A spacecraft with a mounted probe is to be launched on a SpaceX Falcon 9 and released with a 38.81” Lightband separation system. The Spacecraft is represented by a 40” diameter cylinder with 0.015”...

A spacecraft with a mounted probe is to

be launched on a SpaceX Falcon

9 and released with a 38.81” Lightband separation

system.

The Spacecraft is represented by a 40” diameter cylinder with 0.015” thick

walls (only about 4x’s thicker than a soda can wall

thickness!), height of 90”, and has a

mass of 1000kg (2200 lbs).

The material is 6061
-
T6 Aluminum with an allowable yield

strength of 35ksi.

Ignore the thickness of the Lightband.

a)

The SpaceX Falcon Users Guide (April 2020) suggests that secondary struct
ures

should maintain a frequency requirement > 35 Hz and the primary structure

frequency will be assessed using coupled loads analysis.

Assuming your Probe has a

35 Hz frequency and meets the octave rule, what primary structure frequency

requirement would

you start with?

Primary structure frequency requirement (starting estimate) = ____ Hz

b)

The SpaceX Falcon Users Guide (April 2020) provides design loads in an “airplane”

plot per Table 4.2.

What are the design loads for the Spacecraft?

Note: to use an

airpla
ne plot, choose the maximum value in each direction
?

Acceleration in X direction = ____ G’s

Acceleration in Z direction = ____ G’s

c)

Using the design loads in (2b), find the reaction loads, F
x
, F
z
, and bending moment,

M
y
, at the

Lightband
-
to
-
spacecraft interface.

Calculate the Loads Margin of Safety

for the Lightband, using allowable loads provided from Maximum Loads (Table 5.1

from Lightband User Manual).

Use a factor of safety of 1.25.

Provide a Margin of

Safety value for each o
f the axial load (F
z
), shear load (F
x
), and bending moment

(M
y
)
.

d)

Using the same F
z
, M
y

reaction loads (and ignoring the small height of the

Lightband), find the stress margin of safety of the spacecraft, using the 40”

diameter cylinder against the allowabl
e yield stress of Aluminum.

Use a 1.25 factor

4

of safety.

Use a combined stress condition with both F
x

and M
y

occurring

simultaneously.

Use the thin
-
walled cylinder assumptions for area and area moment

of inertia
.

e)

Find the predicted frequency using a fixed

base cantilevered beam frequency

calculation.

Use the thin
-
walled cylinder assumptions for area moment of inertia.

Ignore the Lightband bending stiffness in the frequency calculation
.

Supporting Information:

The relevant properties from the Lightband manu
al are as follows:

MLB bolt circle diameter (
±
0.01 in) = 38.810

Number of fasteners (n) = 60

Maximum Loads

X
LB

axis =

56
,400 lb

Y
LB

or Z
LB

axis =

11
,
61
0 lb

Moment about Y or Z
LB

=

547
,
221

in
·
lb

Bending Stiffness about Y
LB

or Z
LB

±25% =

1
.
60
E+0
9

in·lb
f
/rad

Be careful

–

Lightband chooses X to be axial and Y, Z as lateral! Different than most

spacecraft.

screen-shot-2022-11-10-at-25812-pm-itcsx5mi.png screen-shot-2022-11-10-at-25553-pm-f5xavn0t.png

Nov 10, 2022

SOLUTION.PDF

A spacecraft with a mounted probe is to be launched on a SpaceX Falcon 9 and released with a 38.81” Lightband separation system. The Spacecraft is represented by a 40” diameter cylinder with 0.015”...

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