AEM_360_Homework#5
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AEM 360 ASTRONAUTICS
Homework #5 – Rockets
Name:
none
1.
Circle the most correct answer for each question.
2.
Provide a reference from the course text (chapter and page number).
For questions involving calculations, please show your work.
1.
(
8 points
)
A 1.5 m
2
spacecraft radiator with an emissivity, ε, of 0.75 ejects 110 joules of heat per second (i.e,
watts).
What temperature must it be in degrees Celsius?
Given
:
Stefan-Boltzmann constant,
σ
= 5.67 × 10
–8
W / m
2
K
4
° C = K - 273.15
a.
-59.72° C
b.
203.78° C
c.
-69.37 K
d.
-69.37° C
Reference:
Ch. 13, Pg. 469
2.
(4 points)
Heat pipes are a means of internal active thermal control that provide a heat conduction path
inside a spacecraft.
They transfer heat based on the
a.
latent heat of fusion, the principle of storing additional heat in a liquid as it changes phase to a vapor.
b.
latent heat of vaporization,
the principle of storing additional heat in a liquid as it changes phase to a
vapor.
c.
latent heat of fusion, the principle of storing additional heat in a solid as it changes phase to a liquid.
d.
latent heat of vaporization, the principle of storing additional heat in a liquid as it changes phase to a
solid.
1
E
=
110
1.5
=
73.33
73.333
=
(
0.75
)
(
5.67
∗
10
−
8
)
(
T
+
273.15
)
4
T
=−
69.37
o
C
Reference:
Ch. 13, Pg. 472
3.
(5 points)
Space Shuttle space suits operated at a pressure of only 29.6 kPa (4.3 psi).
Therefore, at 12 hours
before extravehicular activity (EVA, or spacewalk), air pressure inside the Shuttle was lowered from its
normal near-sea level pressure to 70.3 kPa (10.2 psi) to avoid ________________; the EVA astronauts also
had to breathe pure oxygen for 3-4 hours to purge nitrogen from their bodies to avoid nitrogen bubbles in
the blood, which can cause_______________.
a.
decompression problems
; the bends.
b.
depression problems; the bends.
c.
compression problems; the leans.
d.
decompression problems; the leans
Reference:
Ch. 13, Pg. 474
4.
(
7 points
)
A cylindrical rod 10 m long at room temperature, 21° C, has a coefficient of thermal expansion,
α, of 2.22 x 10
-7
/°C .
What will its change in length, ΔL, be at 50° C?
What will the strain, ε, be?
a.
ΔL = 6.438 x 10
-5
m; ε = 6.438 x 10
-6
b.
ΔL = -8.795 x 10
-8
m; ε = -8.795 x 10
-7
c.
ΔL = 8.795 x 10
-5
m; ε = 8.795 x 10
-6
d.
ΔL = -6.438 x 10
-5
m; ε = -6.438 x 10
-6
Reference:
Ch. 13, Pg. 487
5.
(5 points)
Which statement about the launch vehicle acceleration profile shown below is
false
?
a.
The two peaks on the left indicate dual solid rocket strap-on boosters.
b.
The long red line from before 5.0 min to after 15.0 min represents a relatively low thrust third stage.
c.
The maximum g-loading on the vehicle is more than 4.0 g’s
d.
The two peaks on the left indicate increasing acceleration due to decreasing propellant mass with near
constant
thrust.
2
ΔL
=
(
10
)
(
2.22
∗
10
−
7
)
(
50
−
21
)
=
6.438
∗
10
−
5
m
ε
=
6.438
∗
10
−
5
10
=
6.438
∗
10
−
6
Reference:
Ch. 13, Pg. 492
6.
(4 points)
Vibrating an object at its lowest natural frequency, also called its __________________, results
in resonance, which is the tendency for an object to vibrate with increased amplitude (higher peaks), due to
a synchronized, applied, periodic force.
a.
carrier frequency
b.
prime frequency
c.
fundamental frequency
d.
downlink frequency
Reference:
Ch. 13, Pg. 488
7.
(
10 points
)
A communications satellite needs to perform a 12 m / s ΔV maneuver to adjust its orbit.
The
effective exhaust velocity, C, of the reaction control thruster is 1050 m / s and the spacecraft’s initial mass,
m
initial
, is 1100 kg, how much propellant will the maneuver require?
a.
9.950 kg
b.
10.547 kg
c.
11.105 kg
d.
12.500 kg
Reference:
Ch. 14, Pg. 513
8.
(
6 points
)
What is the specific impulse, I
sp
, of the reaction control thruster in Problem 7 above?
Given:
gravitational acceleration constant,
g
o
= 9.81 m / s
2
a.
65.67 s
b.
107.03 s
c.
130.25 s
d.
235.70 s
3
12
=
(
1050
)
ln
(
1100
m
f
)
m
f
=
1087.5001,
m
p
=
1100
−
1087.5001
=
12.5
kg
12
=
I
∗
9.81
∗
ln
(
1100
1087.5001
)
I
=
107.33
s
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Reference:
Ch. 14, Pg. 513
9.
(4 points)
Computing specific enthalpy, h, allows us to separate the energy in a thermodynamic rocket
engine’s exhaust due to the _________________ from the __________________.
a.
subsonic flow; supersonic flow
b.
P
exit
; P
atmosphere
c.
internal energy (heat); mechanical energy (pressure)
d.
converging nozzle section; diverging nozzle section
Reference:
Ch. 14, Pg. 516
10. (4 points)
Which of the following is
not
a reason we want a nozzle to ideally expand the exhaust flow just
to the point where we reduce P
exit
to equal P
atmosphere
?
a.
To maximize pressure thrust so that total rocket thrust is maximized.
b.
To avoid under-expansion, where not all the enthalpy is converted into exhaust exit velocity.
c.
To minimize pressure thrust and maximize exhaust exit velocity and therefore momentum thrust.
d.
To avoid over-expansion, where shock waves rob kinetic energy from the flow, lowering exhaust exit
velocity.
Reference:
Ch. 14, Pg. 516
11. (4 points)
To improve I
sp
for thermodynamic rockets, engineers
a.
try to maximize the combustion temperature while maximizing the molecular mass of the propellant.
b.
try to minimize the combustion temperature while minimizing the charge density of the propellant.
c.
try to maximize the combustion temperature while minimizing the injection pressure of the propellant.
d.
try to maximize the combustion temperature while minimizing the molecular mass of the propellant.
Reference:
Ch. 14, Pg. 516
12. (4 points)
Hypergolic propellants
a.
such as liquid oxygen and liquid hydrogen require an ignition source to initiate combustion.
b.
such as high-test peroxide (HTP) and kerosene (RP-1) are monopropellants that spontaneously combust.
c.
such as hydrazine and nitrogen tetroxide are storable and react on contact with each other.
4
d.
such as water or liquid hydrogen used in nuclear thermal rockets need no ignition source.
Reference:
Ch. 14, Pg. 528
13. (4 points)
Which of the following statements about ion thrusters is
false
?
a.
Ion thrusters are electrostatic thrusters that use an electric field to accelerate an ionized propellant.
b.
Ion thrusters provide relatively high thrust levels up to 1,500 N (337 lb
f
) for interplanetary missions.
c.
The most popular propellant for ion thrusters is xenon due to its high density specific impulse, I
dsp
.
d.
Ion thrusters offer very high I
sp
(10,000 s) with about 90% of the power going to accelerate the
propellant.
Reference:
Ch. 14, Pg. 537
The following scenario applies to Problems #17 - #20:
A launch vehicle must deliver a total ΔV, or ΔV
design
, of 10,300 m / s.
The total mass of the second stage,
including structure and propellant, is 11,800 kg, of which 9100 kg is propellant.
The payload mass is 1850
kg.
The I
sp
of the first stage rocket engine is 370 s and the I
sp
of the second stage rocket engine is 420 s.
The
structural mass of the first stage is 7,800 kg. (Hint:
See Sellers, pg 599, Example 14-3.)
Given
:
2 stages
m
payload
= 1850 kg
m
structure2
+ m
propellant2
= 11,800 kg
m
propellant2
= 9100 kg
m
structure1
= 7800 kg
I
sp1
= 370 s
I
sp2
= 420 s
ΔV
design
= 10,300 m / s
g
o
= 9.81 m / s
2
14. (
8 points
)
What is the change in velocity provided by stage 2, ΔV
stage2
?
a.
ΔV
stage2
=
3886.8 m / s
b.
ΔV
stage2
=
4196.2 m / s
c.
ΔV
stage2
=
4246.1 m / s
d.
ΔV
stage2
=
4526.5 m / s
Reference:
Ch. 14, Pg. 595
5
ΔV stage
2
=(
420
)∗
9.81
∗
ln
(
11800
+
1850
(
11800
−
9100
)
+
1850
)
ΔV stage
2
=
4526.5
m
/
s
15. (
6 points
)
What is the required change in velocity that must be provided by stage 1, ΔV
stage1
?
a.
ΔV
stage1
=
5480.8 m / s
b.
ΔV
stage1
=
5773.5 m / s
c.
ΔV
stage1
=
5943.1 m / s
d.
ΔV
stage1
=
6213.0 m / s
Reference:
Ch. 14, Pg. 595
16. (
10 points
)
What is the initial mass of stage 1, m
initial
?
(This is also the mass of the entire launch vehicle
including the payload at launch.)
a.
M
initial
=
34,118 kg
b.
m
initial
=
99,550 kg
c.
m
initial
=
105,251 kg
d.
m
initial
=
109,148 kg
Reference:
Ch. 14, Pg. 595
17. (
7 points
)
What is the propellant mass of stage 1, m
propellant1
?
a.
m
propellant1
=
83,801 kg
b.
m
propellant1
=
94,709 kg
c.
m
propellant1
=
101,532 kg
d.
m
propellant1
=
105,225 kg
Reference:
Ch. 14, Pg. 595
6
ΔV stage
1
=(
10300
−
4526.5
)
ΔV stage
1
=
5773.5
m
/
s
m
initial
=
e
5773.5
(
370
) (
9.81
)
∗(
7800
+
11800
+
1850
)
m
initial
=
105251.4
kg
m
propellant
1
=
105251.4
−(
7800
+
11800
+
1850
)
m
initial
=
83801.4
kg
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