Results and Discussion of Submarine Sonic Boom Noise Penetration
Analysis
Remarks on input data and model analysis
The input data in the analysis for the Kodiak program, was furnished
by Dr. K. Plotkin, Wyle laboratory, based on scaling laws deduced
from an earlier work by Jarviner and Hill [1] for underexpanded
rocket plumes. The shape of the exhaust plume was determined
up to a downstream station where the Mach disc is located. Together
with the known vehicle geometry, this suffices to arrive at the
F-function needed for the ray/geometrical acoustic calculation,
from which the incident waveform and intensity at the sea level
were obtained. Figure 1 illustrates schematically the plume and
the Mach disc downstream of the rocket and the corresponding Ffunction
distribution. The overpressure data at the sea level contributed
by the omitted plume portion was not available.
Although the contribution from the rear portion of the plume is
relatively weak and has little significance for most predictions/measurements
on the ground, its effects on noise penetration under water may
not be negligible, inasmuch as the plume can not only add considerably
to the signature length, of the waveform, say L', but may alter
the far-field attenuation rate (owing to an unbalanced [total]
impulse which is normally zero). Therefore, in addition to the
analysis made according to the two sets of sea-level overpressure
furnished, three more sets of sea-level overpressure will be considered
in order to access the correct real-plume effects.
While the plume effect should generally be regarded a significant
aspect of the submarine problem for most space-launch program,
the Kodiak program at hand may be expected as an exception. This
is because the smallness of the rocket's weight, thrust, and dimension
make its hydroacoustic impact very minute in comparison with that
found with the Apollo or Atlas launch (which we have examined
earlier). (The rocket thrust delivered at the Minute-Man launch
amounts only to about 1% of that for the Apollo.)
The sound-pressure intensity underwater at the level of 160 db
has been considered potentially harmful to some marine mammal
species [2,3].* This would amount to about
two (2) psf.** On the other hand, intensity
at the 120-130 db corresponding to (rms) overpressure in the percentile
(0.01) psf range, may also affect adversely the behavior and activity
patterns of some fish and mammals. These are believed to be factors
in the recent impact assessment on the program of ocean wave guide
(SOFAR) experiments [3,4,5]. Whereas, the following model analyses
will confirm that the sonic-boom noise generated in the present
program cannot reach well down to the 1 km depth of the SOFAR
channel, an overpressure level at the 0.01-2 psf range does occur
at depth of 0100 meters, according to the following
analysis.
In passing, we note that the 10-2 psf level
mentioned and to be seen below is still well above the 10-1
Pa, or 0.0021 psf, which has been taken to be the back-ground
noise level of the sea in many studies, according to Ref [6].
Also note that acoustic disturbances in the 10-500 Hz frequency
range, as well as in the higher 10-30 kHz have been of concern
in studies with certain whale species [7].***
The acoustic signals in the higher range mentioned was of considered
essential in previous investigations, on account of their relatively
short propagation range, being 10 km or less, owing to a chemical
absorption process according to an existing study [7]. But this
10 km range is by no means short for noise penetration study here.
The results discussed below pertain mainly to the analysis based
on the flat-ocean model, in which the critical dependence
on the rocket-size and its plume effects will become clearly evident.
The two sets of the available sea-level overpressure data are
limited however to a condition corresponding to a wavefield moving
over the (ocean) surface at nearly the sonic speed which
is comparable to that in a superboom. Under this condition, a
solution allowing interaction with a wavy (ground/ocean) surface
is yet to be developed. For this reason, the corresponding wavefield
computations under a wavy ocean has not been performed.
As indicated in an earlier elucidation, this interaction effects
will be significant even for incident waves corresponding to a
"carpet boom" normally found in steady supersonic cruise.
Its importance will nevertheless be discussed on the basis of
an example analyzed earlier at a condition removed from that of
a super/focused boom.
Submarine Sonic-Boom Wavefields Under a Flat Ocean
Two incident sonic-boom wave forms at the sea level furnished
by the Wyle Laboratory, together with three of their variants,
are employed as input surface overpressure data for calculating
five cases of hydroacoustic response in a flat-ocean model. The
sea-level overpressure in the first example was obtained (directly)
from the geometrical acoustic calculation of the PC Boom program,
referred to as the "carpet boom." Its distribution
is shown as solid curve at the top left of Fig. 2 for z=o corresponding
to the sea level. Inspite of the presence of three discontinuities
in the F-function [Fig.1(b)], the waveform arriving at the sea
level takes on nearly N-wave form. The example with this input
waveform will be designated to be Case A. For the second example,
to be referred as Case B, the incident waveform at the sea level
was provided by another version of the PC Boom involving a local modification
of the geometrical acoustic program by adopting partly the Gill-Seebass
model solution to the Tricomi equation. This is the "focal-boom
model" proposed and implemented successfully by Plotkin in
Ref. [8]. The resulting overpressure at the sea level is shown
in dashes also on the top left of Fig. 2 for Z = 0. The rabbit-ear
like spikes near the two ends of the profile in dashes has been
known to be characteristic of waveform from the Gill-Seebass model
as well as several sonic-boom measurements recorded from towers
(above the ground level). The overpressure at each streamwise
location are shown as "dP" (in psf) vs. "x"
(in feet) at six successive depth levels in Fig. 2, corresponding
to distances from the surface Z = 0, 10, 50, 100, 300 and 1,000
feet. Both set of results show that the disturbance magnitude
as well as its manner of attenuation are not much different from
those found in submarine response to aircraft-generated sonic
booms [9,10].
We next examine the importance of, and the need for, a more complete
description of the F function corresponding
to the aft portion of the rocket plume. We consider three plume
extension models, postulating in two of these cases the similarity
between the anticipated Kodiak/MinuteMan waveform and that
of the much larger Apollo/Atlas system in the length scales of
the negative to positive portions of the waveform (at sea level).
The latter scale ratio is found to be approximately nine to one
(9:1) [11]. The sea-level overpressure are shown on the upper
left of Fig. 3 for three examples, Cases C, D and E, labeled,
respectively, in thin solid curve, in dashes, and in dash-dot
curve. They model the plume extension by the addition after the
real shock of Case A (shown in heavy full dots) a linear axial
variation, as depicted. Case C (in thin solid line) has a shorter
plume extension, the length of which is determined by requiring
the positive and negative areas to balance with each other. The
remaining Cases D and E have the same plume extension length called
for by the 9:1 ratio. In Case D, the area on the negative portion
is 1.8 time that in the positive portion, while in Case E with
a greater negative overpressure contribution, the corresponding
area ratio is 2.7. As were the data from the Apollo records during
ascent, the longer tail portions of Cases D and E give a nonvanishing
sink effect in the farfield, noticeable at the larger depths.
These results confirm that, even without accounting for the full
length of the real plume, the overpressure in the range of 0.01
to 2 (mentioned earlier) can be found within a depth of 1,000
ft., or about one third of a kilometer. In Cases
D and E, disturbances at depth of 300 ft. (close to 100 meters)
of the order up to 0.10 and 0.20 psf are predicted even at 1,000
ft. or 1/3 km, below sea level.
The above study based on the flat-ocean model confirms that under
the flight track, the sonic-boom disturbances produced by the
Kodiak Minute-Man model can penetrate under water with overpressure
level comparable to 1 psf at 100 ft. depth and 0.1 psf at depth
as large as 1,000 ft. Unlike the much larger Apollo, Titan or
Atlas Launch vehicles, however, the Minute-Man shot is not expected
to produce acoustic disturbances/noise that can noticeably reach
down to the ocean wave guide in most part of the globe.
Surface Waviness Influence
In the absence of a more appropriate analysis to establish the
importance of the sonic boom and surface wave interaction effect
on the superboom-like domain (which would call for solving a time-dependent,
nonlinear version of the Tricomi equation with a wavy wall boundary),
we shall examine the result of a linear system valid for
a wavefield (horizontal) propagation velocity larger than the
sea-level sound speed analyzed earlier in Ref. [10]. The work
therein sought correction for a flat-ocean response to an incident
N-Wave, based the theory explained earlier. The particular example
given was for a subsonic (wavefield) Mach number under
water MW = 0.402, corresponding to a supersonic
cruise Mach number Mo = 2.1 at the Stratosphere
and a sea level Mach number MA = 1.8207.
The maximum overpressure at the sea level is 2.020 psf in this
case. The wave length of the sinusoidal surface-wave train considered
in this example is comparable to the incident sonic-boom signature
length L ', being 4L '/2¹ Å 261.4 ft.
The maximum surface slope is taken to be d
= 0.1. The root-mean-square values (rms) of resulting overpressure
distributions (with the waviness corrections) are shown in Fig.
4 as solid curves at three depth levels Z = 100, 200 and 300 ft.
The difference from the uncorrected overpressure in the flat-ocean
model (included as dashes) are significant as depth increases.
At Z = 300 ft. depth and beyond, the waviness correction becomes
an effect of the first-order importance, altering the nature and
power of the noise penetration under water.
For incident superboom-like wavefields comparable to those considered
earlier in Case A-E for the flat-ocean model (Figs. 2,3),
the linear theory yields unbounded results and is invalid. Nevertheless,
the important role of the surface waviness influence in the corresponding
nonlinear, elliptic-hyperbolic mixed problem should be convincingly
evident from above.
Impact-Zone 3-D Description
The lateral (horizontal) extent of the impact zone is typically
large compared to its windward/ streamwise dimension (even at
the leading edge of the boom carpet identified with the super/
focused boom (refer to Fig. 5). A high aspect-ratio theory
similar to the lifting-line theory in aerodynamics is therefore
applicable and was demonstrated to work well in Ref. [11]. The
theory reduces the problem to a two dimensional one and
thus justifies the 2-D formulations underlying all the foregoing
analyses. Essential is, however, the proper orientation of the
local coordinates so that the 2-D analysis is carried out for
each span station in a plane normal to the (curved) center
line. By this procedure, contour plots for specified/chosen psf
value of the overpressure may be generated for each depth level,
using data from the 2-D analysis. [This plot has not yet been
prepared for this presentation.]
Descent Boom Impact
The sonic booms generated along most part of the descent trajectory
of the Kodiak plan will propagate along rays which may reach the
ground/sea surface far from the target area sea/ground
surface with much attenuated signals, or can never do so due to
refraction. Significant sonic boom impact occurs, however, near
the very end of the descent phase when the vehicle/missile is
decelerated to low supersonic or subsonic speed, resulting from
bow shock detachment. With the exception of a vertical (downward)
trajectory, a location can always be found in this instance on
the propagating paraboloid-like, detached shock/wave front where
the surface slope is parallel to sea/ground surface. Therefore,
it should not be surprising to find the front of the descent boom
hitting the sea/ground surface at nearly normal incidence, and
this is indeed the case found by the ray-acoustic (PC Boom) computation
for the Kodiak run.
The calculation by K. Plotkin indicates a ray-angle (measured
from the vertical) closes to 6.5°. The speed of the horizontal
wave-field movement may then be estimated to be the product of
cot (6.5°) and the sea-level sound speed corresponding
to a Mach number of 8.78 above the water. This gives a Mach number
1.94 under the water, that is, during a short period at and after
the impact, the responding hydroacoustic wavefield will move supersonically
under the ocean. This means that, unlike the case with ascent
phase, signals will propagation with undiminished strength
to a depth considered larger than the signal wave length, L
', which will be eventually attenuated, however, by 3-D effects.
The foregoing properties of the supersonic under water wavefield
would have been an extremely important aspect of the present study,
if not for the other features shown in the descent-boom "foot print"
according to Plotkin's analysis (Fig. 6). Whereas the maximum
overpressure level in the 0.5-1.0 psf range is comparable to that
in the ascent phase, the contour plot, unlike that in Fig. 5,
takes on an onion-ring like pattern with the higher overpressure
of 1-3 psf being found mainly on the inner ring. Unlike that
in Fig. 5, the zone under 2-3 psf is limited to a transverse dimension
of 2-3 nm, which forms the basis (root) of a relatively narrow
column under water. For this reason, we do not consider
the descent phase is more critical aspect of sonic boom problem
for the Kodiak plan at the present stage, which certainly deserve
attention in a more critical study subsequently.
Cited Reference
1 Javiner, P.O. and Hill, J.A.F. "Universal Model For Underexpansion Rocket Plumes in Hypersonic Flow," Proc. 12th JANNAF Liquid Propulsion Meeting, Nov. 17-19, 1970, Las Vegas (1970).
2 Richardson, W.J. et al., Marine Mammals and Noise, Acad. Press (1995).
3 Howe, Bruce, et al., "Final Environment Impact Statement for Kauai Acoustic Thermometry Experiment of Ocean Climate Program and Marine Mammals Research Project," ARPA, NOAH, State of Hawaii, (1995).
4 Baggeroer, A., and Munk, W., "The Heard Island Feasibility Test," Physics Today, Sept. 1992, pp. 22-30 (1992).
5 Paddock, L., "Undersea Noise Test Could Risk Making Whales Deaf," Los Angeles Times, Tuesday, March 22 (1994).
6 Thompson, P.A., Compressible-Fluid Dynamics, McGraw-Hill, p. 182 (1972); also see Pierce, A.D. Acoustics: An Introduction to Its Physical Principles and Applications, Acoustical Soc. America, Am. Inst. Phys., pp. 60-63 (1989).
7 Howe, Bruce (private communication; also cf. Refs. 2,3 above), Sept. 1997.
8 Plotkin, K.J., "Potential Sonic Boom Focal Zone From Space
Shuttle Reentries,"
WR 89-11, Wyle Lab., (1989); also see Plotkin, K.J., Downing,
M., and Page, J.A., "USAF Single-Event Sonic Boom Prediction
Model: PCBoom 3," High-Speed Res. NASA Sonic Boom Workshop,
NASA Conf. Pub. 3279, pp. 171-184 (1994).
9 Sparrow, V.W., "The Effect On Aircraft Speed On the Penetration of Sonic Boom Noise into a Flat Ocean," J. Acoustical Soc. America, Vol. 97, no. 1, pp. 159-162 (1995).
10 Cheng, H.K., Lee, C.J., Hafez, M.M., and Guo, W.H., "Sonic
Boom Propagation and Its Submarine Impact: A Study of Theoretical
and Computational Issues," AIAA paper
96-0755 (1996).
11 Holloway, P.F., Wilhold, G.A., Jone, J.H. Garcia, F., and Hicks,
R.M., "Shuttle Sonic Boom-Technology and Prediction,"
AIAA paper 73-1039 (1973).
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