Lecture Notes: Calculating Rocket Stability

Introduction

• Presenter: Mike Thompson
• Topic: Mathematical calculations for rocket stability
• Focus on understanding the math behind the calculations

Key Concepts

Rocket Projection and Areas

• Begin by projecting the rocket onto a surface to calculate the area.
• Different parts of the rocket are measured:
  • Triangle: Base 2, Height 1, Area = 1
  • Rectangle (Body): Length 11, Height 1, Area = 11
  • Trapezoid (Tail Cone): Small area, nearly negligible
  • Fins: 2 inches tall, 1 inch tip, 1.5 inches span, Total area = 4.5 square inches

Area Breakdown

• Break rocket into simple shapes: triangles, rectangles
• Calculate each shape’s area separately

Centroid Calculations

Centroid of Rocket Parts

• Triangle: Centroid is 1/3rd up from the base
• Rectangle: Centroid is at its middle
• Trapezoid: Centroid uses a more complex formula
  • Formula: ( \frac{H}{3} \times \frac{2a + b}{a + b} )

Distance Measurements

• Measure from a fixed datum (reference point)
• Adjust calculations based on offset from datum

Calculations and Results

Moment of Areas

• Use sum of moments over sum of areas to find centroid of the entire rocket
• Multiply each fin’s area by 2 (since there are two) to account for both
• Total area of the rocket calculation = 16 and 15/16 square inches
• Center of pressure calculated to be 8.54 inches from the top

Center of Pressure vs. Center of Gravity

• Knowing center of pressure is crucial for stability
• Center of gravity not covered, varies based on other factors

Additional Considerations

Number of Fins

• Common fin configurations: three or four fins
• Adjust calculations for fins by considering projection onto a plane:
  • Use fin length times cosine of the angle for correct area
  • Incorrect calculation leads to a false sense of stability

Conclusion

• Break rocket into simple geometric shapes to simplify calculations
• Ensure center of pressure is behind the center of gravity for stability
• Note: Important to calculate conservatively when determining stability

• Closing: Thanks for watching
• Purpose: Aim to simplify understanding of calculating rocket stability through math