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@mkeeter
Created Dec 13, 2016
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# Sage code to generate NACA airfoil equations
import operator
var('x, y, xc, m, p')
def run(y_chord):
g_chord = vector([1, derivative(y_chord(xc), xc)])
pos_pt = vector([x, y])
pos_chord = vector([xc, y_chord(xc)])
delta = pos_pt - pos_chord
print delta.dot_product(g_chord) == 0
sols = solve(delta.dot_product(g_chord) == 0, xc)
return expand(sols[1].op[1])
def to_prefix(expr):
if expr.operator() == None:
if str(expr) == 'I':
return '0'
return str(expr)
children = " ".join(map(to_prefix, expr.op))
f = {operator.add: "+",
operator.sub: "-",
operator.pow: "expt",
operator.mul: "*"}[expr.operator()]
return "(%s %s)" % (f, children)
def to_func(y_chord):
return """ (define (yc x)
%s)
(define (xc x y)
%s)
(lambda (x y)
(let ((x (xc x y)))
(values x (yc x))))""" % (to_prefix(y_chord(x)),
to_prefix(run(y_chord)))
y_chord_a = lambda x: m * (2*x/p -(x/p)^2)
y_chord_b = lambda x: m / (1-p)^2 * (1-2*p + 2*p*x - x^2)
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