aero: checkpoint

Cargo.toml

@@ -42,6 +42,7 @@ iyes_perf_ui = { version = "0.3.0" }
 bevy_common_assets = { version = "0.11.0", features = ["ron"], optional = true }
 ron = { version = "0.8.1", optional = true }
 serde = { version = "1.0", features = ["derive"], optional = true }
+parry3d = { version = "0.17.2", features = ["parallel"] }
 
 [[bin]]
 name = "yahs"

docs/drag.md → docs/intro_to_drag.md

@@ -1,97 +1,121 @@
-# Aerodynamic Drag Calculations
+# Introduction to Newtonian Aerodynamics
+
 This is a summary of the paper
 [Newtonian Aerodynamics for General Body Shapes](https://ntrs.nasa.gov/citations/19660012440)
 and its implementation in our simulation. It is generated using ChatGPT
 `o1-mini`.
 
 ## 1. Introduction to Newtonian Aerodynamics
+
 Newtonian Aerodynamics applies Newtonian mechanics to predict aerodynamic forces
 such as drag and lift on objects moving through a fluid (like air). This
 approach is particularly useful for objects in supersonic or hypersonic flows.
 
 ## 2. Fundamental Concepts
-### a. Drag Force (Fₓ)
-Drag is the resistance force acting opposite to the direction of an object's
-velocity.
 
-### b. Lift Force (Fᵧ)
-Lift is the force perpendicular to the direction of motion, often associated
-with winged objects.
+- *Drag Force (Fₓ)* is the resistance force acting opposite to the direction of
+  an object's velocity.
 
-### c. Flow Regimes
-- **Subsonic**: Flow speeds less than the speed of sound.
-- **Supersonic**: Flow speeds greater than the speed of sound.
-- **Hypersonic**: Flow speeds significantly higher than supersonic speeds.
+- *Lift Force (Fᵧ)* is the force perpendicular to the direction of motion, often
+  associated with winged objects.
+
+- *Flow Regimes*
+
+  - **Subsonic**: Flow speeds less than the speed of sound.
+  - **Supersonic**: Flow speeds greater than the speed of sound.
+  - **Hypersonic**: Flow speeds significantly higher than supersonic speeds.
 
 ## 3. Newtonian Impact Theory
+
 The Newtonian Impact Theory estimates aerodynamic forces based on the assumption
 that fluid particles impacting the body either stick or rebound elastically.
 
 ### Key Assumptions
+
 1. The fluid is treated as a collection of particles.
 2. Particles impacting the body either stick or reflect off elastically.
 3. The flow is steady and uniform far from the body.
 4. Viscous effects are neglected.
 
 ### Mathematical Formulation
+
 #### a. Pressure Coefficient (Cₚ)
+
 \[ C_p = \frac{P - P_{\infty}}{\frac{1}{2} \rho V_{\infty}^2} \] Where:
+
 - \( P \) = Local pressure on the body.
 - \( P_{\infty} \) = Free-stream pressure.
 - \( \rho \) = Fluid density.
 - \( V_{\infty} \) = Free-stream velocity.
 
 #### b. Newtonian Drag Coefficient (C_d)
+
 \[ C_d = \int \left(1 - \cos(\theta)\right) dA \] Where:
+
 - \( \theta \) = Angle between the local surface normal and the free-stream
   velocity vector.
 - \( dA \) = Differential area element.
 
 ## 4. Calculating Aerodynamic Forces
+
 ### a. Drag Force (Fₓ)
+
 \[ F_x = \frac{1}{2} \rho V_{\infty}^2 C_d A \] Where:
+
 - \( A \) = Reference area (e.g., frontal area).
 
 ### b. Lift Force (Fᵧ)
+
 \[ F_y = \frac{1}{2} \rho V_{\infty}^2 C_l A \] Where:
+
 - \( C_l \) = Lift coefficient.
 
 ## 5. Application to General Body Shapes
+
 The paper extends Newtonian Impact Theory to arbitrary body shapes by
 decomposing the body's surface into differential elements, calculating local
 impact angles, and integrating contributions to overall aerodynamic forces.
 
 ### a. Surface Sampling
+
 To handle complex geometries, the body's surface is sampled at numerous points.
 Each point's normal vector and its angle relative to the flow direction are
 determined.
 
 ### b. Numerical Integration
+
 Due to the complexity of analytical solutions for irregular shapes, numerical
 techniques are employed to perform surface integrals for drag and lift.
 
 ## 6. Enhancements and Corrections
+
 While Newtonian Impact Theory provides foundational estimates, the paper
 discusses enhancements for improved accuracy, including:
+
 - Correction factors based on empirical data.
 - Considering how the body's orientation relative to the flow affects the
   distribution of impact angles.
 
 ## 7. Practical Implementation Considerations
+
 ### a. Computational Efficiency
+
 Sampling the surface at too many points can be computationally intensive.
 Optimal sampling densities should balance accuracy and performance.
 
 ### b. Integration with Physics Engines
+
 Aerodynamic forces must be integrated with the physics engine's update loops,
 ensuring forces are applied correctly based on the body's current state and
 orientation.
 
 ### c. Validation
+
 Comparing simulation results with experimental data to validate and calibrate
 the implemented models.
 
 ## 8. Summary of Mathematical Steps for Implementation
+
 1. **Surface Sampling**: Discretize the body's surface into numerous points.
 2. **Local Impact Angle Calculation**: Compute the angle between each normal
    vector and the free-stream velocity vector.