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Aircraft Parametric Geometry via Blender & Python, 2015

– Trigonometric Method J. Philip Barnes 22 Feb 2015

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Objective, rationale, and study topics

Objective:Define (initially) airfoil geometry with trigonometric functions

Trig. functions are simple, powerful, and computationally efficient

Rationale:Return to basics before implementing more-sophisticated methodsTheory before application to enhance understanding & outcome

Study topics (see next slide):Generate library of modified trigonometric shapesParametrically approximate a given airfoil via X(u) and Z(u)Solve for the leading-edge-radius-to-chord ratio (R = r/c)Include finite trailing edge thickness Consider user inputs and interface to assist and/or automate

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Trig parametric airfoil parameters

x = 1-(1-g)Sin(pu)+ g Sin(3pu)' Z = haLf_edge * (1 - 2 * u) _ + Ziu * Sin(Pi*(1 - u)^eiu) _ - ZiL * Sin(Pi*(0 + u)^eiL) _ - Zcu * Sin(Pi*(1 - u)^ecu) _ + ZcL * Sin(Pi*(0 + u)^ecL) _ + bbb * Sin(Pi * u) _ + dZf * Sin(twoPi * u)

cusps: Low-amplitudeupper/lower inchwormwith high-exponent

Option 3:“g” adder shiftsmax thickness aft

Option 2:upper & lower“Inchworms”(not to scale)

Option 1: Sinewave backbone

uMicrosoft Excel

Macro-Enabled Worksheet

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Trig parametric airfoil example 1 ~ basic half/full sine wave

simple half wave

simple full wavefinite trailing edge

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Trig parametric airfoil example 1A ~ upper/lower inchworms

“old fashioned” max thickness location ~ next up: move thickness aft

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Trig parametric airfoil example 2

afterbody too thick ~ next up: apply upper/lower “cusps”

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Trig parametric airfoil example 3

modern thickness distribution ~ next up: apply camber

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Trig parametric airfoil example 4

contemporary shape ~ next up: reduce pitching moment

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Trig parametric airfoil example 5

high-performance laminar foil, cM < 0 ~ next up: zero pitching moment

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Trig parametric airfoil example 6 ~ Cm=0

zero lift angle and pitching moment largely set by last 5% of meanline

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Leading edge radius calculus study

Microsoft Excel Macro-Enabled Worksheet

Prove: R= r/c = (dZ/du)2/(d2X/du2) @ u=0.5Thus: dZ/du=[R d2X/du2]0.5 @ u=0.5

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Parametric Fuselage – trig. approximation

Microsoft Excel Macro-Enabled Worksheet

cubic-spline basis

Trig. functions provide 99% desiredresult with just 1% of computation

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Sample Application of Method: “Regenosoar”

C:\Users\Philip\graphics\Blender\regen.bl