Team 5 Aerodynamics PDR 2 November 18 2003

Team 5 Aerodynamics PDR #2 • • November 18, 2003 Scott Bird Mike Downes Kelby Haase Grant Hile Cyrus Sigari Sarah Umberger Jen Watson Aero PDR #2 1

Preview • Airfoil Sections and Geometry • Aerodynamic mathematical model • Launch Conditions • Endurance November 18, 2003 Aero PDR #2 2

Walk-Around Data Boom Conformal Pod Engine Landing Gear November 18, 2003 Aero PDR #2 3

Aircraft 3 -view November 18, 2003 Aero PDR #2 4

Wing Geometry • Wing – – – – Airfoil Aspect Ratio Span Chord Planform Area Taper Ratio Dihedral Sweep Angle November 18, 2003 NACA 2412 7 14 (ft) 28 (ft^2) 0 (deg) Aero PDR #2 5

Horizontal Tail Geometry • Horizontal Tail – – – – Airfoil Aspect Ratio Span Chord (average) Planform Area Taper Ratio Sweep Angle November 18, 2003 NACA 0012 5 7 (ft) 1. 38 (ft) 9. 64 (ft^2) 0. 8 5 (deg) Aero PDR #2 6

Vertical Tail Geometry • Vertical Tail – – – – Airfoil Aspect Ratio Span Chord (average) Planform Area Taper Ratio Sweep Angle November 18, 2003 NACA 0012 2 2. 8 (ft) 1. 38 (ft) 3. 9 (ft^2) 0. 73 10 (deg) Aero PDR #2 7

Lift Methodology • Used XFOIL to get NACA 2412 2 -D data – Converted 2 -D data to 3 -D data for wing CLo and CLα • Used XFOIL to get NACA 0012 horizontal tail data – Used method described in Roskam Part VI, CH 8 for CLδe November 18, 2003 Aero PDR #2 8

Aerodynamic Mathematical Model of Lift • CL= CLo + CLα * α + CLδe * δe • CLα = Cl α / (1 + (Cl α / (π * e * A))) [rad-1] • CL = Cl * (CLα/Cl α) • CLδe = CLα_ht * ηht * Sht / Sref * τe [rad-1] – ηht = f (Sht_slip, Sht, Pavailable, U, Dp, qbar) – (Roskam Part VI, CH 8) November 18, 2003 Aero PDR #2 9

Aerodynamic Mathematical Model of Drag • Summation of individual components for CDo – Wing, fuselage, horizontal tail, vertical tail • CD=CDo + k * CL • CDo = Σ CDo(i) November 18, 2003 CDo_wing CDo_horizontal tail – CDo(i) = (Cf * FF * Q * Swet) / Sref • k = 1 / (pi * AR * e) CDo(i) CDo_vertical tail CDo_fuselage CDo_total Aero PDR #2 0. 01 04 0. 00 39 0. 00 13 0. 02 04 0. 03 6 10

Moment Methodology • Used method described in Roskam, Chapter 3 of AAE 421 Book to find individual components of moment equation November 18, 2003 Aero PDR #2 11

Aerodynamic Mathematical Model of Moments • CM = CMo + CMα * α + CMδe * δe – (α and δe in degrees) • CM 0 = Cmac_wf + CL 0_wf*(xbar_cg - xbar_acwf) + CLalpha_h*eta_h*(S_h/S)*(xbar_ach - xbar_cg)*epsilon • CMalpha = (x/cw)*CLalpha_wf*(xbar_cg - xbar_acwf) CLalpha_h*eta_h*(S_h/S)*(xbar_ach - xbar_cg)*(1 – depsilon/dalpha) • CMdele = -CLalpha_h*eta_h*Vbar_h*tau_e November 18, 2003 Aero PDR #2 12

Aerodynamic Mathematical Model Summary • CL= 0. 1764 + 7. 941 (rad-1)* α + 1. 925 (rad-1)* δe – α and δe are in radians • CD =. 036 +. 0522 * (. 1764 + 7. 941 (rad-1) * α)2 • Cm= - 0. 0280 - 0. 1562* α - 0. 0898* δe November 18, 2003 Aero PDR #2 13

Launch Conditions Known Values • W = 49. 6 lbs • S = 28 ft 2 • ρ = 0. 0023328 slug/ft 3 (at 600 ft) • CLmax: To = 0. 8*CLmax = 1. 44 • VTO = 39 ft/s November 18, 2003 Aero PDR #2 14

Launch Conditions from EOM Normal Drag Our Airplane Friction November 18, 2003 Thrust Weight Aero PDR #2 15

Launch Conditions from EOM integration • STO = 76 ft – Constriant of 127 ft • t. TO = 3. 7 s November 18, 2003 Aero PDR #2 16

Endurance Known Values • Bhp = 3. 7 hp • ηp = 0. 40 • Cbhp = 0. 0022 lb/s-hp • Wi = 49. 6 lbf • Wf = 43. 6 lbf – Using 1 gallon @ 6 lbf • L/D = 10. 39 • 12*. 866 (86. 6% of L/Dmax when flying @ Vmin power) November 18, 2003 Aero PDR #2 17

Endurance • V = [2*W/( ρ*S)*(K/(3*CDo))1/2] ½ • (Raymer, eq 17. 33) – K = 1 / ( pi * AR * e ) – Vmin@min power = 32. 5 ft/s • E = (L/D)*[(550*ηp)/(Cbhp*V)]*ln(Wi/Wf) • (Raymer eq 17. 31) E = 75. 5 minutes November 18, 2003 Aero PDR #2 18

Future Work • Resize flaps for landing • Verify known values – Cbhp • Weight reduction from extra fuel (Endurance) November 18, 2003 Aero PDR #2 19

Review of Today’s Presentation • Wing Geometry and Size • 3 -view of aircraft • Aerodynamic mathematical model • Launch Conditions • Endurance November 18, 2003 Aero PDR #2 20

Questions? ? November 18, 2003 Aero PDR #2 21

References • Roskam – AAE 421 Book • Raymer – Aircraft Design: A Conceptual Approach • AAE 251 Book – Introduction to Aeronautics: A Design Perspective November 18, 2003 Aero PDR #2 22

Putting EOMs into MATLAB • Put state space EOMs into MATLAB • Used ode 45 command to integrate EOMs • Inputs to the code are initial conditions for position and velocity – Used x(0) = 0. 1 ft and v(0) = 1 ft/s to eliminate singularities • Code output position and velocity as a function of time November 18, 2003 Aero PDR #2 23

EOM file in MATLAB November 18, 2003 Aero PDR #2 24

November 18, 2003 Aero PDR #2 25