Aircraft Mission Lecture 8 Aircraft Mission Text: Constraints analysis Introduction Concept of Constraints Motori Aeronautici Mathematical model Mar. 22, 2016 Aerodynamic Polar Throttle Lapse Flight phases Mission analysis Introduction Aircraft weights Cruise weight ratio TSFC behavior BCM/BCA Takeoff weight estimation Conclusions Mauro Valorani Università La Sapienza 8.108
Aircraft Mission Agenda Constraints analysis 1 Constraints analysis Introduction Introduction Concept of Constraints Concept of Constraints Mathematical model Mathematical model Aerodynamic Polar Aerodynamic Polar Throttle Lapse Throttle Lapse Flight phases Flight phases Mission analysis Introduction Aircraft weights Cruise weight ratio Mission analysis 2 TSFC behavior Introduction BCM/BCA Takeoff weight estimation Aircraft weights Conclusions Cruise weight ratio TSFC behavior BCM/BCA Takeoff weight estimation Conclusions 3 8.109
Aircraft Mission The difficulties of engine design Constraints analysis Introduction Concept of Constraints Gas Turbine engines exert a dominant influence on aircraft performance Mathematical model Aerodynamic Polar and must be custom tailored for each specific application. Throttle Lapse Flight phases ⇒ Engine Specifications come from Aircraft Specifications Mission analysis Introduction Aircraft weights Cruise weight ratio The design process is both started by and constrained by an identified TSFC behavior BCM/BCA need Takeoff weight estimation Conclusions The process is inherently iterative 8.110
Aircraft Mission The need : Request for Proposal (RFP) Constraints analysis Introduction It’s the mission specification that defines the desired engine Concept of Constraints performance. Mathematical model Aerodynamic Polar Throttle Lapse The aircraft customer describes the desired aircraft performance in a Flight phases document such as a Request for Proposal Mission analysis Introduction Aircraft weights Example: Cruise weight ratio TSFC behavior 1 Takeoff, field is at 2000 ft pressure altitude. Takeoff ground roll must be BCM/BCA less than 2500 m at MTOW Takeoff weight estimation 2 Takeoff rate of climb greater than 1000ft/min Conclusions Subsonic cruise at Best Cruise Mach, maximum range 10000 km 3 Payload of 60000 kg 4 8.111
Aircraft Mission Design Process Constraints analysis Introduction Concept of Constraints Mathematical model Aerodynamic Polar Throttle Lapse Flight phases Mission analysis Introduction Aircraft weights Cruise weight ratio TSFC behavior BCM/BCA Takeoff weight estimation Conclusions Figure: Design process, schematic 8.112
Aircraft Mission A Roadmap Constraints analysis Introduction Concept of Constraints Mathematical model Aerodynamic Polar DESIGN PROCESS ⇒ Constraint and Mission Analysis Throttle Lapse Flight phases Choice of ( T SL / W TO ) and ( W TO / S ) Mission analysis Estimation of W TO to obtain T SL Introduction Aircraft weights ENGINE SELECTION ⇒ Parametric Cycle Analysis and Performance Cruise weight ratio TSFC behavior BCM/BCA Takeoff weight estimation ENGINE COMPONENTS ⇒ Components Sizing Conclusions 8.113
Aircraft Mission Design Process Mission Specs E ffi ciencies (1st attempt) Constraints analysis Introduction CONSTRAINT Desired TSFC Assumed TSFC PARAMETRIC & Concept of Constraints CYCLE Reference flight condition behavior with MISSION Tech limitation Mathematical model h, V, δ T ANALYSIS ANALYSIS Aerodynamic Polar Throttle Lapse Flight phases OFF-DESIGN Mission analysis Thrust Cycle parameters ( β c, T4, BPR, …) Introduction Specific Thrust Ia Aircraft weights Cruise weight ratio TSFC behavior BCM/BCA MASS FLOW Takeoff weight estimation Conclusions Component sizing Cross-section, blade profiles, Geometries combustor, … E ffi ciencies (Actual) Figure: Design process, schematic 8.114
Aircraft Mission The concept of constraints The requirements of the RFP can be converted into a series of functional relationships between: Constraints analysis the thrust-to-weight ratio at sea-level takeoff Introduction Concept of Constraints Mathematical model T SL / W TO Aerodynamic Polar Throttle Lapse Flight phases the wing loading at takeoff W TO / S Mission analysis Introduction Aircraft weights We are looking for equations of the kind: Cruise weight ratio TSFC behavior T SL / W TO = f ( W TO / S ) BCM/BCA Takeoff weight estimation for each of the requirements (flight phases). Conclusions These will represent constraints that have to be attained simultaneously. Of course, many legitimate solutions exist, and none can be identified as optimal or unique. The "best" solution is always given by judgment and compromise. 8.115
Aircraft Mission Constraints Diagram Each requirement gives life to a curve in the constraint diagram . The solution space is the region above all the curves Constraints analysis Introduction Concept of Constraints Mathematical model Aerodynamic Polar Throttle Lapse Flight phases Mission analysis Introduction Aircraft weights Cruise weight ratio TSFC behavior BCM/BCA Takeoff weight estimation Conclusions For a given W TO , a low W TO / S means large wing area and increased drag, while a high T SL / W TO results in a large thrust requirement. One may prefer, therefore, relatively low thrust and high wing loadings . 8.116
Aircraft Mission Constraints Diagram Design points of actual passenger/cargo aircrafts. The selected design point is very sensitive to the application and the preferences of the designer. Constraints analysis Introduction Concept of Constraints Mathematical model Aerodynamic Polar Throttle Lapse Flight phases Mission analysis Introduction Aircraft weights Cruise weight ratio TSFC behavior BCM/BCA Takeoff weight estimation Conclusions 1 lbf ft 2 = 47 . 88 N m 2 8.117
Aircraft Mission Constraints Diagram Design points of actual fighter aircrafts. Constraints analysis Introduction Concept of Constraints Mathematical model Aerodynamic Polar Throttle Lapse Flight phases Mission analysis Introduction Aircraft weights Cruise weight ratio TSFC behavior BCM/BCA Takeoff weight estimation Conclusions 1 lbf ft 2 = 47 . 88 N m 2 8.118
Aircraft Mission Master equation The design process starts by considering the forces that act on the aircraft (modeled as a point mass): lift, drag, thrust, weight . Constraints analysis Introduction Concept of Constraints Mathematical model Aerodynamic Polar Throttle Lapse Flight phases Mission analysis Introduction Aircraft weights Cruise weight ratio TSFC behavior Equation of motion in the velocity direction: BCM/BCA Takeoff weight estimation T cos ( AOA + ϕ ) − D − W sin ( θ ) = W dV Conclusions (15) g 0 dt where AOA is the angle between Velocity and Wing Chord Line, ϕ is the angle between Wing Chord Line and Thrust axis. Multiplying by the velocity V, we obtain the energy conservation equation: � � �� V 2 V sin ( θ ) + d ( T cos ( AOA + ϕ ) − D ) V = W (16) dt 2 g 0 8.119
Aircraft Mission Master equation Assuming small angles of attack (AOA ≈ 0) and small thrust vector Constraints analysis misalignments with V ( ϕ ≈ 0), and recalling that V Sin θ = dh dt : Introduction Concept of Constraints V 2 Mathematical model � � d 2 g 0 + h Aerodynamic Polar V ( T − D ) = dz e = = P s (17) Throttle Lapse W dt dt Flight phases Mission analysis where z e represents the aircraft mechanical energy (kinetic + potential) and Introduction is often referred to as "energy height". Aircraft weights Cruise weight ratio TSFC behavior P s is the time rate of change of the energy height and is called weight specific BCM/BCA excess power . Takeoff weight estimation Conclusions Isolating the thrust-to-weight ratio at LHS: W = D T W + P s (18) V Here, both T and W depend on the flight condition and mission phase. 8.120
Aircraft Mission Master equation: assumptions for T and W Constraints analysis Introduction It is assumed that the installed thrust and the actual aircraft weight are given by Concept of Constraints (SL=Sea Level Static, TO=Take-Off): Mathematical model Aerodynamic Polar Throttle Lapse T = α T SL (19) Flight phases Mission analysis W = β W TO (20) Introduction Aircraft weights where α is the full throttle thrust lapse (dependent on altitude, speed and Cruise weight ratio afterburner on/off) and β depends on how much fuel has been consumed . TSFC behavior BCM/BCA Takeoff weight estimation The equation becomes: Conclusions = β � � T SL D + P s (21) W TO α β W TO V 8.121
Aircraft Mission Aerodynamic polar Constraints analysis Recall that lift can be expressed through the lift coefficient as follows: Introduction Concept of Constraints Mathematical model L = nW = 1 q := 1 2 ρ V 2 SC L = qSC L 2 ρ V 2 Aerodynamic Polar (22) Throttle Lapse Flight phases ⇒ C L = nW qS = n β W TO Mission analysis (23) Introduction q S Aircraft weights Cruise weight ratio and that also drag has a similar expression: TSFC behavior BCM/BCA D = qC D S (24) Takeoff weight estimation Conclusions where C D can be expressed through the aerodynamic lift-drag polar: C D = C D 0 + K 1 C 2 L + K 2 C L (25) 8.122
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