# Knowledgebase Guide

## Overview

The **Knowledgebase** is a reference library of propellants, materials, and engineering equations. It provides the properties needed for calculations in the Solver, Engine Designer, and Rocket Designer.

## Structure

The knowledgebase is organized into four categories:

1. **Fuels & Oxidizers** — Propellant properties
2. **Ablative Materials** — Thermal protection
3. **Structural Materials** — Engine & tank construction
4. **Equations** — Mathematical references

---

## Fuels & Oxidizers

### What are They?

**Fuel**: Hydrocarbon or hydrogen source
- Examples: RP-1 (kerosene), methane, hydrogen

**Oxidizer**: Oxygen source
- Examples: Liquid oxygen (LOX), nitrogen tetroxide (N2O4)

### Key Properties

Each propellant entry contains:

**Chemical Properties:**
- Molecular formula (e.g., O₂ for oxygen)
- Molecular weight (g/mol)
- Density (kg/m³)

**Combustion Properties:**
- **Adiabatic flame temperature (Tc)** — peak temperature of combustion (K)
  - Higher Tc = higher Isp
  - Example: LOX/RP-1 ≈ 3750 K, LOX/LH2 ≈ 3900 K

- **Expansion ratio (gamma, γ)** — specific heat ratio
  - γ = Cp / Cv
  - Affects nozzle performance
  - LOX/RP-1: γ ≈ 1.25, LOX/LH2: γ ≈ 1.26

- **Characteristic velocity (c*)** — ideal nozzle exit velocity
  - Fundamental property of propellant
  - Used to estimate Isp

**Performance Metrics:**
- **Specific impulse (vacuum, Isp_vac)** — seconds
  - Higher = better
  - Example: LOX/RP-1 ≈ 310–320 s, LOX/LH2 ≈ 450 s

- **Specific impulse (sea level, Isp_sl)** — reduced due to ambient pressure
  - Lower than vacuum value
  - Example: LOX/RP-1 ≈ 260 s at sea level

**Mixture Ratio:**
- **O/F ratio** — oxidizer mass per fuel mass
  - Example: LOX/RP-1 optimal ≈ 2.5–2.8
  - Higher ratio = more oxygen = higher T but lower mass fraction
  - Lower ratio = more fuel = lower T but better mass fraction

### Common Propellant Pairs

| Fuel | Oxidizer | Isp (s) | Tc (K) | γ | Notes |
|------|----------|---------|-------|-------|-------|
| RP-1 | LOX | 310 | 3750 | 1.25 | Space-proven, storable |
| Methane | LOX | 330 | 3900 | 1.24 | Better impulse than RP-1 |
| Hydrogen | LOX | 450 | 3900 | 1.26 | Best impulse, cryogenic, low density |
| MMH | N2O4 | 290 | 3400 | 1.20 | Storable, hypergolic (ignites on contact) |
| Hydrazine | N2O4 | 310 | 3700 | 1.24 | Toxic but storable, high density |

### Storage Types

**Cryogenic:**
- Requires refrigeration
- LOX, LH2, LN2, LCH4
- Higher energy density
- Complex ground support needed

**Storable (Room Temperature):**
- RP-1, Methane (marginally), MMH, Hydrazine
- No cryogenic handling needed
- Lower energy density than cryo
- Easier integration

**Hypergolic:**
- Ignites spontaneously on contact (fuel + oxidizer)
- No ignition system needed
- Toxic, corrosive, more expensive
- Examples: MMH/N2O4, Hydrazine/N2O4

### Selection Criteria

**High Performance** → LOX/LH2 (Isp 450 s, but cryogenic complexity)
**Best Balance** → LOX/RP-1 (Isp 310 s, storable, proven)
**Storable Only** → MMH/N2O4 (Isp 290 s, no cryo needed)
**Simple & Solid** → RP-1/LOX or Methane/LOX

---

## Ablative Materials

### Purpose

Ablative materials line the rocket engine chamber to withstand:
- **High temperature** (combustion products: 3500+ K)
- **High pressure** (200+ bar)
- **Erosion** from hot gas flow

### Key Properties

Each ablative material entry contains:

**Mechanical Properties:**
- Density (kg/m³)
- Tensile strength (MPa)
- Compressive strength (MPa)

**Thermal Properties:**
- Specific heat (J/kg·K)
- Thermal conductivity (W/m·K)
- Melting point (K)

**Erosion Properties:**
- **Base erosion rate** (inch/s @ 300 psi reference pressure)
  - Ablative material mass removed per unit time
  - Higher rate = thicker liner needed
  - Example: PAXS ≈ 0.025 in/s

- **Pressure exponent (n)** — power-law sensitivity to pressure
  - `rate(P) = base_rate × (P / P_ref)^n`
  - Lower n = less pressure-sensitive (better for high P)
  - Example: PAXS n = 0.38, KFSI n = 0.35

**Application Notes:**
- Where used: chamber, nozzle, injector
- Temperature limits
- Compatibility with propellants

### Material Classes

**Composites (Rigid):**
- PAXS (polyester + glass) — n = 0.38
  - Common, cost-effective
  - Moderate erosion rate
  - Max temp ~2000 K

- KFSI (silica + phenolic) — n = 0.35
  - Better than PAXS
  - Lower erosion rate
  - Higher temp capability
  - More expensive

- Carbon-Phenolic — n = 0.32
  - Excellent thermal performance
  - Very low erosion rate
  - Very expensive
  - Used on high-end engines

**Elastomers (Flexible):**
- ZIRCONIA (zirconia + silicone) — n = 0.48
  - Flexible (less brittle)
  - Higher erosion rate
  - Absorbs vibration
  - Lower cost than phenolics

- Butyl Rubber — n = 0.50
  - Very flexible
  - High erosion rate
  - Used for low-pressure applications

### Pressure Exponent Explanation

The power law `rate ∝ P^n` comes from **regression rate burning**:

- Composites: n ≈ 0.3–0.4
  - Erosion driven by thermal decomposition
  - Less pressure-dependent
  - Preferred for high-pressure engines

- Elastomers: n ≈ 0.4–0.5
  - Erosion driven by shear stress
  - More pressure-dependent
  - OK for moderate pressures

**High Pressure (>1000 psi):** Use composite with low n
**Moderate Pressure (500 psi):** Elastomer acceptable
**Low Pressure (<300 psi):** Elastomer preferred (lower cost)

### Selection Guidance

| Application | Material | Reason |
|-------------|----------|--------|
| High-perf liquid rocket | KFSI or Carbon-Phenolic | Low erosion rate, high pressure capable |
| Medium-perf liquid | PAXS | Good balance, cost-effective |
| Hybrid rocket | KFSI (fuel grain liner) | Low ablation to preserve geometry |
| Solid rocket | Composite | Erosion from particles & hot gas |
| Low-cost experiment | Butyl or PAXS | Adequate performance, lowest cost |

---

## Structural Materials

### Purpose

Structural materials form the engine chamber and rocket tanks. They must:
- Withstand internal pressure (hoop stress)
- Resist corrosion from propellants
- Perform at operating temperature
- Balance weight vs. strength

### Key Properties

Each structural material entry contains:

**Mechanical Properties:**
- **Yield strength** (MPa) — stress at which permanent deformation begins
  - Higher = thinner walls possible = lighter
  - Example: Aluminum 6061-T6: 275 MPa, Inconel 718: 1240 MPa

- **Young's modulus** (GPa) — stiffness
  - Higher = less deflection (stronger)

- **Density** (kg/m³) — weight per volume
  - Lower = lighter vehicle
  - Example: Al: 2700, Ti: 4430, SS: 8000

**Thermal Properties:**
- Melting point (K) — temperature limit
- Coefficient of thermal expansion (CTE)
- Thermal conductivity

**Other:**
- Cost (relative)
- Machinability
- Availability

### Material Comparison

| Material | Density | Yield | T_melt | Cost | Best For |
|----------|---------|-------|--------|------|----------|
| Al 6061-T6 | 2700 | 275 | 933 | 1× | Prototype, pressure-fed |
| SS 304 | 8000 | 215 | 1726 | 3× | Corrosion resistance |
| Inconel 718 | 8190 | 1240 | 1600 | 10× | High-performance engines |
| Ti-6-4 | 4430 | 880 | 1941 | 15× | Lightweight, space |
| CFRP | 1600 | 600+ | 700 | 20× | Lowest weight |

### Hoop Stress Calculation

For cylindrical pressure vessels:
```
σ_hoop = (P × r) / t
```

Setting equal to yield with safety factor:
```
t = (P × r) / (σ_yield / SF)
```

Higher yield strength → thinner walls → lighter mass

### Material Selection

**Pressure-Fed Engine (200+ bar, chamber):**
- **Inconel 718** — withstands high pressure & heat
- **Titanium** — lighter alternative
- **Aluminum** — cheap but needs cooling design

**Rocket Tanks (20–50 bar):**
- **Aluminum 6061** — standard, proven, affordable
- **Titanium** — if weight critical
- **CFRP** — lowest weight, highest cost

**Low-Pressure Systems:**
- **Aluminum** — sufficient, cheapest
- **Stainless Steel** — if corrosion concern

---

## Equations Reference

### Fundamental Relations

**Thrust (momentum equation):**
```
F = ṁ · Ve + (Pe - Pa) · Ae
```
- ṁ = mass flow rate
- Ve = exit velocity
- Pe = exit pressure
- Pa = ambient pressure
- Ae = exit area

**Specific Impulse:**
```
Isp = Ve / g0  (vacuum)
Isp = (Ve - (Pe - Pa) / ṁ · Ae) / g0  (sea level)
```
- g0 = 9.81 m/s² (gravitational acceleration)

**Rocket Equation (Tsiolkovsky):**
```
ΔV = Isp · g0 · ln(m_initial / m_final)
```
- ΔV = velocity change (delta-v)
- m_initial = wet mass
- m_final = dry mass

### Isentropic Flow (Nozzle Design)

**Temperature at exit:**
```
Te / T0 = (Pe / P0)^((γ-1)/γ)
```

**Density at exit:**
```
ρe / ρ0 = (Pe / P0)^(1/γ)
```

**Mach number from area ratio:**
```
A / A* = (1/M) · [(2/(γ+1)) · (1 + (γ-1)/2 · M²)]^((γ+1)/(2(γ-1)))
```
- A* = throat area
- A = arbitrary section area
- M = Mach number
- (requires numerical inversion via bisection)

**Characteristic velocity:**
```
c* = √[2 · (γ+1)/(γ-1) · R · T0 · (2/(γ+1))^((γ+1)/(γ-1))]
```

### Thrust Coefficient

```
CF = √[2γ²/(γ-1) · (2/(γ+1))^((γ+1)/(γ-1)) · (1 - (Pe/P0)^((γ-1)/γ))]
    + (Pe - Pa)/(P0) · (Ae/At)
```

### Chamber Thermodynamics

**Energy balance (no losses):**
```
Cp · (T0 - Te) = Ve² / 2
```
- Cp = specific heat at constant pressure

**Chemical equilibrium:**
Determine T0, γ from propellant properties and stoichiometry
(computed via NASA CEA code or thermodynamic tables)

### Drag & Atmosphere

**Drag force:**
```
Fd = 0.5 · ρ · v² · Cd · A
```
- ρ = air density (depends on altitude)
- v = velocity
- Cd = drag coefficient (~0.25 for rockets)
- A = reference area

**US Standard Atmosphere (piecewise):**
```
T(h) = T0 - L·h  (troposphere, 0–11 km)
P(h) = P0 · (T(h)/T0)^(-g/(R·L))
ρ(h) = ρ0 · (T(h)/T0)^(-(g/(R·L) + 1))
```
- L = lapse rate ≈ 6.5 K/km
- R = gas constant

### Hoop Stress (Pressure Vessels)

**Thin-walled cylinder:**
```
σ_hoop = P·r / t
```
With safety factor:
```
t = P·r / (σ_yield / SF)
```
Mass:
```
m = 2π · r · t · L · ρ  (cylinder)
m = 4π · r² · t · ρ  (hemispherical dome)
```

### Mass Fraction

**Payload fraction:**
```
fp = m_payload / m_wet
```

**Structure fraction:**
```
fs = m_structure / m_wet
```

**Propellant fraction:**
```
fp = m_propellant / m_wet
```

Sum: `fp + fs + fpayload = 1`

Typical rockets: `fs = 0.10–0.20` (10–20%)

---

## Using Knowledgebase in Design

### Importing Propellant Properties

1. **Solver**: Drag `chamberTemperature`, `expansionGamma` onto workspace
2. Check knowledgebase for propellant pair (LOX + RP-1)
3. Enter T0 from knowledgebase → solver computes Isp
4. Verify with reference Isp in database

### Cross-Checking Ablation

1. **Engine Design**: Select PAXS ablative
2. **Check Pressure Exponent**: 0.38 (from knowledgebase)
3. Verify erosion rate correction is applied
4. Compare remaining thickness to safety margin (>0.5 inch)

### Material Trade-Studies

1. **Rocket Design**: Compare materials
   - Aluminum: 1000 kg tanks
   - Titanium: 600 kg tanks (lighter, more expensive)
   - CFRP: 350 kg tanks (lightest, most expensive)
2. Use mass to compute TWR, delta-v
3. Pick best balance for mission

---

## Future Enhancements

- **User contributions**: Allow adding new materials/propellants
- **Temperature corrections**: Adjust properties with temperature
- **Material compatibility**: Show fuel/material interactions
- **Cost database**: Include material & propellant costs
- **References**: Link to papers & technical data sources
- **Lookup plots**: Interactive charts (Isp vs. O/F, etc.)

---

## References

- NASA SP-273: Liquid Rocket Engine Combustion Instability.
- Huzel, D. K., & Huang, D. H. (1992). Modern engineering for design of liquid-propellant rocket engines. AIAA.
- Rocket Propulsion Elements (8th ed.). Sutton & Biblarz.
- US Standard Atmosphere 1976. NASA TM-X-74335.
- CEA (Chemical Equilibrium with Applications). NASA Glenn Research Center.

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**Last Updated**: 2025-02 | **Status**: Current