Page 41 - Spring 2015

Concorde was a technological marvel that astounded the world with its beauty and speed. Its sonic boom was its Achilles heel, but was it the cause of those mysterious east coast noises?
an altitude where the local sound speed is equal to the speed of the aircraft. Because the sound speed is proportional to the square root of the absolute temperature, this requires a temperature four times the temperature at the altitude of the Mach 2 Concorde. The required temperature would be reached in the thermosphere at an altitude of 160 kilome- ters (see Figure 6). Garwin (1978) hypothesized that what he called a “hyperboom,” somehow got detached from the aircraft when it maneuvered and propagated at a very high altitude at a speed faster than that of the aircraft and could reach the US coast over an hour before the aircraft. More- over, Garwin, a longtime opponent of the Concorde (Sulli- van, 1978), also hypothesized that the thermospheric waves could negatively alter the tenuous thermosphere, thereby causing chemical reactions and winds (Garwin, 1978).
On March 8, 1978, in a meeting attended by Presidential Sci-
ence Advisor Frank Press, Transportation Secretary Brock
Adams, NRL Director Alan Berman, Stone, and Garwin
charged that the NRL had erred and that the Concorde was
the culprit in the east coast booms and also may be causing
At the March 8 meeting, the NRL was tasked by Adams and Press to investigate the Stone-Garwin hypothesis, that is, specifically to determine what does happen to the upward going Concorde sonic boom as it propagates to and from its turning point in the thermosphere. Adams also requested that Press arrange for an independent review of the Navy’s results.
The NRL assigned the task to Peter Rogers and John Gard-
ner. Rogers and Gardner developed a model for the ther-
mospheric propagation of the sonic boom from Concorde
aircraft. In the model they considered, only those booms
that were refracted to the ground by the sound velocity gra-
dient in the thermosphere (above 100 kilometers). From
their model, they determined the boom strength as a func-
tion of altitude and the ground pressure both on and off the
flight path. The model utilized a realistic atmospheric model
of the density, temperature, and composition of the atmo-
sphere versus altitude and included nonlinear stretching and
attenuation of the wave, the effects of the turning-point and
linear acoustic attenuation. The results are presented in Fig-
ure 7 (Rogers and Gardner, 1980). Figure 7 shows the pre-
dicted ground pressures for the initially upward and initially
downward waves as a function of distance from the ground
track. The abrupt lateral cutoff was determined by the re-
turning rays, which were refracted upward before reaching
the ground. The solid lines show the results, which consid-
ered both nonlinear effects and linear attenuation, whereas
In-line equations and symbols pg. 13 - Concorde Booms
the destruction of the thermosphere. In-line equations and symbols pg. 13 - Concorde Booms
Garwin’s environmental argument was based on the conser-
the dashed lines show the results obtained using the nonlin- ear theory alone. The dominant signal was from the initially
In-line equIna-tliionneseaqnudatsiyomnsboanlsdpsgy.m13bo-lCsopngc.o1r3de- CBonocmorsde Booms
In-line equations an2d symbols pg. 13 - Concorde Booms downward wave. The highest pressure level (about 0.30 pas-
v#a1tion oMf en=evrg/yc.=Thpe/ ρacoustic Mac#h2numvber of a sound wave ac
cals) occurred about 400 kilometers from the ground track.
The pressure measured on the ground track was a minimum anvd #w2as abovut 0.10 pascals for the initially downward wave. This is because the ray paths along which the shocks propa- gate were less steeply inclined at lateral locations compared with the on-track rays. Thus, on-track rays traveled to much higher altitudes where they incurred much larger losses due to the extremely low density at altitude. It should be noted that the predicted secondary boom levels that arrived from the thermosphere were more than an order of magnitude less than the secondary boom levels propagated from the strato- sphere and lower mesosphere (see Figures 3 and 7). This is in contrast to the primary carpet booms where the pressure was a maximum (about 100 pascals) along the ground track and decreased to zero at the lateral cutoff.
Rogers and Gardner (1980) concluded that thermospheric returns from the Concorde are of sufficiently low amplitude
is a dimensionless measure of the strengt#h1of aMsou=ndv /wc a=vep,/ ρc2 #2
v
ac
#w3hich wMou(lzd b) e/ Mind(i0ca) tive of the effect of the wave on its en-
acTP ac
#1 2 M #=1 v / c#M=3 p /=ρvMc/ c (=z p )/ /ρMc #2(0)
v 2 ac TP 2ac , #w4here vρi(s0)t/hρe(zac)oustic particle velocity. Garwin’s model
vironm#1ent. IMn th=evf/acr =fiepld/ ρ, cit is givacen b#y2 ac ac
TP
s h o w e#d3 t h a t M a c ( z T P ) / M a c ( 0 ) w a s p r oa c p oT rP t i o#n4a a alc c t oT P ρ ( 0 )a c/ ρ ( z T P ) ,
#3 M#(3z )/M (0z))/M (0) where TP is the altitude at the turning point.
#5 z
#4 ρ(0)/ρ(z )
#4 ρ#(40) / ρ#(z5ρ)(0) /zρ(z ) TP TP TP
For the Mach 2 Concorde at the turning point (160 kilome-
#6 Mac TP
ters), the density is 1.14 × 10-12 grams per cubicMcentimeter, #5 z#5 #z6
#5zTP TP TP ac
more than nine orders of magnitude smaller than it is on the
ground, resulting in a very#6large M#6at thaMt altitude. Garwin’s
#6 Mac ac
In caption for Figure 2
linear model included the effect of spreading of the conical
wave front but was subject to criticism because it did not
#7 Δp
include nonlinearity, refraction, linear attenuation, and the
In caption for Figure 2
#7 Δp
In captionInfocraFpitgiuornef2or Figure 2
focusing at the turning-point caustic where adjacent rays
cross. #7 Δp#7 Δp #7 Δp
ac
In caption for Figure 2
| 39