SUMMARY OF AERODYNAMIC VIBRATION

EFFECTS ON A.L.L. TURRET

P. MERRITT
L. SHER

Air Force Weapons Laboratory, Kirtland AFB NM

The use of a laser system in an aircraft requires an understanding of
the effects of the airborne environment on the laser system. The time
averaged intensity of the laser at the target will be reduced if the
optical elements of the system are caused to be jittered. The airborne
environment provides sources of angular and linear vibrations that cause
laser beam jitter. These vibrations can come fom the vehicle itself or, if
the optical elements are exposed or vented to the airstream, this can
provide a direct torque disturbance on the optical elements. Figure 1
schematically depicts these two main sources of jitter. In the upper
figure, the optical element is shown on bearings which give it two degrees
of freedom. The mirror would actually be surrounded by a telescope
housing which would be rotated to point the beam. When the use of a
window is precluded, such as for very high power, the external airstream
provides a direct torque excitation to the mirror. In general, for a
arbitrary pressure distribution, the torques on the mirror would be

= - // y p(x,y,t)dxdy
A

My(t) = // X p(x,y,t)dxdy

A

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If the pressures were constant in space over halves of the mirror, e.g.,
p(x,y,t) = Pj^(t) y>0

p(x,y,t) = p 2 (t) y<0

then

M^(t) = 0.08 D3 [p^Ct) -p^(t)]

M (t) = 0

y

where D is the mirror diameter. The torque is seen to scale with diameter
cubed. Given the power and cross spectra of the pressures then the power
spectrum of the torque would be

<I>^x(f) = (. 080^)2 [cj)^ +4)^ -2Rei|j^ ^ ]

Pi P2

PiP

1^2

where denotes a power spectrum and denotes a cross spectrum. For

Pj^ and p 2 equal but uncorrelated, or perhaps correlated 180° out of phase,

one sees that a torque will still result.

The optical system is pointed at the target by using some type of
optical tracking system. However the primary mirror, the one disturbed by
the pressure fluctuations, is inertially stabilized by using gyroscopes
attached to the back of the mirror. A simplified schematic of such a
system is shown in Figure 2. If the transfer function from torque, T^ to
mirror motion, e, is calculated it is found to be;

(e/T^) = (l/JJ/(s^ +

This transfer function is a constant, 1/K^, for low frequencies, and reduces
at 40 dB per decade above the corner frequency This indicates that

the system only rejects low frequencies by the strength of its torquer.

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Higher frequency torques are rejected by the inertia of the primary mirror
and its structure. The closed loop bandwidth, K^/J, is typically 100 Hz,
therefore the response of the telescope mirror to direct torques may be
considered as two frequency regions, from d.c. to K^/J, and from K^/J to
infinity. The following equations permit us to consider the previous
developed PSD expressions based on pressure, to evaluate the mean square
error,

K^/J

= J for 2/tf < K^/J

2 °

£ = /“ (4>^/J2u)'‘)du) for 2nf > K^/J

K^/J

The other effect of the flow is the motions of the turret induced by
the steady and fluctuating pressure. The motion of the turret can be
coupled to the optical elements by several mechanisms which are shown in
Figure 3. The motion of the turret in response to the aerodynamically
generated torques, T^, are determined by the inertia of the turret, J^,
and its mounting compliance, K. A mechanical transfer function from torque
to angular motion, 0, results in a transfer function of the same form as
developed for the mirror motion. Therefore, at low frequencies the motion
of the turret is (0/T^) = (1/K)

At high frequencies

(0/T^) = (1/Juj2)

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The first flights of the Airborne Laser Laboratory (ALL) in the Cycle I
test program gave an indication that the optical jitter, e, varied with the
flight dynamic pressure, q^, see e.g. Figure 4. Since the net pressure
difference either across the mirror or across the turret is the quantity
of interest it makes sense that the torque, and thus the jitter will scale
with q^. Theoretically it, probably makes more sense to use the difference
between stagnation pressure P° and static pressure as the dependent
variable, i.e. ,

P°-Poo = Kp°/Poo)-1] Poo

The function P°/Pqj, is a complicated function of Mach number and specific
heat. For M<0.6, one can approximate the above to within 10% by

P°-Poo = ^ Poo ^00^

Early tests of a dummy turret with a cavity on a KC-135 in which
fluctuating pressures were measured, Reference 1, indicated numerous
acoustic resonances and torque levels approaching 2000 inch lbs on the
exposed mirror. A comprehensive test series in wind tunnels, reference 2,
led to dramatic reductions in the levels of fluctuating torques on the
mirror to the order of 50 in lbs by the addition of external fences on the
Advanced Pointing and Tracking. In addition, the acoustic resonances were
reduced in intensity. In the next flight program of the Airborne Laser Labo-
ratory, Cycle II, the actual pointing and tracking telescope was instrumented
with pressure transducers, see Figure 5, which were differenced and suitably
scaled for telescope area and moment arm to indicate torque. The results are
shown in Figure 6, where the torque spectrum for wind tunnel results and for
the airborne measurements are shown. The torque spectra have been normalized
by

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Where L - Aperture diameter
M - Mach Number
P - free stream pressure

and

S = V/L

Where V - free stream velocity.

The wind tunnel data shown in Figure 6 was obtained using the on gimbal
telescope model used for the Large Pointing System test series. An attempt
was also made to use the 0.3 scale APT model test results, however poor
correlation was obtained. It was discovered that the APT model was not
vented internally and thus did not match the actual airborne telescope
which is vented to the turret.

The magnitude of the torque measured for the modified flight turret
was insignificant in terms of the jitter generated. An attempt to corre-
late a pressure measurement in the cavity with the jitter of the telescope
is shown in Figure 7. Just observing the pressure spectrum and the jitter
spectrum, one might be tempted to infer that the pressure spectrum is
driving the jitter. However, the coherence spectrum shown at the center
shows correlation only at several high frequency spikes. The coherent
power between pressure and jitter indicated only about 3 percent of
the jitter was correlated with pressure fluctuations. Follow-on tests
with a window installed over the cavity yielded essentially the same
telescope jitter as the open cavity again verifying the direct aero-
dynamics torques on the mirror were insignificant.

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The Cycle II test series conducted numerous tests to explore the
potential variables that influence system jitter. Based on the measure-
ments of fluctuating pressures in the cavity, it was concluded that the
vibration of the turret was the main source of jitter excitation. Attempts
to correlate jitter with dynamic pressure are shown in Figure 8, which
shows a large spread in the data. However by restricting several variables,
the correlation of jitter with dynamic pressure, in particular the circled
data points, was much more obvious. However a lack of angular instrumenta-
tion made it impossible to acquire data during Cycle II to accurately
correlate turret vibration with flight parameters such as dynamic pressure
and Mach number.

Prior to Cycle III flight testing the Air Force acquired some precision
angular displacement transducers to install on the turret. These transducers
along with several pressure transducers were installed on a dummy turret
in the initial flight tests of the ALL for Cycle III. Further, it was
possible to define a series of tests where one flight parameter was varied
while holding others fixed. In particular, a series of tests were run
where q^ was held constant and Mach number changed, and a similar series
where the Mach number was held constant and the q^ was changed.

The flight tests have yielded some interesting and unexpected results.
Figure 9, shows the effect on roll angular vibration when changing q^ with
Mach held constant. The data indicates that the vibration does change
linearly with q^ but it also shows a distinct dependency on Mach number.

The higher Mach number shows considerably less vibration. The effect is
further amplified by referring to Figure 10 which shows the effect of

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changing Mach number while holding a constant dynamic pressure. The data
shows a nonlinear decrease in vibration with increasing Mach number. The
spike in Figure 10 labeled "Shudder experiment" is another interesting
aspect of the vibration. The ALL crew had described a strong vibration
effect at .51 Mach number. In the data of Figure 10 labeled Mission 5 the
pilot attempted to "feel out" the high vibration point and hold it for
several seconds. The plotted spike in the data confirms the aircraft
"Shudder Area".

It was also possible to analyze the flight test data for frequency
content. This data is shown in Figures 11 and 12. The effect of changing
while holding Mach number constant appears to change the entire level
of the PSD with little effect on the frequency content. This is shown as
Figure 11. However, when the Mach number was lowered, a distinct increase
in low frequency vibration, below 20 Hz was obvious, see Figure 12. The
low Mach numbers must change the flow pattern over the turret in such a
way that the airflow imparts a much stronger driving torque to the APT
turret.

Pressure measurements on the external pressures at 4 points on the
dummy turret were taken concurrent with the vibration data. Figure 13 is
included to show the pressure from a transducer labeled R103 which was at
the vertical center of the turret and 50 degrees CCW from the leading edge

and transducer R104 which was at vertical center and aft. It is interest-
ing to see that the pressure measurements follow the same trend as the

vibration measurements. Notice that the 50° transducer shows more variation
the PSD at various Mach numbers, but the aft transducer contains consider-
able more energy in the PSD. The RMS level plots of the transducers were

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similar in shape to the angular vibration shown in Figure 10.

The data now available well documents the base motion response of the
turret to air loads during flight. This data can be used to select flight
conditions for this aircraft that will yield low base motion. However the
data does not provide an understanding of the physics of the aerodynamic
phenomena. If the vibration is to be reduced by using different fairings
or if this data is to be used to design a future turret, the physical
basis of the airflow needs to be understood. Since this paper has pointed
out that turret base motion is the major driving source for jitter, it
would be most beneficial to pursue this analytical area. Probably wind
tunnel tests are not the correct approach since the problem requires
convolving structural design of the turret with aerodynamic loading.
However, a large amount of flight data is available, including pressures,
angular, and linear vibration data.

In conclusion, this paper has summarized the effects of the airborne
environment on a pointing and tracking system using a turret external to
an aircraft. The data has covered a series of flight tests and a span of
seven years. The two major airborne effects were shown to be direct
pressure loading of optical elements and vibrations of the entire turret.
The direct optical loading problem has been minimized by clever fence
designs for the turret, however the turret vibration problem is a poorly
understood area. A large amount of data has recently been obtained to
document the turret vibration but a physical understanding of the problem
is yet to be attempted.

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REFERENCES

1. "Estimation of Steady and Unsteady Torques Acting on a Large Cavity

Fairing into the Airstream," GD Convair Div, Fort Worth, TX, Report
No. F2A-453, September 1971.

2. Van Kuren, James T. , et al, "Acoustic Phenomena of Open Cavity

Airborne Cassegrainian Telescopes", AIAA paper No. 74-196, AIAA
12th Aerospace Science Meeting, Jan 30, 1974.

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FLOW INDUCED TURRET VIBRATION

Figure 1. Sources of Aerodynamic Jitter.

524

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SI6NAL

FKOPORTIONAl
TO IIRAOR

■OTIO« viMo INERTIAL

INERTIAL

RATE

/

6

Figure 2. Servosystem Diagram for Gyro Stabilized Pointing Mirror

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FLIGHT
CONDITIONS
DYNAMIC
PRESSURE.
MACH NO..
REYNOLDS NO..
ETC.

ANGULAR

VIBRATION

Figure 3. Coupling Paths Between Vibration and Beam Jitter.

I

I

I

I

CO

— <r

O CD

I—

00

hsi

or —I
o —
z m

CO

Figure 4. Stabilization Jitter from Cycle I Versus Dynamic Pressure.

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I

Figure 5. Location of Pressure Transducers for
Cycle II Flight Tests.

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529

(IN-LB)^/Hz

(^)

10 “^

10

-5

10 “®

10 ~^

FLIGHT:

TUNNEL:

8,080 Meters
.82 MACH
AZIMUTH 40°
ELEVATION 35°

SEA LEVEL
.85 MACH
AZIMUTH 45°
ELEVATION 45°

10 ~®

J

10

1

STROUHAL NO.

Figure 6. Correlation of Wind Tunnel and Flight Test Torques.

FLIGHT 64

19:26:20

EL STAB.
ERROR
PSD

COHERENCE
EL STAB./K8

K8 PRESSURE
TRANSDUCER
PSD

dB

Figure 7. Coherent Correlation of Pressure Fluctuations
and Stabilization Jitter >

530

531

100

ELEVATION

STAB.

ERROR

PERCENT

DYNAMIC PRESSURE (PSI)

PARAMETERS
HELD CONSTANT:

1) RAMP/FULL/OPEN

2) AZ = 90^ EL = 0"

3) EYELID OPEN

4) RATE MODE

Figure 8. Correlation of Cycle II Stabilization Jitter With Dynamic Pressure.

Figure 9. Correlation of Turret Vibration With Dynamic
Pressure for Constant Mach Number (Vibration
levels are nns).

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ROLL (MILLIRADIANS)

.4 .5 .6 .7

MACH

Figure 10. Correlation of Turret Vibration With Mach Number,
Dynamic Pressure Constant at 1.25 psi (Vibration
levels are rms).

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Figure 11. PSD's of Turret Vibration for Two

Different Dynamic Pressures, Constant Mach.

Figure 12. PSD's of Turret Vibration for Changes in
Mach Number and Dynamic Pressure.

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PRESSURE (PSI) SQ/HZ

Figure 13

PSD Analyses of Pressure Transducers on Exterior
Surface of Dummy Turret.