Calculating Offset Curves defined by NACA Formula The Next CEO of Stack OverflowCalculating Second Moment of Area of NACA AerofoilsIntersection of 3D curves parameterised by piecewise defined functionsProduct rule for curvespaths and curvesParallel curve to a sine waveDistance between 2 skew lines (Weird Result?)Curves in 3D, cartesian coordinatesEstimating a derivative of a linear data series using a parabolic fitExercise on parametric curvesFormula for the offset curve of an ellipsoid?Parallel/Offset 3D curve
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Calculating Offset Curves defined by NACA Formula
The Next CEO of Stack OverflowCalculating Second Moment of Area of NACA AerofoilsIntersection of 3D curves parameterised by piecewise defined functionsProduct rule for curvespaths and curvesParallel curve to a sine waveDistance between 2 skew lines (Weird Result?)Curves in 3D, cartesian coordinatesEstimating a derivative of a linear data series using a parabolic fitExercise on parametric curvesFormula for the offset curve of an ellipsoid?Parallel/Offset 3D curve
$begingroup$
I need to be able to scale an aerofoil so that it creates a new offset aerofoil.
I'm going to be using the notation as suggested to me in my previous question.
Taking:
$$ 0 le t le 1\ \u(t) =begincases
frac MP^2(2Pt-t^2), & 0le t< P \
frac M(1-P)^2(1-2P+2Pt-t^2), & Ple tle 1
endcases\
dot u(t) = fracdudt(t)=
begincases
frac2MP^2(P-t), & 0le t< P \
frac 2M(1-P)^2(P-t), & Ple tle 1
endcases\
v(t)=fracT0.2(a_0sqrt t+a_1t+a_2t^2+a_3t^3+a_4t^4)$$
With
$$alpha(t) = (t + v(t)dot u(t)w(t), u(t) - v(t)w(t))$$
as the formula for defining the $x$ and $y$ coordinates for the lower surface.
I then use this formula to create the offset points, with d being the offset distance:
$$x_d(t)= x(t) + fracd times y'(t)sqrtx'(t)^2+y'(t)^2$$
$$y_d(t)= y(t) - fracd times x'(t)sqrtx'(t)^2+y'(t)^2$$
Solving for the variables I need:
$$x'(t)=1+ dotv(t)dotu(t)w(t) + v(t)ddotu(t)w(t) + v(t)dotu(t)dotw(t)$$
$$y'(t)=dotu(t) - [dotv(t)w(t) + v(t)dotw(t)]$$
I can then substitute in the required variables. The problem I'm having is I've done this and coded it Python and it just defines all the points in one fixed y and x location at a distance d vertically from the origin. There's every chance my code is wrong but I just wanted to get my maths checked.
calculus curves
asked Mar 19 at 21:21
Darth VaderDarth Vader
1267
$endgroup$
add a comment |
$begingroup$
I need to be able to scale an aerofoil so that it creates a new offset aerofoil.
I'm going to be using the notation as suggested to me in my previous question.
Taking:
$$ 0 le t le 1\ \u(t) =begincases
frac MP^2(2Pt-t^2), & 0le t< P \
frac M(1-P)^2(1-2P+2Pt-t^2), & Ple tle 1
endcases\
dot u(t) = fracdudt(t)=
begincases
frac2MP^2(P-t), & 0le t< P \
frac 2M(1-P)^2(P-t), & Ple tle 1
endcases\
v(t)=fracT0.2(a_0sqrt t+a_1t+a_2t^2+a_3t^3+a_4t^4)$$
With
$$alpha(t) = (t + v(t)dot u(t)w(t), u(t) - v(t)w(t))$$
as the formula for defining the $x$ and $y$ coordinates for the lower surface.
I then use this formula to create the offset points, with d being the offset distance:
$$x_d(t)= x(t) + fracd times y'(t)sqrtx'(t)^2+y'(t)^2$$
$$y_d(t)= y(t) - fracd times x'(t)sqrtx'(t)^2+y'(t)^2$$
Solving for the variables I need:
$$x'(t)=1+ dotv(t)dotu(t)w(t) + v(t)ddotu(t)w(t) + v(t)dotu(t)dotw(t)$$
$$y'(t)=dotu(t) - [dotv(t)w(t) + v(t)dotw(t)]$$
I can then substitute in the required variables. The problem I'm having is I've done this and coded it Python and it just defines all the points in one fixed y and x location at a distance d vertically from the origin. There's every chance my code is wrong but I just wanted to get my maths checked.
calculus curves
asked Mar 19 at 21:21
Darth VaderDarth Vader
1267
$endgroup$
add a comment |
$begingroup$
I need to be able to scale an aerofoil so that it creates a new offset aerofoil.
I'm going to be using the notation as suggested to me in my previous question.
Taking:
$$ 0 le t le 1\ \u(t) =begincases
frac MP^2(2Pt-t^2), & 0le t< P \
frac M(1-P)^2(1-2P+2Pt-t^2), & Ple tle 1
endcases\
dot u(t) = fracdudt(t)=
begincases
frac2MP^2(P-t), & 0le t< P \
frac 2M(1-P)^2(P-t), & Ple tle 1
endcases\
v(t)=fracT0.2(a_0sqrt t+a_1t+a_2t^2+a_3t^3+a_4t^4)$$
With
$$alpha(t) = (t + v(t)dot u(t)w(t), u(t) - v(t)w(t))$$
as the formula for defining the $x$ and $y$ coordinates for the lower surface.
I then use this formula to create the offset points, with d being the offset distance:
$$x_d(t)= x(t) + fracd times y'(t)sqrtx'(t)^2+y'(t)^2$$
$$y_d(t)= y(t) - fracd times x'(t)sqrtx'(t)^2+y'(t)^2$$
Solving for the variables I need:
$$x'(t)=1+ dotv(t)dotu(t)w(t) + v(t)ddotu(t)w(t) + v(t)dotu(t)dotw(t)$$
$$y'(t)=dotu(t) - [dotv(t)w(t) + v(t)dotw(t)]$$
I can then substitute in the required variables. The problem I'm having is I've done this and coded it Python and it just defines all the points in one fixed y and x location at a distance d vertically from the origin. There's every chance my code is wrong but I just wanted to get my maths checked.
calculus curves
asked Mar 19 at 21:21
Darth VaderDarth Vader
1267
$endgroup$
I need to be able to scale an aerofoil so that it creates a new offset aerofoil.
I'm going to be using the notation as suggested to me in my previous question.
Taking:
$$ 0 le t le 1\ \u(t) =begincases
frac MP^2(2Pt-t^2), & 0le t< P \
frac M(1-P)^2(1-2P+2Pt-t^2), & Ple tle 1
endcases\
dot u(t) = fracdudt(t)=
begincases
frac2MP^2(P-t), & 0le t< P \
frac 2M(1-P)^2(P-t), & Ple tle 1
endcases\
v(t)=fracT0.2(a_0sqrt t+a_1t+a_2t^2+a_3t^3+a_4t^4)$$
With
$$alpha(t) = (t + v(t)dot u(t)w(t), u(t) - v(t)w(t))$$
as the formula for defining the $x$ and $y$ coordinates for the lower surface.
I then use this formula to create the offset points, with d being the offset distance:
$$x_d(t)= x(t) + fracd times y'(t)sqrtx'(t)^2+y'(t)^2$$
$$y_d(t)= y(t) - fracd times x'(t)sqrtx'(t)^2+y'(t)^2$$
Solving for the variables I need:
$$x'(t)=1+ dotv(t)dotu(t)w(t) + v(t)ddotu(t)w(t) + v(t)dotu(t)dotw(t)$$
$$y'(t)=dotu(t) - [dotv(t)w(t) + v(t)dotw(t)]$$
I can then substitute in the required variables. The problem I'm having is I've done this and coded it Python and it just defines all the points in one fixed y and x location at a distance d vertically from the origin. There's every chance my code is wrong but I just wanted to get my maths checked.
calculus curves
calculus curves
asked Mar 19 at 21:21
Darth VaderDarth Vader
1267
asked Mar 19 at 21:21
Darth VaderDarth Vader
1267
asked Mar 19 at 21:21
Darth VaderDarth Vader
1267
asked Mar 19 at 21:21
Darth VaderDarth Vader
1267
asked Mar 19 at 21:21
Darth VaderDarth Vader
1267
1267
add a comment |
add a comment |
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