Roll Mode (Roll Subsidence)

Concept: The Roll Mode, also known as Roll Subsidence, describes how quickly an aircraft stops rolling once the ailerons are neutralized after a roll has been initiated. It is primarily governed by the roll damping derivative (Cl_p), which represents the rolling moment generated opposing the roll rate. This is typically a stable, non-oscillatory (aperiodic) mode – the roll rate simply decays exponentially.

Physical Origin: When an aircraft is rolling, the downward-moving wing experiences a slightly increased angle of attack, while the upward-moving wing experiences a decreased angle of attack. This difference in AoA creates a differential lift, generating a rolling moment that opposes the existing roll rate. This inherent aerodynamic damping causes the roll rate to decay once the initiating control input (aileron) is removed. The larger the wingspan and the faster the speed, generally the stronger the roll damping.

Flight Test Proposal:

1. Setup:

   • Select an aircraft model.

   • Configure mission for a typical cruise speed and safe altitude (e.g., 1000m).

   • Set data recording window (e.g., 0-30 seconds).

   • Trim the aircraft for stable, wings-level flight.

2. Excitation:

   • Apply a distinct aileron input (e.g., hold 'P' key for 1-2 seconds) to establish a moderate roll rate.

   • Sharply neutralize the ailerons (release the key).

3. Hands-Off: Do not make any further control inputs.

4. Observation & Recording: Observe the roll rate decaying back to zero. Record the data.

Data Analysis:

1. Load Data: Use the visualization tool.

2. Key Plots:

   • Roll Rate (p_roll_rate) vs. Time: This is the primary plot. Observe the exponential decay of the roll rate after the aileron input ceases (look for when roll_demand_attained returns to zero).

   • Roll Angle vs. Time: Shows the aircraft settling into a constant bank angle after the roll rate becomes zero (if no other disturbances occur).

   • Roll Control (roll_demand, roll_demand_attained) vs. Time: Useful to identify precisely when the control input was neutralized.

3. Identify Parameters:

   • Time Constant (τ): Estimate the time it takes for the roll rate to decay to approximately 37% (1/e) of its initial value after controls are neutralized. A smaller time constant indicates stronger damping (larger magnitude Cl_p). The roll rate p(t) can be approximated by p(t) = p0 * exp(-t/τ), where p0 is the rate when controls are neutralized.

References: (Same as previous stability modes, focusing on lateral dynamics)

• Nelson, R. C. (1998). Flight Stability and Automatic Control.

• Phillips, W. H. (2004). Mechanics of Flight.

• Etkin, B., & Reid, L. D. (1996). Dynamics of Flight: Stability and Control.