Rockets

PTYS206-2March 25, 2008

Schedule

• Today– Essay review– HW review– Start on Rockets and Spaceflight

• Thursday– HW due– More on Rockets– Start on satellite communications

• Next Tuesday– Satellite Communications

• Next Thursday– Science Fiction

Essay Marking Key UGH Painful to Read. NAS Not A Sentence. This usually indicates a grammatical problem. WW Wrong Word. A word has been used incorrectly. Check a dictionary. NS No Sense. The sentence indicated makes no sense as written. NC No Content. The sentence indicated does not add significant content

to the essay. UI Useless Information. HP Hodge podge Paragraph. The paragraph indicated contains too

many weakly connected ideas. WA Weak Antecedent. It is unclear which noun goes with the pronoun. WN Wrong Number. Usually indicates disagreement between the number

(singular or plural) of the subject and verb. WT Wrong Tense. Indicates that the verb has the wrong tense (past,

future, etc.). OS Out of Sequence. The sentence indicated is not in a logical

sequence. SM Superfluous Modifier. The indicated adjective or adverb is

unnecessary. CM Confused Metaphor. The attempted metaphor does not work.

Plagiarism

• Copying very short phrases of 3-4 words isnot great, but it difficult to avoid and mayhappen unconsciously.

• Copying clauses is worse.• Copying entire sentences is a clear violation

of ethical standards and will result in a failinggrade.

• Copying many complete sentences is evenworse.

Comments on Essays

• Some are very good, many not so good, someindicate an alarmingly low level of literacy.

• The most common problem is insufficient effort onthe writing. Now you know what the standards are.

• If you are really concerned, I’ll look at another draftbefore the final.

• Misuse of words is common. Use your dictionary.Read more books.

• It is impossible to overstate the importance of goodwriting skills to your impending career. Work on this!

Some General Comments

• The first sentence in the essay is the most important.Make it good!

• The first paragraph is the most important. Make itgood!

• Every paragraph should have one main point. Thispoint should be introduced in the topic sentence. Thetopic sentence should be as specific as possible.

• Write concisely! Work hard to shorten your essay.Remove all non-essential sentences and clauses.The reader will love you for it.

Good Intro Sentences

• The first sentence should introduce the main ideaand say why it is important.

• Do not start listing details right away, but do not betoo general either.

• Most essays erred with introductory sentences thatwere far too general.

• For example, “Mankind has always been fascinatedby the heavens.” is a horrible intro sentence.

• A good test is: Does the sentence apply specificallyto this essay, or could it be used in a thousandothers?

The Bulwer-Lytton Fiction ContestThe Worst First Sentences of All Time

http://www.bulwer-lytton.com/lyttony.htm

Modern Form of Newton’s Third LawNewton’s Third Law: For every action there is an equaland opposite reaction.

Modern Version: Momentum is conserved.

“Conserved” to a physical scientist means that thequantity in question does not change. So, if we areanalyzing some event, conservation of momentummeans that the momentum after the event is the same asthe momentum before the event.

Momentum is equal to the product of the massand velocity of an object.

There are many conservation laws in physics.Unfortunately, we cannot study them all.

Action and Reaction

As Applied to Rockets

Momentum Conservation

Before

Rocket is stationaryMometum is zero

(M + m)V= 0

After

Momentum must still be zero.

MVR + mVf = 0, soVR = -(m/M)Vf

Negative means oppositedirection

Vf

VR

upward

down-ward

The speed of the rocket exhaust is critical

Rocket ExampleCalculate the mass of fuel needed to accelerate a 1000 kgrocket to escape velocity on Earth. Assume that theexhaust speed is 3 km/s (a typical value). Remember thatescape velocity on Earth is 11 km/s.

Rocket ExampleCalculate the mass of fuel needed to accelerate a 1000 kgrocket to escape velocity on Earth. Assume that theexhaust speed is 3 km/s (a typical value). Remember thatescape velocity on Earth is 11 km/s.

We have

MVR + mVf = 0

m = -(VR/Vf)M

Vf = -3 km/s, VR = 11 km/s, M = 1000 kg = 103 kg, so

m = (11/3)103 = 3.7×103 kg.

The fuel has more mass than the rocket!

Jet Engines and High Speed Exhaust

The following designmaximizes the exhaustvelocity for a chemical rocket.

The constriction in the nozzleis critical (called a de Lavalnozzle). This design producessupersonic exhaust velocity. Itis used in all gas combustionrockets.The nozzle was developed by Swedish inventor Gustaf deLaval in 1897 century for use on an impulse steamturbine.[1]This principle was used in a rocket engine byRobert Goddard. Walter Thiel's implementation of it madethe V2 rocket possible, and very nearly all modern rocketengines that employ hot gas combustion use de Lavalnozzles.

Multistage Rockets

The rocket velocity isgiven by

VR = -(m/M)Vf

To make VR as largeas possible, we shouldmake M (the rocketmass) as small aspossible. This leadsto the idea of multi-stage rockets.

Play the Movie

Myths about Rockets and Spacecraft

• Once in space, rocket engines are off and rocket ison unpowered flight, following an orbital trajectory.The goal of the launch is to place the rocket on theright orbit. Spacecraft don’t accelerate, changedirection, stop or do anything else exciting.

• The space shuttle is a glider.• Spacecraft have tiny thrusters to make small

adjustments to their orbit. The typical force is 1Newton (i.e. the weight of a 0.1 kg object on Earth).

• Sometimes spacecraft carry an engine and fuel inorder to slow down enough to get into orbit about aplanet.

Gravitational Assists

Voyager and the Grand Tour

Cassini Trajectory

Play Movie

Electric PropulsionElectric propulsion is analternative to chemicalpropulsion. Theprinciple is the same, butinstead of chemicalexhaust ions are ejectedfrom the engine at highspeed. The ions can beaccelerated to muchhigh velocities thanchemical exhaust,making ion enginesmore efficient in somecircumstances.

Most importantly, ion enginescan run continuously andspacecraft powered by ionengines are no longer on pureorbital trajectories.

Xenon Ions Provide Thrust

m i v i → ← m e v e =

750-kg Dawn spacecraft ∆v = 10-5 m/s

Dawn Mission to Ceres and Vesta