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Old 08-01-2010, 07:33 PM
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Fuselage Lofting with Rhino, A Tutorial

Fuselage Lofting with Rhinoceros 3Dtm

+Gil


Background


Smooth contoured surfaces whether they describe a ship’s hull, the contour of an automobile or that of an aircraft all stem from mathematically derived curves based on sections of a cone known as conic sections. These curves include the line, hyperbola, parabola, and ellipse (the circle is a special case of the ellipse). Prior to computer graphics curves contained in sets known as French Curves were used to manually draw curves through plotted points to form concatenated curves. The advent of computer graphics allowed mathematically derived conic sections to be derived instantaneously on the screen. The computer graphics industry standardized this format of curve generation, collectively known as NURBS (Non-Uniform Rational B-Splines), it facilitates interoperability of geometric data sets between different CAD software packages.

“Lofting” is the process of defining the external geometry of an aircraft. It also includes its shipbuilding counterpart and is now used to describe the process for a number of other areas where smoothly contoured surfaces are a requirement.

Rhinoceros 3D by Robert McNeel & Associates is subtitled as “NURBS Modeling for Windows”. This claim doesn’t really seem to hit home even for many long time users even though it’s touted as the main reason for the software’s existence. Rhino’s lofting command has long remained a mystery for some reason. Rhino’s in-house tutorials and those from external sources do not seem to adequately express the power of this command. This brief tutorial shows how to use Rhino’s loft command to quickly and accurately “skin” a fuselage from a 3 View drawing.

Drawing the Profile Lines


A drawing of a P-47D, found on the web, was downloaded and prepped using Photoshop to be used as reference bitmaps for top, right and front views. Place the bitmaps in the proper views and adjust each view's scale to match the other references (Pictureframe command has been used to place the images in this tutorial).

Use either a “control point curve” or “interpolate point curve” to trace the top profile line of the fuselage in the right view. Shown below is a rendered “drawing box” view of all three views. Note that a reference centerline has been drawn. This becomes important later on.



Use as few drawing points as possible to draw the curve. More can be used but will become unwieldy if too many are used. Note also that the trace begins just aft of the forward engine cowl.

Use the mirror command to flip the top profile line vertically. Make sure the “Ortho” cursor control radio button is on. This keeps the edit points orthogonal with one another. Turn on the bottom profile lines “edit points” and adjust each to the fuselage side view bottom reference curve as shown below.



Next select the top trace and using the “rotate” command (“copy yes” on) rotate a copy of the top trace 90 degrees as shown below. Turn on the rotated lines edit points and with the cursor “Ortho” mode switched “on” adjust each point to the side reference line in the top view.


Using the “Curve from 2 View” command, generate the bottom and top of the “box” curves. These curves maintain tangency at the top of the cross section (see below).


Trial Loft


These five traces are enough to try a trial loft. Select the “Surface > Loft” command. It will ask to select the lines to loft. Select the lines in this order; top, top right, side then bottom right, then bottom followed by enter. A floating menu will appear. Select “Loose” under style and “do not simplify” button under “Align Curves”. Depress “Ok” or “Enter”. The following shows the resulting test “loft”.



Looking at the “Front View” it's evident that, although the fuselage loft conforms to the side and top profiles, it does not conform in cross section (see below).



Adjusting the Cross Section


This next step shows the real power of using NURBS to “skin” fuselages. The adjustment is achieved by using the “Average 2 Curves” command. By generating curves “in between” those already established the shape of the cross section can be changed to converge on the desired shape. Although it requires several “trial lofts” to converge it doesn’t require that much time to accomplish.

Study the following finished loft and see how it differs from the original “First Loft”. The original three loft lines are now joined by five additional blue curves that bring the cross section into conformance.



Further Thoughts


Rhino includes a command called the “Cage” command which literally applies edit points around an object to ease the task of manipulating the surface. The above tutorial is along similar lines providing a technique using successive approximation to transform profile lines from three view drawings into three dimensional surfaces.

Lines used to loft the surfaces can each be given a separate layer which makes it easy to select and manipulate them.

A way of back checking your work is to take “sections” of the developed surface at the same reference points as those contained in the current three view drawing to see how well they match one another. I haven’t tried playing with the “Cross Section” (Csec) command which generates curves sectionals from profile lines though they look to be particularly applicable.

Surfaces, once generated, can be selected and their edit points can be turned on and manipulated. A point of interest is that all the line manipulation commands will operate on a group of selected control points which is very nice to have in a situation where the cross section of the fuselage transitions from one geometry to another (i.e. “pear” shaped to circular).

I haven’t explored the full depth of this technique yet, but have tried it on enough examples that indicate it to be one of the most powerful tools that I’ve come across.


Further Reading:


“Lofting and Conics in the Design of Aircraft”, Derek Morrison and Gregory Neff, Purdue University Calumet, Indiana. Proceedings of the ASEE Illinois/Indiana Section Conference, March 13-15, 1997, Indianapolis, Indiana, page 222 - 227.
Lofting & Conics in Aircraft Design
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