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Unformatted text preview: AB 201 Final Exam Spring 2009
(2 hours, open book) 1. (50%) Earth to Jupiter Hohmann transfer A spacecraft is to be sent from Earth to Jupiter using a Hohmann transfer. You may
assume that the eccentricity of both planetary orbits is negligibly small. am, = 5.2028 AU, 1AU = 149.6 - 106km, as," = 1.327 -10“km3 /sec2 10 a) Find the total AV required (in km/sec).
5 b) Find the time of ﬂight (in days).
5 0) Determine the eccentricity of the transfer orbit. [o (1) Draw a cartoon and show the precise position of Jupiter with respect to Earth on the day of departure from Earth. Also show where Earth will be on the day of arrival
at Jupiter. [0 e) How often do opportunities for Hohmann transfers to Jupiter occur (in days)? (0 f) When the spacecraft is at point B on the transfer trajectory, what is its speed (in
km/sec)? 2. (50%) Boeing 747-400 data Weight = 870,000 lb/ mass = 394,846 kg at takeoff
Weight = 585,000 lb/mass = 265,590 kg at landing wing area s = 5951 £12 = 553 m2 mean chord c = 29.5 ft = 9.0 m wingspan (wingtip to wingtip) = 211.4 ft = 64.4 m
Oswald efﬁciency factor e = .87 C = .95 LMax CD0 = .06 The airplane is powered by 4 General Electric CF6-80 turbofans with 57,900 lb or
223,132 Newton thrust each. 1 meter/sec = 1.944 kt, 1 ft = .3048 meter .4 , 4 “V... ..__. A A ref: — ._'.’:.T1:VZ::.“““““““"4124112;. . .. 4 a) Find the stall speed of the airplane in level ﬂight at sea level on a standard day.
Assume the airplane is at takeoff weight. Express the result in m/sec and knots. b) The nominal cruising speed of the airplane is 490 kts = 910 km/hr @ 31,000 ft.
Find the temperature and density @ 31,000 ft. What is the lift coefﬁcient CL at cruise? Assume the airplane has consumed 100,000 lb
of fuel since takeoff. c) The actual stall speed of the airplane on approach (low enough to consider as
sea level) is 156 kts (w/ ﬂaps fully extended). What is the lift coefﬁcient CL of the airplane on approach? By how much (in %) has the use of full ﬂaps increased the lift coefﬁcient (over the
value at cruise, from part (b))? Assume airplane has landing weight. d) What is the calculated takeoff distance (in m and in ft) of the airplane on a standard day at sea level? (Just for comparison with your theoretical result, the ﬂight manual
value is 10,561 ft.) e) The analysis that yields the takeoff distance formula you used in part (d)
assumes that the takeoff distance is the distance required to accelerate to a speed of 1.2 V3. (This is in fact the VS that you found in part (a).) What is the takeoff speed in
knots? Suppose that there is a headwind of 20 kts. Then the airplane needs less of a groundspeed to achieve an airspeed equal to 1.2 VS . Derive a new takeoff distance formula that allows for a headwind.
Find the takeoff distance of the airplane on a standard day when the airplane has this
20 kt headwind. f) If all four engines were to stop, with the airplane at 30,000 ft MSL (mean sea level)
over Champaign (alt = 750 ft MSL), what is the maximum gliding range of the
airplane (in km or miles)? :1 g) The published maximum speed of the airplane in cruise is 507 kts = 942 km/hr at 31,000 ft .
The maximum speed obviously occurs when the maximum thrust is applied.
i) How will the drag be related to the thrust at maximum speed? ii) What is the drag coefﬁcient of the B-747 at maximum speed? ...
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- Spring '09
- Takeoff, takeoff distance, Jupiter Hohmann, takeoff distance formula