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Intro to Aerodynamics - Learning Objectives -. At the end of this talk you will be able to: Answer the question “ How do the disciplines of structures & materials, aerodynamics and propulsion jointly set the performance of aircraft, and what are the important performance parameters? ”
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Intro to Aerodynamics- Learning Objectives - At the end of this talk you will be able to: • Answer the question “How do the disciplines of structures & materials, aerodynamics and propulsion jointly set the performance of aircraft, and what are the important performance parameters?” • Estimate the performance of aircraft using empirical data and thus begin to develop intuition regarding important aerodynamic, structural and propulsion system performance parameters • Explain wind tunnel scale testing • Become familiar with typical drag behavior for representative shapes
A MATHEMATICAL MODEL OF THE PHYSICAL SYSTEM Assumption: Level flight at steady speed V L (Lift) Weight of aircraft changes in response to fuel burned T (Thrust) D (Drag) V How can we integrate this to determine how long it takes to burn all of the fuel? W (Weight)
SOME IMPORTANT PARAMETERS Propulsive system efficiency: Thus, These parameters are fairly constant during steady level flight Aerodynamic efficiency: Lift-to-drag ratio = L/D
MANIPULATING THE EQUATION Rewriting using the important design parameters: Rearranging and integrating with initial and final conditions: Integrating from the initial to final conditions:
THE BREGUET RANGE EQUATION propulsion system efficiency fuel energy/mass Fuel + payload + structural weight aerodynamic efficiency payload + structural weight
AERODYNAMIC EFFICIENCY TRENDS Babikian, Raffi, The Historical Fuel Efficiency Characteristics of Regional Aircraft From Technological, Operational, and Cost Perspectives, SM Thesis, Massachusetts Institute of Technology, June 2001
Boeing 747-400: Range Estimate • From the published data: • Assuming that all fuel is burned: • From published data: • Assume initial weight is MTOW (max take-off weight) • The Breguet range equation gives: • Published data gives B747-400 range as 13,400 km
Boeing 747-400: Sensitivity Analysis • Suppose that the design goals are not met, e.g. L/D is 1% lower than initial design goal • Consider the scenario that the airplane has been built so that the fuel tanks cannot be increased (fuel weight is fixed), the empty weight is fixed, etc. • Further, as the airplane has been designed with a specific range in mind, the range is fixed (e.g. the B747-400 has to be able to fly 12,700km). • The only option is to reduce payload until the range can be met at the reduced L/D. • Question: What is the impact on the payload weight? • For L/D = 17, a 1% decrease is d(L/D) = -0.17 • What is the • Breguet range equation gives:
Boeing 747-400: Sensitivity Analysis Given the operating empty weight (OEW) = 179,000 kg and the average passenger (including baggage) weight is 90 kg: A 1% decrease in L/D results in ~30 passengers decrease in allowable payload at max range
Aerodynamic Design • Aerodynamic design combines wind tunnel testing with computational modeling • Error in computational approaches exist because: • Partial differential equations being solved have modeling error (turbulence modeling) • Computational solutions include discretization errors • Recent studies have shown that modeling and discretization errors are equally important • Error in wind tunnel approaches exist because: • Scale errors (i.e. tunnel model is not at exactly same conditions as actual aircraft) • Wind tunnel wall effects distort flow from atmospheric flight
Wind Tunnel Scale Testing • Wind tunnels rely upon scale testing (technically called flow similarity) • Consider the drag on an aircraft as being dependent upon a handful of parameters:
Drag Coefficient • Define a non-dimensional drag quantity, the drag coefficient: • Now, the drag coefficient is dependent on non-dimensional parameters
