IWTLP - Learn Programming by Doing

Aerodynamics is the study of the motion of air and the forces acting on solid bodies moving through it. For aerospace engineering, understanding aerodynamics is fundamental to aircraft design, performance analysis, and flight safety.

The Four Forces of Flight

The physics of flight is elegantly captured by four fundamental forces that act on an aircraft:

LIFT - The upward force that opposes weight, primarily generated by the wings
WEIGHT - The downward gravitational force acting through the aircraft's center of gravity
THRUST - The forward force generated by propulsion systems, opposing drag
DRAG - The rearward force of resistance as the aircraft moves through air

These forces must be balanced for steady, level flight: Lift = Weight and Thrust = Drag.

Understanding Lift Generation

Lift is produced by the wings through two primary mechanisms:

Bernoulli's Principle

As air flows over the airfoil (wing cross-section), it travels a longer path over the curved upper surface than the flatter lower surface. This creates faster flow on top and slower flow below, resulting in lower pressure above and higher pressure below. This pressure differential creates an upward force.

The mathematical expression of Bernoulli's equation shows:

P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}

Where $P$ is pressure, $\rho$ is air density, $v$ is velocity, and $g$ is gravitational acceleration.

Newton's Third Law

The wing also deflects air downward (downwash). By Newton's third law, every action has an equal and opposite reaction, so the downward force on the air creates an upward force on the wing.

Lift Equation

The total lift produced can be calculated using:

L = \frac{1}{2} \rho v^2 S C_L

Where:

$L$ = Lift force
$\rho$ = air density
$v$ = velocity
$S$ = wing area
$C_L$ = coefficient of lift

Types of Drag

Understanding drag is crucial for aircraft efficiency:

Parasitic Drag

Parasitic drag consists of three components:

Form Drag - Drag due to the shape of the aircraft and pressure differences
Skin Friction Drag - Drag due to the viscosity of air and friction with the surface
Interference Drag - Drag created by the interaction of airflow between different components

Induced Drag

Induced drag is a byproduct of lift generation. It's caused by the three-dimensional flow around the wingtips, creating wingtip vortices. Higher angles of attack (needed for more lift at slow speeds) create more induced drag.

D_i = \frac{L^2}{\frac{1}{2}\rho v^2 \pi b^2 e}

Where $b$ is wingspan and $e$ is the Oswald efficiency factor.

Drag Polar

The total drag coefficient can be expressed as:

C_D = C_{D0} + \frac{C_L^2}{\pi e AR}

Where:

$C_{D0}$ is the zero-lift drag coefficient (parasitic drag)
$AR$ is the aspect ratio of the wing

Angle of Attack

The angle of attack ( $\alpha$ ) is the angle between the chord line of the airfoil and the relative wind. As angle of attack increases, lift increases up to the critical angle of attack, where stall occurs.

Airfoil Design

Modern airfoils are optimized for specific flight conditions:

Symmetric airfoils - Equal performance in positive and negative angles of attack, good for aerobatic aircraft
Cambered airfoils - Optimized for typical forward flight, providing better efficiency
Supercritical airfoils - Designed for high-speed flight, delaying shock wave formation

Reynolds Number

The Reynolds number indicates the ratio of inertial forces to viscous forces:

Re = \frac{\rho v l}{\mu}

Where $l$ is a characteristic length (chord for wings) and $\mu$ is dynamic viscosity. It determines the nature of the flow (laminar vs turbulent).

Real-World Application: The Lift-to-Drag Ratio

The lift-to-drag ratio ( $L/D$ ) is a crucial measure of aerodynamic efficiency. A higher $L/D$ ratio means the aircraft produces more lift for the same amount of drag, improving fuel efficiency and range.

For example:

A typical glider might have $L/D$ = 40:1
A commercial airliner might have $L/D$ = 15-20:1
A fighter jet might have $L/D$ = 8-12:1 (sacrificing efficiency for maneuverability)

Example Calculation

If an aircraft weighs 100,000 N and has an $L/D$ ratio of 20:1, its drag in level flight is:

D = \frac{W}{L/D} = \frac{100,000}{20} = 5,000 \text{ N}

This means the engines only need to produce 5,000 N of thrust to maintain level flight.

Your Challenge: Wing Loading Analysis

In this exercise, you'll analyze how wing loading affects flight performance.

Goal: Calculate the stall speed for different wing loadings and understand the trade-offs in aircraft design.

Key Variables

# Aircraft specifications
weight = 1500  # Weight in kg
gravity = 9.81 # m/s²
mass = weight * gravity  # Weight force in Newtons

# Wing specifications
wing_area_small = 15  # m²
wing_area_large = 25  # m²

# Air conditions at sea level
air_density = 1.225  # kg/m³

# Airfoil performance
max_lift_coefficient = 1.4  # Typical for general aviation

Your task is to calculate the stall speed for both wing configurations using the lift equation. The stall speed occurs when the wing reaches its maximum lift coefficient for a given configuration.

Hint: At stall, Lift = Weight, so:

\frac{1}{2} \rho v^2 S C_{L_{max}} = Weight

Solve for $v$ to find the stall speed.

# TODO: Calculate stall speed for both wing configurations
stall_speed_small_wing = 0
stall_speed_large_wing = 0

# Print results
print(f"Stall speed (small wing): {stall_speed_small_wing:.2f} m/s")
print(f"Stall speed (large wing): {stall_speed_large_wing:.2f} m/s")

What are the advantages and disadvantages of each wing configuration? How does wing loading affect performance?

Fundamentals of Aerodynamics