Rocketry
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Newton's Third Law explains how rockets work: fuel ejected from the nozzle exerts an equal and opposite force on the rocket, causing it to accelerate upwards. Specific impulse measures a rocket engine's efficiency - how fast it ejects fuel for a given amount of thrust. Higher specific impulse means less fuel is needed. The nozzle helps increase fuel velocity and specific impulse using the continuity equation, but must be carefully designed to avoid instability from overexpansion or loss of efficiency from underexpansion. As a rocket burns fuel, its mass ratio - initial to final mass - increases, improving acceleration according to Newton's Second Law. Forces acting on a rocket include weight, drag, thrust, lift, and gravity.
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- 1. Physics Of A Rocket Sandeep Arakali Physics 1A
- 2. Equal force in opposite direction Thrust from exhaust Newton’s Third Law Newton’s Third Law explains how a rocket takes off. It states that for every force, there is an equal and opposite force. A rocket takes off by ejecting fuel forcefully from its nozzles. The high-velocity fuel hitting the ground exerts an equal force on the rocket in the opposite direction, causing it to go up.
- 3. Δp = 50 Ns Mfuel = 5 g Isp = 30 m/s Less Efficient Engine More Efficient Engine Δp = 150 Ns Mfuel = 2 g Isp = 75 m/s Isp = 30 m/s Isp = 75 m/s Specific Impulse Momentum is conserved in a rocket. A change in momentum is called an impulse. Impulse is the amount of force exerted over a given time (Δp = FΔt). In rocketry, the specific impulse refers to the impulse per a given mass of fuel. Specific impulse is the same as the speed of the fuel if the units are multiplied using dimensional analysis. The faster the fuel is ejected, the less fuel is actually needed to produce the same shift in momentum. Therefore, specific impulse is a measure of a rocket engine’s efficiency. Specific impulse is abbreviated Isp.
- 4. Fuel Combustion Chamber Reasonable specific impulse Large specific impulse Small specific impulse Overexpanded: loss of stability occurs Underexpanded: loss of efficiency occurs Ambient: just right Nozzle Continuity Equation The continuity equation applies to fluids in motion. It states that the area of a pipe’s opening is inversely proportional to the velocity of the fluid inside (A1v1 = A2v2). This means that as the area of the pipe opening gets smaller, the velocity of a fluid inside has to increase to match the smaller opening. This principle is used in the nozzle to increase the velocity of the fuel leaving, thereby increasing the specific impulse. However, the nozzle cannot be narrowed too much, or the speed of the fuel will overwhelm the rocket and cause it to be unstable. The nozzle width is carefully controlled and changed throughout the flight for maximum efficiency without losing stability.
- 5. Mass Ratio The mass ratio measures the efficiency of the rocket itself. It is the ratio of the initial mass of a rocket to its final mass. The higher the mass ratio, the more fuel the rocket sheds, and the lighter it becomes. According to Newton’s Second Law, force equals mass times acceleration. The more mass the rocket sheds, the greater acceleration it willexperiencegiven a constant thrust. Therefore, the rocket becomes more efficient as the flight progresses. The mass ratio quantity was derived from Tsiolkovsky’s equation which stated that Δv = veln(mass ratio). It can also be seen that the mass ratio affects the change in velocity given a constantvelocityof fuel or ve.
- 6. Space Drag Earth Atmosphere-space boundary Weight/Gravity Thrust Lift Lift Forces Acting On A Rocket The forces acting on a rocket are weight, drag, thrust, lift and gravity. Weight is its gravitational pull on earth (W = mg). Drag refers to air resistance and atmospheric friction as the rocket leaves the atmosphere. Thrust is the force that propels the rocket upwards as shown in slide 1. Lift is usually very small on most rockets. Lift is the sideways stabilizing force on the fins caused by Bernoulli’s principle. Finally, gravity is the universal force that acts on the rocket. It is exerted by any celestial body that the rocket comes close to.
- 7. Adcock, George. Rocket Science – The Very Basics. 20 Mar. 2009. 1 Jul. 2009. <http://www.brighthub.com/science/space/articles/29607.aspx>. Braeunig, Robert. Rocket Propulsion. 2007. 2 Jul. 2009. <http://www.braeunig.us/space/propuls.htm>. Forces On A Rocket. 17 Nov. 2005. National Aeronautics and Space Administration (NASA). 2 Jul. 2009. <http://exploration.grc.nasa.gov/education/rocket/rktfor.html>. “Rocket.” Wikipedia. 3 Jul. 2009. <http://en.wikipedia.org/wiki/Rocket>. Bibliography
- 8. THE END