The Fundamentals of Flight

To master long-range drone fabrication, we must first understand the equilibrium of forces acting upon an aircraft in steady flight. This module covers the core principles that dictate whether an airframe stays in the air or returns to the build plate in pieces.

1. The Force Equilibrium

For a plane to maintain straight and level flight, the four forces must be in balance. We represent this equilibrium through the following relationships:

$\text{Lift}=\text{Weight}$ $\text{Thrust}=\text{Drag}$

If $\text{Lift}>\text{Weight}$, the aircraft climbs. If $\text{Thrust}<\text{Drag}$, the aircraft decelerates.

2. The Lift Equation

Lift is generated by the pressure difference between the upper and lower surfaces of a wing. The amount of lift produced is calculated using the standard Lift Equation:

$L=\frac{1}{2}\rho v^{2}S{C}_L$

Where:

• $\rho$ (rho): Air density (kg/m³)
• $v$: Velocity of the aircraft (m/s)
• $S$: Wing surface area (m²)
• $C_L$: Coefficient of lift (determined by the airfoil shape and angle of attack)

Impact for MNR_FAB

When we 3D print wings, the surface roughness (layer lines) can impact the boundary layer of air, potentially reducing the $C_L$ or increasing the stall speed.

3. The Drag Equation

Drag is the aerodynamic force that opposes an aircraft's motion through the air. In our drone builds, reducing drag is the key to increasing battery life.

$D=C_d\frac{\rho v^2}{2}A$

• $C_d$: Drag coefficient (how "slippery" the drone is)
• $A$: Cross-sectional area

Note that velocity is squared ($v^2$). This means doubling your speed quadruples the drag, requiring eight times the power!

4. Wing Loading

One of the most important metrics for our printed planes is Wing Loading, which determines how "heavy" the plane feels in the air:

$W_L=\frac{m\cdot g}{S}$

A higher $W_L$ means the drone must fly faster to generate enough lift to stay airborne, which is a common challenge with heavy 3D-printed airframes.

Summary Checklist for Fabrication

1. Optimize Airfoil: Choose a $C_L$ profile suited for your mission speed.
2. Minimize Surface Area ($A$): Reduce frontal profile to combat $v^2$ drag.
3. Weight Reduction: Every gram reduced lowers the required lift.