ASE 102 - Practice Final 1

ASE 102 - Practice Final 1 - Introduction to Aerospace...

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Unformatted text preview: Introduction to Aerospace Engineering ASE 102 Final Examination May 15, 2004 Name Problem 1 Please state whether the following statements are true or false: (1) There are very few stars like the Sun in our galaxy. (1) (2) The ailerons of an airplane control the roll motion. (1) (3) Hydrogen filled balloons were used for reconnaissance during the Civil War (1861—1865). (1) (4) Igor Sikorsky flew the first helicopter in 1903. (1) (5) Wernher von Braun was responsible for the design of the Saturn rocket that put astronauts on the Moon. (1) (6) The Northrup B-2 “stealth” bomber is nearly invisible on radar. ( 1) (7) Saturn’s satellite Titan is the largest satellite in the Solar System. (1) (8) US. reconnaissance satellites were developed, in part, to monitor and verify arms control agreements. (1) (9) The lifting force provided by the wings of an aircraft is proportional to the lift— to-drag ratio of the airplane. (1) (10) A turbo jet engine has a higher trust—to-weight ratio than a reciprocating aircraft engine. (1) (l 1) Newton obtained the law of gravitation by comparing the period of the Moon with the gravitational acceleration on the surface of the Earth. (1) (12) An aircraft with its center—of—mass above the center of lift is unstable. (1) (l 3) The Bell V~22 tilt—rotor aircraft can fly at supersonic speed. (1) (14) The exhaust velocity of a rocket depends on the square root of the temperature in the combustion chamber. (1) (15) The rudder of an airplane controls the pitch of the airplane. (1) (16) The Wright brothers used a Wind tunnel to design the wings of their airplane. (1) (17) There is strong evidence that there are animals on Mars. ( 1) (18) The planet Venus has a very dense atmosphere. (1) (19) An air cooled radial engine produces less drag on an aircraft than a liquid cooled in—line engine. (1) (20) A glider, in order to fly properly, must have very low aspect ratio wings. (l) Problem II A high altitude hydrogen filled balloon has a diameter of 100 meters. The balloon weighs 5,000 kgms and carries a payload of 20,000 kgms. (a) What altitude does the balloon reach? Assume that the balloon has a spherical shape at maximum altitude. (5) (b) At night, the temperature of the air decreases so that the balloon displaces only half the air that it does at full altitude in the day time. At what altitude does the balloon fly at night? (5) Problem 111 Titan is a satellite of the planet Saturn. It orbits the planet at a distance of forty million kilometers in a nearly circular orbit. What is the period of the orbit? Use the data in the attached table to calculate your answer. (20) Problem IV (a) Calculate the velocity that a rocket must reach to leave the Earth’s gravitational field. Assume that the rocket leaves from the surface of the Earth. To solve this problem, calculate the total work that must be done to move the rocket from the surface of the Earth by performing the integral of ngr where E6 is the force of gravity and the limits of the integral are the radius of the Earth RE and infinity. The total work calculated must be equal to the kinetic energy of the rocket at the surface of the Earth if it falls to the Earth from infinity. Thus, equating the two yields is what is called the “escape velocity.” (15) (b) What is the relationship between the escape velocity and the orbital velocity of an object in a near Earth orbit at altitude, h, where the altitude is much smaller than the radius of the Earth RE? (5) Problem V On July 25, 1909, Louis Bleriot flew a small airplane across the English Channel from Calais to Dover, a distance of 40 kilometers. He asked his friend, Louis Charles Breguet, to calculate how much fuel he would have to put in his airplane. Bleriot told Breguet that the aiiplane had a top speed of 50 kilometers per hour and had a total dry mass of 1000 kilograms. The lift—to—drag ratio of the airplane was 10 and the value of the constant k/eg was 100 kilometers. On the day of the flight, a wind was blowing from Dover to Calais at 15 kilometers per hour. How many kilograms of fuel did Breguet tell Bleriot to carry? (15) Problem VI An F—14 with wings extended is normally launched from an aircraft carrier with a catapult mounted on the bow of the ship. The F-14 weighs 55,000 lbs fully loaded. During the launch maneuver, the carrier is moving at 40 miles per hour into a head wind of 20 miles per hour. The aspect ratio of the wings is 20 and the wing thickness is one foot. What speed must the catapult provide to the F-14 so that it is flying when it leaves the ship? Note: Because of the different definitions of “pound” in the English system for the weight and the density, the force in the lift equation must be multiplied by g — 32ft/sec2 ~ to get the right answer. (15) SZZ GZZ Planetary Constants* Sidereal , , Apparent Mean Diameter Mass N Sym- Semimajor Period Eccen- Inclination Angular ame bol Axis ofOrbit (mean solar tricity E 1° , Diameter days) . cliptic (equatorial) km 03 = 1 O = 1 E0 = 1 Sun 0 31’59’13 (mean) 1,393,000 109.3 1.000 332,488 Moon C 383,403 ka 271321661 0.05490 5° 8'33" 31/05” (mean) 3,476 0.273 2—711h—X107 0.012304 n r/ _ n 1 Mercury § 0.387099 87.9693 0.20562 7 0012 4.7 12.7 5,000 0.39 6.12 X 105 0.0543 Venus 9 0.723331 224.7008 0.00681 3 23 38 919-6475 12,400 0.973 4081645 0. 8136 - 1 Earth 1.0 00 0 A , . . $ 0 0 365 2564 0 01674 0 00 00 12,742 1 000 332,488 1.000 1 M 1. . . '.' — '.' . an (37‘ 523688 686 9797 0 09333 1 5101 3 5 25 1 6,620 O 520 3,248,200 0.1080 Ceres @ 2. 767303 1681.449 0.07653 10 36 56 0126—0766 770 0.060 Eros (4%) 1.458296 643.230 0.22297 10 49 4o 0’.’02—0?3 20 0.0016 jupiter ‘21 5.202803 4332.588 0.04837 1 18 28 3078—5010 139,760 10. 97 1 0:7 4 318.35 Saturn 1') 9.538843 10759.201 0.05582 2 29 29 1419—2016 115,100 9.03 3—39—9 95.3 Uranus CT) 19.190978 30685. 93 0.04710 0 46 22 31’4—4’52 51,000 4. 00 221870 14. 58 Neptune ‘1’ 30.070672 60187. 64 0.00855 1 46 38 272—234 50,000 3.90 191310 17.26 1 l . . . ¥—— . Puto E 39 51774 90737 2 0 24684 17 18 48 360,000 0 93 . . Mean . Mean . Inclination Velocity Name Density R$1§hn of Equator Oblatenms (33:21:? Albedo of Escape TSEP' ‘ g/cma 1 t0 Orbit EB :11, km/scc Sun 1.41 24 E165 (equatorial) 7°10f5 0. 0000 27.91 618 5,750 Moon 3.34 27 9321661 6°40’.7 I 0.165 0.07 2.4 277 Mercury 5.0 88510 0.00 0.36 0.07 4.2 446 Venus 4.9 0.00 0.86 0.59 10.2 326 Earth 5 . 52 23556334509 23°26’59” 1/297 1.00 0.29 11.2 277 Mars 4. 2 24537m22 .“58 25°12’ 1/192 0.40 0.15 6 .4 225 Ceres 0.06 167 Eros 51116m 34° 230 Jupiter 1.33 91‘50'n to 9115611: 3°6f9 1/15.4 2.64 0.44 60 121 Satum 0.71 10*‘14m to10h 38m 26°44’.’7 1/9.5 1.17 0.42 36 90 Uranus 1.26 101‘7 98?0 1/14 0.91 0.45 21 63 Neptune 1.61 151.18 29° 1/45 1.12 0.52 23 50 Pluto 44 * The values in this table are taken from a similar table in Russell, Dugan, and Stewart, Astronomy 7, except for Rabe’s masses for Mercury and Venus and Trumpler’s value for the radius of the solid surface of Mars. The mass of Mars is calcu- lated from Woolard’s calculations on the orbit of Deimos. Kuiper has reviewed the literature and added measurements of his own on the radii of the planets and their satellites; his table ofthese values was not available to me until the above table was in page proof. His values for the radii differ from the above values as follows: Mercury, 0.38; Venus, 0.967; Mars, 0.523; Uranus, 3.72; Neptune, 3.38; Pluto, 0.45. His radii for the satellites of jupiter are somewhat less than those used in the text. No important conclusion of this book is changed by the substitution of his values for those used; T Mean distance from the earth. 1 Sec discussion in the text. ...
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