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Topic: Rocket equation

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	Starships of the Mind - by Bruce M. Bowden - Chapter Four (Site not responding. Last check: 2007-10-13)
		Within a rocket, a quantity of the mass being carried on board, the fuel, is expelled with a certain kinetic energy in the direction opposite the desired direction in which the rocket is to move.
		The derivation of the rocket equation begins with a finer analytical snapshot of the rocket at an arbitrary moment and leads to a relationship between time, exhaust velocity, acceleration and the rocket mass.
		This rocket is ideal: the exhaust is exactly opposite the direction of travel, the burning is uniform, the conversion of chemical to kinetic energy is efficient, there are no extraneous influences upon the rocket such as magnetic fields or a resisting medium.
	www.scientium.com /specials/sotm/chap04.htm (2522 words)

	Rocket Tutorial from ATI Space and Defense Technical Training Courses (Site not responding. Last check: 2007-10-13)
		The center of mass of the total system, subsequently consisting of the particles remaining in the rocket and the particles in the exhaust, follows a trajectory determined by the external forces, such as gravity, that is the same as if the original particles remained together as a single entity.
		As the altitude of the rocket increases along its trajectory, the surrounding atmospheric pressure decreases and the thrust increases because of the increase in pressure thrust.
		By the rocket equation, assuming a specific impulse of 300 seconds, the fraction of the separated mass consumed by the propellant for the apogee maneuver is 46 percent from Cape Canaveral, 40 percent from Kourou, and 39 percent from the equator.
	www.aticourses.com /news/rocket_tutorial.htm (3806 words)

	Some Rocket Motor Calculations (Site not responding. Last check: 2007-10-13)
		Since there is gas pressure P in the front of the rocket motor wall and little gas pressure at the back 5 of the rocket motor, a reaction thrust F is produced in the rocket motor.
		Then, the equation (1) may be used to for the reaction thrust force F produced by the rocket motor.
		The mass flow rate M in a rocket motor is assumed to be constant along the length of the rocket motor.
	science.radioelectronics.biz /thermoManual2/rocketCalculations.html (2199 words)

	Tsiolkovsky's equation (Site not responding. Last check: 2007-10-13)
		Tsiolkovsky's rocket equation, named after Konstantin Tsiolkovsky who first derived it, considers the principle of a rocket: a device that can apply an acceleration to itself (a thrust) by expelling part of its mass with high speed in the opposite direction, due to the conservation of momentum.
		The Saturn V rockets used in the Apollo space program and the ion thrusters used in long-distance unmanned probes are good examples of this.
		The rocket equation shows a kind of "exponential decay" of mass, but not as a function of time, but as a function of delta-v produced.
	equation.net.ru (553 words)

	That's Why They Call It Rocket Science
		The rocket seems to tear itself apart and in an instant is transformed from an icon of humanity's great achievement to a scattering of high-tech trash raining down from the sky in flaming bits.
		Rocket engines represent a significant fraction of the overall mass of the empty rocket stage, so they must achieve a high thrust-to-weight ratio to lift themselves—and the rest of the rocket and payload—into orbit.
		That modern rockets have achieved their current level of reliability is a testament to the dedication and skill of the teams that design, build, and launch them.
	www.aero.org /publications/crosslink/winter2004/02.html (1628 words)

	Rocket Principles
		Under the influence of the rocket thrust and gravity, the acceleration is
		Under the influence of the rocket thrust in a gravity-free environment, the acceleration is
		To explore the effects of the various parameters on the motion of the rocket, you may substitute numbers in any of the boxes.
	hyperphysics.phy-astr.gsu.edu /hbase/rocket2.html (237 words)

	Rocket Motion
		This equation says that the rocket changes momentum due to its loss in mass (which is just the mass of gas expelled) times its initial velocity plus the mass of the rocket times its change in velocity.
		All that is missing for your degree in rocket science is the ability to apply the rocket equation to typical problems.
		This equation ignores air resistance, the weight of the rocket body itself, and does not take into account the fact that the force of gravity reduces with height (we need integration to do that problem), but nevertheless is pretty accurate for characterizing most rocket launches, including the Space Shuttle.
	dept.physics.upenn.edu /courses/gladney/mathphys/subsubsection3_1_3_3.html (1170 words)

	Untitled
		Atmospheric resistance harms us in two ways: not only does it provide physical resistance to the rocket's movement through the air (drag), but it also hinders the escape of the propellant out the back end: which is to say it slows that down, or lowers the c in the equation.
		Since the rocket spends more time in vacuum, the average exhaust velocity during the flight is going to be higher than 10615; precisely what it will be can be calculated, but the calculations are sensitive to the flight path, and that's sensitive to the structural weight; meaning there's enough room for experts to disagree.
		The result was that many rocket engineers fell into the habit of thinking of rocket motors as part of an artillery system; they were ammunition, and it was pointless to build them for anything else.
	home.earthlink.net /~jerryp/SSX.html (6904 words)

	Range vs. difficulty for ballistic missile development.
		In fact, the function of the rocket nozzle is to expand the combustion gas in such a fashion that it cools and constitutes a largely uni0directional jet.
		As the gas expands in the rocket nozzle, it repeatedly pushes on the material of the nozzle (except in the direction of the exit circle), and as the rocket nozzle diameter increases with distance from the throat, the gas expands and cools itself.
		So one has an equation relating the two, and specifically giving the rate of increase of rocket momentum as determined by the rate m (in grams/second) at which mass is exhausted, together with the velocity Ve of the exhausted mass.
	www.fas.org /rlg/980327-range.htm (1503 words)

	EBTX - The Rocket Equation-Tsiolkovsky and Interplanetary Space Travel
		This equation (and variations) has stood the test of time and experience and should be applicable to all rocket type situations wherein the astronauts take their fuel along with them and use it to "push off of".
		Since the rocket "burn" is even and continuous, we can average the whole mass of exhaust as 75% of light velocity (for every bit going at 80% there is a corresponding bit going at 70%).
		Fuel is fed to the rockets through tubes running the length of the tether originating from a tanker stationary at the point of rotation of the entire apparatus.
	ebtx.com /mars/rocketeq.htm (1615 words)

	app-a2
		A step rocket is one rocket riding piggyback on top of another so that their velocity increases during burning are additive, a concept recognized as early as the seventeenth century.
		Using the perfect gas equation, rocket exhaust velocity can also be expressed as a function of three ratios: specific heat, nozzle exit pressure to combustion pressure, and combustion gas temperature to the mean molecular mass of the gases.
		This equation can be obtained by algebraic combinations of the basic thermodynamic relationships of' the equation of state for a perfect gas, conservation of energy, reversible adiabatic (isentropic) gas expansion.
	www.hq.nasa.gov /office/pao/History/SP-4404/app-a2.htm (5787 words)

	Artemis Project: Introduction to the Rocket Equation
		Since nuclear rockets and matter-antimatter engines aren't exactly off-the-shelf technology (yet), just look at the chemical rockets.
		To calculate the fuel burns, invert the rocket equation:
		Delta-M for a rocket engine burn is Mo - Mf; that's the total of the fuel plus oxydizer used during the burn.
	www.asi.org /adb/06/07/04/11/rocket-eqn-primer.html (392 words)

	Rocket Propulsion
		The thrust force of a rocket motor is the reaction experienced by the motor structure due to ejection of the high velocity matter.
		The rocket and fuel have a total mass M and the combination is moving with velocity v as seen from a particular frame of reference.
		The equation expresses that, when a particle is acted upon by a force F during a given time interval, the final momentum p2 of the particle may be obtained by adding its initial momentum p1 and the impulse of the force F during the interval of time.
	www.braeunig.us /space/propuls.htm (4923 words)

	The Rocket Equation (Site not responding. Last check: 2007-10-13)
		This equation lets us calculate the mass of propellant that will be required to accelerate a rocket of a given mass to a given velocity.
		Roughly 10% of the mass of a rocket on takeoff is "dead weight" – the mass of the empty rocket structure.
		Assume the first stage will accelerate the rocket to one quarter of its orbital velocity, but that it will have all the atmospheric drag (since air resistance decreases rapidly with altitude, most of the air resistance occurs in the first few km of travel).
	www.carlton.paschools.pa.sk.ca /chemical/mtom/contents/chapter1/req.htm (662 words)

	Rocket Thrust Equation
		The amount of thrust produced by the rocket depends on the mass flow rate through the engine, the exit velocity of the exhaust, and the pressure at the nozzle exit.
		Since the oxidizer is carried on board the rocket, rockets can generate thrust in a vacuum where there is no other source of oxygen.
		That's why a rocket will work in space, where there is no surrounding air, and a gas turbine or propeller will not work.
	www.grc.nasa.gov /WWW/K-12/airplane/rockth.html (400 words)

	Rocket Lab
		The first number in the name is the rockets average thrust in N. Finally, the last number is the delay time in seconds between the burnout of the rocket and the ejection of the parachute.
		Several measurements will be needed for each rocket launch including the apogee (maximum altitude) of the rocket, the flight time till apogee and the initial and final mass of the rocket engine.
		The second number on the rocket engine name is the number of seconds until the charge is supposed to detonate, but for real rockets the time till the charge varies wildly from this number.
	www.users.csbsju.edu /~jcrumley/332_2004/rl/rocket_lab.html (3572 words)

	Chemical Rocket Launcher
		According to the above formula, which is know as the rocket equation, a high velocity of exhaust gas is needed to launch massive cargo.
		Rocketeers often talk of specific impulse, which is measured in seconds and is proportional to the exhaust gas velocity.
		To maximize the specific impulse, some researchers attempt to build rockets propelled by pure hydrogen heated either by electric current, or a laser, or microwaves, or a nuclear reactor.
	www.nas.nasa.gov /About/Education/SpaceSettlement/Nowicki/SPBI101.HTM (754 words)

	Program rockfile - Updated 10/16/06
		In the previous exercise we extended the water rocket analysis to include evaluation of the upward velocity of the rocket throughout the flight.
		Unlike the nonlinear differential equations for volume V and velocity u (equations 7 and 10), equation 11 can be directly integrated using the Trapezoidal method which we developed in Lab 5.
		The very jagged cumulative height plot is a result of using a very unconventional numerical quadrature technique to solve the set of three differential equations, when in fact we should be using a standard differential equation solving method.
	www.ent.ohiou.edu /~et181/rocket/rockfile.html (945 words)

	Theory (Site not responding. Last check: 2007-10-13)
		The equation I use in this application is one known to spacecraft designers everywhere called the Rocket Equation.
		construct in the equation is the natural (or base-e) logarithm of the argument -- in this case, the ratio of starting mass to final mass.
		Please note that this form of the Rocket Equation does not factor in the influence of external forces on the spacecraft such as gravity or air resistance.
	www.clanseger.org /vrs/isp/theory.html (281 words)

	rocket equation (Site not responding. Last check: 2007-10-13)
		The rocket is going at a certain velocity and the object that is thrown out has the same velocity as the rocket before it is thrown.
		It doesn't matter how fast the rocket is going when the object is expelled; it is the force needed to achieve the relative exit speed for a given mass of gas that increases the speed of the rocket.
		Notice that the rocket gains momentum (expressed as a positive value) and the gas loses momentum and is expressed as a negative value.
	ed-thelen.org /rocket-eq.html (911 words)

	rocket equation
		First derived by Konstantin Tsiolkovsky in 1895 for straight-line rocket motion with constant exhaust velocity, it is also valid for elliptical trajectories with only initial and final impulses.
		The rocket equation, which can be obtained from Newton’s laws of motion, shows why high effective exhaust velocity has historically been a crucial factor in rocket design: the payload ratio depends strongly upon the effective exhaust velocity.
		In its simplest form the rocket equation can be written as:
	www.daviddarling.info /encyclopedia/R/rocket_equation.html (188 words)

	Week 10 ase 201 (Site not responding. Last check: 2007-10-13)
		In space, there is no gravity and no atmosphere, so the equation for velocity as a function of time is very simple and can be solved by hand, Near the earth, gravity is a constant force, and the velocity equations are still solvable by hand.
		When a realistic model of drag is included, the equation for velocity becomes nonlinear and is no longer easy to solve by hand.
		are the mass of the rocket and the payload, and
	www.ae.utexas.edu /courses/ase201/assign_dir/rocket.html (416 words)

	Classical mechanics: rocket motion (Site not responding. Last check: 2007-10-13)
		Rockets are perfect for space travel because they carry their fuel and oxygen supply with them.
		At initial time t, the rocket is moving with velocity v and has a mass M.
		Therefore, the rocket equation that describes the motion for any time t is simply
	classicalmechanics.net /RocketMotion.htm (818 words)

	FundRoc 2-4 (Site not responding. Last check: 2007-10-13)
		One of the most basic and often used rocket equations is called the "ideal rocket equation." It relates exhaust speed and mass ratio to the resulting change in speed,
		For a rocket, reactive force is due entirely to its change in mass by expelling exhaust gas at speed, c.
		is the change in rocket speed, "ln" is the natural logarithm and MR is its mass ratio.
	www.innovatia.com /Design_Center/FundRoc_2-4.htm (191 words)

	Liquid Air Cycle Rocket Equation by Steven S. Pietrobon (19 Dec 1994)
		We derive this from the fact that the effective thrust of a rocket equation is that obtained by accelerating the propellant mass continuously entering the engine up to some exhaust speed v_e (the energy being obtained from the combustion of a fuel and an oxidiser).
		This is the LACE Rocket Equation (probably discovered yonks ago, but what the heck, it was fun deriving it).
		Using the rocket equation and v_e = 4400 m/s we have v(T) = 6123 m/s.
	www.islandone.org /Propulsion/LACE.html (1048 words)

	Rocket -- from Eric Weisstein's World of Physics
		Let u be rocket speed relative to a stationary observer and v be exhaust speed relative to a stationary observer
		which is not true, since a rocket may go faster than its propellant exhaust velocity.
		Sutton, G. Rocket Propulsion Elements: An Introduction to the Engineering of Rockets, 6th ed.
	scienceworld.wolfram.com /physics/Rocket.html (72 words)

	SCRAM Rocket Equation by Steven S. Pietrobon (20 Dec 1994)
		For a SCRAM powered rocket incoming air is slowed down to some supersonic speed v_s to allow the fuel enough time to burn with the oxygen in the air.
		Assume a 5:1 O/F ratio for the rocket powered flight (a lower ratio is used for vacuum operation to get better v_e, whereas 6:1 is used for sea level operations where higher thrust is desired).
		If we assume that rocket powered 300 m/s is required to go into and out of orbit (150 m/s each way) then using the rocket equation we require
	www.islandone.org /Propulsion/SCRAM.html (587 words)

	Various rockets parameters simulators (Site not responding. Last check: 2007-10-13)
		I have written 3 javascripts simulators based on the "Rocket Equation".
		Basically it say that with a given quantity and type of a propellant/oxydiser your rocket will accelerate till there is no more fuel to burn.
		After that the rocket speed stay at this last speed until it encounter something large and heavy!
	perso.orange.fr /jplr/English/ideas/consid.htm (90 words)

	Ideal Rocket Equation
		The forces on a rocket change dramatically during a typical flight.
		Now, if we consider the instantaneous mass of the rocket M, the mass is composed of two main parts, the empty mass me and the propellant mass mp.
		The limits of integration are from the initial mass of the rocket to the final mass of the rocket.
	exploration.grc.nasa.gov /education/rocket/rktpow.html (618 words)

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