Introduction

XFLR5 is a powerful analysis tool for low-Reynolds number aerodynamics. It calculates aerodynamic forces and moments for a specific geometry, allowing the user to iterate until the control authority is sufficient.

Theoretical Approach

Control surface sizing in XFLR5 relies on determining if the generated moments (Pitch, Roll, Yaw) are sufficient to achieve desired flight conditions. The key metrics are the Control Derivatives, which quantify the change in force or moment per degree of deflection (\(\delta\)).

• Elevator Sizing: Governed by the pitch control derivative (\(C_{m_{\delta_e}}\)) and the ability to trim at \(C_{L_{max}}\) (landing speed) and \(C_{L_{min}}\) (high speed/dive).

• Aileron Sizing: Governed by the roll control derivative (\(C_{l_{\delta_a}}\)) to ensure sufficient roll rate.

• Vertical Stabilizer/Rudder: Governed by directional stability (\(C_{n_{\beta}}\)) and yaw authority (\(C_{n_{\delta_r}}\)).

XFLR5 Workflow for Sizing

The sizing process is an iterative loop: Define Geometry \(\rightarrow\) Analyze Control Power \(\rightarrow\) Resize \(\rightarrow\) Repeat.

Step 1: Airfoil Preparation (The Flap Function)

XFLR5 does not simulate moving parts dynamically in the 3D view. You must create "flapped" versions of your airfoils to represent deflected surfaces.

1. Navigate to Module \(\rightarrow\) Direct Design.

2. Select your base airfoil (e.g., NACA 0012).

3. Right-click on the airfoil pane and select Set Flap.

4. Input parameters:

   • Hinge Location: Typically \(70-80\%\) chord (\(x/c = 0.7 - 0.8\)).

   • Angle: Create versions for deflection (e.g., \(+10^\circ\), \(-10^\circ\)).

5. Save these as new airfoils (e.g., NACA0012_Elev_Down10).

Step 2: Plane Geometry Definition

In Wing and Plane Design, you must manually assign these flapped airfoils to the specific span-wise sections of your wing or tail.

• For Ailerons: Split your main wing geometry so you have a distinct "tip" section. Assign the flapped airfoil only to this outer section.

• For Elevators: Usually, the entire horizontal stabilizer uses the flapped airfoil.

Step 3: Stability Analysis (The "Control" Loop)

To check if the surface size is adequate, use the Stability Analysis (Type 2 or Type 7 polars).

Method A: The Trim Check (Elevator Sizing)

1. Define an analysis (Type 2: Fixed Lift or Type 1: Fixed Speed).

2. Run the analysis with your neutral elevator (\(0^\circ\)).

3. Observe the \(C_m\) vs \(\alpha\) graph. The crossing point (\(C_m = 0\)) is the trim angle.

4. Test Authority: Swap the tail airfoil to the deflected version (\(+10^\circ\)) in the plane editor and re-run the analysis.

5. Compare the new trim point using the relationship: \[\Delta C_{m} = C_{m_{\delta_e}} \cdot \delta_e\] If the elevator cannot trim the aircraft at the desired high \(C_L\) (landing speed) with max deflection, the elevator chord or span must be increased.

Method B: Control Derivatives Calculation

In newer versions of XFLR5 (and its successor flow5), you can define "Control Parameters" in the Analysis definition window.

1. In the Analysis settings, select the Controls tab.

2. Set a "Gain" for the elevator/aileron.

3. Run a Stability Analysis (Type 7).

4. View the log file or "Stability Derivatives" output. Look for: \[\begin{aligned} C_{m_{\delta}} &= \frac{\partial C_m}{\partial \delta} \quad \text{(Pitch authority)} \\ C_{l_{\delta}} &= \frac{\partial C_l}{\partial \delta} \quad \text{(Roll authority)} \end{aligned}\] If these values are lower than historical data for your aircraft type (e.g., typical trainer \(C_{l_{\delta_a}} \approx 0.15 - 0.25 / \text{rad}\)), increase surface area.

Sizing Criteria Summary

When analyzing the graphs, use the criteria in Table 1 to decide if resizing is necessary.