Trajectories

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+# Rocket Design Guide
+
+## Overview
+
+The **Rocket Design** tool calculates vehicle mass budget, tank geometry, structural requirements, and generates 3D models. It integrates engine data from the engine designer and computes the complete rocket's performance characteristics.
+
+## Main Sections
+
+### Vehicle Geometry
+Define tank configuration, dimensions, and structural layout.
+
+### Tank Structure
+Calculate wall thicknesses, masses, and pressurant requirements.
+
+### Nose Cone Design
+Select and visualize nose cone shapes (conical, ogive, Von Kármán).
+
+### Mass Budget
+Integrate all components (engines, tanks, payload, structure) to compute total mass and performance metrics.
+
+### 3D Visualization
+Interactive three.js model showing tanks, nose cone, and flight orientation.
+
+---
+
+## Vehicle Geometry
+
+### Tank Configuration Options
+
+**Tandem (Sequential):**
+- Two cylindrical tanks stacked vertically
+- Fuel (lower), Oxidizer (upper)
+- Domes: hemispherical on both ends
+- **Advantage**: Compact, simpler plumbing
+- **Disadvantage**: Longer vehicle
+
+**Coaxial (Concentric):**
+- Outer tank (fuel) surrounds inner tank (oxidizer)
+- Reduces diameter
+- Inner tank: flat bulkheads (simpler)
+- **Advantage**: Compact, low diameter
+- **Disadvantage**: More complex, thermal management
+
+**Single Tank:**
+- One tank with both propellants mixed
+- Rarely used for high-performance (lower Isp)
+
+### Tank Dimensions
+
+**Inputs:**
+- `outerRadius` (mm) — outer tank radius
+- `propellantVolume` (L) — total propellant quantity
+- `tankConfiguration` — tandem, coaxial, single
+- `ullagePercent` (%) — pressurant volume as % of propellant
+
+**Key Relationship:**
+```
+Ullage volume = propellant volume × (ullage% / 100)
+Effective volume = propellant volume × (1 + ullage%)
+```
+
+Ullage accommodates:
+- Thermal expansion of propellant
+- Gas bubble for pump inlet
+- Margin for fill level uncertainty
+
+### Tank Geometry (Tandem Case)
+
+**Dome Volume (hemispherical):**
+```
+V_dome = (2/3) × π × R³  (one hemisphere)
+V_domes = (4/3) × π × R³  (both domes)
+```
+
+**Cylindrical Section:**
+```
+L_cyl = (V_eff - V_domes) / (π × R²)
+```
+
+**Total Tank Length:**
+```
+L_total = L_cyl + 2R  (two dome heights)
+```
+
+**Example:**
+- R = 1.5 m, V_prop = 5000 L, ullage = 10%
+- V_eff = 5000 × 1.1 = 5500 L
+- V_domes = 4/3 × π × 1.5³ ≈ 14.1 m³ = 14100 L (larger than prop!)
+- Need smaller R or accept small L_cyl
+
+**Note**: For smaller rockets, domes dominate volume. Design must account for this.
+
+---
+
+## Tank Structure
+
+### Pressure Sources
+
+**Pressure-Fed System:**
+```
+P_tank = 1.2 × P0_chamber  (pressure margin)
+```
+Typical: P0 = 200 bar → P_tank = 240 bar
+
+**Pump-Fed System:**
+```
+P_tank = 2 MPa (minimum for turbopump inlet)
+```
+Much lower pressure (pump provides most acceleration)
+
+**Selection affects:**
+- Wall thicknesses (direct proportionality)
+- Mass (linear with pressure and wall thickness)
+- Propellant pump requirements
+
+### Structural Material Properties
+
+Available materials from knowledgebase:
+- **Aluminum 6061-T6**: density 2700 kg/m³, σ_y = 275 MPa
+- **Stainless Steel 304**: density 8000 kg/m³, σ_y = 215 MPa
+- **Inconel 718**: density 8190 kg/m³, σ_y = 1240 MPa
+- **Titanium 6-4**: density 4430 kg/m³, σ_y = 880 MPa
+- **CFRP (Carbon Fiber)**: density 1600 kg/m³, σ_y = 600 MPa
+
+**Selection factors:**
+- Cost (Al < SS < Ti < CFRP)
+- Weight (CFRP < Ti < Al < SS)
+- Corrosion (SS, Ti, CFRP better; Al needs coating)
+- Temperature (Inconel for hot engines; others at T < 150°C)
+
+### Wall Thickness (Hoop Stress)
+
+**Hoop stress formula:**
+```
+σ_hoop = (P × R) / t
+```
+
+**With safety factor:**
+```
+t = (P × R) / (σ_yield / SF)
+```
+
+**Cylindrical section mass:**
+```
+m_cyl = 2π × R × t × L_cyl × ρ_material
+```
+
+**Dome mass (two hemispheres):**
+```
+m_domes = 4π × R² × t × ρ_material
+```
+
+**Total tank mass:**
+```
+m_tank = m_cyl + m_domes
+```
+
+### Example Calculation
+
+**Tandem LOX/RP1 Tank:**
+- Radius: 1.0 m
+- Pressure: 240 bar = 24 MPa
+- Material: Aluminum 6061-T6
+  - σ_y = 275 MPa
+  - ρ = 2700 kg/m³
+- Safety Factor: 2.5
+
+**Wall Thickness:**
+```
+t = (24 MPa × 1.0 m) / (275 MPa / 2.5)
+  = 24 / 110
+  ≈ 0.218 m = 2.18 mm
+```
+
+**Cylindrical Section (assume L_cyl = 3 m):**
+```
+m_cyl = 2π × 1.0 × 0.00218 × 3.0 × 2700
+      ≈ 110 kg
+```
+
+**Domes:**
+```
+m_domes = 4π × 1.0² × 0.00218 × 2700
+        ≈ 74 kg
+```
+
+**Total tank mass:** ~184 kg
+
+---
+
+## Pressurant System (Pressure-Fed Only)
+
+### Helium Requirements
+
+For pressure-fed engines, pressurant gas maintains tank pressure throughout burn.
+
+**Ideal gas law:**
+```
+P × V = n × R × T
+```
+
+**Helium mass:**
+```
+m_He = (P_tank × V_prop) / (R_He × T)
+```
+
+Where:
+- `P_tank` — tank pressure (Pa)
+- `V_prop` — propellant volume (m³)
+- `R_He` — helium specific gas constant = 2077 J/kg/K
+- `T` — temperature (K), typically 293 K (20°C)
+
+**Example:**
+- P_tank = 24 MPa = 24×10⁶ Pa
+- V_prop = 5 m³
+- T = 293 K
+
+```
+m_He = (24×10⁶ × 5) / (2077 × 293)
+     ≈ 20 kg
+```
+
+### Helium Bottle Mass
+
+Helium stored in high-pressure bottle. Typical storage pressure: 250 bar.
+
+**Bottle mass (conservative):**
+```
+m_bottle = 4 × m_He
+```
+
+Rule of thumb: bottle is 4 times the helium mass. (More sophisticated: use MEOP analysis.)
+
+**Total pressurant system:**
+```
+m_pressurant = m_He + m_bottle
+```
+
+Example: 20 kg He → 80 kg bottle → 100 kg pressurant system
+
+**Note**: This is a major mass penalty for pressure-fed systems. Pump-fed systems avoid this.
+
+---
+
+## Nose Cone Design
+
+### Available Profiles
+
+Three aerodynamic nose cone shapes, all with L = 2 × R (length = 2 × base radius).
+
+**Conical:**
+- Simple linear profile
+- `r(x) = R × (x / L)`
+- Sharpest tip, moderate drag
+
+**Tangent Ogive:**
+- Smooth circular arc meeting base tangentially
+- `ρ = (R² + L²) / (2R)` (radius of curvature)
+- `r(x) = √(ρ² - (L - x)²) - (ρ - R)`
+- Smooth, less drag than conical
+- Common in rocketry
+
+**Von Kármán:**
+- Power law profile minimizing drag
+- `θ = acos(1 - 2x/L)`
+- `r(x) = (R / √π) × √(θ - sin(2θ)/2)`
+- Theoretically optimal for transonic flight
+- Used on high-performance rockets
+
+**Selection Criteria:**
+- **Conical**: Simplest to manufacture, sharp tip
+- **Tangent Ogive**: Better aerodynamics, smoother base transition
+- **Von Kármán**: Best drag coefficient (Cd ≈ 0.15 vs 0.25 conical)
+
+### 3D Visualization
+
+Nose cone is rendered using THREE.js `LatheGeometry`:
+- Profile points sampled from mathematical formula
+- Rotated around vertical axis to create 3D shape
+- Interactive rotation/zoom in 3D viewer
+
+---
+
+## Mass Budget
+
+### Components
+
+**Structure:**
+- Tank walls and domes: `m_tanks`
+- Other structure (nosecone, bay, interstage): `m_other`
+- Engine dry mass (from engine designer): `m_engine`
+
+**Propellant:**
+- Fuel + oxidizer: `m_propellant`
+
+**Pressurant (pressure-fed only):**
+- Helium + bottle: `m_pressurant`
+
+**Payload:**
+- Avionics, recovery system, instruments: `m_payload`
+
+### Calculation
+
+**Dry mass (no propellant):**
+```
+m_dry = m_tanks + m_other + m_engine + m_pressurant + m_payload
+```
+
+**Wet mass (with propellant):**
+```
+m_wet = m_dry + m_propellant
+```
+
+**Payload fraction:**
+```
+fraction_payload = m_payload / m_wet
+```
+
+**Structure fraction:**
+```
+fraction_structure = m_tanks / m_wet
+```
+
+**Thrust-to-weight ratio:**
+```
+TWR = F_thrust / (m_wet × g)
+```
+
+### Example Mass Budget
+
+Small LOX/RP1 rocket:
+
+| Component | Mass (kg) | % |
+|-----------|-----------|-----|
+| Tanks (structure) | 200 | 14% |
+| Engine | 50 | 3.5% |
+| Pressurant (He + bottle) | 100 | 7% |
+| Avionics + recovery | 30 | 2% |
+| **Dry mass** | **380** | **26.5%** |
+| Propellant (LOX + RP1) | 1050 | 73.5% |
+| **Wet mass** | **1430** | **100%** |
+
+**Performance:**
+- TWR = 150 kN / (1430 kg × 9.81 m/s²) = 10.7
+- Delta-v (no gravity loss): 310 s × ln(1430/380) ≈ 1300 m/s
+
+---
+
+## 3D Model Components
+
+### Tank Rendering
+
+**Cylindrical body:**
+```javascript
+<TankSection
+  radius={1.0}
+  length={3.0}
+  position={[0, 0, 0]}
+/>
+```
+
+Renders:
+- Cylinder: `CylinderGeometry`
+- Top dome: `SphereGeometry` (hemisphere)
+- Bottom dome: `SphereGeometry` (hemisphere)
+
+**Material:** MeshStandardMaterial with color (red = fuel, blue = oxidizer)
+
+### Nose Cone Rendering
+
+**LatheGeometry:**
+- Takes profile curve (array of points)
+- Rotates around Y-axis to create 3D surface
+- Smooth, aerodynamic appearance
+
+**Example:**
+```javascript
+const profile = noseConeProfile('tangent-ogive', 0.5, 1.0, 24)
+const geometry = new THREE.LatheGeometry(profile, 24)
+```
+
+### Scene Setup
+
+**Lighting:**
+- Ambient light (0.6 intensity)
+- Directional light from top-right
+- Shadows enabled for depth
+
+**Camera:**
+- Orbit controls (rotate, zoom, pan)
+- Auto-fit to model bounds
+- Perspective view (60° FOV)
+
+---
+
+## Workflow: Design Complete Vehicle
+
+### Step 1: Import Engine
+1. Go to **Design > Engine**
+2. Configure combustion (LOX/RP1, 200 bar, etc.)
+3. Size structure (Inconel, 3.0 SF)
+4. Export as JSON
+5. Return to **Design > Rocket**
+6. Upload engine JSON
+→ **Result**: Engine dry mass auto-populated
+
+### Step 2: Configure Tanks
+1. Set tank configuration: **Tandem**
+2. Set outer radius: **1.0 m**
+3. Set propellant volume: **5000 L**
+4. Set ullage: **10%**
+→ **Result**: Calculated tank length, dome geometry
+
+### Step 3: Design Tank Structure
+1. Select material: **Aluminum 6061-T6**
+2. Set safety factor: **2.5**
+3. Select feed system: **Pressure-Fed**
+→ **Result**: Wall thickness, tank mass, pressurant requirements
+
+### Step 4: Set Payload
+1. Enter payload mass: **50 kg** (avionics, recovery)
+→ **Result**: Dry mass updated
+
+### Step 5: View Mass Budget
+→ **Result**:
+- Wet mass: 1550 kg
+- Dry mass: 450 kg
+- TWR: 10.2
+- Delta-v (vacuum): 1320 m/s
+
+### Step 6: Adjust Nose Cone
+1. Select shape: **Von Kármán**
+→ **Result**: 3D model updates with optimal nose cone
+
+### Step 7: Export & Simulate
+1. Export vehicle JSON
+2. Go to **Design > Trajectory**
+3. Import vehicle & engine data
+4. Run flight simulation
+→ **Result**: Altitude, downrange, apogee, landing site
+
+---
+
+## Advanced Topics
+
+### Multi-Stage Rockets
+
+Not yet implemented, but conceptually:
+- Stage 1: Large engines, heavy structure
+- Stage 2: Smaller engines, lighter structure
+- Interstage adapter: mass penalty
+- Staging sequence: defined by velocity requirements
+
+Implementation would require:
+- Multiple vehicle definitions (or list of stages)
+- Trajectory system that handles stage separation
+- Cumulative mass and thrust calculations
+
+### Composite Materials
+
+CFRP offers best strength-to-weight but requires special analysis:
+- **Fiber direction** — properties vary with orientation
+- **Matrix** — epoxy, vinyl ester
+- **Layup schedule** — [0°/90°/45°] typical
+- **Microbuckling** — axial compression limit
+- **Matrix cracking** — transverse tensile limit
+
+Advanced model would include:
+- Classical laminate theory (CLT)
+- Ply-by-ply failure criteria (Tsai-Wu, Hashin)
+- Buckling analysis (Timoshenko, finite element)
+
+---
+
+## Troubleshooting
+
+### Tank too long?
+- Reduce ullage percentage (lower to 5%)
+- Increase radius (larger tank, shorter cylinder)
+- Split into multiple smaller tanks
+- Switch to coaxial configuration
+
+### Vehicle too heavy?
+- Switch to lighter material (CFRP)
+- Reduce safety factor (if acceptable)
+- Decrease payload mass
+- Use pump-fed system (avoids pressurant)
+
+### Nose cone looks wrong?
+- Verify radius and length (L = 2R)
+- Try different shape (Von Kármán usually best)
+- Check 3D viewer isn't zoomed in too far
+
+### 3D model not rendering?
+- WebGL must be enabled
+- Check browser console for Three.js errors
+- Ensure geometry dimensions are reasonable (not NaN)
+
+---
+
+## References
+
+- NASA SP-8007: Structural Design and Test Factors of Safety for Spaceflight Hardware
+- Huzel, D. K., & Huang, D. H. (1992). Modern engineering for design of liquid-propellant rocket engines.
+- Rocket Propulsion Elements (8th ed.). by Sutton & Biblarz.
+
+---
+
+**Last Updated**: 2025-02 | **Status**: Current (v3 — Domed Tanks)