Daniel Guggenheim Airship Institute
Akron, Ohio
DESCRil'TION OF SE!iLF -PROP~LL ... U A1RSIIIP MODEL 01· l: 4 } INF.NC.SS RATIO
FOR USh IN \',ATh'R TANK TESTS
Report on Item 2, Contract NOs-68971
In order to make the comparison between test results obtained with two
models of different fineness ratio more direct, it seemed desirable to
make the new model the aame volume ae the 1/150 scale "A.lcron" model, and
to make the contour similar. This oonsidero.tiou requires that at a givsn
fraction of the length the radiue ahall be a col'.letant fraction of the
maximum radius for both 111odels. Thue, if the radius of either model is
plotted in percent of' tho maximum radius ae ordinates atainst fractional
distances of' the total length frorn the tail as abscissae, both model a will
have the same profile .
From these two conditions the overall longth and maxi mum diameter for a
model of 1:4 fineness cac be determined. ror, let r • radiue of the model
at the etation x inohes from the tail, a the cross-section at the same point,
.-! the total model length in inches and R and S the maximum radius and oross£
uction reepeotively. Then for both models ,
r • R • r(~/jJ) and
s • S • F( ...., /,fJ
~here f(X~) and F(X/~ are coefficients relating the local radius and
oroea aeo~ion with the ..aximum values. Then V, the model volume (which
must be the same for botr ·~odels), is liven by the relation:
I V• / •·dx • J~ ('Y J)dx.
But since /} ( X/j')d: 1s so"'e cO•~•tant times ,/ , the model length
()
V • k • .,.,J and
"J. • v2 • k·S1 ·~ • k•S2 ·~
where s1 , s2 and .-11• ~ are the maximum oroes aeotion and total length of
the two models, 'eapeotively. Knowing S end ,,,/ for the 1/150 eoale "Akron"
model and having eiven that the length of the ne codel ie four times the
maximum diameter, the dimensions are determined. The distance from the tail
to given stations in the nc, 'l model will then be to the similar dimeneion
in tho old model as ~/..&J. while the radius at a given station in the new
modol will be to the radius at the oorresponding etation in the old model as
R~/R 1 • The coordinates of the new model contour were calculated in this
mfnner and plotted to a suitable scale. The coordinate• used to lay out
the model template were then taken from the curve thus obtained. Table 1
gives the dimensions of the lr4 model 1rofile. The volume wa~ checked by
graphically evaluating the integral ;-.ta.ax.
0
.... u ... ~ .. "'"'c VUUV.LU& .n.L~CU.&..P •uD".Lvl.l v V
Akron, Ohio
2
Tho fine or the 1:4 model ~re designed to be s similar in shape ae poesibl
to the fine of thc'~kron"model. Applying to th fine the simple rules u1ed
in obtainin the model contour ould hove resulted in an area con1lderably
smaller than seemed neoeeeery to give the n w model atabil1ty characteriatios
imil r to the "Akron" model. A criterion propo1ed by H. R. Liebert 11
as follo (see ~1g. l):
S • k • 1:· K2-K1) l +12/§ -
where S • required fin area
,,~l • volume of ship
L • dietanoe from rudder axle to C.B.
K1 and ·2 •virtual mass coefficients for an ellipsoid of the
m~el finenes ratio
q • ~E • the width between ed e of fine squared,
divided by total area of fins plus rea through
hull lying between fin•
k • con tant deter ined from pr vioue successful design1.
Sub tituting known values from the "Akron" model, k booomes 0.75. Accordingly.
the !'in area and poEition s varied until thie value v s obtained for k.
t the amo time, tho general sh pe of th fin a de as nearly s po1eible
like the "Akron" typo fine . 1-ig. 2 i;ivea detail• of the fin form used. The
fin con tant k for thie shape is r . o. The location of the rudder axi1
wa . \. nearly constant, bein O.O!H.>L from the tail for the now model and
O.OE~> ..f rrom the tail for the "Akron lOdel.
In goneral, the new 1:4 model is 1imilar in construction to the free-flight
model of the "Akron". (This was described in th Reporte on Iteme 11 nd 12
of Contr ct NJ -47286). The hull ie de up of five separate maGneeium
alloy castings esembled to~ether and fini1hed accurately to the model contour.
Tho sep rate sectione aro held in lignment by pairs of ball-bearing
hinge joint on vertical axee. A s 11 amount of olearnnce bet een adjacent
parts per mite the model to bend or deflect ot the four hin ed croee-aectione.
Tho deflections re about vertical tr nsv rse axes, nd are restr ined by
utiff coil prings connecting the adjacent p rte at the eides of the model.
Accordingly, the deflections are proportion l to the bending moment exietin
t the cro e-section perpendicular to th hinge axis, and the defleotione
{and hence, bondin moments) are recorded by a pu h-rod and lever system
Which ctuatee diamond scratching on a rot tin polished glass cylinder.
Due to the relatively longer fins in the 1:4 model tho two rear eectione at
which b nding momenta are measured re not located tho eamo as in the old
mod _· . In . • 11Akror." 11odel t'r • ~ inged oros1-aeotione were located at
.2341, .3u1.J, . 567.l and . 730,,/. In the new model, tne hinged oroseeectiona
re 1.Jcated at . 20,,I, . 1. 4.J, .5t 7,/ nd . 7'.>5.J .
The motive po ·er for the model le provided by eight dry cells inetnlled in
the t o forward seotione and connected to 1/20 hp, 6 volt, ehunt- round
el otric motor. Thie motor drives t o 3" propellere mounted on outrig ere
through a double bevel gear drive. Motor speed ( nd hence, propeller epeed)
Daniel Guggenheim Airship Institute
Akron, Ohio
11 varied by in1erting resistance in the armature oircuit. The motor switoh
ia operated by a push rod extendin through a flexible rubber diaphragm in
the top of the model. The switch ia designed to shut off the motor automatically
after the propellers have turned a certain number of revolutione. Aa
in the model previouely constructed, an eleatrioally driven vibrator is provided
which traoee a wave form on a drum carrying soaped paper tape and driven
by the motor. Thie enablee the motor speed to be determined throughout the
run.
Rudder motion is controlled as before by a cylindrical oam which turns one
revolution for each oyole of operation of the motor. The cam actuates a bell
crank, one end of which moves in a short arc approximately along the oenter
line of tho model. An axial wire baok to the rudder linkage transmit• the
desired motion to t he ruddere.
The gla•~ cylinder on which bending moments are recorded is driven through
double worm reduction from the propelling motor.
Fib. 3 ia a schematic drawing ehowing an approximate layout of all the
various iteme in the model. Fig. 4 is a Fhotoc;raph showing the center seotion,
h1le Fig. 5 ii a photograph showing the intorior of the two nose and
two tcil ~eotions.
f ittinge are provided in the top of the mode l so that the launching apparatus
devised for the self-propelled "Akron" rnrJdel oun be utilized. The motion of
the model in teete ie photographed the eume wuy os deaeribed before. Similarly,
provi1ion is made for measuring momenta t two section~ only during
one teet run, the other sections being looked, so that teet runs have to be
repeated to measure the moments at all four seotlons. A ref'inement added
to the "Akron" model after some teete had been run was included on this r.todel •
'l'his conaieta of a small lit;ht bulb set flush in the upper surfaoe of the
model nnd oonneoted in parallel with ths electric motor. Thie light goe1
on and ahuta off with the motor. Thia makes it possible to tell on the film
reoording the model motion when the motor etarte and how long it runa.
The moments of inertia of the different eectione about their hinge axe1 were
computed ae described in the report on Item 11, Contract NOe-47286, aeeuming
a weight distribution in equilibrium with buoyant forces and uniform distribution
aeroes cross-section!. The~e moments were determined experimentally
and adjusted to the desired values by properly locating the extra eight•
neoe!sary to submerge the model. The moments of inertia of the eeotion1
were measured by the method outlined in the re ort on Item 11, Contract
NOs-47286. The moment of inertia of the entire model about the traneveree
axis throueh the oenter of buoyancy wae measured as before by determining
the period or torsional oeoillation when euspended on a ca librated wire.
The metacentrio height was detormjned by two separate methods. In the 11rst
method, the nose and tail caps were removed and ateel plates drilled and
buahed on the model oenter liue were atta oied at the ends. fhe model ~s
then suspended by these holee on small pine held in the lathe centers. The
moment required to balance it when rotMted 90° was then meaeured anci from
the known total weight, the dietanoe from the center line to the center of
gravity was oomputed. Since the center of buoyancy is located on the model
oenter line, this gave the metacentric height direotly. lhe polar or rolling
4
Danie Guggenheim Airship ln1titut e
Akron, Ohio
moment of inertia Ip waa determined by observin the frequency of vibration
uain a calibrated spring at a me eured dietance from the axia to re•train
the model in the 90o rotated position. This method had been used on the
"Akron" model, but it was suspected that the friction of the pins in the
buahings might be excessive. Accordingly, short rode were faetened to the
steel end platea and the model e suapended on a pair of level rail• by
these rode. The metacentric height 1'9.1 obtoined e before by measuring the
monent required to intain the model rolled 90o and the moment of inertia
• a likewise determined. The two detenninatione of the metaoentrio height
re very oonsiatent, but the rolling moment of inertia ae determined by
the l tter method was almoet 15°/o higher than tho firat value obtained.
Thie 1 tter volue ne thought to btt more accurate, ae it could eaeily be
seen that the vibration1 ere subject to lee! damping by thie method or
suspen ion. Table II i•es a comp rieon bet ecn the computed and experimental
values for the v rioua moments of inertia.
The rolling moment of inertia measured about the center line of the model ia
greater than the required rollin moment about the oonter of gravity by the
mount h 2 ·!!. , where
g
h • diatanoe between the longitudinal axis through the
center of gravity and the center line of the model,
in inohea (metacentric height for the airship model)
\'i • total weight or the model, in pound1, end
g • gravitational acceleration in in/aeo •
bout, <t_ of model • Ip about longitudinal ax11 + h • • .!.
through center of gravity g
liav1n
roll in
r vity
determined Ip bout the center line and h experimentally, the required
moment of inertia about the longitudinal axia throu h the oenter of
B computed from the abov relation.
The noomputed" values of Ip end h lieted ill Table II were obtaiued aa followa:
the computed moment of inertia for the "Akron" model about the vertical
transverse axle through the oenter of buoyancy a i• 69.7 w-seo -in. The oor-reaponding
moment of inertia for the 1:4 model ie 43.6 U-eeo2-1n.
The ratio of these values i~ accordingly
69.7 • 1.60
43.6
The lengths of the two models ore, respectively, 62.26 and 43.6 inches, eo
that the ratio or tho lengths squared i•
(
62.26\a • l 66
48. 26•) •
6
Uaniel Guggenheim Airship !netitute
Akron, Uhio
Accordingly, the moment of inertia about a transverse axis through the oenter
of buoyancy is approximately proportional to the length of the model squared.
Since no design data for e full site rigid airship of 1:4 fineness ratio ie
available to use in estimating the rolling moment of inertia of the model,
it VlBS assumed that the rolling moment of inertia would be proportior.al to
the equare of the maximum radius and that the metacentric height would be
directly proportional to the radius. The scaled-down value of the rolling
moment about tho center of gravity for the "Akron" model i~ 6.2 0-sec2-in,
hile the metacentric height is 2.5 inohee. The maximum radiue ie 5.312
inohe1. The maximum radius of the ls4 model i 6. 033 inches. Then lp, the
rolling moment about a longitudinal axie through the center of gravity, for
the ls4 model should be giver approximately by the relation:
Ip ./u.o~")J
6.2 \5.312 •
from which Ip • 8.0 1-eeo4-in. ~imilarly, the metaoentric height
the ne model should be given by the proportion
from whioh
h
2.6 •
6.033
5.312
h • 2.64 inches.
'
h for
A with the "Akron" model, the experimental ratio IP/h is considerably
higher than ~ould be desired, but the experimental reaulta of Table Il
are the beet that oould be obtained ·dthout greatly increasing constructional
dif.ficultiea . In any oaee, this lack of similarity would have em.all effect
on the hull bonding moments oc~aeioned by a 1ide guat •
• B.L.
Akron, Ohio
2-6-40
Diatance from Tail
in inche1
0
0.5
l
2
3 '
4
5
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
43
44
45
46
47
47.5
48
48.264
TABLE I
Radiua
in inches
0
0.84
1. 20
1.76
2.21
2.60
2.98
3.32
3.93
4.44
4.86
s.20
5.48
5.68
5.83
5.93
5.99
6.03
6.033
6.03
6.01
6.95
5.84
5.64
5.32
4.89
4.58
4.22
3. 75
3.17
2.28
1.64
0.80
0
Daniel Guggenheim Air ship Insti t ute
Akr on, Ohio
Cro11 Section
in 1q.in.
0
2.2
4.5
9.7
15.3
21 .2
27.9
34.6
48.5
61.9
74.2
85.0
94.4
101.3
106.8
110.5
112. 7
114.2
114.3
114.2
113.5
111.2
107.2
100.0
88.9
76.2
65.9
55.9
44.2
31.6
17.2
8.1
2.0
0
Length - 48.26"
Maximum diameter - 12.0711
Volume - 3795 cu. in.
•
Distance from Tail
in inches
TABLE I
Radius
in inches
Daniel Guggenheim Airship Institute
Akron , Ohio
Cross Section
in sq.in.
F = c -<rs.>< 100,es-? :( v 2..
--
c ::-
~o
28
30
32
34
36
38
40
42
43
44
45
46
47
47.5
48
48.264
,&<3 v~ xC
·V
-r- •
6.0~
6.033
6.03
6.01
5.95
5. 84
5.64
5.32
4.89
4. 58
4.22
3. 75
3.17
2 .28
1.64
0.80
0
!f 00
I (J ~"O
3! D
G '!GO
0 I rJ
114.2
114.3
114.2
113.5
111.2
107.2
100.0
88 .9
76.2
65 .9
55.9
44.2
31.6
17.2
8.1
2.0
0
Length - 48.2611
Maximum diameter - 12.07"
Volume - 3795 cu.in.
Doniel Guggenheim Airship Institute
Akron. hio
TABLE II
Moment of Inertia in *-aeo -in
Tail section
Two tail 1eotion1 locked together
iwo no1e eeotiona looked together
~oae 1eotion
Entire model about tranaver!e axis through C.B.
Entire model, about longitudinal axis through
oenter or gravity (Ip)
etaoentrio height (h) in inohea
...
, ./r-1eo ..
Computed Experimental
1.668 1.67
7.16 6.96
17.4 17.0
3.07 3.07
43.6 42.6
8 .0 4.72
2.84
2.82 S.63
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Daniel Guggenheim Airship Institute
Akron, Ohio
Fig. 4. Photograph ehowing center section of self-propelled model.
a - 6 volt eleotrio motor
b - cross shaft driven through worm reduction
c - worm wheel driving poli!hed glass cylinder
(glass cylinder is directly behind worm wheel)
d - electrioally driven vibrator
e - drum carrying soaped p&per tape on which vibrator reoorde
f - motor switch
g - bell crank operating rudders
h - levers carrying diamond points which scratch bending
moment records on glass cylinder
j - oam governing rudder motion
l - outrigger
•
..
Daniel Guggenheim Airship In1titute
Akron, Ohio
Fig. 5. Photograph showing interior of t'ro nose and two 'IF
tail aeotion1. ~
•