Thoughts on Measurement Activity Planning

1
payload
Systems Problem 4Lecture Notes
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Learning objectives

• After completing this SP4 and SP5 you will have
• Applied material from 8.01, (Unified
  thermodynamics) and Unified fluid mechanics to
  develop a model for a single stage water rocket
• Demonstrated an ability to integrate a system of
  ordinary differential equations using a
  spreadsheet
• Explored how external aerodynamics, structural
  weight, propellant mass fraction, payload mass,
  internal fluid mechanics and thermodynamics
  jointly determine the dynamic behavior of a
  single stage water rocket.
• Demonstrated an ability to describe conceptually
  how the performance of the water rocket changes
  as a function of important design parameters
• Developed a preliminary design for a water rocket
  that you and a partner may build and test for SP6

SP4
SP5
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3 stages
Stage 3 Ballistic Gravity and drag forces
Stage 2 Quasi-static adiabatic expansion Water
ejected from rocket Gravity, drag, thrust forces

• Stage 1
• Quasi-static adiabatic expansion
• as rocket lifts off launch rod
• Constant mass

4
Three state variables
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Open items

• Initial conditions
• Modeling stage 1
• Thrust (Ti)?
• Exit velocity (uei)?
• Integrating the equations
• Analyzing the results
• Developing a design rationale

6
Modeling the gas expansion

• Work change in energy
• Adiabatic, quasi-static
• g 1.4 for air

pressure
volume
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Thrust from the momentum equation

• Force time rate of change of momentum

8
Forward Euler finite difference equations
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My spreadsheet