1. Sophomore Engineering Clinic I September 25, 2014 Blackboard Back of Room Section 12- Miller Section 13- Reed Section 13- Reed 1 Section 9- Tole Section 10- Cesare Section 11- Tole

2.  Physics/mathematical modeling  Figures and tables  Rocket testing Today’s Schedule

3.  Do you think mathematical models were used in the production of this commercial? http://www.youtube.com/watch?v=7vrorg79aNM Mathematical Modeling in Engineering

5. Bottle Rocket Physics  What forces are acting on the rocket?  Thrust from expelled water  Weight of bottle, water, clay  Drag from air resistance

6. Free Space Bottle Rocket Physics  What external forces are acting on the rocket?  None ….No gravity, No drag  Newton’s Third Law  Momentum is conserved if F ext =0  Change in momentum of the rocket is equal and opposite to the change in the momentum of the water ( and also any residual air)  ∆V rocket = (∆m_water/m_rocket) Ve where Ve is the escape velocity of the water or the air ∆P rocket ∆P water Ve ∆V rocket

7. Bottle Rocket Flight has two stages x d h cot(θ)

8. How do we obtain range d? For θ=45 o, rocket is down range a distance h at the end of burn This is a small correction ( <2m ) to the calculated range d l

9.  There are a few methods of doing this:  All are based on conservation of energy and momentum principles  Some models are more complex than others  You can decide how simple or complex you need to make your model  We are focusing on an approximate work-energy model Bottle Rocket Mathematical Models

10. Bottle Rocket Model

11. Work- Energy Model

12. Work-Energy Model Review W = Work P i = Initial pressure in the bottle V i = Initial volume of air in the bottle V f = Final volume of air in the bottle m = Avg mass of rocket during burn ρ = Density of water V w = Volume of water in the bottle v = Velocity of rocket g = Gravity h = Height at the end of the burn d = Distance Θ = launch angle

13. “Exact” Numerical Model Conservation of Energy Introduce Time Introduce Momentum for Mass Flow Total Thrust, Exit Velocity Pressure Volume Velocity Exit Velocity Mass Flow Thrust ΔMomentum Δ Volume of Air in Rocket Δ Velocity of Rocket Δ Mass of Rocket Δ Volume of Air

14. Water θ=45 o

15.  According to the equations, what happens if the amount of clay is increased? Does this make sense?  F = ma  The clay moves the center of mass towards the nose of the rocket and provides stability  What does that mean for your design? Clay

16.  What is the purpose of the fins?  What would happen if your fins are too big or too small?  Some rockets are not flying straight. Why? Fins

17.  You are expected to:  Compare your best design to the experimental model. Did you obtain similar results? If not, why?  Discuss your parametric design results in light of the bottle rocket physics. Do your results make sense based on the laws of physics? Physics in your Bottle Rocket Report