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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 methods
Theory before application to enhance understanding & outcome
Study topics (see next slide):
Generate library of modified trigonometric shapes
Parametrically 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
cusps: Low-amplitude
upper/lower inchworm
with high-exponent
x = 1-(1-g)Sin(pu)+ g Sin(3pu)
'
Z
+
+
+
+
Option 3:
“g” adder shifts
max thickness aft
= 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)
_
_
_
_
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Option 2:
upper & lower
“Inchworms”
(not to scale)
Option 1: Sinewave backbone
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Trig parametric airfoil example 1 ~ basic half/full sine wave
simple half wave
finite trailing edge
simple full wave
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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
Prove: R= r/c = (dZ/du)2/(d2X/du2) @ u=0.5
Thus: dZ/du=[R d2X/du2]0.5 @ u=0.5
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Parametric Fuselage – trig. approximation
cubic-spline basis
Trig. functions provide 99% desired
result with just 1% of computation
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Sample Application of Method: “Regenosoar”
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