2.3 Aircraft Performance
2.3.2 The Flight Path Angle
The FPA and the aircraft vertical profile are related to each other. A higher FPA assures a higher vertical profile. If community noise impact were the only concern, high FPAs would naturally be preferred for lower noise on the ground, at least when the aircraft is close to the runway. However, in
noise abatement approach and arrival procedure design, many other factors must also be taken into account.
The FPA is also related to required engine thrust. During constant CAS level flight where FPA equals zero, engine throttle must be fully engaged to overcome drag. As the FPA at which the aircraft is descending becomes steeper, the required engine thrust to maintain a constant speed (such as a given CAS) will decrease. The FPA for constant CAS idle descent represents a critical condition. If the FPA is steeper than the FPA for constant CAS idle descent, speedbrakes must be extended to maintain the given CAS or the CAS will increase during descent. Sustained use of speedbrakes during descents is not desirable because it reduces comfort, increases airframe noise, and wastes the aircraft gravitational potential energy. Thus, constant CAS idle descent represents the upper bound of the magnitude of FPAs from an aircraft performance point of view.
To illustrate the relationship between idle descent FPA and aircraft aerodynamics, consider a simplified case – instantaneous constant true speed descent under zero wind. Because wind is assumed to be zero, the true speed V and true airspeed Vr have the same value. The simplified free body diagram is shown in Fig. 2-15. In the figure, Ȗ denotes FPA, which is negative for descent, and Ti denotes installed idle thrust, which is approximately equal to zero.
V X Ti J
D
mg
L
Z
J
Figure 2-15 Simplified free body diagram for constant true speed idle descent.
For constant true descent, both vertical and horizontal accelerations are zero. The force equations are thus
0 cos ) (
sin
L
J
Ti DJ
(2-7)0 sin
) (
cos T D mg
L
J
iJ
(2-8)From Eq. (2-7), the FPA for constant true speed idle descent can be derived as
¸¹
¨ ·
©
§ L
D Ti
J
atan (2-9)Ignoring the installed idle thrust, the FPA for constant true speed idle descent becomes
D L
atan
J
(2-10)It can be seen from Eq. (2-10) that the FPA for constant true speed idle descent is determined by aircraft L/D ratio. The lower the L/D ratio, steeper the FPA will be and vise versa. As mentioned earlier in Subsection 2.2.2, for any given aircraft, the L/D ratio is a function of the lift coefficient and the aircraft configuration (flap/slat and landing gear positions). From Eq. (2-8) and the first half of Eq. (2-4), it can be derived
With the drag polar for a given aircraft configuration known, Eq. (2-10) and Eq. (2-11) can be solved iteratively to obtain the FPA for constant true speed idle descent. Under normal operational conditions, Cd << Cl and the magnitude of FPA J is small. Eq. (2-11) can be approximated by the lift coefficient for
Based on the discussion in Subsection 2.2.2, the L/D ratio decreases with the decrease in speed. It is thus expected that the magnitude of FPA for constant true speed idle descent will increase as the speed decreases. On the other hand, if the speed is adjusted (by proper trimming) to keep the term mg/V2 in Eq. (2-12) constant as the aircraft weight varies, the lift coefficient will remain the same; hence, the L/D ratio will remain the same. In other words, the descend speed corresponding to the highest L/D ratio (or the shallowest constant true speed idle descent FPA) varies with the aircraft weight. At heavier weight, the descent speed corresponding to the highest L/D ratio is higher.
Because of the nonlinear relationship between CAS and TAS, and the possible wind changes along altitude, aircraft acceleration is normally not zero during constant CAS descent. The computation of FPA for constant CAS idle descent is thus more complicated. Nonetheless, the analysis of the FPA for constant true speed idle descent does provide insight to the relationship between FPA and aircraft aerodynamic performance, and descent speed. Detailed derivation of the equations used for computing the FPA for idle constant CAS descent is provided in Subsection A.4.3 of Appendix A. They are not iterated here for the sake of clarity.
FPAs for constant CAS idle descent were extracted from the output files of simulation runs described in section 2.2.3. Since FPAs for constant CAS idle descent did not change much for different altitudes with in the range (sea level to 10,000 ft) examined, average values for each CAS value were used to represent the FPA for that speed. The results are presented in Fig. 2-16. The magnitude of FPAs for constant CAS idle descent above CAS 200 kt up to 240 kt (clean configuration) were approximately 3 deg for the given simulation conditions. Below CAS 200 kt, the magnitude of FPAs for the constant CAS idle descent increased rapidly as speed decreased, because flap/slat extensions were initiated at approximately that speed. At 140 kt, the magnitude of FPAs for constant CAS idle descent were about 7 deg – landing gear had been deployed at that speed.
In a practical approach procedure design, the aircraft would normally decelerate as it approaches the runway threshold. Should the aircraft decelerate to about 140 kt, it would normally have been established on the final approach. At that time, the FPA would normally be determined by the ILS glide slope which
is about 3 deg. In other words, as the aircraft decelerates and gets closer to the runway, thrust must be added to maintain stabilized flight because the FPA to remain on glide slope would be far shallower than the FPA required for constant CAS idle descent at low speeds. The requirement to add engine thrust to counter the increased drag – because of the deployment of flaps/slats and landing gear at low speeds and the need to remain on the glide slope – essentially limits the area where noise abatement approach procedures are effective in reducing community noise impact. For this reason, noise abatement approach procedures can not be effective in reducing noise impact once the aircraft is established on the final approach as long as a conventional 3 deg glide slope is used.
Calibrated Airspeed, kt
Flight Path Angle,deg
140 150 160 170 180 190 200 210 220 230 240
-8 -7 -6 -5 -4 -3 -2 -1 0
B757-200 B767-300
Figure 2-16 Average FPAs for constant CAS idle descent.
A special case is a noise abatement approach procedure that is some times referred to as steeper approach. This procedure resembles a glide-and-dive vertical profile, i.e. an initial approach segment with normal FPA and a final approach segment with steeper FPA (steeper than the normal 3 deg glide slope). If the FPA is steep enough, the final approach could also be performed at or near idle thrust even when the speed is relatively low. However, the majority of commercial jet aircraft are not certified for steeper approaches. The London City Airport is one of the few airports that require the glide-and-dive type steeper approach procedures – only aircraft capable of making an approach at 5.5 deg (-5.5 deg FPA) or steeper are permitted to land at the airport.
The use of different FPAs is also important in satisfying ATC restrictions. For example, if an “at or above” altitude restriction is imposed at a point relatively far from the runway, the FPA between that point and the next lower altitude restriction must be steeper than a certain value. In some cases, the ATC dictated minimum FPA could be slightly higher than the FPA for the constant CAS idle descent corresponding to the assigned CAS for that segment. If this happens, speedbrakes will have to be frequently extended to add drag to keep the aircraft on the vertical path and maintain the assigned speed.
This is not desirable because it increases pilot workload. If other conditions permit, the assigned speed for the segment could be lowered so that the FPA for constant CAS idle descent corresponding to the new speed would be higher than the ATC required minimum FPA. With the new speed, an idle descent segment satisfying the altitude restrictions may be built, and be executed without excessive use of speedbrakes11.
Knowledge of the magnitude of FPA for constant CAS idle descent for various conditions such as aircraft type, weight range, altitude, speed, and wind (which will be discussed in the following chapters) is thus a valuable tool for the design of noise abatement approach and arrival procedures.