New concepts in passenger airliner design will have the range to cross the Pacific in a single flight and the efficiency to make it economical [16. 29]. These new designs will require the use of temperature-resistant, lightweight materials and advanced control systems. Noise control is an important issue in modern aircraft designs since most airports have strict noise level requirements. One interesting concept is the Boeing Sonic Cruiser depicted in Figure P7.10(a). It would seat 200 to 250 passengers and cruise at just below the speed of sound.
The flight control system must provide good handling characteristics and comfortable flying conditions. An automatic control system can be designed for the next generation passenger aircraft.
The desired characteristics of the dominant roots of the control system shown in Figure P7.10(b) have a ζ = 0.707. The characteristics of the aircraft are ωn = 25, ζ = 0.30, and т = 0.1. The gain factor K1, however, will vary over the range 0.02 at medium-weight cruise conditions to 0.20 at lightweight descent conditions.
(a) Sketch the root locus as a function of the loop gain K1K2.
(b) Determine the gain K2 necessary to yield roots with ζ = 0.707 when the aircraft is in the medium-cruise condition.
(c) With the gain K2 as found in part (b), determine the ζ of the roots when the gain K1 results from the condition of light descent.
Figure P7 10
(a) A passenger jet aircraft of the future.
(b) Control system.

Aiteraft dynarmics KErs + I Controller Actuator Yis) + Pitch rate Ris) s 100) Rate gyro