AIAA Team Aircraft Design Competition 2009-2010
Introductory Lectures on Aerospace Design Oct. 30th, 2009
University of Southern California
Sina Golshany
Lecture-3 Mission, Performance & Preliminary Sizing,
Mission & Preliminary Mission Analysis
Notes on lecture’s objective – The goal of this lecture is to present to you the extents of aircraft performance evaluation. – Theoretical backgrounds are fairly extensive and complicated and therefore not presented here. (They can be found in ESDU performance data items, Roskam’s book on performance and many others) – We will use Advanced Aircraft Analysis (and possibly the AP software if budget allows) to perform the computations
Mission & Mission Analysis – Aircraft Mission: A Series of flight tasks executed to achieve a certain goal Aircraft Mission: Flight Segments -Flight Conditions (Atmospheric Conditions: More on that next) -Flight Parameters ( Flight Speed, Altitude, Climb Parameters, Thrust Setting, -Statistical Mission Analysis: Performed based on suggested typical values - Fuel Burn Causing Variation of Weight Over Mission
Standard Atmosphere - Temperature Variations: Influences on all other atmospheric parameters
Standard Atmosphere - Density & Viscosity Variations:
Mission Profile, Commercial
– A representation of the tasks performed during flight • It is usually a given – but occasionally it’s details and generalities are subject to optimization and are design driven • Example of a step climb performed to reduce fuel burn.
Mission Profile: Military vs. Civil Flight – Range – Endurance
– Radius of action – Endurance
Mission Profile: Parameterization
Fuel Fraction for mission segment i: M ff ,i
Wi − ∆WFuel = Wi
J. Roskam
Total Fuel Fraction for a mission: n
M ff = ∏ M ff ,i = M ff ,1 ⋅ M ff , 2 ⋅ M ff ,3 ⋅ ...⋅ M ff ,n i =1
Both Wi and ΔWfuel are computed using statistical methods: Wi : is the initial weight minus the fuel burn up to i. - Initial weight is computed using weight regression - Fuel burn of each segment is computed using statistical methods assuming certain inputs such as SFC & Approximate times taken.
Mission Profile Segments:
– The most basic method of analyzing a mission – Used for preliminary sizing
Aircraft Performance Evaluation An introduction to principles & Methods
Performance Parameters: Dependencies – The selection of configurationn is done by
comparative performance evaluation. – Performance evaluation can be done in different levels of detail: – By neglecting minor physical details it is possible to perform simplified evaluation. – By including minor effects (No Acceleration, No change in ‘g’ as altitude changes, thrust vector passing trough center of gravity, all motion on the horizontal plane, no yaw and climb simultaneously, …) --- Sensitivity Analysis are performed
Performance Parameters: Accuracy Comparison
– Example: Rate of Climb Accuracy, Simplified vs. Complete Equations
– It is considerably close in case of the R/C – Presented by ESDU 92019
Field Performance Parameters: – Airfield Performance: -Takeoff & Landing Distances -Runway Forces, even tyre spray effects!
An important market aspect of aircraft performance Alternative ways to shorten the takeoff run or landing distance are well received by the airlines.
Field Performance Parameters: – Typical Takeoff & Landing Profiles:
Climb Performance Analysis – Complicated multi-dependent Analysis: – Propulsion, and Aerodynamics (LS & HS)
Climb Performance: Notion of γ and α: – Flight path angle (γ) can be (and often is) different than angle of attack (α):
Cruise Performance Analysis: Speeds – Complicated multi-dependent Analysis: – Propulsion, and Aerodynamics (LS & HS) – Thrust vs. Velocity Analysis:
Cruise Performance Analysis: Range – Range and Endurance Estimations are sometimes presented in terms of a Weight-Range* chart:
*More often called Payload-Range chart
Sensitivity Analysis – Rate of Change of aircraft weight due to change in aircraft performance (or parameters such as SFC) – Performed using the mission profile data. – An Example:
– Interpretation and significance of sensitivity analysis of a mission profile
Weight Engineering The Essential Elements
Weight Engineering : – Goal: to estimate the weight, mass distribution and inertial properties of the plane, without knowing too much details about the structural configuration. – Extremely important: – As we saw, all sensitivity parameters are in form of derivatives of weight. – Reason is that weight has a significant impact on almost every performance parameter one could think of. – Also weight is directly related to the cost of acquisition and operation of the aircraft: – It is incredibly important from optimization standpoint
Weight Analysis: Fidelity Level – Mission Based weight estimations (Class I) – Geometry/performance based weigh estimation (Class II) – Statistical Weight Estimation (As a starting point or to confirm class I analysis) – General Elements: • No closed loop formulation for major weight components (i.e. wing, fuselage, empennage,…). • Major components are formulated as functions of TOGW (Takeoff Gross Weight), So iterations are necessary to solve weight equations. • Weight figures constantly change during design phases. • Calibration is often necessary to ensure quality of the
Example of Weight Tables
Example of Weight Results
Weight of the aircraft was reduced From ~139000 lbs. to 135700 lbs. over 4 iterations.
Mass Distribution & C.G. Location
– Mass distribution (i.e. location of the Center of Gravity) determines the general longitudinal location of wing installation. – C.G. Travel should be limited to a small number – It is generally desired to have heavy non verifying items (such as engines) installed in mid-fuselage range. Compromises could be made in favor of noise.
Example of CG Location & Travel
– Exterior geometry of Tranquillus
Example of CG & Landing Gear
– Case study of Aquila Transient Trainer Jet
– Case study of the Phoenix Flyer
Moment of Inertia
– It is a measure of distribution of mass with respect to the location of center of gravity. – It is also a measure of tendency of the aircraft to resist rotation about any of it’s principal axis:
Estimation of Moment of Inertia:
– Could be estimated using empirical methods:
I xxB =
2 w
b Wgross R
2 x
4g
2
I yy B =
L Wgross R 4g
2 z
2
I zz B =
2 z
e Wgross R 4g
– Where Radiuses of Gyration (Rx , Ry , Rz ) are computed via statistical data. – Parameter e however is a geometric parameter:
bw + L e= 2 – Moment of Inertia is estimated in detail after the configuration is fixed and interior arrangement is determined
Initial Sizing & Optimization Sizing Charts & Carpet Plots
Preliminary Sizing: – Performed to estimate basic parameters to satisfy all performance requirements Simultaneously. – The two most important parameters to be influenced by performance requirements are the Wing Reference area Sw and the required Takeoff Thrust TTO of the engines. – It can be done in two different ways: • By Numerical Iteration (Jetsizer) – Basically varying the wing area and thrust of the engine in a performance model until all performance requirements are satisfied. • By Sizing Charts & Regulation Requirements (AAA) – Solving the performance equations & plotting the results…more on that after carpet plots
Concept of Sizing Chart – Solving the performance equations, it is possible to obtain solutions for wing area and engine thrust that are adjusted for the weight of the aircraft. – The intermediate sizing parameters are: • Wing Loading (Weight/Wing Area) • Thrust to Weight Ratio ( Net Thrust/Takeoff Weight)
– Analysis is usually performed to size for the following requirements: • • • •
Stall Speed (2 case of: 1-Clean 2-with flaps extended) Takeoff Distance Landing Distance Maximum Cruise Speed
– Sizing Charts are an irregular case of carpet plots.
Example: Sizing Chart Construction – Sizing for Stall Speed…
Example: Sizing Chart Construction – Sizing for Takeoff Distance Added…
Example: Sizing Chart Construction – Sizing for Maximum Cruise Speed Added…
Example: Sizing Chart Construction – Sizing for Landing Distance Added…
Example: Final Results for Aquila – Desirable Region is Hatched, Design Point Selected
Example: Final Results for Tranquillus – Desirable Region is Hatched, Design Point Selected
– Note that this needs to be updated as design
Concept of Carpet Plots – A technique to represent two functions of two separate variable simultaneously:
Example of application of Carpet Plots – Fuel Burn & Max Takeoff Gross Weight are plotted by changing AR and Sweepback Angle of the wing:
Example of application of Carpet Plots& Operational Empty – Max Takeoff Gross Weight
Weightare plotted by changing AR and Sweepback Angle of the wing:
Simplified Aircraft Sizing Tool Exploring Jetsizer
Configuration for efficiency Group Assignments
Group Assignments: – Assignments are to be done in 4 groups. – Each overtake one of the configurations numbered 1-4. – Each group will have 2 Excel Files: • 1- Jetsizer: Performing the calculations (Different for each group) • 2- Carpet Plot File (Same for all groups) – Each Group is tasked with performing two similar trade studies on each airplane. – Please Contact Sina if you have any questions. – Shouldn’t take more than 1 h to complete
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Questions?