Formula & Calculator
Phugoid Mode Period (Approx.)
Approximate period of the long-period, lightly-damped phugoid oscillation in airspeed and altitude.
Interpretation
Phugoid mode period: T_ph ≈ 2π·√2 · V/g, where V is airspeed, g is gravity. It is the long‑period oscillation in speed and altitude. Example: V=100 m/s → T_ph ≈ 2π×1.414×100/9.81 ≈ 90.5 s.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| T_ph | Phugoid period | s |
| V | Trim airspeed | m/s |
| g | Gravitational acceleration | m/s2 |
What it means
The phugoid mode is a low‑frequency, usually poorly damped oscillation involving exchange between kinetic and potential energy. Its period is approximately proportional to speed, independent of altitude. The approximation assumes small perturbations and no drag. The phugoid is important for pilot control and for autopilot design. It is often lightly damped and may require active damping. Understanding phugoid behaviour is essential for flight test and for evaluating longitudinal stability.
Worked example
Phugoid Period – Two Examples
Real‑World| Parameter | Value |
|---|---|
| V | 60 m/s |
| Parameter | Value |
|---|---|
| V | 100 |
Common mistakes
- Phugoid mode period (approx.): T_ph ≈ 2π·√2 · V / g.
- V: Trim speed (m/s).
- g: Gravitational acceleration.
- Long‑period oscillation, typically poorly damped.
- Approximate formula; full analysis includes derivatives.
Applications
The phugoid mode period, T_ph ≈ 2π√2·V/g, is the long‑period oscillatory mode involving exchange of kinetic and potential energy. It is a slow, lightly damped mode that affects speed and altitude variations. Engineers use this to ensure adequate damping (through auto‑throttle or pilot input) and to assess ride quality. The period depends on airspeed; faster aircraft have longer periods. By understanding phugoid dynamics, aerospace engineers can design control laws that either damp the mode or make it acceptable to pilots, improving flight safety and comfort.
- Longitudinal dynamic stability analysis
- Auto‑throttle and speed control system design
- Pilot‑induced oscillation avoidance
- Flight test mode identification
- Ride quality and passenger comfort assessment
Frequently Asked Questions
It gives an approximate period of the long‑period, lightly damped phugoid oscillation in airspeed and altitude. It is a fundamental mode of aircraft longitudinal dynamics.
Tph = phugoid period (s)
V = trim speed (m/s)
g = acceleration due to gravity (9.81 m/s²)
It affects the aircraft’s response to long‑term disturbances and pilot workload. The phugoid is usually lightly damped and can be uncomfortable if not controlled.
- Assuming the phugoid mode depends strongly on aerodynamic derivatives, when to first order it depends mainly on trim speed.
- Using the formula for speeds where the approximation is invalid (e.g., very low or very high speeds).
- Confusing the period with the time constant.
For an aircraft at V = 150 m/s, Tph ≈ 2π√2 × 150 / 9.81 = 8.886 × 15.29 ≈ 135.8 s (≈ 2.3 minutes).
The period increases with true airspeed, so at higher altitudes (where TAS is higher for a given Mach), the period is longer.
For a given speed, the period is independent of weight; however, heavier aircraft fly at higher speeds for a given lift coefficient, so the period may change.
The phugoid damping is determined by the derivative of drag with respect to speed. A larger drag‑speed coupling gives more damping.
Autopilots must control the phugoid mode, either by providing damping or by using speed‑hold modes.
The formula assumes a constant lift‑to‑drag ratio and small perturbations; for more precise analysis, the full linearised equations must be used.