Goals
The fins must withstand in-flight conditions.
- Fins and leading edges should not deform from in-flight temperatures.
- Fins should be structurally stable.
The fins shall stabilize the rocket.
- (Stability margin criteria)
The fins shall be aerodynamic.
- (Goals for determining fin and leading edge shape)
Thermal Analysis
Medusa's fins will experience much higher stagnation temperatures than Phoenix's. Approximations of maximum stagnation temperatures at the leading edges have been calculated using simulation data.
Parameters derived from simulation data
To determine an upper bound for expected stagnation temperatures, we take data from the point when the rocket reaches maximum velocity (and consequently, max stagnation temperature) in each stage.
Stage 1
Atmospheric temperature at height of max velocity T = 275.15K
Free stream velocity c = 625.45 m/s
Ratio of specific heats γ = 1.4
Max Mach number M = 1.91
Stage 2
Atmospheric temperature at height of max velocity T = 223.25K
Free stream velocity c = 1216.06 m/s
Ratio of specific heats γ = 1.4
Max Mach number M = 4.14
Calculations
Stagnation temperature equation T_s = T*(1+\frac{\gamma-1}{2}*M^2)
Stage 1
Ts = 475.90K | 202.75°C | 396.95°F
Stage 2
Ts = 988.53K | 715.38°C | 1319.68°F
Note that aluminum melts at 660°C.
Design Considerations
Since stagnation temperatures could exceed the melting temperature of aluminum during the second stage, the fins need to be designed with heat resistance in mind. This can be achieved by either applying a protective coating over aluminum fins or manufacturing the fins out of a more heat-resistant material.
(research here)
Conclusion
Stability
Aerodynamics
Leading edge shape (WIP)