A facility was constructed for the study of water-entry,

water-exit, and underwater trajectory behavior of

small momentum-propelled missiles for varied trajectory

launching angles, missile accelerations and velocities,

wave fields and conditions of cavitation. A unique feature

is the electromagnetic missile propulsion system.

The facility is made principally of non-magnetic and

electrically non-conducting materials to permit the determination of missile accelerating force from the reactive force on the launching coil

Ellis, A. T.

Waugh, J. G.

Caltech Authors - Main

The Variable-Atmosphere Wave Tank 
by 
J, G . Waugh>:• and A. T. Ellis** 
A facility was constructe d for the study of water-entry, 
water-exit, and unde rwater trajectory behavior of small 
momentum-propelled missiles for varied trajectory 
launching angles, missile accelerations and velocities, 
wave fields and conditions of cavitation. A unique 
feature is the electromagnetic missile propulsion sys-
tern. The facility is made principally of non-magnetic 
and electrically non-conducting materials to permit the 
determination of missile accele rating force from the 
reactive force on the launching coil. 
The Variable-Atmosphere Wave Tank at the California Institute 
of Technology, Pasadena, California, is a new facility designed for 
the study of water-entry, water-exit, and underwater traj e ctory be-
havior of small momentum-propelled missiles for varied trajectory 
launching angles, missile accelerations and velocities, wave f i elds , 
and conditions of cavitation. 
>:< Consultant, Propulsion Division , Underwater Ordnanc e Department, 
U . . S. Naval O:::dnance Test Station, 3202 E. Foothill Blvd., 
Pasadena, Cal ifornia 
>:<>:c Associate Professor of Applied Mechanics, Hydrodynamics 
L abo:::atory, California Institute of Technology, 1201 E. California 
Blvd. , Pasadena, California 
Description of F a cili ty 
The diagram in Fig. 1 and the photograph in Fig. 2 show a 
reduced-pressure vessel constructed almost entirely of 2-inch-thick 
1ucite sheet. The three flanged sections, bolted together with nylon 
bolts and sealed with 0-rings ar e a wave generation section, a test 
section, and a wave-absorption section. The tank rests on four sup-
ports provided with screws for height adjustment and leveling. The 
two inner tank supports are heavy laminated wood piers with fiber-
impregnated plastic bases and adjusting screws. The two outer tank 
supports are made of steel and the tank end-plate as~ociated with 
the wave-generation equipment is of stainle ss steel. The floor of 
the tank is about 3 feet from ground level. 
Access ports with covers are provided 1n the wave-generation 
and absorption sections. A trolley hand hoist, directly above the 
test section, facilitates removal and replacement of the turret cover. 
All covers are fitted with 0-rings to make them airtight. Tank 
a1r pressure can be lowered to the vapor pressure of water, thus 
providing a range of cavitation numbers within the tank. Water of 
the high clarity necessary for metric stroboscopic photography is 
maintained with a Millipore filter. 
Test Section 
The 5. 6-foot-long test · section (Figs. · 1 and 2) is provided with 
a 2-foot turret to allow some aerial trajectory. The turret has a 
removable airtight cover for missile loading and recovery. A nylon 
fabric backstop, impervious to moisture and molds, is mo~ted in 
2 
the turret to halt missiles after water exit. The backstop, attached 
with nylon cords to eye-bolts at the corners of the turret, can be 
moved to one side for tank access. 
Three 1-foot-diameter holes in the floor of"the test section 
provide for mounting missile launching systems. One hole is di-
rectly beneath the turret for vertical or near-vertical upward launch-
ings; the other two are on either side for oblique launchings into the 
turret. The missile may be launched either into the advancing wave 
or away from · .it. When not in use, the holes are fitted from under-
neath with plates so constructed as to make the channel bed uniform-
ly level. 
The tank and supports near the test section a .re constructed 
of plastics and wood that are non-magnetic and electrically non-
conducting to permit determination of missile virtual or added mass 
by means of an electromagnetic missile propulsion system that is 
described later. The action of this system is illustrated in Fig. l, 
which shows a steel sphere launched vertically upwards from a 
well, mounted beneath the central hole of the tank floor by means 
of a missile accelerating or launching coil. Different types of wells 
that could be used are shown in Fig. 3. In other applications, the 
launching coil (in suitable housing) could be submerged (as in Fig . 2) 
and missiles launched under water in any direction. The system 
could also be used for water-entry launching tests. 
Propulsion System 
A unique feature of the tank is its I"r?-agnetic propulsiol"). system 
for small missiles. A sphere or spherical shell of large magnetic 
3 
permeability is located on the axis of a coil of wire whose radius 
is large compared to the sphere (to minimize hydrodynamic inter-
ference) and the coil-winding cross-section. Since the coil-winding 
eros s- section is small, the magnetic field generated by a current 
in the coil is very nearly a product of the number of turns times 
the field due to the current in a single turn. The large coil radius 
makes the electromagnetic coupling between the coil and sphere 
rather poor, but it does provide for a relatively simple mathemati-
cal treatment which assumes that the average magnetic field of the 
coil is not appreciably affected by the presence of the sphere. If 
a pulse of current passes through the coil when the sphere is on 
axis, but not in the center of the coil, the sphere . will be drawn 
toward the coil center with a force proportional to the spatial 
gradient of the energy in the magnetic field. The field energy 1s 
proportional to the square of the current and hence if the current 
is turned off when the sphere reaches the coil center, the sphere 
will continue in its path along the coil axis without deceleration 
from magnetic forces. A means is thus provided for propulsion 
that does not depend on the presence of a nearby object or disturb-
ance such as an explosion or gas release. Examples of accelerati n g -
coil launchings are shown in Figs. 4 and 5. 
The wave tank and coil holder were constructed of non-mag n e tic 
--""' c-.. -
force on the coil due to their presence. In this case, the force on t he 
coil is equal and opposite to the propelling force applied to the missile. 
4 
The coil may therefore be instrumented externally and direct 
measurements of this force may be made without any attachments to 
- w • • • • • • 
-=~ ~ ~:'J_j .:...:. =. ::· .. :..:-.. -~-.. :. :.~ ::. .-. :.::. 6. -= c.. ::.~..:_.:.-
ally recorded displacement-time records, these data may be used 
to yie ld information on virtual mass and drag under conditions o f 
suddenly accelerated motion. The accele r ation may be from rest 
or from motion with an already established wake. The former case 
should agree with established theory for short times but the latter 
is a more difficult situation in which data are needed to guide theory. 
Forces due to eddy currents in the missile are small compared 
to magnetization forces when the rate of change of the field from 
the coil is nqt too g reat. An eddy current drive could have been 
used were it not for the · fact that this would make it more difficult 
to obtain an impulse of appreciable duration. To impart sufficient 
momentum to the missile, a short-duration impulse would involve 
large missile (and fluid) accelerations that could introduce unwanted 
cavitation or other effects undesirable for some tests. 
Since the propulsion force on the magnetic sphere is a true 
body force rather than a contact force, it avoids the possibility of 
generating elastic waves within the sphere itself that might be objec-
tionable if one were interested in hydroelastic effects and did not 
want extraneous waves to be generated. 
As an indication of performance of the system, a . l-inch-
diam e ter stainless steel sphere attained an underwater velocity of 
approximately 90 fps in 2 inches of travel from rest for an ex-
penditure of 1, 500 watt- seconds of electrical energy when a 
5 
1 - 1 / 2- i ncn-I. D. accelerating coil ''-' Ci..S use d. Witn an 8 - i:-:. c :-... -I. ::). 
coil, a velocity of about 50 fps was observed for about 20, 000 watt-
seconds of energy. The great reduction in efficiency with coil size 
was to be expected. Althoug h sufficient energy is available for 
present working needs, another capacitor bank, that will provide a 
total of 54,000 watt-seconds, is planned. In applications w h ere a 
small coil is permissible, v e locities o f the order of 500 · fp s should 
be possible. The period of acceleration of the missile may be varied 
by adjusting parameters in the ele ctrical circuit and the missile may 
e ven b e made to describe oscillations if desired. 
Wave Sys tem 
The tank wave channel (Fig. 1} is 15 feet long, 1- 1 /2 f eet 
wide , and 2 f e et high. The maximum (undisturbed} water leve l for 
wave studies is about 1-1/2 f e et. A rig id flap, hinged at the bottom 
of t h e channel, and actuated by an adjustable crank and controlle d-
spe e d gear-motor system, is used to generate prog ressive waves 
from l to 3 feet in length and up to 3 inches in amplitude. It is 
situated 1-l /2 feet from the end of the channel so that fluctuation 
in water level behind it would be moderate and less than flap h e i g ht 
f or all flap amplitudes. The distance f rom the w a ve generator t o 
the cen ter o f the test section is 5-l/2 feet, almost four times th e 
maximu:n wave depth. l Theory indicates that the · extraneous dis-
1 J ame s Ross and C. E. Bowers. 11 Laboratory Surface Wave E q uip-
ment11, St. Anthony Falls Hydraulic Laboratory. University of 
M i nnesota, Minneapolis, M inn., Proj e ct Report No. 38, November 1953 . 
6 
turbances of the water at t he wave generator become negligible in 
two or three wave depths of travel; hence essentially free waves 
should obtain in tho teet aaction. 
This method of generating waves was chosen because the 
long est wave contemplated for study is about 3 feet in length, a 
relatively short length compared to the water depth. 2 Theory 1n-
dicates that this generator is suitable for pr o -=.ucing such waves. 
Moreover, it does not possess a large inertia characteristic, is 
easily regulated, and the flap motion required t~produce a desired 
wave is calculable. 
No wave absorber lS presently planned because the wave channel. 
extending 8 feet beyond the center of the test section. is sufficiently 
long that four of the longe st waves (3 feet) can pass the center of 
the test section before the reflected waves return. It is believed 
that the wave train will stabilize and tests can be completed within 
this period. Tests of longer duration may require a wave absorber. 
Conclusion 
The unique construction of the Variable-Atmosphere Wave Tank 
and associated launching equipment may provide a means to estimate 
hydrodyn amic forces on the accelerated missile from reactive forces 
on the launching coil. and hence a means to obtain information on 
virtual mass and drag. Moreover, the laWlching equipment may pro-
vide a means to study missile and associated cavity behavior under 
2 Ibid. 
7 
unusual conditions, e. g., a cavitating missile that is stopped 
sudd e nly or made to oscillate back and forth by electromagnetic 
forces. 
A c knowle d gements 
The authors are indebte d to G. W. Stubstad of the U.S. Naval 
Ordnanc e Test Station for helpful comments and suggestions. 
This work was supported by the Department of the Navy, 
Bureau of Naval Weapons, Contract Nl23( 19)59369 to the 
California Institute of Technology, and Task Assignment No. RRRE-
0400l/216-l/R009-0l-Ol to the U.S. Naval Ordnance Test Station. 
8 
J. G. Waugh A. T. Ellis 
Captions for Illustrations 
Fig. 1. Diagram of Variable-Atmosphere Wave Tank. 
Fig. 2. Variable-Atmosphere Wave Tank Adapted for Vertical 
Water - Exit Studies. A missile-accelerating coil is inside the 
tank directly beneath the turret. 
Fig. 3. Wells for L aunching Missiles with Accelerating Coils . 
A coil for oblique launchings is shown. 
Fig. 4. Cavitating l-Inch-Diameter Steel Sphere Launched 
Vertica lly Upward by Submerged Accelerating Coil. Sphere velocity 
approximately 65 fps with atmospheric pressure over the water 
surface. A rubber cushion over the coil prevents possible damage 
on missile fall-back. Exposure time (flash duration) approximately 
one microsecond. 
Fig. 5. Water-Exit Behavior of l-Inch-Diameter Steel Sphere 
L a unched Vertically Upward by Submerged Accelerating Coil. 
S phere velocity approximately 50 fps with atmospheric pressure 
over the water surface. Exposure time {flash duration) approx-
imately one microsecond. Time between successive exposures 
1/1500 second. 
WAVE-GENERAT ING 
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The Variable-Atmosphere Wave Tank

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The Variable-Atmosphere Wave Tank

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