Vehicle Design and Performance
You may answer no more tharl
of the foilowillg two questions:
A. Vehicle Design and Performance (Aeronautics)
B. Vehicle Design and Performance (Astronautics)
Vehicle Design and Performance (Aeronautics)
An aircraft sizing study is performed, using -the following independent design parameters.
m
C
Aa
f
gross takeoff mass
takeoff wing loading
aspect ratio
airfoil thicknessJchord ratio
CL
lift coefficient
From these, simple structural, aera,powcrplant, and weight models are then used to derive
numerous relevant dependent parameters. S o r n ~examples are
b = \lrnsAR/z
wing span
wing (fuel) volume
v 21 0. 5b3/A2
V = J w
flightspeedattakeoffmass
fk = VSJvb
average-chord Reynolds number
power-specific fuel consuxnption
HFC = PSK(mengi,,, . . .)
drag coefficient
CD = C2JTAI cdp(&, CLvi) + . . .
Mruei = m ( l - f
,,) - mstructure(m,
C, A?. . .) - mengine
. . . allowable fuel mass
+
A payload/gross mass fraction of f,, = O,l is assumed, The assumed structural material
properties correspond to common composites. The Breguet range is then finally examined,
ultimately as a function of the independent parameters.
In a sizing study, the gross mass is varied over a wide range rn = I . . .I00 000 kg (small UAV
to large transport). All the other irldepcndent parameters are optimized so as to maximize
the range R at each specified ~ n .The resulting optirnun~R is shown in Figure 1, and the
associated optimum Pn and C are shown in Figures 2 and 3.
I) In Figure 1, what physical effects cause R to increase as m is increased from 1kg to about
20000 kg? What causes the slight decreme a m increases beyond 20000 kg. Hint: examine
the variables in the Rreguet expression.
2) In Figure 2, why is the optimum /R largest for an intermediate mass? What causes is to
decrease on the left of this maximum? On the right of this maximum?
3) In Figure 3, the optimum wing loading increases very nearly as m1/3. What physical
principle is responsible for this?
4) The assumed material properties are rlow upgradeci to match exotic higher-strength and
higher-stiffness composites, and the sizing study is repeated. Briefly describe how each of
the curves in the three figures would change.
Figure 1: Range R versus mass m. All other pnrarncters optimized for maximum range.
1
10
7 00
1000
10000
1
f OOOOO
m (kg)
Figure 2: Aspect ratio A! optimized for rnaxirllurn range, versus mass m.
Figure 3: Wing loading C optinnixed for maxirnum range, versus mass m.
---
Vehicle Design and Performance (Astronautics)
.--
Two competing architectures for lunar exploration must bc compared in terms of their total departure mass in low
Earth orbit (LEO), see Figure 1. Each architecture uses a slightly different set of modules and operational sequence.
Lunar Surface
Lunar Surface
-I-..
LLO
-----
- - m a - -
CM
i
. -:i
1
:. \. "I,unar Orbit Rendezvous"
,;
:
"Moon Directn
p
LE
---
----------------SM
Earth
Earth
Figure 1: (left) "Moon Direct", (right) "Lunar Orbit Rendezvous"
Moon Direct: The Command Module (CM), Ascent Stage (AS), Descent Stage (DS) and Trans-Lunar Stage (TLS)
leave together fiom low Earth orbit (LEO). The mans-lunar injection burn is provided by the TLS. Upon amval in low
lunar orbit (LLO) the TLS fires again to circularize the orbit around the Moon and is subsequently abandoned. The
CM-AS-DS descend to the Moon together, with the DS providing descent propulsion and stabilization on the surface
(landing gear). AAer surface expIoration is complete, the CM-AS lift off together with the AS providing propulsion
and the DS being left behind on the surface. The AS fires again in CLO to provide trans-Earth injection for the CM.
The CM enters Earth's atmosphere directly for a ballistic reentry.
Lunar Orbit Rendezvous: The CM-SMand LM-AS-DS leave low Earth orbit together with the SM providing both the
AV for trans-lunar injection and circularization in LLO. The LM-AS-DS descend to the lunar surface with the DS
providing descent propulsion and stabilization on the surface (landing gear). During surface exploration the CM-SM
waits in orbit. After surface exploration i s complete, the LM-AS lift off together with the AS providing propulsion
and the DS being left behind on the surface. The LM-AS and CM-SM rendezvous in orbit and the astronauts transfer
from the LM back to the CM.T h e empty LM-AS are abandoned in lunar orbit. The SM fires to provide trans-Earth
injection for the CM and is subsequently jettisoned. The CM enters Earth's atmosphere directly for a ballistic reentry.
a) Compute the total departure mass in LEO [kg] for both architectures and compare.
b) Explain why one architecture is superior to another in terms of departure mass.
C)
At what ratio of masses LMICM wonld both architectures be equivalent in terms of deparhre mass?
d) What criteria, other than mass, must be considered for architecture selection?
Data to be used: I,=400 [s], CM=6000 [kg], LM=2000 [kg], assume all tanks and engines are massless.
AV:
LEO+ LLO
circularize at LLO
LEO+ Lunar Surface
Lunar Surface 3 LLO
T.l,r>+
LEO
3400 m l s
1100 d s
2200 mls
2200 rnls
1 100 mls
(trans-lunar injection)
(trans-Earth iniectionl
MIT OpenCourseWare
http://ocw.mit.edu
16.842 Fundamentals of Systems Engineering
Fall 2009
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