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Four-seat light aircraft by the vortex-lattice method: trim, span loading, drag polar, neutral point and stability derivatives with and without the fuselage

Tool	Vortex Lattice Analysis
Source	Margason, R. J., and Lamar, J. E. (1971). Vortex-Lattice FORTRAN Program for Estimating Subsonic Aerodynamic Characteristics of Complex Planforms. NASA Technical Note D-6142, National Aeronautics and Space Administration, Washington, DC. Hough, G. R. (1976). "Lattice Arrangements for Rapid Convergence." In Vortex-Lattice Utilization, NASA SP-405, National Aeronautics and Space Administration, Washington, DC, pp. 325–342. The aircraft is illustrative; the two reports are the sources the method is verified against.
Level	Graduate

Problem

An illustrative low-wing four-seat aircraft (wing, horizontal tail, fin and fuselage, described by spans, chords, taper, sweep and positions) flies level at 55 m/s and 1,000 m with a mass of 1,100 kg and the centre of gravity 2.20 m aft of the nose. Trim it with the elevator and find the lift, induced and total drag, span efficiency, the neutral point and static margin with and without the fuselage, the stability derivatives, the stall-onset speed and the maximum lift-to-drag ratio.

Inputs to Enter

Wing: span 11 m, root chord 1.63 m, taper ratio 0.693, unswept quarter-chord line, dihedral 5°, root incidence 2°, tip twist −3°, NACA 2412 camber line, root leading edge at x = 1.75 m, z = −0.35 m; aileron over the outer 40 % of the semi-span with 25 % chord
Horizontal tail: span 3.4 m, root chord 0.95 m, taper 0.684, sweep 2.5°, incidence −1.5°, root leading edge at x = 6.0 m, z = 0.25 m, elevator 40 % chord; fin: height 1.45 m, root chord 1.2 m, taper 0.5, sweep 22.5°, root at x = 5.75 m, z = 0.3 m, rudder 40 % chord
Fuselage: length 7.3 m, maximum diameter 1.2 m, nose 1.8 m, tail cone 4.3 m, drag area 0.14 m², wing carry-over on
55 m/s at 1,000 m (ρ = 1.1117 kg/m³, Mach 0.163); mass 1,100 kg, c.g. at x = 2.20 m, z = −0.10 m; section c_l,max 1.5, strip polar c_d = 0.0075 + 0.006 (c_l − 0.2)²; normal lattice density (278 panels)

Open the Vortex Lattice Analysis tool (loaded with this example)

Answers

Reference area 15.178 m², mean aerodynamic chord 1.3949 m, aspect ratio 7.97 (closed forms of the tapered wing)
Trim: α = 2.206°, elevator +3.664°; C_L = 0.4227, Trefftz-plane C_Di = 0.00726, span efficiency e = 0.957, total C_D = 0.02628, L/D = 16.08
C_Lα = 5.504 per rad; neutral point at x = 2.380 m, static margin 12.9 % of c; without the fuselage 2.482 m and 20.2 %: the fuselage moves the neutral point 0.102 m forward and lowers C_nβ by 0.0525
About the c.g.: C_mα = −0.700, C_nβ = +0.0184, C_lβ = −0.0710, C_lp = −0.508, C_mq = −11.85, C_nr = −0.0580: statically stable in pitch, yaw and roll
Stall onset on the wing at 16 % of the semi-span: α = 11.40°, C_L = 1.289, 31.5 m/s (61.2 kt); maximum L/D = 17.63 at C_L = 0.647 (44.5 m/s); wing-root shear 5,578 N and bending moment 12,449 N·m

Notes

The tool's default inputs are this case (the Conventional template in simple mode); press Submit. The numbers are the tool's own solution of an illustrative aircraft, not a printed example. The solver is checked by test_vortex_lattice.php (13,781 checks) against NASA SP-405 (rectangular wing of aspect ratio 2, p. 328: C_Lα 2.4743 against 2.474; Warren-12 planform, pp. 330–331), NASA TN D-6142 sample cases 5 to 7 (within 0.1 to 1.5 %), NACA TM 77 (ground effect) and an independent numpy implementation; the page by test_vortex_lattice_page.php (584 checks: every template, analysis kind, the grids, AVL import and the derivative set read by the Aircraft Stability Analysis tool). Linear inviscid theory: profile drag and stall enter only through the entered section values, and the fuselage terms are slender-body estimates.