# What is an acceptable phugoid oscillation duration?

What is an acceptable settling time for the phugoid mode in a large aircraft?

As a more specific question, what is the settling time when the aircraft (say, a B747 or an A320) switches from Climb to Cruise phase at the top-of-climb?

Here is the response of a 180 passenger high-subsonic twin-jet simulator: the first period takes about 87 seconds.

Conditions:

From the trimmed position, excite the phugoid mode by applying longitudinal control in one direction in order to change airspeed by approximately 10 kts, then release.

Initial conditions:

• COG 0.2205 MAC
• Pressure altitude 35,000 ft
• Engine N1 rotor speed 87.47% (both engines)
• Calibrated Airspeed 264.54 kts
• Gross weight 66,360 kg

EDIT

To answer the additional question of when the resulting motion amplitude would be below 0.1 deg, I made a kind of a digital simulation according to this block diagram:

and then tuned spring stiffness C, inverse inertia 1/M, and damping constant K until the resulting response overlaid the original aircraft one. The resulting motion gets to a max. amplitude of 0.1 deg in about 1,600 sec - 27 minutes.

• What do you think is the approx. settling time, maybe when the amplitude goes below 0.1 deg?
– Raj
Nov 20 '17 at 17:14
• The peaks setlle down over time, a lime through the peaks looks like a first order response. I'll see if I can make a ROM on < 0.1 deg later in the day. Nov 21 '17 at 0:05

Normally this is in the tens of seconds.

An approximation for the undamped phygoid frequency is: $$\omega_P = \frac{2\cdot g}{v}\cdot \left(1-\frac{c_{mv}\cdot c_{L\alpha}}{c_L\cdot c_{m\alpha}}\right)$$

Nomenclature:
$g\;\;\;\;\;$Gravitational acceleration
$v\;\;\;\;\;$Flight speed
$c_{mv}\;\;$Speed stability (change in pitch moment over speed)
$c_{L\alpha}\;\;$Lift curve slope
$c_{L}\;\;\;$Lift coefficient
$c_{m\alpha}\;$Static stability (change in pitch moment over angle of attack)

• Isn't straight and level flight actually made up of infinitesimally small Phugoid oscillations? Do air-planes really fly perfectly straight? Could you enlighten me?
– user18035
Nov 20 '17 at 13:28
• Can you comment on the oscillation just after the top-of-climb? Is it phugoidal in nature? And it follows the same frequency formulae as is in the answer?
– Raj
Nov 20 '17 at 17:18
• @AnandS: I fail to see a difference between infinitesimally small oscillations and straight flight. Damping ensures that those oscillations die down (except in some gliders), so yes, a well-designed airplane does fly perfectly straight if we neglect that it follows the curvature of the earth. Nov 21 '17 at 8:10
• @Raj: Those oscillations (if they occur at all) are short-period oscillations. Nov 21 '17 at 8:11

Let's first address OP's first question:

What is an acceptable settling time for the phugoid mode in a large aircraft?

Phugoid is a hands-off (i.e. pilot and autopilot off) rigid-body mode, with or without Stability Augmentation System. MIL-STD-1797B specifies a damping ratio of at least 0.04 for Level 1 handling quality. The typical phugoid period is around 90 seconds. This converts to a settling time (within 2% of trim speed) of around 24 minutes. This is so long which makes settling time itself not a particularly good measure for phugoid.

Now onto,

What is the settling time when the aircraft (say, a B747 or an A320) switches from Climb to Cruise phase at the top-of-climb?

Leveling off from climb is not hands-off. A well-tuned autopilot should be deadbeat with minimal overshoot and oscillation. The time scale is also vastly different; we are talking about settling time on the order of a seconds (not half an hour). And this not phugoid.

• Mil-F-8785C is rescinded, however exact same requirements carried over to new milspec. So your answer still holds true. Strangely enough, civilian counterpart Part 25 section 25.181 is not even bothering to give any requirements for phugoid. I think that’s because phugoid is a nuisance mode. Oct 31 '19 at 21:45
• @Kolom Is MIL-STD-1797A the replacement?
– JZYL
Oct 31 '19 at 22:04
• 1797B is the new one Oct 31 '19 at 22:11
• This should be the accepted answer. Nov 4 '19 at 5:37