Understanding the Spiral Mode

What is the Spiral Mode?

The Spiral Mode is another fundamental lateral-directional dynamic mode of an aircraft. Unlike the oscillatory Dutch Roll, the Spiral Mode is typically a slow, non-oscillatory (aperiodic) mode. It describes the aircraft's long-term tendency in roll and yaw after being disturbed from wings-level flight.

Stable Spiral Mode: If disturbed into a bank, the aircraft will slowly return to wings-level flight on its own.
Neutral Spiral Mode: If disturbed into a bank, the aircraft will tend to maintain that bank angle and continue turning at a constant rate.
Unstable Spiral Mode: If disturbed into a bank, the bank angle will slowly but continuously increase, leading to a tightening spiral dive if not corrected by the pilot.

The stability of this mode varies greatly between aircraft designs and flight conditions. Many general aviation aircraft have a mildly unstable spiral mode.

Physical Origin: Balance of Lateral & Directional Stability

The Spiral Mode's behavior depends critically on the balance between the aircraft's lateral stability (Dihedral Effect, Cl_beta) and its directional stability (Weathercock Stability, Cn_beta).

Imagine the aircraft is slightly banked to the right:

Sideslip due to Bank: While banked, gravity causes the aircraft to start slipping slightly towards the lower wing (a right sideslip, positive β).
Competing Moments:
- Directional Stability (Cn_beta): The right sideslip acts on the vertical tail, creating a yawing moment to the right, trying to align the nose with the direction of slip (relative wind).
- Dihedral Effect (Cl_beta): The right sideslip acts on the wings (due to dihedral/sweep), creating a rolling moment to the left, trying to level the wings.
The Balance Determines Stability:
- Stable Spiral: If the dihedral effect (Cl_beta) is relatively strong compared to directional stability (Cn_beta), the tendency to roll wings-level dominates. The aircraft generates a left roll, which reduces the bank angle and the associated sideslip, eventually returning the aircraft towards straight-and-level flight.
- Unstable Spiral: If the directional stability (Cn_beta) is relatively strong compared to the dihedral effect (Cl_beta), the tendency to yaw into the turn dominates. As the aircraft yaws right (into the bank), the outer (left) wing travels faster than the inner (right) wing. This speed difference creates more lift on the outer wing, causing a rolling moment to the right, which increases the bank angle. This increased bank leads to more sideslip, reinforcing the yaw into the turn and the roll into the bank, creating a slowly tightening spiral.
- Neutral Spiral: If the effects are perfectly balanced (rare), the aircraft maintains the established bank and turn rate.

Other factors like roll damping (Cl_p) and yaw damping (Cn_r) also play roles, but the fundamental behavior is driven by the Cl_beta vs. Cn_beta balance.

Flight Test Proposal using OpenFlight Simulator

This test aims to observe the aircraft's spiral stability tendency. This requires patience as the mode is slow.

1. Setup:

Aircraft Selection: Choose an aircraft. Results will vary significantly based on the aircraft's stability characteristics defined in its YAML file.
Mission Configuration (default_mission.yaml):

# AIRCRAFT PARAMETERS

aircraft_name: "SF25B.yaml" # Name of the aircraft aerodynamic data file in \🏭_HANGAR\📜_Aero_data

# FLIGHT TEST PARAMETERS

initial_velocity: 32 # Initial velocity in m/s

initial_altitude: 2000 # Initial altitude in m

# FLIGHT RECORDING PARAMETERS

start_flight_data_recording_at: 3 # start recording in seconds after start of flight

finish_flight_data_recording_at: 300 # finish recording in seconds

# VISUALIZATION PARAMETERS

scenery_complexity: 0 # 0 = four checkered quadrants (good for old GPUs), 1 = low, 2 = medium or 3 = high detail

show_force_vectors: "true"

show_velocity_vectors: "true"

show_trajectory: "true" # "true" or "false", to show the trajectory of the aircraft

- Ensure the data recording window is long enough to observe the slow divergence or convergence (e.g., 0 to 300 seconds or more).
Trim: Start the simulation and allow the aircraft to settle into stable, wings-level, straight flight. Minimize any initial roll or yaw rates.

2. Excitation:

Once trimmed, gently establish a shallow bank angle (e.g., 5-10 degrees):
- Briefly apply a small amount of aileron (e.g., tap 'P' or 'O') until the desired small bank is achieved.
- Carefully neutralize all controls (aileron and rudder). Ensure no residual roll or yaw rate is being commanded.
Hands-Off: Do not make any further control inputs. Let the aircraft fly undisturbed for an extended period (1-5 minutes).

3. Observation & Recording:

Carefully observe the aircraft's bank angle and heading in the 3D view and GUI.
- Does the bank angle slowly increase? (Unstable Spiral)
- Does the bank angle slowly decrease back towards zero? (Stable Spiral)
- Does the bank angle remain roughly constant? (Neutral Spiral)
The simulator backend will record the data to CSV.

Data Analysis

Use the Flight Data Visualization tool or other software to analyze the generated CSV data over the entire recording period after the initial disturbance.

Load Data: Load the CSV file.
Key Plots:
- Roll Angle vs. Time: This is the primary plot. Look for a slow, steady trend after the initial disturbance settles: increasing, decreasing, or staying relatively flat.
- Heading or Yaw Angle vs. Time: Should show a continuous change if the aircraft is turning (associated with bank). The rate of change might increase if the spiral is unstable.
- Yaw Rate (r_yaw_rate) vs. Time: Should settle to a near-constant value (for neutral/unstable) or decay towards zero (for stable).
- Sideslip Angle (beta_DEG) vs. Time: Should remain small but might show a slight bias depending on the turn coordination.
Interpret Results:
- Increasing Bank Angle: Indicates an unstable spiral mode.
- Decreasing Bank Angle (towards zero): Indicates a stable spiral mode.
- Constant (non-zero) Bank Angle: Indicates a neutral spiral mode.

Online Resources:

- Wikipedia: Article on "Spiral divergence". (https://en.wikipedia.org/wiki/Spiral_divergence)

This test requires patience but provides valuable insight into the long-term lateral-directional tendencies of an aircraft design.

EXERCISE:

In a single slide of a presentation answer the following questions:

Plot the relevant flight data for your flight (as shown above)
Is your mode stable?
Do you think the behavior you get is realistic? Why?
If this aircraft limit load factor is 2.5, could this trajectory be achieved in reality?
Is this mode dangerous for flight? Why?

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