Rail Exit Velocity¶
Why It Matters¶
The rocket must achieve sufficient velocity before leaving the launch rail for the fins to provide aerodynamic stability. Below this velocity, the rocket may:
- Weathercock into wind
- Fly unstable trajectory
- Tip over on the pad
Minimum Rail Exit Velocity¶
Rule of Thumb
Minimum rail exit velocity: 50 ft/s (15 m/s)
Recommended: 60-80 ft/s for margin of safety
Physics¶
Rail exit velocity depends on:
\[V_{exit} = \sqrt{V_0^2 + 2 \cdot a_{avg} \cdot L_{rail}}\]
Where:
- \(V_0\) = Initial velocity (0 for standing start)
- \(a_{avg}\) = Average acceleration during rail travel
- \(L_{rail}\) = Effective rail length
Simplified:
\[V_{exit} = \sqrt{\frac{2 \cdot F_{avg} \cdot L_{rail}}{m}}\]
Where:
- \(F_{avg}\) = Average thrust force (N)
- \(m\) = Liftoff mass (kg)
Minimum Rail Length¶
Rearranging for rail length:
\[L_{rail} = \frac{m \cdot V_{exit}^2}{2 \cdot F_{avg}}\]
Peregrine Calculations¶
Estimated Values¶
| Parameter | Value |
|---|---|
| Liftoff Mass | ~6 lbs (~2.7 kg) with H motor |
| Target Exit Velocity | 60 ft/s (18 m/s) |
Example: AeroTech H180W¶
| Parameter | Value |
|---|---|
| Average Thrust | 180 N (40 lbf) |
| Liftoff Mass | ~2.7 kg |
| Min Rail Length | Calculate below |
\[L_{rail} = \frac{2.7 \cdot 18^2}{2 \cdot 180} = \frac{874.8}{360} = 2.4 m \approx 8 ft\]
Rail Length
An 8-foot (2.4m) rail should provide adequate exit velocity for the Peregrine on H motors.
Standard high-power rail lengths: - 6 ft (1.8m) - marginal for heavy rockets - 8 ft (2.4m) - good for most HPR - 10 ft (3m) - excellent margin
Simulation Verification¶
OpenRocket/RockSim calculate rail exit velocity:
Insert simulation results here
| Motor | Rail Length | Exit Velocity | Status |
|---|---|---|---|
| H180W | 6 ft | TBD | TBD |
| H180W | 8 ft | TBD | TBD |
| H100W | 8 ft | TBD | TBD |
Wind Considerations¶
In windy conditions:
- Higher exit velocity needed
- Consider longer rail
- Or postpone launch if marginal
Rule: Add 10 ft/s to minimum for each 10 mph wind.