Rocket Equations Quick Reference

Equations for finding your rocket's peak altitude and motor delay.

Definition of Terms

• m = rocket mass in kg (see below)
• g = acceleration of gravity = 9.81 m/s²
• A = rocket cross-sectional area in m²
• C_d = drag coefficient = 0.75 for average rocket
• r (rho) = air density = 1.22 kg/m³
• t = motor burn time in seconds (NOTE: little t)
• T = motor thrust in Newtons (NOTE: big T)
• I = motor impulse in Newton-seconds
• v = burnout velocity in m/s
• y₁ = altitude at burnout
• y_c = coasting distance
• Note that the peak altitude is y₁ + y_c
• t_a = coasting time => delay time for motor

Note on the rocket mass: you usually know the empty (no motor) mass of your rocket m_r. You can usually find the loaded mass of your motor, m_e, and the mass of the propellant, m_p. Both Estes and Aerotech provide these numbers in their spec sheets and with the motors. Then

• average mass during boost is m_r + m_e - m_p/2
  use this value for all but the y_c, q_a, and q_b calculations.
  
  
• mass during coast is m_r + m_e - m_p
  use this value for the y_c, q_a, and q_b calculations.