Drag Computation
The Importance of drag Its effects on aircraft performances On the Concorde, one count drag increase (ΔC D =.0001) requires two passengers, out of the 90 ~ 100 passenger capacity, be taken off the North Atlantic run. A drag decrease is equated to the decrease in aircraft weight required to carry a specified payload for the required distance. One advanced fighter study found the drag sensitivity in supersonic cruise was 90 lb/ct and 48 lb/ct for subsonic and transonic cruise.
The Importance of drag For one executive business jet the range sensitivity is 17 miles/drag count. Advanced supersonic transports now being studied have range sensitivities of about 100 miles/drag count. Conclusion A minor changes in drag can be critical!
The Importance of drag Its effects on the company The economic viability and future survival of an aircraft manufacturer depends on minimizing aerodynamic drag while maintaining good handling qualities to ensure flight safety and ride comfort. A company was willing to invest $750,000 for each count of drag reduction. Examples: Boeing 767, 777 Airbus A340
The Importance of drag The designing for low drag and the ability to estimate drag is at the heart of aerodynamic design Initial drag estimates can dictate the selection of a specific configuration concept in comparison with other concepts early in the design phase. The drag projections have a huge effect on the projected configuration size and cost, and thus on the decision to proceed with the design.
Issues on Drag Drag cannot yet be predicted accurately with high confidence levels (especially for unusual configuration concepts) without extensive testing. No one is exactly sure what the ultimate possible drag level really is that can be achieved for a practical configuration. To this extent, aerodynamic designers are the dreamers of the engineering profession.
The efforts on drag estimation and reduction Conferences Aerodynamic Drag, AGARD CP-14, 1973. Aircraft Drag Prediction, AGARD-R-73, 1985. Drag Reduction Techniques, AGARD-R-787 AIAA CFD Drag Prediction workshop, 001 AIAA progress series book Thrust and Drag: Its Prediction and Verification, AIAA, New York, 1985.
Objective of this chapter To introduce the key concepts required to use computational aerodynamics to evaluate drag.
Outline Nomenclature and Concepts Farfield Drag Analysis Induced Drag Zero Lift Drag Friction and Form Drag Estimation Supersonic Wave Drag Trim Drag Current Issues for Drag Calculation Using CA
Some Different Ways to View Drag - Nomenclature and Concepts Simple Integration Concept Consider the distribution of forces over the surface. pressure force shear stress force due to the presence of viscosity An integration over the surface results in an estimate of the drag. This approach is known as a nearfield drag calculation. Disadvantages This integration requires extreme precision remember that program PANEL did not predict exactly zero drag The results are difficult to interpret for aerodynamic analysis Exactly where is the drag coming from? Why does it exist, and how do you reduce it?
Fluid Mechanics: This viewpoint emphasizes the drag resulting from various fluid mechanics phenomena. This approach is important in conceiving a means to reduce drag. Providing a means of computing drag contributions in a systematic manner. friction drag form drag induced drag wave drag The term can be confusing!
Friction Drag The Terms on Drag Skin friction drag is caused by the actual contact of the air particles against the surface of the aircraft. depends mostly upon the wetted area. Form Drag ( Pressure Drag) caused by the separation of air that is flowing over the aircraft. Viscous separation drag which depends upon the location of the separation point on the body.
Parasite Drag Skin friction drag + Form drag Induced Drag Induced drag is the drag created by the vortices at the tip of an aircraft's wing. Drag forces are a strong function of lift. Wave Drag caused by the information of shocks at supersonic and high subsonic speeds. Wave drag is a form of pressure drag.
Aerodynamics: This approach combines the fluid mechanics viewpoint with more practical considerations. Thinking in terms of contributions from a variety of aircraft features. The basic contributions from each component must be included. individual component contributions to drag base drag Drag owing to a base pressure lower than the ambient pressure; it is a part of pressure drag. inlet drag with spillage boattail drag camber drag trim drag aeroelastic effects on drag
Performance: To calculate the performance of an airplane it is natural to define drag as the sum of the drag at zero lift and the drag due to lift. C D = C D 0 + C L πare Each term is a function of Mach number, Reynolds number (or altitude), and the particular geometric configuration (flap deflection, wing sweep, etc.). The value of the Oswald efficiency factor, E, is defined as a function of the lift coefficient and Mach number.
Performance: To take into account the effect of wing camber and twist, drag polar become asymmetrical about the C L = 0 axis. C D = C D + ΔC D + K( C 0 m m L C L )
A fluid mechanics refinement: transonic wave drag Transonic flow The wave drag arises at subsonic speeds when the flow accelerates locally to supersonic speeds, and then returns to subsonic speed through a shock wave. Drag divergence Mach number, M DD The Mach number at which the rapid drag increase occurs At drag divergence the additional transonic drag is divided between the explicit shock drag and the shock induced additional profile drag.
A fluid mechanics refinement: transonic wave drag Definitions of the drag rise Mach number dc D dm C L = conts. = 0.1 or ΔC D = 0.000 Details of wave drag increases at transonic speeds
An flight mechanics refinement: trim drag The requirement of steady flight can lead to control surface deflections that increase the drag. The cases of significant drag: The shift in the aerodynamic center location with Mach number for supersonic aircraft. The use of airfoils with large values of the zero lift pitching moment about their aerodynamic center The configurations with variable wing sweep
A practical aspect of aero-propulsion integration: thrustdrag bookkeeping The drag of the airframe is affected by the operation of the propulsion system a spillage drag the boattail drag over the external portion of the nozzle; Depend on the nozzle setting Approach thrust-drag bookkeeping.
Aerodynamic-structural interaction: aeroelastic effects on drag aerodynamic loads aerodynamic loads structure change of drag change of drag deformation
Farfield Drag Analysis Approach Estimate the drag on a body by considering the overall momentum balance on a control volume surface well away from the body. Advantage Less sensitive to the detailed calculations of surface pressure and integration of the pressures over the surface to obtain the drag.
Derivation (1) where q is the disturbance velocity vector Control volume for farfield drag evaluation.
Derivation () Using linearized flow relations and the small disturbance relations:
Derivation (3) The equation became: Where v r is the radial component
Derivation (4) The integral over I is zero as x -. The integral over II as x, corresponds to the so-called Trefftz Plane. The integral over III is the wave drag integral, which is zero for subsonic flow, and when any embedded shock waves do not reach III.
Drag Categorization & Farfield Drag Analysis Drag = friction drag + induced drag + wave drag + form drag 1 D = ρ [( M 1) u + v + w ] dydz ρ uvrrdθdx II III Farfield Drag Analysis
Consider the integral over II The induced drag integral 1 ρ [( M 1) u + v + D i = w ] dydz 1 ρ [ v + D i = w ] dydz Far downstream, u 0 Using Green s theorem II ( v + w ) ds φ = φ dc n c D i 1 = ρ φ φ dc n c
In this Trefftz plane, the integral vanishes around the outside contour as R and the integrals along AB and CD cancel. The only contribution comes from the slit containing the trace of vorticity shed from the wing. The value of φ is equal and opposite above and below the vortex sheet,and φ = w n
D i = b / 1 ρ ( Δφ) x= b / w dy Relation between φ and circulation Δφ x= = Γ(y) Using lifting line theory w x= ( y) = 1 π b / b / γ ( η) dη y η γ ( η) = d Γ / dy Relation between the trailing vorticity strength and the change in circulation D i ρ 4π b/ b/ = b/ b/ dγ( y dy 1 ) dγ( y dy ) ln y 1 y dy dy 1
D i ρ 4π b/ b/ = b/ b/ dγ( y dy 1 ) dγ( y dy ) ln y 1 y dy dy 1 Comments on this equation This result shows that the induced drag is a function of the Γ distribution (spanload) alone. The spanload distribution is responsible for the induced drag. Because of the double integral we can get the total drag, but we have lost the ability to get detailed distributions of the induced drag on the body. This is the price we pay to use the farfield analysis.
Drag Computation() Induced Drag Friction Drag Form Drag Wave Drag
Drag = friction drag + induced drag +wave drag + form drag 1 D = ρ [( M 1) u + v + w ] dydz ρ uvrrdθdx II III Farfield Drag Analysis
Induced Drag The induced drag is a function of the Γ distribution (spanload) alone. D i ρ 4π b/ b/ = b/ b/ dγ( y dy 1 ) dγ( y dy ) ln y 1 y dy dy 1
Induced Drag The three-dimensional flowfield over a lifting surface does result in a drag force, even if the flow is inviscid. This is due to the effective change in the angle of attack along the wing induced by the trailing vortex system. It is one part of the total drag due to lift and written as. C D i CL = π AR e e in this equation is known as the span e. How to evaluate e?
Determination of e D i ρ 4π b/ b/ = b/ b/ dγ( y dy 1 ) dγ( y dy ) ln y 1 y dy dy 1 representing as Γ a Fourier Series Γ = U b n= 1 A n sinθ and D i πρ U b = na 8 π L = ρ U 4 b n= 1 A 1 n where CD i = C L πar e 1 [1 + A e = n( A = n n 1 ) ]
where CD i = C L πar e 1 [1 + A e = n( A = n n 1 ) ] Comments These expressions show that e max = 1 for a planar lifting surface. If the slit representing the trailing vortex system is not a simple flat surface, and C di is based on the projected span, a nonplanar or multiple lifting surface system can result in values of e > 1.
Comments Induced drag is a function of circulation distribution alone, independent of Mach number except in the manner which Mach number influences the circulation distribution (a minor effect in subsonic and transonic flow). Given Γ, e can be determined by finding the A n s of the Fourier series for the simple planar wing case.
Program LIDRAG A simple Fourier analysis of the spanload to determine the e using a Fast Fourier Transform for single planar surfaces. For an elliptic spanload, the e is 1.0 For a triangular spanload, the e is 0.78. You can try other distributions of spanload
How to Make e Bigger Exploiting non-planar surface concepts such as winglets Canard configurations Using advanced wing tip shapes on nominally planar configuration.
Multiple Lifting Surfaces Munk's Stagger Theorem The induced drag of a multi-surface system does not change when the elements of the system are translated parallel to the direction of the flow, provided that the circulation distributions on the elements are left unchanged. The fore and aft positions of multiple lifting surfaces do not affect drag as long as the circulation distribution remains fixed.
Application of the theorem to aerodynamic design If the lifting elements are in the same plane, then the sum of the spanloads should be elliptic for minimum drag.
Zero Lift Drag (subsonic) Friction drag Form drag The importance of streamlining A wire and airfoil with the same drag
Zero Lift Drag (subsonic) Approach A typical turbulent flow skin friction formula (for one side of a flat plate surface only) is used to evaluate friction drag The form factor is used to account for effects due to thickness and additional trailing edge pressure drag.
Formulation C D 0 C F S S wet ref FF Form factor A turbulent flow skin friction C F = 1.455.58 [log Re] For planar surface t t FF = 1+ 1.8( ) + 50( c c For bodies d 1.5 d FF = 1+ 1.5( ) + 7( l l ) 4 ) 3
C D 0 C F S S wet ref FF Comments These simple formulas are used in conceptual design, and provide good initial estimates until more detailed calculations using the boundary layer methods. Some configurations can now take advantage of at least some laminar flow, with its significant reduction in friction drag. Advanced airfoils can have as much as 30 to 40% laminar flow.
Program FRICTION Computing the skin friction and form drag over each component, including laminar and turbulent flow. Including compressibility The input requires geometric information the Mach and altitude combination, or the Mach and Reynolds number Valid from subsonic to moderate supersonic speeds (about M3) Providing an estimate of laminar and turbulent skin friction suitable for use in aircraft preliminary design.
Wave Drag Drag = friction drag + induced drag + wave drag + form drag 1 D = ρ [( M 1) u + v + w ] dydz ρ uvrrdθdx II III Farfield Drag Analysis
Consider the integral over III D w = lim r ( ρ r π 0 dθ + uv r dx) If u,v r 0 as r then D w = 0 For the subsonic flow, D w = 0 For the supersonic flow _ ρ U = l l 0 0 '' D( θ ) w S ( x1) S ( x)ln x1 x dx1dx 4π '' Where S(x) the cross-sectional area distribution, and satisfies S'(0) = S'(l) = 0.
Consider the integral over III Comments on the wave drag integral The method is available in a program known as the Harris Wave Drag program. The Mach number doesn t appear explicitly. A refined analysis for bodies that aren t extremely slender extends this approach by taking slices, or Mach cuts, of the area through the body at the Mach angle. For non-axisymmetric bodies D w = 1 π π 0 D w _ ( θ ) dθ
1 0 1 '' 1 '' 0 _ )ln ( ) ( 4 ) ( dx dx x x x S x S U D l l w = π ρ θ where the S(x) values represent the area from an oblique (Mach angle) cut to find the cross section area of the aircraft at a specific theta. = π θ θ π 0 ( _ ) 1 d D D w w
l _ ρ U '' '' D( θ ) w = S ( x1 ) S ( x)ln x1 x dx1dx 4π 0 l 0 The importance of the distribution of the cross-sectional area To minimize the integral the area change should be very smooth. Low drag is achieved by minimizing the maximum crosssectional area. Increasing the fineness ratio decreases the wave drag.
Area rule Proposed by Richard Whitcomb at the NACA It states that the body should develop in a smooth fashion as the air moves around and along the body, with no sudden discontinuities. The total aircraft area distribution should form a smooth progression. For wing-body configuration, results in the distinctive area ruled, or coke bottle, fuselage shape.
The validity of area rule The key result obtained by Whitcomb The increase in drag for a wingbody combination
The famous application of the area rule YF-10, F-10, F-106 YF-10 When it first flew, the prototype is unable to break the sound barrier
F-10 The fuselage fineness ratio and area distribution had been increased and refined. The fuselage mid-section cross-sectional area had been reduced The cockpit canopy was reduced in cross-section with a near triangular cross-section The cockpit and the side-mounted engine inlets were moved forward to reduce their sudden area build-up, or impact on the fuselage area. The aft fuselage bustles ( 裙撑 ) were retained to avoid the rapid collapse of the cross-sectional area at the delta wing trailing edge. It was able to fly at low supersonic speeds (M = 1.).
Area ruling of F-10A airplane
Zero lift drag for the YF-10 and F-10A airplanes The resulting change in drag from the YF-10 to the F-10 was about 5 counts
F-106 The F-10 configuration was completely redesigned incorporating a more refined, integrated area rule. Further slimmed down by a reduced weapon bay capacity and shortened and repositioned engine air intake ducts, and powered by a fifty percent more powerful engine. It was capable of routine Mach + speeds.
Estimation of wave drag D w = 1 π π 0 D w _ ( θ ) dθ l _ ρ U '' '' D( θ ) w = S ( x1 ) S ( x)ln x1 x dx1dx 4 π 0 l 0 Harris wave drag program At each roll angle θ a number of x-cuts are made. Determining the cross sectional area distribution of the aircraft Evaluating the integral numerically. Typically, 50 to 100 x-cuts are made for each of from 4 to 36 θ values.
Estimation of wave drag Validation of the wave drag program
Examples: F-16 The revision is to improve the contour forward and aft of the maximum cross-sectional area to fill in the shape This is the original area distribution Small aircraft are much more difficult to lay out to ensure a smooth distribution of area.
Trim Drag surface lift requirements for trim
What is trim drag? Control surface deflections change the drag from the reference undeflected value. This difference in drag could be termed a trim drag.
Where trim drag comes from? For a given flight conditions the total lift must be fixed. Any change in lift on the trimming surface requires a change in lift on the primary surface. The change in lift on the primary surface will result in additional drag, i.e. trim drag.
Cases with Big Trim Drag Trim drag is especially important for several specific classes of aircraft. Supersonic aircraft A.C. shift from subsonic to supersonic flight. To control trim drag as well as stability, fuel is transferred fore and aft between subsonic and supersonic flight. Variable sweep wing aircraft Aerodynamic center locations vary with sweep Potentially leading to high values of trim drag The maneuvering aircraft high trim drag at high lift coefficients, severely limiting sustained turn performance.
Minimum drag for different configurations For aft swept wings aft tail configurations the minimum trimmed drag occurs at a slightly unstable center of gravity (5-10%). For canard configurations minimum trim drag at slightly more unstable conditions (15%). Forward swept wing canard configurations even more unstable to achieve minimum trimmed drag the X-9 is about 30-35% unstable
How to Reduce Trim Drag New configurations Innovative configurations for small trim drag Using stability and control augmentation systems Allowing the designers much more freedom in the choice of a center gravity location Controlling C.G. placement in a configuration
Canard Configuration Canard concept are often considered advantageous because both the canard and wing supply positive lift to trim.
Current Issues for Drag Calculation Improving the accuracy of drag computation for complex configurations How to reduce drag reducing drag due to lift tip shaping use of winglets tip sails reducing skin friction drag. laminar flow through passive means (NLF) suction using riblets to reduce turbulent friction reduction
Summary The importance of drag in aircraft design Nomenclature and Concepts Don t be confused by the all those terms! Far-field Drag Analysis Formulation Induced Drag Program LIDRAG Multiple Lifting Surfaces Zero Lift Drag: Friction and Form Drag Program: FRICTION.f Supersonic Wave Drag Trim Drag
Homework 4 Get a copy of FRICTION from Mason's web site. Repeat the check case in the user's manual. Select a aircraft and then examine its skin friction values by using the program FRICTION.
Input for Friction.f reference Area SCALE number of component Wetted Area t/c for planar surf. or d/l for body Reference Length Component type Mach number, Altitude (in 1000 feet) Transition location