere had the
po ten tial to simulate testing in a reduced
pre ssu re a tm os ph ere of a bo ut 2 psia, since the
density of helium is about one seventh that of
air.
There are two m ajor sourc es of
measure ment error in air (entrained and
entrapped air). F or the he lium m eth od to be
successful, it must reduce both by the same
percentage. Our experiments show this to be
the case. The percentage reduction in MO I was
the same whether we redu ced the pre ssure to 2
ps ia or replaced the atmosphere with helium.
W e repeated this experiment with a number of
tes t ob ject s ha pe s.
2. M os t hig h a cc ura cy M O I a nd PO I
instru m en ts are bu ilt with gas bearings.
That me ans th a t the gas discharged
from the be arin g m us t be co ntinu ally
p um ped ou t in o rd er to m ain tain a
va cu um , making it difficult to obtain a
go od va cu um .
3. A va cuu m cha m ber req uires a large
expensive vacuum pu m p. C on sid er ab le
electrical po w er is e xp en de d e ve ry tim e
the vacuum chamber is evacuated, and
additional energy is required to keep the
pumps runn ing so the air flo wing
through the gas bearing is removed.
4. There is no convection cooling in a
va cu um , so motors and elec tro nic
circu its in standard mass properties
instru m en ts will tend to overheat and
fail. Some compo n e nts can be moved
outside the ev acu ated s pac e, but oth ers
have to be protected by intermittent, low
service factor o peration, or special
cooling m eth od s. T he se co mponen ts
i n tr o d u c e
some
measurement
un ce rtain ty du e to temperature variation
during the operating cycle.
Advantages of helium atm osphere testing over
vacuum testing -- The primary advantages are
low er c os t an d g rea ter c on ve nie nc e.
1. T he massive, expensive vacuum
chamber a nd th e va cu um pum p are
eliminated. Helium testing can be done
in a sim ple , lightw eig ht, sealed cha m ber.
For very large parts, the entire test area
can be sealed with plastic film and serve
as a sp ac e e nv iron m en t.
5. Th e g as be arin g in th e instrument
works very differently in a vacuu m than
in air, so that a special bearing design is
req uire d fo r us e in a va cu um .
2. Less operator time is required to run
a test. Evacuation tim e for a vacuum
chamber is far greater than helium
pu rg e tim e. Heliu m is introduced at the
top of the chamber and w he n it is
detected flowing out of a vent at the
b otto m, the chamber is ready for testing.
6. The cost of a special mass properties
inst ru me nt for use in a vacuum is at
least 10% higher than a conventional
instru m en t.
3. Te st se tups in a vacuum chamber
cannot readily be changed without reintroduci ng air and re-evacuating the
cha m ber. A glove box can be us ed in
the helium chamber. For large test
cham bers, techn icia ns ca n w or k in
scuba gear or with Scott packs in a
helium environment.
Realistically,
technicians cannot work in a vacuum
chamber and the vacuum must be
released and the chamber re-evacuated
for any adjustment to the test. I n a
helium filled room, a simple airlock can
How good a vacuum do you need? -- To
elim ina te the effect of air, you do not ne ed to
cre ate the near perfect vacuum of o uter space.
The relationship between air mass error and
atm os ph er ic pres su re is linear. For example,
reducing the atmospheric pre ssu re fro m 14 .7
ps ia to 2 psia will reduce the effec t of the
entrained and enclosed air by a factor of 7.25.
By m ea su rin g th e mom ent of inertia first at
atm os ph er ic pressure, and then at 2 psia, you
have two da ta p oin ts fro m wh ich to ex trap ola te
the m ea su red va lue in a v ac uu m .
4
be us ed , s o th e room need not be
purged and refilled.
The effect of these changes was minimal but
gave us additional confidence in the test setup.
W e then w ere ab le to d ete rm ine tha t the drift
wa s du e to hu m idity (see ne xt para grap h).
4. T he M O I (or P O I) instrum ents re quire
little redesign.
A proprietary Space
E lectronics gas bearing design works
equ ally well in air or helium and the
electrical co m po ne nts a re eq ua lly w ell
co ole d in e ither atm os ph ere .
Hum idity effects -- The drift was finally traced to
a hum idity effect. Ou r first test objects w ere
made of paper and cardboard. These had
appare ntly ac hie ve d m oistu re e qu ilibrium with
the am bie nt a tm os ph ere . Th e v ac uu m , with
zero hum idity, drew m oisture from the test
objects, redu cin g their weig ht an d M O I. T his
effect was m easurable. The tests w ere re-run
w ith non-adsorbent test o b je cts an d w e
observed that the humidity effect was eliminated.
Results of low pressure simulation using a
helium atm osp here -- It was determ i ned by
these tests tha t m ea su ring M O I i n a helium
environment of 1 atmosphere pres su re is
equivalent to o pe ra ting in air at a pressure of
about 4 inches of Mercury (2 psia). Even though
w e had chosen test objects which had different
proportions of e ntra ine d a nd en trapped air, the
results wer e th e s am e fo r all tes ts. This is
ex ac tly what one might suspect based on the
rela tive d en sity o f air an d h elium .
Sensing when the cham ber w as filled with
helium -- O ur n orm al pr oc ed ure wa s to
introduce helium into the evacuated cham ber .
When the pressure returned to 1 atmosph ere,
the escape of gas from the vent was proof that
the ch am be r w as filled w ith he lium . H ow ev er , in
those tests where we did not evacuate the
ch am be r, w e fille d it with helium from the top to
minimize the mixing of air a nd he lium . W e used
3 methods to determine when the chamber was
filled with helium.
A s our test data shows, the data points using
helium appear on ea ch curve at a density which
is slightly greater than would be predicted from
the theore tical density of helium . We we re
puzzled by this at first, but then it occurred to us
that the helium is probably mixed w ith a s m all
amount of air, increasing its density. In any
ev en t, the magnitude of error which results was
less than 0.08% for the cone sha ped objects.
1. W e placed a deflated plastic bag
loosely over the vent. When helium
started to flow from the ve nt, it ros e into
the ba g, filled it, and ev en tually caused
the bag to rise in the air, mu ch as a hot
air balloon is filled and rises.
NOTES
In the p roce ss o f pe rform ing the se tests , a
nu m be r of inte res ting e ffects we re o bs erv ed .
2. The second method was to place a
ca nd le in an inve rted jar a t the ve nt.
When helium rose into the jar and
disp lace d th e a ir, the c an dle we nt o ut.
Te m pera ture effect -- Wh e n th e M O I
m ea su rem en ts we re first perform ed, there
seemed to be considerable drift.
We als o
noticed when the cover of the test chamber was
removed, the escaping helium was quite cold.
W e qu es tione d w he the r the drift w as d ue to
tem pera ture variation. Two m odifications w ere
made:
3. T h e tw o prev iou s m etho ds wor k w ell
but do not lend themselves to
c o n ti nu o u s u se in a production
en viro nm en t.
Comm ercial oxygen
sen sors are av ailab le.
W e have
installed two of these on our measuring
instrumen ts. The first sensor is placed
in the chamber and
1. A thermom eter was mounted in the
sid e of the ch am be r to m on itor
temperature.
2. The helium was passed through a
copper coil in a room -tem pera ture water
bath b efore e ntering the test cham ber.
5
Figure 1 - M OI o f En trap ped/Entra ined Air
6
Prope rty
Air
Helium
D en sity
(lb/ft 3)
at 20oC
.0754
.0104
Ab so lute V isco sity
at 20oC
Micropoise
181
194
Specific Heat
joule/gm oC
Co nstan t Pressu re
at 20oC
1.006
5.24
Th erm al C on du ctivity
at 0 oC
joule/cm sec oC
2.41
14.15
used to verify when the oxygen has been
displaced by helium. The second se ns or is
mounted outside the instrument and is us ed to
wa rn the tes t op er ator if the o xy ge n le ve l is
reduced to 90% of its norm al le ve l p e r O S H A
standards.
chamber listed e arlier apply for this case. A
helium environment has the effect of reducing
this noise floor by approximately a factor of 7.
Center of gravity
If ce nter of g ra vity is
measured by the sp in pr oc es s, then the sa me
advantages liste d a bo ve for PO I ap ply to this
process. If CG is measured by de tectin g s tatic
unbalance m om en ts, the n th e w eig ht of a ir
introduces an erro r du e to bu oy an cy. T his
buoyancy effect only occurs for sealed objects.
The de ns ity of a ir is 0.0 75 lb/ft 3. If one side of an
object disp lace s 1 ft 3 more than the other side,
and the center of buoyancy of that sid e is at a
radius of 3 ft, then a m om en t of 2 .7 lb-inc h is
created.
The significance of this mom ent
depends on the w eig ht of the tes t item . If the
test item we igh s 1 00 0 p ou nd s, the n th is res ults
in an error in CG of 0.003 inch. If the test item
weighs 100 pounds, then the error is 0.027 inch.
If the test item is a thin lightweight space object
such as a decoy, the n it could weigh as little as
1 po un d. Th e res ulting error in CG would be
2.700 inch! Measuring the C G i n he lium will
reduce the buoyancy error by a factor of 7.5. As
in the ca se of the m om en t of ine rtia
m ea su rem en t, the m easurement in air and
helium ca n b e e xtra po lated to yield the CG in a
va cu um .
Purging air from sealed test objects -- This is a
m ea su ra ble effect when air is entra pped inside
a lightw eig ht, h igh vo lum e te st ob ject. If the
helium m et h od is to b e fu lly e ffe ctiv e, this air
mu st be rep lace d b y h elium . If the tes t ob jec t is
not tightly sealed, this can be accomplished by
sim ply waiting until the air has disp ers ed into the
helium atm osp here . If there are a ny op en ing s in
the test object, they should be oriented down so
the helium w ill rise through them an d displace
the air inside. It should be noted that if the test
object is tig htly s ea led , air m ay be inte ntion ally
trapped ins ide w he n th e v eh icle is in space and
no atte m pt sh ou ld be m ad e to pu rge it.
Product of inertia Spin b alanc e m ach ines are
ca pa ble of very high sensitivity, particularly if the
test item is rotated at a relatively high speed,
since the force due to POI unbalance increases
as the sq ua re o f the sp ee d. How eve r, a ir
turbulence has the effect of negating the
advantage of higher spin speed. Air turbulence
increases the noise floor of the mea sureme nt, so
that t he unbalance signal is obscured by the
forces introduced by the air flowing past the
outer su rfac e o f the test o bje ct. Placing the test
object in a vacuum eliminates this prob le m.
H o w ever, the same objections to a vacuum
Effect of helium on the test operator
helium used in this test procedure will be
7
The
exh aus ted to the atm osp here and will be mixed
with the air that the op era tor b rea the s. W ill this
present a hazard ? T h e answer is no, for the
following reas on s: H eliu m is n ot tox ic, a nd in
fact is intentionally used by scuba divers to
reduce the inciden ce o f the "ben ds". H elium
rises very quickly, since it is so mu ch lighter than
air. In a large industrial building, the 1 C F M of
helium used by th e instrument will rise to the
ceiling and not change the composition of the air
the operator breathes. In a small room, the
helium will eventually displace the air, so that the
operator co uld experience a lack of oxygen.
Ho we ver, well before this happen s, the operator
w ill note tha t he is sta rting to so un d lik e D on ald
Duck when he talks. As a fu rth e r s afe g ua rd , w e
have insta lled an oxygen sensor on all of our
instru m en ts w hich use helium. A warning tone
sounds when the oxygen level decreases to 90%
of its normal concentration.
helium or air as the bearing ga s, an d to
anticipa te
a n y o t h er
p ro b le m s
associated with the use of helium as the
gas bearing medium.
For ea ch tes t ob jec t, M O I w as m ea su re d in air at
atm os ph er ic press ure. Ba rom etric pressure was
recorded. Pressure was then reduced, and
mea suremen ts made at 15, 20, 25, and 28
inches Hg vacuum. The test chamber was then
backfilled with he lium to atm osp heric pre ssure
and MO I was me asured. The data wa s plo tted
and extrapolated linearly to perfect vacuum
co nd itions .
The change in M OI from the vacuum value for
each of the vacuum conditions and helium was
then plotted as % MO I error due to entrained
and entrapped atmosphere vs a bs olu te
atm os ph er ic pre ssu re. The magnitude of the
error du e to air varied from nearly 19 percent of
vacuum MO I for a very thin walled cylinder
rotated about its transverse ax is to near zero for
a so lid steel sphere. Most test items were made
of 0.007 inch thick mylar, so that the effect of air
would be m ore drama tic.
Cost of Helium In March, 1991, the cost of
helium wa s $ 84 for a 29 1 ft 3 bottle. About 1
CFM is required for th e ins trum en t. In addition,
a vo lum e of helium equal to the volume of the
test cham ber will be required. Typically, about
$15 wort h o f helium is required for one
m ea su rem en t. Th is is a tiny fraction of the cost
of buying a vacuum chamber and expending the
en erg y to p um p th e a ir ou t.
The he liu m atmosphere value of MO I was then
plotted as a s trai ght horizontal line.
The
intersection w i th the MO I vs air pressure line
co ns iste ntly fell a t an air atm os ph er ic equivalent
press ure of 4 to 5 inch es Hg ab so lute pressure.
This agrees with the pred iction of 4.25 inches
based on the relative den sities o f helium and air.
Description of test method
It was the intent of these tests to determine the
fea sibility of measu ring M OI of various test pa rts
designed for use in spa c e in a helium
atm osp here at 1 a t m o s p h e re p ressure
(nom ina lly 14.7 Psia) as a substitute for
measuring these parts in a partial vacuum. The
objectives of this study were:
1.
T o d e t er m i n e t h e le v e l o f re duced
press ure air (vacuum) equivalent to the
helium environment for various tes t part
shapes. The shapes measured were; 2
cones, 2 cylinders, 1 solid sphere, and 1
flat pa ne l.
2.
T o d e t e rm i n e c o rr e c ti on fa c tors to
extrapolate test part MO I in vacuum
ba se d o n h elium atm os ph ere res ults
3.
T o d e v e l o p a g a s b ea rin g M O I
instrumen t su itable for o pe ratio n w ith
8
Figure 2 - Helium/Vacuum Test Setup
9
a 5.25 inch diameter and 14 inch height; the
other had a 4.25 inch diameter and 17 inch
he igh t. Because of their shape, they had greater
entrained and entrapped air than the cones
(which we re o f the sa m e th ickne ss m ylar).
Therefore, the effec t of air was greater (19% vs
10% for the co ne s). Eve n w ith this large error in
air, w e were still able to predict the MO I in a
vacuum with high accuracy. For the shorter
cylinder, the value of MO I in a vacu um was
1.68265 lb- in 2. If we calculate the MO I in a
vacuum using the M O I in a ir and the M O I in
helium, then this calculated value is within 0.14%
of the true va lue in va cu um . Fo r the longer
cyli nder, the value of MO I in a vacuum was
2.12335 lb-in 2. If we ca lcula te th e M O I in a
vacuum using the MO I in air and the M O I in
helium, then this calculated value is within 0.22%
of the true value in vacuum.
Tes t Resu lts
Open Cones-- Thin walled cones are comm on
shapes for ce rta in types of space vehicles. T w o
cones w e re te ste d . O n e co n e w as 4 .6 75 inch
diameter by 16 inches long . The other cone was
5.75 inch diame ter by 13 .75 inch es long . Bo th
we re open on one end and had a wall thickness
of 0.007 inch. They were oriented to measure
M O I ab ou t an ax is p ar alle l to the base at about
1/3 the height. This was nominally through the
C G . Bo th cones exhibited slightly less than 10%
error in air (this number could have been
decreased by m aking the co ne m aterial thicker).
For the sh orte r co ne , the va lue of MO I in a
vacuum was 0.6 15 04 lb-in 2. If we calculate the
M O I in a vacuum using the MO I in air and the
M O I in h eliu m , then this ca lcu lated va lue is
w ithin 0.12% of the true value in vacuum. For
the long er c on e, th e v alu e o f M O I in a vacuum
was 0.72390 lb-in 2. If w e calculate the MO I in a
vacuum us ing the M O I in a ir and the M O I in
helium, then this calculated value is within 0.08%
of the true value in vacuum . As described
pre viously, the m ea su re d v alu es in h elium
indicated a density slightly higher tha n w ou ld be
predicted from the theoretical density of helium.
W e believe this is b ec au se the he lium is
pr ob ab ly m ixed w ith a sm all amo unt of air,
increasing its density. The helium data should
fall on the cu rve at a pressure of 4.14 inches of
me rcury. Instead, the longer cone was at 4.77
inches and the shorter cone was at 4.73 inches.
This sma ll difference was not enough to cause a
sign ifican t erro r in the pre dicte d v alu e o f M O I.
So lid Sph ere-- T he precision-lapped stainless
steel sphere had a diameter of 4.0078 inches
and w as roun d w ithin 5 m icroinche s. A s w ou ld
be expected, the effect of air was negligible (less
than 0.01%). This data was not plotted.
Conclusions
We have deve loped a new
method of testing which simulates the vacuum of
outer space without requiring a large expensive
vacuum chamber. This method involve s first
measuring the object in air, th en m ea su rin g it
ag ain in a helium environment, and extrapolating
the va lue s to yie ld th e m as s p ro pe rtie s in a true
va cu um . Experimental data on a number of
shapes indicates tha t this meth od w orks ve ry
w ell.
Space Electronics has developed
instruments which use helium to lubricate the
gas bearing in the instrum ent, so the y are
co mpatible with this method. This discovery
sh ou ld make it possible to m easure very large
ob jects (such as assem blies used in a space
station) witho ut requ iring a vacu um cha m ber.
Flat Plate-- The flat plate was a .120 inch thick
lucite 5½ by 16 inches. MO I was measured
about the short axis. The flat plate was selected
as a test part bec aus e it had n o en trappe d air.
N ote that the relationship between the MOI
measured in helium and that at an atm os ph er ic
press ure of 4.14 inch es o f me rcury is the sa me
as ot her shapes, indicating that the same
form ula ca n b e u se d fo r an y sh ap e o bje ct (i.e.
the same relationsh ip exists for both entrained
and entrapped air). The value of M O I in a
vacuum was 9.7 11 76 lb-in 2. If we calculate the
M O I in a vacuum using the MO I in air and the
M O I in helium , then this ca lcu lated va lue is
within 0.05% of the true value in vacuum.
Open Cylind ers-- T he se test pa rts were thinwalled pla stic tubes open at both ends. One had
10
Figure 3 - M OI v s. Chamber Pressu re - O pen C ylind ers a bo ut C ross Axis
11
Figure 4 - M OI v s. Chamber Pressu re - O pen C on es a bo ut C ross Axis
12
Figure 5 - MO I vs Ch am ber Press ure - Th in Recta ngu lar Plate
13
Tes t Data
Short Cylinder
Vac
Ab s. Press ure
MOI
0
30.14
1.92892
15
15.14
1.81009
20
10.14
1.77191
25
5.14
1.72454
28 .5
1.64
1.68811
30.14
0
1.68265 *
HE
30.14
1.72176
Calculated **
Deviation
1.68033
-.14%
Calculated **
Deviation
2.11864
-.22%
Long Cylinder
Vac
Ab s. Press ure
MOI
0
30.14
2.51772
15
15.14
2.33161
20
10.14
2.25853
25
5.14
2.18978
28
2.14
2.14811
30.14
0
2.12335 *
HE
30.14
2.18515
* Extrapolated Data Point
** Ca lculated from Air and HE data a t Atm . Pressu re
14
Short Cone
Vac
Ab s. Press ure
MOI
0
30.14
.674765
15
15.14
.646299
20
10.14
.635092
25
5.14
.626813
27
3.14
.620793
30.14
0
.615040 *
HE
30.14
.624402
Calculated **
Deviation
.614329
-.12%
Calculated **
Deviation
.723320
-.08%
Long Cone
Vac
Ab s. Press ure
MOI
0
30.14
.792282
15
15.14
.757376
20
10.14
.746159
25
5.14
.736432
27
3.14
.730344
30.14
0
.723900 *
HE
30.14
.734811
* Extrapolated Data Point
** Ca lculated from Air and HE data a t Atm . Pressu re
15
Flat Plate
Vac
Ab s. Press ure
MOI
0
29.56
9.97983
7
22.56
9.91993
10
19.56
9.89673
15
14.56
9.84724
20
9.56
9.80396
25
4.56
9.75381
27.25
2.31
9.73270
29.56
0
9.71176 *
HE
29.56
9.75242
* Extrapolated Data Point
** Ca lculated from Air and HE data a t Atm . Pressu re
16
Calculated **
Deviation
9.70694
-.05%