Air Loads. Airfoil Geometry. Upper surface. Lower surface
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1 AE1 Jha Loads-1 Air Loads Airfoil Geometry z LE circle (radius) Chord line Upper surface thickness Zt camber Zc Zl Zu Lower surface TE thickness Camber line line joining the midpoints between upper and lower surfaces. Chord line straight line joining end points of camber line (length=c) Camber max. distance of camber line from chord line (expressed as %c; usually less than 5%c) Zu=(Zc+Zt) Z l =(Zc Zt) TE
2 Forces and Moments l m F d V F Angle of attack f (, M, R ). V For air foil, Lift co efficient N Drag co efficient Pitching moment coefficient S S c1( unit span) C l C d 1 l Vc d qc Arbitrary ref. pt. (generally c/4 or cg) C l qc m m qc l lift F cos d drag Fsin m pitching moment AE1 Jha Loads-
3 AE1 Jha Loads-3 Wing Planform c /4 ¼ chord line s=b/ Cr y LE LE C(y) TE Ct Aerodynamic characteristics generally based on gross wing area (assumed extended up to fuselage centerline) Exposed wing (only outside fuselage) area used for skin friction drag b b b / b S ( c c) c( y) dy c (1 ) wing r t r 0 Wing aspect ratio, A Wing taper ratio, c / c t b S wing r
4 AE1 Jha Loads-4 Mean Aerodynamic Chord Mean Aerodynamic Chord (MAC), b / c ( y) dy b/ 0 c b / c ( y) dy c 0 0 cydy ( ) b/ b 1 y ( ) ( ) mac c y ydy 0 S 6 1 ( Aerodynamic center at (1/4) c for subsonic M ) S 3 r 1 1 Wash in tip Wing twist along span Wash out Root Root tip + y/s=1.0
5 AE1 Jha Loads-5 The V n Diagram (Flight Envelope) A CL max boundary Stall area Vs, 1 g 3 1 B V* +7.5 Positive limit load factor 150 V4 300 Vcruise 450 V5 C Max q Max. speed boundary. M = 0.85 approx. Ve (knots) Stall area CL max boundary 3.0 E Negative limit load factor D V n (velocity-load factor) diagram for a typical Jet Trainer (1 knot = 1.15 mph)
6 AE1 Jha Loads-6 V n Diagram Limit load is the safe limit up to which there is no permanent deformation Ultimate load factor Structural failure occurs when n>nultimate V n (velocity load factor) diagram includes both aerodynamic and structural limitations and establishes maneuver boundaries. Curve A B: aerodynamic limit on load factor, imposed by (CL)max 1 ( C ) L max n V max W / S Pt1 C C, n n L Lmax Pt C C, n n L Lmax max max Pt 3 Outside flight envelope As V increases, n possiblealsoincreases( V ) max 4
7 AE1 Jha Loads-7 V n Diagram Horizontal line B C: Positive limit load factor of the structure 1/ n W AtV V wherev C C C S Lmax max *, *, L Lmax Line C D: high speed limit set by maximum dynamic pressure (design dive speed, VCD) At higher speeds, undesirable instabilities (like flutter, aileron reversal, divergence, buffeting etc.) may occur. VCD =1.5 x Vmax,cruise (max. cruise velocity) (FAR part 5 airplanes) For supersonic aircraft, (Vmax/a sl ) = Max. Mach no. in level flight + 0. (a=speed of sound)
8 AE1 Jha Loads-8 V n Diagram Maneuver pt. B: CL and n are simultaneously at their highest possible values. Highest Instantaneous Turn Rate (V*=corner velocity) 1 SL SL V e 1 V Sea level density; V Equivalent air speed ( EAS) e density at flight altitude; V Trueair speed ( TAS) Curve A E: Negative CLmax limit (flow separation from bottom surface) Line E D: Negative limit load factor (Why different from the positive nmax? skin thickness)
9 AE1 Jha Loads-9 Air Load Distribution on Lifting Surfaces Use high (CL max) limit and max q limit points for load calculations on wings. Spanwise lift distribution is proportional to the circulation at each span station. For an elliptical planform, lift distribution is elliptical. For nonelliptical wings, use Schrenk s approximation (semi empirical) to estimate lift distribution ( Load distribution on a wing is the average of actual planform shape and an elliptic shape of the same span and area. ) y Trapezoidal : c( y) Cr 1 (1 ) b elliptic 4S y Elliptical : c( y) 1 average b b Wing planform Rectangular planform Schrenk s method is not applicable to highly swept wings (such as delta wings) due to vortex flow
10 AE1 Jha Loads-10 Shear Forces and Bending Moments Beam (wing) with distributed load Support shear reaction shear Support moment reaction Compression Tension Ultimate Load on each wing, L w ( W * n*1.5/ ) moment
11 AE1 Jha Loads-11 Shear Forces and Bending Moments For any span station, the shear force is simply the sum of the vertical loads outboard of that station (or, the integral of distributed load) Bending moment at any station equals the sum of product of load at each outboard station and its distance from the station For a positive Bending Moment (as shown in the figure), the internal forces produce compression on upper part and tension on lower part Wing weight is proportional to. Halving (t/c) increases wing weight by 41%. Wing weight is typically 15% of total empty weight of aircraft Add fuel weight to empty wing weight to obtain gross wing weight Chordwise lift distribution may be approximated as shown below 1 t/ c actual Approx c 1.0 c
12 AE1 Jha Loads-1 SF, BM, Torsion Calculation (1) Pick load cases from V n diagram (max AoA, max dynamic pressure, max. negative AoA, etc.) () Calculate total lift force (approx. normal force); Load on each wing, L w ( W * n*1.5/ ) (3) Approx. wing as strips from center line totip (e.g., 10 strips of of 10% semi span each) (4) Distribute lift force on each strip using Schrenk s approximation (6) Estimate shear force and bending moment (7) Use wing center of pressure at 5% chord (subsonic speeds) (8) Using same strips as in (3), calculate torque about front spar location (say, 15% chord). Then sum torque values from tip to root
13 AE1 Jha Loads-13 Example - SF, BM, Torsion Calculation Rectangular wing: chord = 0.5 m, span = 4 m, TOGW = 5,000 N, nmax = 4 Wing area = sq m, AR = b/c =8 Calculate total lift force (approx. normal force) on each wing: L w ( W * n*1.5/ ) =15,000 N (Ultimate load on each wing) Distribute Lw along wing span using strips of equal width Use 3 strips for this example problem Chord for elliptical wing 4S y 4() y y cy ( ) b b (4) 4 y-station Wing chord, c Elliptical c(y) Average chord
14 AE1 Jha Loads-14 Example - SF, BM, Torsion Calculation Distribute lift force on each strip using Schrenk s approximation Calculate strip area = (Average of geometric and elliptical chord)*width = Average chord*0.667 Calculate factor for lift distribution: Lw = (factor)*(sum of strip areas) 15,000 N = (factor)*(0.965 sq m) factor = 15,544 N/sq m Strip Strip area Lift on each strip N N N
15 AE1 Jha Loads-15 Example - SF, BM, Torsion Calculation Estimate shear force and bending moment SF at any y station = sum of lift force outboard of y station BM at any y station = sum of (lift force * distance) outboard of y station For calculating distance, assume lift acting through the center of strip width y-station Shear Force, N Bending Moment, N-m ( ) ( ) Calculate torque about 15% c using wing center of pressure at 5% c (good approximation at subsonic speeds); sum torque values from tip to root Strip Torque, N-m ( ) ( )
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