Basic Physics of Rocket Propulsion How Newton's Third Law and Conservation
Momentum Propel Rocket
Apollo 15 Begins its Journey to the Moon - NASA
Rocket propulsion from toy water rockets to the space shuttle can be understood in terms of either Newton's third law or the law of conservation of momentum. There is an old myth that rockets need something to push against to move forward. The fact that rockets work in space far from anything to push against provides convincing evidence that this myth is incorrect. What then propels rockets forward? Rocket propulsion can be explained equally well with either of two fundamental laws of physics: Newton's third law or conservation of momentum.
Newton's Third Law Newton's third law states: "For every action, there is an equal and opposite reaction." The key to understanding the concept con cept behind these words is action reaction pairs. If A applies a force on B, the reaction must be that B applies an equal but opposite force on A. There can be no third object involved.
Read more at Suite101: Basic Physics of Rocket Propulsion: How Newton's Third Law and Conservation of Momentum Propel Rockets http://mechanical physics.suite101.com/article.cfm/basic_physics_of_rocket_propulsion#ixzz0vP9bSuzE physics.suite101.com/article.cfm/basic_physics_of_rocket_propulsi on#ixzz0vP9bSuzE In a rocket engine some type of (usually) chemical reaction spits the burned rocket fuel out of the back of the rocket. Via this chemical reaction, the rocket exerts a strong backward force on the burned rocket fuel. According to Newton's third law the required reaction is that the burned rocket fuel exerts an equal forward force on the rocket. This force accelerates the rocket forward. Newton's third law explains the rocket's forward propulsion. Because Newton's third third law says nothing about pushing against something, the rocket does not need to push against anything to accelerate forward.
Law of Conservation of Momentum An object's momentum is its mass multiplied by its velocity: momentum equals mass times velocity. Momentum, like velocity, is a vector quantity. It includes direction. If an object changes the direction of its motion, its velocity and momentum both The law of conservation of momentum applies only to isolated systems, which have no external forces acting on them. Momentum conservation states that the total momentum of an isolated system must remain constant. Physicists say that any q uantity, such as momentum or energy, that must remain constant co nstant is conserved. A rocket sitting on a launch pad or at rest in space has a zero velocity and total momentum. If the rocket and the fuel inside the rocket is an isolated system, then the total momentum of the rocket and fuel must remain zero as the rocket launches. When the rocket ignites, violent chemical reactions in the rocket fuel thrust the burned rocket fuel out the back of the rocket at a high rate of speed. This burned rocket fuel has a large backwards momentum. However the total momentum of the rocket fuel system must be conserved and remain zero. If the burned fuel has a backwards momentum, the rocket must have an equal forward momentum. The rocket must accelerate forward to get the needed forward momentum.
The backward and forward momenta add up to zero because momentum is a vector. The two momenta have opposite signs. If the forward momentum is positive, the backward momentum is negative. The equal positive and negative numbers add to zero.
The rocket has a forward momentum so that the rocket and fuel system keep the zero total momentum when the burned fuel has a backward momentum. These principles apply to any rocket from a toy water rocket to the launch of the space shuttle. They also apply to more than rocket propulsion. For example, a gun recoils when fired because of the same principles. p rinciples.
Newton's Laws of Motion The Relationship between Forces and Motion Explained
Isaac Newton - Wikimedia Commons
Newton's three laws of motion prove relationships between the forces acting on a body and the motion of the body. Isaac Newton’s three laws of motion were first published in his Philosoph his Philosophiae iae Naturalis Naturalis Principia Mathematica Mathematica in 1687. The laws form the basis b asis for classical mechanics and Newton used them to explain many results concerning the motion of physical objects.
Newton’s Three Laws First Law: Bodies move in a straight line with a uniform speed, or remain stationary, unless a force acts to change their speed of direction. Second Law: Forces produce accelerations that are in proportion to the mass of a body ( F=ma) F=ma) Third Law: Every action of a force produces an equal and opposite reaction.
Forces
Newton used Galileo’s principle of inertia as the basis for his first law. It states states that bodies do not move or change their speed unless a force acts. Effectively, bodies that are stationary will not move unless a force is applied to them while bodies that are moving at a constant speed will keep moving at that speed unless a force acts upon them. A force (such as a push) supplies an acceleration that changes the velocity of the body. This first law can be hard to appreciate in the everyday world. While a push may start an object in motion, the object will eventually slow down due to friction with the surface on which it is travelling. Friction causes a force which makes the object slow down. However, Newton’s law can be seen to operate in special situations where friction is absent. The nearest such situation would be events in space but even there forces such as gravity are at work. Nevertheless, Newton’s first law provides the the groundwork from which an understanding of forces and motion
Acceleration Newton’s second law of motion relates the size of the force to the acceleration it produces. The force needed to accelerate an object is proportional to the object’s mass. Therefore, heavy objects need greater force to accelerate them than lighter objects. This second law can be expressed algebraically as F=ma as F=ma where force (F) equals mass (m) times acceleration (a). By turning this definition around, the second law could be expressed so that acceleration a cceleration is equal to force per unit mass. For a constant acceleration, force per unit mass is also unchanged. So the same amount of force is needed to move a kilogram mass whether it is part of a small or large body.
Action Equals Reaction Newton’s third law states that any force applied to a body produces an equal and opposite reaction force in that body. Effectively, for every action there is a reaction. The opposing force is felt as recoil and the recoil force is equal in size to that originally expressed.
Newton's Third Law For the time being, we will skip the second law and go directly to the third. This law states that every action has an equal and opposite reaction. If you have ever stepped off a small boat that has not been properly tied to a pier, you will know exactly what this law means.
A rocket can lift lift off from a launch pad only when it expels gas out of its engine. The rocket pushes on the gas, and the gas in turn pushes on the rocket. The whole process is very similar to riding a skateboard. Imagine that a skateboard and rider are in a state of rest (not moving). The rider jumps off the skateboard. In the third law, the jumping is called an action. The skateboard responds to that action by traveling some distance in the opposite direction. The skateboard's opposite motion is called a reaction. When the distance traveled by the rider and the skateboard are compared, it would appear that the skateboard has had a much greater reaction than the action of the rider. This is not the case. The reason the skateboard has traveled farther is that it has less mass than the rider. This concept will be better explained in a discussion of the second law.
With rockets, the action is the expelling of gas out of the engine. The reaction is the movement of the rocket in the opposite direction. To enable a rocket to lift off from the launch pad, the action, or thrust, from the engine must be greater than the mass of the rocket. In space, however, even tiny thrusts will cause the rocket to change direction. One of the most commonly asked questions about rockets is how they can work in space where there is no air for them to push against. The answer to this question comes from the third law. Imagine the skateboard again. On the ground, the only part air plays in the motions of the rider and the skateboard is to slow them down. Moving through the air causes friction, or as scientists call it, drag. The surrounding air impedes the action-reaction. As a result rockets rockets actually work better in space than than they do in air. As the exhaust gas leaves leaves the rocket engine it must push away the surrounding air; this uses up some of the energy of the rocket. In space, the exhaust gases can escape freely.
Rocket Thrust Equation and Launch Vehicles The fundamental fundamental principles of propulsion and and launch vehicle vehicle physics physics by Robert A. Nelson A satellite is launched into space on a rocket, and once there it is inserted into the operational orbit and is maintained in that orbit by means of thrusters onboard the satellite itself. This article will summarize the fundamental principles of rocket propulsion and describe the main features of the propulsion systems used on both launch vehicles and satellites. The law of physics on which rocket propulsion is based is called the principle of momentum. According to this principle, principle, the time rate of change of the total momentum momentum of a system of particles is equal to the net external force. The momentum is defined as the product of mass and velocity. If the net external force is zero, then the principle of momentum becomes the principle of conservation of momentum and the total momentum of the system is constant. To balance the momentum conveyed by the exhaust, the rocket must generate a momentum of e qual magnitude but in the o pposite direction and thus it accelerates forward. The system of particles may be defined as the sum of a ll the particles initially initially within the rocket at a particular instant. As propellant is consumed, the exhaust products are expelled at a high velocity. 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 g ravity, that is the same as if the original particles remained together as a single entity. In deep space, where gravity may be neglected, the center of mass remains at rest.
Mr. Hayhurst's Quick and Easy Bottle Rocket Much of this information was "borrowed" from Jake Winemiller of N.E.R.D.S. Inc. and observations of many rockets launched in competitions in which I have participated. Please treat it with respect. Also remember that this is only a start. You have to do the testing and the minor adjustments. Problem
Create one bottle rocket that will fly straight and remain aloft for a maximum amount of time. Materials
Two 2-liter bottles One small plastic cone (athletic) Duct Tape Scissors String
Manila Folder Large Plastic Trash Bag Masking Tape or Avery Paper reinforcement labels (you'll need 32/chute.) Hole punch
Procedure
Cut the top and the bottom off of one bottle, so that the center portion or a cylinder remains.
Tape the cylinder to another bottle to create a fuselage (a place to store the parachute).
Get the boxes; fins will be made from it. Cut three shapes out of the folded bottom in the shape that the diagram shows. Your fins will be triangular.
The next drawing indicates how the fin should look once folded.
Mark straight lines on the bottle by putting the bottle in the door frame or a right angle and trace a line on the bottle with a marker. Use these lines as guides to place the fins on the bottles.
Make three fins and tape them on the rocket. Be sure that the fins are spaced equally around the rocket body. This can be achieved by using a piece of string
and wrapping it around the bottle and marking the string where it meets the end. Mark the string and lay it flat on a meter-stick or ruler. Find the circumference of the bottle by measuring the length of the string to the mark. Once you know the circumference, then you can divide it by three to find the distances the fins should be separated.
Use the athletic cone to make your nose cone. Use fairly rigid scissors and cut the bottom square off of the cone. Depending upon your project's mass limitations, place a golf ball sized piece of clay in the tip of the cone. This will add mass to the cone and give the rocket/cone more inertia. Then, using scissors, trim the cone to make it symmetrical. (Hint: the diameter of the bottom of the cone should be a little wider than the diameter of a 2-liter bottle.
Attach the the cone with with string string to the top top of the the other two-liter two-liter bottles bottles so that it looks looks like the diagram. Tie a knot in the end of each piece of string to give it more friction and tape it using a piece of duct tape to the inside of the cone and to the inside of the rocket body.
Many students have trouble with their nosecone getting stuck on the top of the rocket and not coming off. This can be prevented by making a pedestal for the cone to sit on. It should be high enough up so that there is space between the cone and the top of the parachute compartment. You can make a pedestal out of
the same material you will make the fins, the manila folder. Make three mini-fins, invert them and tape them on the rocket where the cone should sit.
Making the Parachute
Don't forget a good parachute has shroud lines that are at least as long as the diameter of the canopy. Lay your garbage bag out flat. Cut off the closed end. It should look like a large rectangle and be open at both ends. Lay down the bag on a flat surface and smooth it out.
The bag has a long side and a short side and is open at both ends. Fold it in two so that the short side is half as long as it was originally.
Make sure the edges are perfectly lined up during each fold. Now fold it in half along the long axis.
Make a triangle with the base of the triangle being the closed end of the previous fold.
Now fold it again. Fold the hypotenuse so that it lines up with the right side of the triangle in the above drawing.
Examine the base of the triangle and find the shortest length from the tip to the base. This is the limiting factor for chute size. The most pointed end will end up being the middle of the canopy. For an example; if you want the diameter of the chute to be 34 inches then measure 17 inches from the center of the canopy (the most pointed side of the parachute) along each side, mark it and then cut it.
After cutting cutting it, unfold unfold it. If If you have have been successful successful there should be be two canopies.
Fold the canopy in half, then into quarters, then into eighths. Carefully crease the folds each time. Crease it well and fold it again. Now the canopy is divided into 16ths. Unfold the parachute. Notice the crease marks. Get masking tape and put a piece around the edge at each fold mark. You may also use Avery reinforcement tabs. Place one on both the inside and outside of every crease, making sure that they are overlaid on top of each other. Punch holes through every piece of masking tape or Avery tab pairs and use these to attach the kite-string shroud lines.
As mentioned mentioned earlier earlier the minimum minimum length length of the shroud line should should be the the same length as the diameter of the canopy. After punching punching the the holes fold fold the canopy canopy in half. Pick Pick four holes holes and tie the shroud lines to the holes. After doing this tie the four lines together at the end most distant from the canopy. Repeat this four times until the chute is completed. Once you have it complete attach it inside the fuselage. Generally a couple of pieces of duct tape will hold the parachute to the rocket. Pack the parachute loosely and put the nosecone on the rocket. You are now ready to launch your rocket.
Carefully read the safety instructions. Fill the rocket half full of water, place on the launch pad, pressurize, and launch.
Be safe, and have fun!
Newton's Laws
P
An early scientist by the name of Sir Isaac Newton studied the motion of objects and came up with three observations. These observations became known as Newton's Three Laws and started a branch of science known as Newtonian Physics. P hysics. Water rockets travel slowly (250 miles per hour) compared to the speed of light (186,000 miles per SECOND) so the laws of Newtonian physics work quite well for our simulation purposes. (If we were simulating events that occur near the speed of light we would have to take into account relativistic effects. This branch of dynamics is called Einsteinan physics named after physicist Albert Einstein.) Einstein.) Newton's first law is: Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it. Note here that a uniform state of motion can also be standing still. The magnitude of the velocity vector just happens to be zero. Newton's first law is a simple simple statement of the laws of momentum and inertia. Newton's second law is: The relationship between an object's mass (M), it's acceleration (A), and the applied force (F) is F=MA. This is the fundamental equation for all dynamics p roblems. The force F is the total or summation of all forces acting on the mass M. Newton's third law is: for every action there is an equal and opposite reaction. This is illustrated by imagining two ice skaters standing in a line. If the skater in back pushes the skater in front, the front skater will go forward and the back skater will go backward. back ward. That is sort of what happens with rockets. As the exhaust is pushed out of the nozzle, the rocket is pushed in the opposite direction with equal force.
C Si
Me M
R
Rocket Thrust To calculate the acceleration of a rocket, we must know the thrust and mass. Since F=MA, to get acceleration, divide both sides of the equation by M and you get A=F/M. The equation for thrust on a rocket is F=mass flow rate times exit velocity. The mass flow rate is how much mass is leaving the rocket each second. The exit velocity is how fast the exhaust is traveling. Often times, the mass flow rate changes from moment to moment. Also, as mass leaves the rocket, the mass of the rocket is decreasing. The acceleration of a rocket is continually changing and a prediction must take all this into account. During a water rocket rocke t launch, there are three phases pha ses of thrusting; water flow, sonic (choked) air flow, and subsonic (unchoked) (unchoked ) air flow. The study of water flow is called incompressible fluid dynamics. (Water isn't really incompressible but it compresses so little that it can be treated as such for most applications.
ask
Water Flow The thrust produced during the water flow portion of a water rocket flight can b e calculated by using the Bernoulli equation. This equation simply accounts for the energy content of a fluid in a steady state process. (There are many types of energy en ergy that are constantly trading places. Just a few types of energy are potential, kinetic, electrical, chemical, thermal, nuclear, photonic, acoustic.) The Bernoulli equation has many terms that take into account many types of energy exchange. For our purposes here, we can justifiably neglect most of these terms because that type of energy exchange is not taking place. The relationship that represents the water flow in a water rocket is:
where P=bottle pressure, =water mass density, V=water velocity, and g=gravitational constant. If we assume that the initial water velocity inside the bottle (V1) is zero and
As S
the gauge pressure outside the bottle (P2) is zero, this equation reduces to:
. If we use the
uni units of of sl slugs/ ugs/fft^2 t^2 in in our our dens densit ity y ter term, m, the the gr gravi avitati ational onal cons consta tant nt canc cancel elss out out to mak makee
compute exit velocity then by
. We We
. The mass flow rate is the throat area times velocity
times density. But thrust is
So
but
which yields We have simplified the equations by neglecting neg lecting fluid turbulence, fluid viscosity, fluid friction, and other things. These neglected factors combined only account for a very small percentage of the total thrust so this approximation is pretty good. The instantaneous chan ge in weight of the water rocket
as previously mentioned is
but
so
For water rockets using air as the pressurizing agent, the critical pressure is This means that if, after all the water has been exhausted, the remaining air pressure in the bottle is above 27.8 psia (or 13.1 psig), you will get sonic or choked flow at the throat. The air inside the bottle will still be subsonic, but the air expanding outside the bottle will will be supersonic. You can sometimes hear a crack or bang just after launch with a high pressure launch. This is a mini sonic boom. Great way to attract attention at the start of a launch party. When the air pressure is above the critical pressure, and you have sonic flow at the throat, the mass flow rate can be calculated by the following equation:
where
=mass flow rate =throat area =chamber pressure =gravitational constant =characteristic gas velocity The characteristic gas velocity is a measure of the thrust producing abilities of a given gas. The equation for C* is:
where =ratio of specific heats (1.4 for air) =gravitational constant =absolute temperature of gas =universal gas constant =molecular weight One interesting characteristic of sonic flow is that the conditions at the throat are independent of the downstream pressure. Noticed that the mass flow rate equation does not have ambient pressure in it. Once critical pressure is achieved, the mass flow rate will not increase with a decrease of ambient pressure. The actual exhaust velocity (but not mass flow rate) of supersonic flow depends upon the expansion ratio of the nozzle and surrounding conditions. The ratio of exit plane area to throat area is called the expansion ratio. You have seen rockets that have an exit cone. This increases the gas velocity even further to produce more thrust. If you have hav e choked (sonic) flow at the throat, the conditional relationships along the exit cone are: as the cross sectional area increases, the pressure and temperature drops and the velocity increases. There is, of course, a limit on how far you can expand the gases. If you expand to much, the exit plane pressure will be below ambient pressure and this
will have a diminishing influence on the thrust. It can be shown (through a lot of calculus) that the optimum thrust is achieved when the exit ex it plane pressure just equals ambient pressure. If the exit plane pressure is greater than ambient, the flow is said to be underexpanded. Conversely, if the exit plane pressure is below ambient, the flow is said to be overexpanded. For our water rockets, we don't usually have an exit cone because the duration of choked flow is so short. Our water rockets have an expansion ratio of one. The equation for thrust for compressible gases is: =chamber pressure =throat area
where
=thrust coefficient The equation for thust coefficient is: is:
where =expansion cone half angle =ratio of specific heats =exit plane pressure =ambient pressure =chamber pressure =expansion ratio To find the exit plane pressure
iteration: =expansion ratio
, we have to solve the following relationship by numerical
wh e re
=ratio of specific heats =exit plane pressure =chamber pressure As you can see, many calculations are required to determine the actual rocket thrust.
Subsonic (Unchoked) Flow Once the chamber pressure drops below the critical pressure, the flow becomes unchoked. Now the downstream pressure has an influence on the conditions at the throat. The mass flow rate equation
for unchoked flow is: As all the compressed air is expelled, the thrust drops to zero and the water rocket has attained its maximum velocity. Gravity and wind resistance slow the water rocket down to the stopping point and the rocket falls back to earth.
Simulation Results For a simulation of a 2 liter bottle with initial air pressure of 1 00 psig and 20% water volume vo lume the following are the results: Launch Launch Water Water Burnout Burnout Superso Supersonic nic/Su /Subso bsonic nic Deceleration Press essure Transition Equilibrium Time (sec)
0. 0
0.042
0.074
0.088
0.104
Altitude (ft)
0. 0
3 .2
12.2
16.9
22.4
Pressure (psig)
100
69.2
13.1
4 .1
0. 0
Velocity (ft/sec)
0. 0
202
325
332
326
Acceleration (ft/sec/sec)
0. 0
12,294
1,102
0
-671
Water burnout is when all the water is exhausted ex hausted and just air remains in the bottle. There is still pressure (69 psi) which continues to provide thrust. Since the pressure is is above the critical pressure, choked flow occurs at the throat and you have supersonic exhaust. When the pressure drops to the critical pressure (13.1 psi) the flow changes to unchok ed but there is still a little energy left in the a ir. When the chamber pressure gets down to 4.1 psi, the drag on the bottle equals the thrust produced so you get no net acceleration. This is is the point of maximum velocity. By the time time the pressure inside the bottle equalizes, the velocity has dropped d ropped by 6 ft/sec and gravity and drag will bring the bottle to zero velocity. Notice that 1/3 of the velocity is obtained by the residual air in the bottle after the water is gone. This is but a brief introduction into the world of rocket science. Alot of fun as you can see!! Fins
