Pitching Moment Due to Thrust-Line Offset
If the engine thrust line does not pass through the vertical CG, a pitching moment is introduced by thrust change. For many transport aircraft, the thrust line is below the vertical CG, and increasing thrust results in a desirable nose-up pitching moment and a subsequent angle-of-attack increase and pitch attitude increase.
For the MD-11, if all three engines are used equally, the resultant thrust line is near the vertical CG, and this effect is small. If only the wing engines are used, which are nearly 10 ft below the nominal vertical CG, the nose-up pitching moment is signi.cant. The center engine of the MD-11 is approximately 20 ft above the vertical CG and causes a strong nose-down pitching moment with thrust increase.

Flightpath Angle Change Due to the Vertical Component of Thrust
If the thrust line is inclined to the .ightpath, as is commonly the case, an increase in thrust increases the vertical component of thrust, which causes a vertical acceleration and a resulting increase in .ightpath angle. For a given aircraft con.guration, this effect increases as pitch attitude increases.
For the MD-11, the combined short-term effect of a thrust increase is to produce a nose-up .ightpath response shown in .gure 8; this .gure is a time history of the step throttle increase of the wing engines at 220 kn. Thrust responds within about 1 sec. Pitch attitude and the resulting angle of attack increases about 0.3° , and airspeed increases for the .rst 12 sec. With the increased angle of attack, drag increases, and as pitch attitude increases, the component of weight along the .ightpath becomes signi.cant, decreasing airspeed.
When using only the wing-mounted engines for control, the pitching moment from thrust offset is the strongest component, and a throttle advance increases pitch attitude and angle of attack such that the long-term effect is an oscillatory climb at a reduced trim airspeed. The reverse is also true: A reduction in wing engine thrust causes a descent at increased airspeed.

Phugoid
The phugoid is the longitudinal long-period oscillation of an airplane. Phugoid is a motion in which kinetic and potential energy (speed and altitude) are traded; it may be excited by a pitch, thrust, or velocity change. For the MD-11, the bare airframe phugoid is lightly damped; .gure 9(a) shows a .ight example in light turbulence. This phugoid oscillation, with the same airplane con.guration and .ight conditions as in .gure 4, was excited by a pullup, which results in a lightly damped oscillatory climb at constant throttle. Note that the angle of attack changes and is 180° out of phase with airspeed. With throttles .xed, a slight oscillation in EPR occurred from the changing .ight conditions. The speed is low enough that Mach effects are not signi.cant. The EPR and thrust increase with decreasing airspeed contributes to destabilizing the phugoid.
Airspeed,
kn

Flightpath
angle,
deg

Rate of
climb,
ft/sec

Angle of
attack,
deg

Throttle
angle,
deg

EPR
970579

Figure 8. Response to open-loop step throttle increase, MD-11, LSAS off, center engine idle, PCA off, gear down, .aps up, 15,000 ft.
13,500
13,000 Altitude, ft 12,500
12,000

 Phugoid initiaby pullup  ted 
 

6.0
5.5
Angle of attack, 5.0 deg
4.5
4.0

 
Faired angl e 
of attack 

1.3
1.2
EPR
1.1
1.0

Right 
Left 

0 25 50 75 100 125

Time, sec
970580
(a) Time history of phugoid, LSAS off, gear down, .aps up, light turbulence, .xed throttles, center engine at idle, initiated by an elevator pullup and release.
Figure 9. MD-11 phugoid oscillation.
Figure 9(b) shows a nonlinear simulation of a phugoid at the same conditions as those of the .ight data. Similar trends are shown. The angle-of-attack change is primarily from pitch rate damping. Properly sized and timed throttle inputs can damp unwanted phugoid oscillations; reference 2 discussed these techniques.
　
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