Estimation of Performance Airspeeds for High-Bypass Turbofans Equipped Transport-Category Airplanes
Journal of Aviation Technology and Engineering
Estimation of Performance Airspeeds for High-Bypass Turbofans Equipped Transport-Category Airplanes
Nihad E. Daidzic
AAR Aerospace Consulting
Conventional Mach-independent subsonic drag polar does not replicate the real airplane drag characteristics exactly and especially not in the drag-divergence region due to shock-induced transonic wave drag. High-bypass turbofan thrust is a complicated function of many parameters that eludes accurate predictions for the entire operating envelope and must be experimentally verified. Fuel laws are also complicated functions of many parameters which make optimization and economic analysis difficult and uncertain in the conceptual design phase. Nevertheless, mathematical models and predictions have its important place in aircraft development, design, and optimization. In this work, airspeed-dependent turbofan thrust and the new fuel-law model were used in combination with an airplane polynomial drag model to estimate important performance speeds. Except for the airframe-only dependent control airspeeds, all performance speeds are airframepowerplant dependent. In all analytical considerations one ends up with polynomials of the 4th order that have no closed-form solutions. A real positive-root seeking numerical procedure based on the family of Newton-Raphson methods was used to extract performance airspeeds for variable in-flight weights and altitudes in the ISA troposphere. Extensive testing of the accuracy and convergence of the Newton-Raphson nonlinear equation solvers was conducted before performance speed calculations. A fictitious long-range wide-body transport-category airplane was modeled in combination with a pair of high-bypass and ultra-high bypass ratio flat-rated turbofans. Procedure employed here can be easily extended to cases when fitted, measured drag and thrust data is given in arbitrary polynomial forms. Sensitivity analysis is performed on minimum-drag airspeed and maximum aerodynamic efficiency. Transonic wave drag considerations are introduced.
Transport-category airplane; High-bypass turbofan; Thrust; Fuel law and TSFC; Drag polar; Performance airspeeds; Newton-Raphson nonlinear equation solvers; Transonic wave drag
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About the Authors
Dr. Nihad E. Daidzic is president of AAR Aerospace Consulting, LLC. He is also a full professor of aviation, adjunct professor of mechanical
engineering, and research graduate faculty at Minnesota State University. He has a PhD in fluid mechanics and ScD in mechanical engineering. He was
formerly a staff scientist at the National Center for Microgravity Research and the National Center for Space Exploration and Research at NASA Glenn
Research Center in Cleveland, OH. He has also held various faculty appointments at Vanderbilt University, University of Kansas, and Kent State
University. His current research interest is in theoretical, experimental, and computational fluid dynamics; micro- and nano-fluidics; aircraft stability,
control, and performance; and mechanics of flight, piloting techniques, and aerospace propulsion. Dr. Daidzic is ATP and ‘‘Gold Seal’’ CFII/MEI/CFIG
certified with flight experience in airplanes, helicopters, and gliders.
Introduction
In order to optimize airplane operation and predict its
performance in the conceptual design phase, early estimates
of control and performance airspeeds are important. Much of
the aircraft field and cruise performance capabilities depend
on the set of control and performance airspeeds, such as,
rotation, takeoff safety, climb, maximum- and long-range
cruising, and reference landing speeds. Pilots essentially fly
airplanes by reference to set of optimum airspeeds. Best
flight practices depend much on the ability of pilots to
maintain set airspeeds optimized for each phase of flight.
Completed aircraft prototypes must undergo
experimental verification before being certified. Aircraft
manufacturers obtain such specific information by performing
numerous repetitive, tedious, and expensive flight tests
(Daidzic, 2013; FAA 2011)
. Flight testing campaigns do
not normally contribute much to understanding of flight
physics, but are a required step toward particular airplane
certification
(EASA, 2007; FAA, 2013; JAA 2007)
.
Indeed, all limitations, control, and gross performance
figures entering approved airplane operational/flight
manuals (Airplane Flight Manual and Flight Crew Operations
Manual) must be based on measured data
(Daidzic, 2013;
Eshelby 2000)
. Airframe and engine characteristics cannot
be presently modeled and simulated with fidelity,
reliability, and accuracy required to substitute measured test
data for certification purposes
(Eshelby, 2000)
.
Although validation of analytical and computational
calculations and wind-tunnel scale experiments must be
verified during flight tests, nevertheless, the analytical
methods provide deeper understanding of the fundamental
flight physics and enable local an (...truncated)