Interpolate Points tool should results match across different cad progs?


#1

Hi,
V4 and V5
Would a curve drawn through points using InterpolatePoint command match a curve drawn through the same points drawn in other CAD progs such as Autocad, Catia, Turbocad etc ?

I have received such a curve for an aerofoil section and Rhino gives slightly more of a bulge at the leading edge so I wonder if there should be variation or mathematically is there only one course a curve could and should take, in which case which one is correct ?

Steve


(Menno Deij - van Rijswijk) #2

It depends on how the curve is interpolated (algorithm) and how it is parametrized exactly. This has to do with the values of the knots.

In the Rhino InterpCrv command you have the option of choosing knot style (Chord, Uniform and SqrtChord). These values influence the final shape of the curve. Sometimes very subtly, sometimes dramatically.


#3

Any idea which option (…and values if one is then faced with a choice of such) is best for plotting aerofoil sections ?

Steve


(Pascal Golay) #4

Hi Steve- if the points are evenly spaced, as seems likely, use Unform knot spacing. Remember to check Help.

-Pascal


#5

hi,
uniform gives a ‘hump’ above leading edge in the otherwise smoth curve as does sqrdChord though this one less so and chord gives best smooth fit, as chord is an aerofoil term maybe this is why !

Steve


(Menno Deij - van Rijswijk) #6

Even though chord is indeed an aerofoil term, it is a mere coincidence that they are the same. Another word is distance parametrisation, or sometimes arc length parametrisation.

From the help page: http://docs.mcneel.com/rhino/5/help/en-us/commands/interpcrv.htm

[quote]
The spacing between the picked points is used for the knot spacing. This makes curves that have widely varying point spacing behave better than uniform curves.[/quote]


#7

Chord is a mathematical/geometrical term going back to the ancient Greeks…

…therefore long before man learned to fly or understood the concept of airfoils…

Chord is from the Latin chorda meaning bowstring.

–Mitch


(David Cockey) #8

I’d use Chord or possible Sqrtchord parameterization for an airfoil. The points defining the shape should be closer together near the leading edge where the curvature and rate of change of curvature is higher than further aft.


#9

The points defining the shape should be closer together near the leading edge where the curvature and rate of change of curvature is higher than further aft.

So one would think David, but the rule is 2.5 5 7.5 10 etc percent chord axis spacing (the vert lines that have the sections points on the end through which the curve must run), even with 1.25% as an extra , such leading edge curve needs in my book a few more as different knot options can see differences there and that cant be right !

Steve


(David Cockey) #10

Who’s “rule”? What you describe is what’s given in some sources for some airfoils. In other cases more points are given. If equations are available for the airfoil thickness and camber such as for NACA 4-digit and 5-digit sections then an arbitrary number of points can be generated.

Usually the leading edge radius is also given. This can be used to refine the curve. Generate an interpolating spline though the points for the upper surface other than the point at the leading edge (typically 0,0). Then create an arc with the leading edge radius from the leading edge going the other way. Now use BlendCrv (not Blend) between the upper surface curve and the leading edge radius curve. Adjust the control points in BlendCrv until the curvature plot is satisfactory. Save the result. See attachment for an example of a NACA 16-006 thickness curve using this method.

Airfoil Example.3dm (52.8 KB)