Principles of Rocketry Water Rocket Investigation – Background Theory Principles of Rocketry Photo courtesy of Tau Beta Pi MindSET Program © Copyright 2015. All rights reserved. www.cpalms.org

What Do You Think? Why do bottle rockets fly? Why do we have to use water, or do we? Will it fly without water? If a little water works well, will a lot of water work better? Will it fly best when it is totally full? What volume of water works best? © Copyright 2015. All rights reserved. www.cpalms.org

What is a Rocket? A chamber enclosing a gas under pressure A balloon is a simple example of a rocket. Rubber walls compress the air inside. Air escapes from the small opening at one end and the balloon flies. Photo courtesy of Tau Beta Pi MindSET Program © Copyright 2015. All rights reserved. www.cpalms.org

FORCES The cause of acceleration A push or a pull one body exerts on another It is a vector quantity The magnitude or size is the strength of the force The direction of the force is the direction in which the push or pull is applied The SI unit of force is newtons (N) © Copyright 2015. All rights reserved. www.cpalms.org

Balanced vs. Unbalanced Forces Balance force - forces on an object that are equal in size and opposite in direction The net force on the box is zero because the two forces cancel each other. DOES NOT CHANGE VELOCITY Unbalanced force – result in a net force which causes acceleration Net force – overall force acting on an object after all forces are combined • Forces in the same direction add up, ex. pushing a car • Forces in opposite direction subtract, ex. Tug a war Photos courtesy of Pearson Prentice Hall © Copyright 2015. All rights reserved. www.cpalms.org

Newton’s Three Laws 1. Objects at rest will remain at rest and objects in motion will remain in motion in a straight line unless acted upon by an unbalanced force. 2. Force equals mass times acceleration. 3. Every action has an equal and opposite reaction. © Copyright 2015. All rights reserved. www.cpalms.org

1. Objects at Rest, in Motion Force of GRAVITY At Rest: Forces are balanced. The force of gravity on the rocket balances with that of the launch pad holding it up. In Motion: Thrust from the rocket unbalances the forces. As a result, the rocket travels upward (until it runs out of fuel). Note: Thrust from the rocket’s engines acts downward producing an upward reaction on the rocket REACTION from Thrust Photo courtesy of Northbridge Public High School © Copyright 2015. All rights reserved. www.cpalms.org

2. F=mA Force equals mass times acceleration. The pressure created inside the rocket acts across the area of the bottle’s throat and produces force (thrust). Mass represents the total mass of the rocket, including its fuel. The mass of the rocket changes during flight. As fuel is rapidly used and expelled, the rocket weighs less and accelerates. Thrust continues until the engine stops firing. Mass Force Acceleration Thrust Force produced as fuel rapidly exits, accelerates rocket. Photo courtesy of Northbridge Public High School © Copyright 2015. All rights reserved. www.cpalms.org

3. Action and Reaction A rocket takes off only when it expels gas. Action: The rocket pushes the gas out of the engine. Reaction: The gas pushes up on the rocket. The Action (Thrust) has to be greater than the weight of the rocket for the reaction (liftoff) to happen. (Bottle & Water Mass) X (Bottle Velocity) EQUALS (Ejected Water Mass) X (Ejected Water Velocity) UP DOWN Essentially, the faster the fluid is ejected, and the more mass that is ejected, the greater the reaction force on the bottle. Photo courtesy of Northbridge Public High School © Copyright 2015. All rights reserved. www.cpalms.org

DESIGN CONSIDERATIONS Water Rockets DESIGN CONSIDERATIONS Additional concepts to consider for the advance students Photo courtesy of Tau Beta Pi MindSET Program © Copyright 2015. All rights reserved. www.cpalms.org

  Inertia Inertia is the tendency of an object to resist any change in motion. It is associated with the mass of an object. Desired Path of Motion  Wind Direction (Trajectory) A bottle rocket that is HEAVIER has MORE Inertia, because it has MORE mass. MORE Inertia will offer GREATER resistance to a change in direction. Therefore the wind will have LESS effect on a bottle with MORE INERTIA. A LIGHTER bottle rocket has LESS inertia because it has LESS mass. LESS inertia means the rocket will have LESS resistance to change in direction. Consequently, the wind has a GREATER effect on the rocket’s path of motion.   Photos courtesy of Northbridge Public High School © Copyright 2015. All rights reserved. www.cpalms.org

Center of Mass The Center of Mass is the exact point about which all of the mass of an object is perfectly balanced. All matter, regardless of size, mass, or shape has a center of mass. Around this point is where an unstable rocket tumbles. Spinning and tumbling takes place around one or more of three axes: roll, pitch, and yaw. Any movement in the pitch and yaw axes directions can cause the rocket to go off course Photo courtesy of NASA Project Mercury spacecraft © Copyright 2015. All rights reserved. www.cpalms.org

Center of Pressure The Center of Pressure (CP) is the location where the ‘pressure forces’ acting on a rocket are balanced. The CP exists only when air is flowing past the moving rocket. (Based on surface area) Flowing air pushing against the rocket, can cause it to roll and sway around the most stable point (CM). It is important that the CP of the rocket is located toward the tail and the CM is located toward the nose. . Photo courtesy of Rocket Physics Blog Spot © Copyright 2015. All rights reserved. www.cpalms.org

DRAG DRAG = Air Resistance Air Resistance causes friction which slows down the Rocket. Friction always works in the opposite direction of the Rocket’s motion. (Even when a rocket is descending, drag counteracts the rocket’s motion!) UP DOWN MOTION (Reaction) MASS EXITING (Action) Photo courtesy of Northbridge Public High School © Copyright 2015. All rights reserved. www.cpalms.org

effect on blunted bodies, easily separate, thus reducing TIPS: REDUCING DRAG Drag has a significant effect on blunted bodies, such as the Nose Cone below. A Round or Contoured Nose Cone allows Air to easily separate, thus reducing the effects of Drag More AERODYNAMIC or pointed nose cone: This causes the air to “part” around the bottle. More Aerodynamic fins: Thinner, more streamlined fins reduce drag. Position fins toward the tail of the rocket (moves CP!). Photo courtesy of Tau Beta Pi MindSET Program © Copyright 2015. All rights reserved. www.cpalms.org

BALLAST  BALLAST: any mass added to a vehicle to improve STABILITY and increase INERTIA. Wind Direction  Air Resistance (DRAG) Ballast Center of Mass Photo courtesy of Northbridge Public High School Stability: Ballast towards the nose cone will shift the center of mass forward. Inertia: More weight (ballast) increases inertia and will prevent a bottle’s path of motion (or Trajectory) from being prematurely overcome by DRAG & WIND FORCES........CAREFUL! Too much Ballast will make the vehicle too heavy (Newton’s 3rd Law). © Copyright 2015. All rights reserved. www.cpalms.org

Rocket Fin Shapes Square/Trapezoidal Fins yield MORE stability, but create MORE drag. Triangular/ Epsilon Fins introduce LESS drag, but yield LESS stability. © Copyright 2015. All rights reserved. www.cpalms.org

Stability How can you increase Rocket Stability? Lengthen the rocket (This moves the center of mass further forward than the center of pressure) Add mass to the nose cone or nose piece Bend the fins to cause it to spin, Caution! (Spinning the rocket will consume energy. This energy will not be used to gain any more altitude) Extend fins towards the end of the rocket. Heavy rockets have more inertia and therefore more stability Watch Out! Too much weight will not allow the rocket to travel fast enough and it will prematurely run out of thrust, therefore, preventing it from reaching its intended destination. © Copyright 2015. All rights reserved. www.cpalms.org

(Highest Point of Trajectory) Trajectory is the curved path of an object traveling through space. NOTE: Even objects thrown or launched vertically have a trajectory. Photo courtesy of Tau Beta Pi MindSET Program Trajectory Path Apogee (Highest Point of Trajectory) (Launch Angle) X (Distance Traveled) Factors that Affect Bottle Trajectory: Newton’s 3 Laws of Motion Flow Rate of Fuel Existing - Bottle Internal Pressure - Air/Fuel Volumes - Air/ Fuel Densities Mass of Bottle Air Resistance/Drag Affects - Atmosphere Pressure/Temp - Bottle Aerodynamics Gravity © Copyright 2015. All rights reserved. www.cpalms.org

TRAJECTORY PHASES The Boost Phase of a rocket refers to COAST Photo courtesy of Tau Beta Pi MindSET Program BOOST PHASE The Boost Phase of a rocket refers to the initial period in which the rocket produces THRUST to power itself forward. Water Rockets are considered to be under Boost Phase up until the last drop of water is expelled. COAST PHASE The Coast Phase of a rocket refers to any period during flight that the rocket is not being actively powered. Water Rockets enter into Coast Phase immediately after Boost Phase ends; the rocket will remain in Coast Phase until it impacts the ground. © Copyright 2015. All rights reserved. www.cpalms.org

THE END Sources: Northbridge Public High School - http://www.nps.org/sites/default/files/page/2011/10/water_rocket_physics_and_principles_18621.pdf Rocket Physics BlogSpot - http://rocketphysics.blogspot.com/ NASA Project Mercury - http://hubpages.com/hub/NASA-Project-Mercury-Spacecraft-and-Space-Suit Tau Beta Pi MindSET Program - http://tbpmindset.org/modules/SECME/Rockets/Rockets_Lecture.pdf © Copyright 2015. All rights reserved. www.cpalms.org