Monthly Archives: August 2011

p3_Final_Natalie Levinson

Cellular Breakdowns and Warping the Path: A Study in Volumetric Sculpting

Precedent: Vertical Village

Precedent: Richard Serra's walkable sculptures


My original project proposal stemmed from a precedent I had found called Vertical Village – a skyscraper city design generated with Galapagos using a Voronoi algorithm. At first, I wanted to apply the same process to a local site, Wilson Auditorium. However, I soon realized that what attracted me to the design was the sculptural quality of the spaces within, not the endless possibilities or the gradual evolutionary process. Therefore, I moved my investigation to manual manipulation of polygons in Maya, choosing a site adjacent to Wilson on the hillside. The goal of this investigation was to create a walkable landscape that heightened one’s awareness of their relationship with space. The powerful sensation that results from simply tilting walls along a path has been explored by Richard Serra with his walkable metal sculptures. However, his sculptures focus entirely on the path, while Vertical Village focuses primarily on occupiable space. I chose to include both in my project.


40'x20'x5' polygon box, with 3 divisions in the x & y directions

Polyextrude the back row 10', the middle row 5'

Cut faces tool, using the above menu options to offset pieces. After each cut, use the Fill tool to turn the hollow fragments back into solids.

Use the Separate tool to isolate pieces and delete as desired to form walkable voids

One fragment at a time, select each face and extrude them inward to create a frame on each surface. Without de-selecting, use the Smooth tool to soften the lines. Turn off all on/off options in the right panel to make the changes visible. Keep in mind that the number of divisions in the right panel controls how smooth the outlines appear (1-3 is a safe range). Once satisfied with the result, delete the interior faces.

If desired, extract views for atmospheric renderings.

Once the Maya model is complete, production of the physical model may begin. I chose Pepakura, a free online program that "unfolds" the planes of the Maya solids and makes a printable template.

Import the Maya model into Pepakura. If the planes of the model don't pierce each other, then Pepakura generates a clean, printable template as a jpeg file. For a $30 membership, Pepakura allows you to save your files and convert them to vector files if desired.


My project was cellular and biomorphic in nature. In retrospect, Pepakura probably wasn’t the best fabrication medium for a large number of tiny, complex units. Cutting, folding, and reassembling proved much more difficult and time-consuming than expected, despite the helpful tabs and numbered edges that the program generated on the template. Also, the limits of an 8.5″x11″ sheet weren’t appropriate for this project. In the future, I would use a more durable material such as chipboard at a larger scale.

Regardless of the challenges that arose in fabrication, the design succeeds in its ability to sculpt occupiable space. It creates tension with its heavy-looking masses hovering above the walking path, and the tilting wall that leans toward the path heightens this effect. The organic hollowing of the units emphasizes the cellular composition of the pieces, and invites viewers to explore these spaces.

I explored a landscape, but cellular breakdowns and volumetric shifting translates easily to any scale, from buildings to product design. Zaha Hadid’s “Space Bar”, shown below, demonstrates volumetric shift at the level of a product. Incorporation of the unfamiliar, such as a series of ellipse-shaped frames, into the everyday, generally orthogonal landscape of a building interior presents a stark contrast, encourages investigation, and tangibly alters human interaction surrounding the unfamiliar conditions in the space.

Zaha Hadid's "Space Bar" demonstrates an unconventional manipulation of space at a more human scale.

p3_final_Andy McCarthy_#001

Practical Application: P3 – Wall Segment

Some comments on my P1 post pointed out that there are very few brick-laying robots available for contemporary architects to use.  Although this is true, my intention for the post was to show how bricks could be lain in the future, and that this wouldn’t necessarily affect construction now.  I was imagining that one day everything would be built with technological precision by robots.  After doing a bit more research into fluid forms made of brick, I came across the Church of Christ the Worker, designed by the Uruguayan architect Eladio Dieste.  He designed a roof for the church with a thin membrane of brick, only one wythe wide.  The double-curvature catenary arch he invented is called a gaussian vault.  The church was designed in 1950 and completed in 1956.  I’m not sure if it took six years to build, but every part of the church was built by hand and onsite using scaffolding that connected taught rope.  Even though a robotic arm can build a complex brick wall, so can the human hand.

Cristo Obrero:

Image courtesy of

Image courtesy of

Grasshopper script of Christ the Worker:

Dieste GH 6.ghx

Fabrication technology today makes more precise stencils, dies, and molds than the handiwork of the 1950s.  The CNC machine and powder printing machine can make molds with great specificity for poured concrete modules.  The laser cutter can create amazingly accurate dies, which is what I originally thought I would use to lay out the concrete slabs.  I decided to build a retaining wall/bench for my final project, one without mortar but a highly durable epoxy.  This project was just a demonstration, and since I wouldn’t be gluing each course to the ones below and above it, I decided to plot stencils of the layout on 36″-wide rolls.  The plots had to be exactly to scale, with just enough information per sheet to place the slabs correctly.  A 7′-long, 3′-wide stencil was plotted for each of the six slab courses in this retaining wall segment.  A black outline showed the location for that particular slab, plus a gray outline of the slab that was just lain below it.  This way every slab’s location was demarcated by the location of the slab below it.  Originally I planned to laser cut a length-wise die for the undulating wall, and have those six dies anchored by two dowels, one on each side of the wall segment.  This would have hypothetically worked as well.  At the final critique Ming suggested that several top-to-bottom dies could have also been used to ensure accuracy of the wave surface.  The success of this project is its exploration of constructing a parametric design without using heavy machinery.

I first tried a script by Walter Zesk.  It only allowed one course of bricks to be created, so I changed everything on the script that was for curves into surfaces.  However, what I ended up with was too twisty.

I first tried the script by Walter Zesk. It only allowed one course of bricks to be created, so I changed everything on the script that was for curves into surfaces. However, what I ended up with was too twisty.

A parametric design for a brick structure allows for many changes to the variables and parameters of a project that would be incalculable for a 20th century architect.  This wall segment was built by hand after first using standard-performance computers, affordable and user-friendly software, and the use of complex, although accessible, fabrication technology.  There were many options for each student to choose from in designing their final project.  Some students had higher performing computers and chose to work outside of the lab.  Some people downloaded software that wasn’t available on the Daap computers, specifically Galapagos, which was used in one project.  Most students used Maya or Rhino/Grasshopper.  Most students laser cut or powder printed their projects.  For my project, I found that the software that can modify parameters for the most nuanced result was Grasshopper.  In GH the parameters such as wall height, wall width, module dimensions, the number of courses and the space between them, etc, are connected to number sliders.  The range of variation was set, and I would adjust the parameters with the sliders to find the best outcome.  However, there were a few scripts that were published on the internet, including Ming’s site, that used sliders to modify voxels and how they were stacked.  It took three tries to find the most direct result.

Ultimately, I used Ming Tang's explode script to make the project.

Ultimately, I used Ming Tang's explode script to make the project.

I then sectioned each brick course.

I then sectioned each brick course.

After sectioning the brick layout, I plotted six 3'x7' stencils.

After sectioning the brick layout, I plotted six 3'x7' stencils.

The retaining wall/bench was originally conceived as a seat for about three people.  It was ultimately designed as a wall that had three nooks where people could step into from the sidewalk and send a text message, or wait for a car to pull around.  The wave is like a shelf or high bench at some points, and like a wall with a slight lean backwards at other points.  Because retaining walls must resist the lateral force of the earth they hold back, the orientation of the concrete slabs would be best lain parallel to that force.  However for a seat, the preferred orientation would have the 16″ side perpendicular to the person, not the 8″ side.


First attempt using Walter Zesk’s script (

make CA wall along curve 2 wythes

make CA wall along curve 2 wythes, modification

Ming Tang’s explode script (


I later found a very good script by Ted Ngai (


Watch the R-O-B at work in Chinatown:

p3_Kevin Donovan

Presentation PDF

My Grasshopper Defnition

I began project three with the simple idea of developing a new, dynamic ventilation system. For form, I looked at forms ranging from the natural, such as how the spines of a beaver work, to existing precedents of roof systems like those of world cup stadiums. I took cues from Alienware’s Area 51 Desktop and its active mechanical ventilation and began contemplating how I could improve upon the design in both efficiency and stylistic response.  I eventually recalled an image of a type of steel cladding that consisted of a field of interlocking diamonds, which set the direction for my actual form.

When I initially began building the actual panel that would come to be replicated across my “field,” I did not specifically know which program I would be doing my final version, so to develop exactly wanted it all to look like, I did study iterations of the diamond panel in SketchUp in order to determine the size and proportioning.

I experimented a bit with translating the geometry into Maya, but found it too hard to control from a precision standpoint, so I turned to Grasshopper/Rhino. As my first time working on my own with no real direction in such a fairly unfamiliar program, I began with a simple starting point on the origin (0,0,0). From there I executed a series of movies to build the other points which would create the surfaces. These movements were all controlled in proportion by functions so that regardless of how big the initial length of the panel was, it would maintain its shape and depth. Once I had the points, I created surfaces using the 4-Point Surface command. In order to save myself some time, I only created surfaces for half of the panel and then simply mirrored that half about the YZ axis (I will come back to this soon enough)

The definition for my diamond panel.

The finished diamond panel.

The Grid.
In order to have a surface that could be completely closed off, I had to develop a grid system that allowed my panels to interlock. I started off with a simple surface that I could control the size of, once again, in functionally constrained proportions with incrimentation based off of the panel sizes so that regardless of either the size of the panel or the size of the grid, all would fit and function. To allow the panels to interlock, I culled the number sets coming out of the surface grid and shifted every other row half the width a panel. When my created geometry was applied to the grid, however, I discovered that it would still mirror my panels based on the global ZY axis as opposed to that of each local panel. This was remedied by defining a vertical surface in my panel with already existing points and then using that as the plane of mirror.

The definition for my interlocking grid.

Image Reaction.
The final and possibly most important function of my project is the reaction to “heat,” interpreted in the form of an image file. In order to develop the ventilation of panels, images were imported into the file and inherently overlaid onto whatever the current size of the grid was, with each pixel of the image porting out a value of color value from 0.0 to 1.0. This value was multiplied by a factor of 90 to determine the rotation for each individual panel which grasshopper did a surprisingly great job distributing the values back over the grid. This allowed any panel in a zone with a white, or hot, value to self-adjust as open to ventilate, and vise-versa for any panel sitting on a pixel with a black, or cool, value. The result is a kinetic composition with potential response to a number of conditions such as sun exposure, programmatic light issues, and ventilation necessity.

Finished definition.

My fabricated version.

Protected: p3_George Faber_final presentation

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p_3 Molly Wimmel

The objective of my project was to explore the relationship between curved and angular spaces, especially the transition between the two. At first I thought I would achieve this by creating a surface pattern and altering this as I moved across the surface, but I decided my idea would be more effective if I incorporated it into the actual shape of the object, as opposed to just using it as a 2D detail.

I also wanted to incorporate fashion design into my final, so I chose to make a dress. I created four curved and angular shapes in Maya, then lofted between them. From there, I was able to experiment with a lot of shapes based on those four original curves. I then imported my geometry into Rhino, exploded the shape, and used the smash command to flatten all my pieces so that they could be laser cut out of leather.

My final in Maya, before exporting to Rhino.

This project was related with performance based design because I was able to explore a number of shape possibilities. I plan on fabricating this full size and in that case, I would use my original curves as the constants for bust, waist, and hip measurements. These general measurements would control what the general outline of the figure would be, but I would still have some control over what the final outcome was by twisting and rotating the curves.

The major issue I ran into with regard to fabrication was that the leather I used was relatively thin (I had originally chosen it because I needed something thin enough to hand stitch through but that was heavy enough to hold its shape once sewn). Because the leather was thin, it stretched and bubbled significantly as I sewed it. If I was going to manufacture this full scale, I would want to explore other fabrications, as well as ways of using boning or wire as support underneath the exterior shell. If bubbling was unavoidable, I’d want to work more with it to make the bubbling look more purposeful/like an intentional design element.

In conclusion, I think this was a very successful first run at this project. There are definitely still a lot of issues I’d want to work out before making a final, but at this point I think I could adjust the pattern to fit a model and then enlarge it to produce a first muslin. I would also want to make a few other small scale models to experiment with other fabrics and seaming techniques.

It was nice to find a connection between fashion and parametric design. Going into my pre-junior year, I hadn’t been able to use digital pattern making software until this class. Using parametric modeling programs to develop a pattern opens up significant possibilities with respect to silhouette and design. Patterning a garment such as this without digital help would take a lot of unnecessary work and multiple samples. Using parametric design cut out a lot of this and allowed me to focus more on the original silhouette and less on how I was going to go about making a pattern for the garment.

P3_Final_Sarah Mapel_001

Project 2

Utilizing Maya and its various capabilities, Project 2 was a visualization of squaring a number and the complexity that results from this process. Starting with the number two, I bisected a square into two parts in both directions, and then divided the square with two diagonals. I then proceeded to apply various affects to this base layer. These affects I carried through consistently with the other two layers, which were studies of divisions into four parts with four diagonals, and sixteen parts with sixteen diagonals.

The overall final form of the screen design was inspired by various organic shapes that transform themselves to be useful, yet appealing means of cladding a building, providing shading, or acting as an interactive art exhibit. The diminishing voids from layer to layer on the final screen work especially well for creating limited lines of sight with a consideration for temperature control combined with the benefits of day lighting.

Project 3

The Lily is the result of parametric and non-linear thinking and design applied to an initial goal. This objective began with the hopes of creating modular pieces that would fit together without any extraneous connections while operating in such a way that the individual pieces would create many different shapes when combined together, depending on the orientation and the number used. This thought was initially inspired by the VLightDeco IQ Puzzle Pendant Jigsaw Lamp (seen below).

Throughout the design process, my parameters became more defined and specific, resulting in a slightly different final product than what I had initially intended. These included tessellation qualities, in order to conserve materials, flat-pack capability, so that the unassembled product could be shipped conservatively and cheaply, and finally, I wanted each individual piece to have a built-in means of connecting to the other pieces so that no glue, tape or other adhesive was necessary. Thus, the only component that would be shipped would be the pieces ready to be assembled, further enhancing the flat-pack capability.

These parameters were directly linked to the final component operating as a performance-based design. Not only did it satisfy all the rules laid down, but it also had an appealing aesthetic quality that could be used by a wide variety of audience members. Furthermore, it is flexible, can take on a varied number of shapes, and can be coordinated so that the user can interchange components depending on the color of the surrounding environment.

Created entirely via sketching and numerous experimentations with scissors and paper, the parametric design process was not carried out in the way many may imagine, but was conducted without computer aided design programs such as Autodesk Maya or Grasshopper for Rhino. Despite the fact that I did not employ technology as we know it, I shared many similarities with those who do utilize computer programs to aid in parametric thinking. Like them, I did not have a clear image of what I wanted my final product to look like – I merely had a set of rules that I was determined to follow. However, rather than tracing my thought process through a Grasshopper script or similar means, the results of my design development where visible in the discarded physical paper models.

Although I was very pleased with the finished result, the means to that end did provide some problems along the way – foremost of which revolved around the constraints of fabrication. Experimenting with paper and scissors was all well and good for the “rough drafts,” as I like to call them, but the transition to a more resilient, long-lasting material proved difficult. The first attempt at this involved laser cutting a thin acrylic in the hopes that it would be strong enough not to wrinkle (as the paper had), but flexible enough that the bends in the material would not cause it to snap. However, after a few attempts at laser cutting, the acrylic proved to be a failure. It did not score without breaking, and attempting to bend the material freehand typically resulted in it snapping and becoming unusable. I also envisioned a final product with multiple color options, rather than the milky white and clear that the acrylic embodied, so I went in search of another solution. I finally landed upon a thick, strong construction paper that came in a variety of colors and would score without breaking. Although this material worked fine for the final product for the time being, if this design were to be mass produced, a much more resilient material would have to be found. The construction paper was great as long as one were careful with it, but overtime, wear and tear would ultimately show.

In the future, I hope not only to improve upon the materiality of the design, but hope to take this idea further to try to come up with variations on volume, shape, and color. To do this, I may have to tweak the parameters to potentially invent an entirely new form, but it would also be interesting to see if I could keep the parameters the same, but come up with an entirely new form that still satisfied all the requirements, reflecting the notion that the Grasshopper plug-in, Galapagos, employs: there are many solutions for the same problem, but not all of them may be the best one. I believe that the Lily is definitely one of these solutions, but I also believe that there are many more, and the best one is still waiting to be found.

The link to the powerpoint presentation about the Lily is listed below.



p3_final_Jessica Helmer_#001

Beginnings: P2 – Fractal Screen

At the beginning of the quarter I was interested in using parametric programs to design architecture with fractal properties. Choosing where and when to repeat the fractal pattern, I could create areas of greater or less density to control light, visual access or even express load transfers in a structure. For our first project, a three-layer screen, I chose to go with a simple branching pattern using the “interactive split” and “triangulate” tools in Maya.

P3 – Light Column

Even though I deviated from the fractal patterns for the final project, I still wanted to continue to work with the idea of a pattern with various levels of density and transparency in order to control light. I came across three precedents that would help me in my design.

The first precedent comes from designer Pierre Poussin and his Mitosis Courtyard in downtown Toronto. The courtyard included light columns, made up of a laser cut steel shell wrapped around a frosted polycarbonate cylinder which housed programmable LED’s.

Image courtesy of

Pierre’s pattern varied little in scale, however, and I imagined my light column to be more opaque where it met the floor, and more transparent as it met the ceiling. I imagined a density gradient similar one that I found on the website of SOM employee, John Locke.

Image courtesy of

I also imagined that the column could meet the floor and ceiling in a gradual, sweeping motion. The pattern on the column could then continue onto the ceiling, much like the bamboo cladded restaurant found at the Tang Palace in Hangzhou, China.

Image courtesy of

Combining all of these principles I set out to create my light column. I chose to work almost exclusively in Maya and probably took the “long way” around many steps. Because of this, however, I was exposed to a wider range of tools and operations within the program and now feel very comfortable using Maya to design future projects. There were, of course, many iterations that were abandoned and much trial-and-error involved. In the end, I chose to make a column where the apertures 1) increased in diameter and 2) increased in the number of sides as you moved up the column.

The Steps:

My first steps were much like Ming’s “Wood Mirror” tutorial series on I also created a video tutorial series for the column design. Links to my videos can be found in the references section at the end of this blog.

1) I started with a NURBS surface which I bent using the sculpt geometry tool and a simple gradient image. I used soft select and scale tools to alter the grid to my liking.

2) I then created a separate polygon cone with a subdivision axis of 3. I set a driver/driven key on this shape so that it would increase in diameter and in the number of subdivision axes as you moved in the Z direction (long axis of the NURBS plane).

3) I then used Ming’sduplicate with input node script to populate the NURBS surface with the polygon cone. Since the cone had a driver/driven key set, the shapes changed in diameter and subdivision axes as they populated the NURBS plane. They also follow the bend of the NURBS plane that I had set through the sculpt geometry tool.

4) Exporting the shapes (and not the NURBS plane) into Rhino, I used the section tool to cut a straight section through the bottom of the large hexagonal cones and through the tops of the triangle cones.

5) Importing these curves back into Maya, I projected them onto a new NURBS surface and used the trim tool to cut out apertures from those projected shapes.

6) Using the non-linear bend tool I wrapped the NURBS plane into a column (I merged the edges of the seam together in step 8 after I converted the NURB to a polygon). I also used the non-linear twist tool to add further interest to the shape.

7) I applied the lattice deformation tool to create the funnels on either end of the column. This simulated how the column met the ceiling and floor.

8 ) To give the column some thickness for renderings or powder printing, I first converted the NURB into a polygon, merged the edges of the seam together, and extruded. For structural rigidity, I made my powder printed model relatively thick. For my renderings, I extruded less.

9) To create the ceiling effect seen in the final rendering, I used the stitch vertices tool as well as the soft select tool to scale and rotate the pattern.

Final Thoughts

I imagined that this would be a cladding, laser cut from steel and wrapped around a polycarbonate light insert, as in Pierre Poussin’s mitosis column. However, as pointed out in the review, it can certainly be structural just like Frank Lloyd Wright’s mushroom columns in the Johnson Wax building or like Nervi Giatti’s Wool Mill. The pattern and thickness of the ceiling pattern can easily be altered to better reflect structural loading and one could cast it out of concrete or steel.

The rendered scene as a whole reminded me of an ocean theme. The columns themselves are reminiscent of certain coral and the ceiling pattern gives the effect of rippling water. I imagined that lighting effects could enhance this feel. Overhead LED lighting that change in intensity and color, combined with the shadows of the ceiling pattern, could create some very cool “underwater“ effects on the floor.

I’ve found that rendering certain lighting effects in Maya is much harder than I thought. I’m interested in furthering my knowledge in this area so I can create a comprehensive scene that properly reflects what I imagined it to be.


The following links are swf flash movie tutorials for the column:

Click here to view the original power point presentation

P03 Final_Nicholas Schoeppner_001

For the sun shade project, I wanted to achieve an interesting composition for any building to utilize using the three layers required for the project. I researched a few shading techniques on other building and discovered that the shading created with the use of thin, intricate shapes with more void than solid were the most intriguing patterns. So, in my project, I tried to incorporate this with inspiration from a bee’s nest being deformed by a heavy weight being placed on it.

Using Autodesk Maya, I was able to imagine what that “beehive” would look like after deformation. I used the soft select tool on selected vertices and manipulated them in areas where shape changes would take place. I key framed my first stage and last stage of transformation then created an animation snapshot to get multiple middle pieces. I then chose the most appropriate section and extruded all three with Ming Tang’s super extrude script. After digital design was completed, I tried to send it to the RPC for fabrication with a laser cutting but my voids were too large which meant the laser would cut through areas I did not want it to. In order to fix this I had to mess with the file in Rhino and manipulate the shapes to be the proper distance apart.

Project 2 required us to develop an object that is parametrically controlled so I chose to deal with structural elements and how we can manipulate them to fit any building shape. In order to start with this concept, I decided to use a building currently under construction that had a unique shape and unique structural challenge. The Santiago Calatrava designed Transportation Hub at the World Trade Center seemed to be the correct precedent for exploration. Calatrava used Autodesk Maya for his final design which does not bode well to parametrically controlling the shape, spacing and height of the structural columns so I decided to write a Grasshopper script that achieved the same basic form, but also allowed for changes to be easily made.


In order to achieve this, I first began with a range of points in a linear direction. The number of points controlled the number of columns I would eventually have. I then needed to create a parabolic curve that also translated in the z direction for the height, not just the x and y direction. For this I plugged a function into my range with {sin(x/y)*z} as the equation, allowing me to adjust a slider which controlled the height, frequency and the open angle. Using two of these sine curves with the same points, I connected them with a line, thus creating the skeleton for the columns. To model the columns, I created two distinct shapes along the points of both curves and connected them with a loft using each line as an axis for every column. In order to create the top pieces (the shading element for the interior of the building), I simply rotated the columns I created along the top sine curve and used a non-uniform scale to control the different cross section and length of these members. To make the Calatrava inspired building a three dimensional reality, I mirrored my previous geometries which allowed the entire building to be manipulated parametrically with just a few sliders. At the end of my script are areas dedicated to rendering an animation* and flattening the pieces for laser cutting, so they can be ignored if neither are needed for other future designs with this script.

The shape I created was just an exploration on using Grasshopper and no other modeling program to create an architectural structure. This script can be easily manipulated to place columns along a linear grid or with random points in space.  All that has to be done is replace the sine function with the shape of preference for the designer and the columns should be just as easy to manipulate.

To view my video, follow this link:

For fabricating this project, I wanted the physical model to be able to rotate just like the digital model was able to do. I designed the laser cut pieces to have holes in the ends of the acrylic pieces so they could connect with a dowel or bolt, allowing them to rotate freely depending on the shading required.  My model is nine inches long in the center column which creates a problem when using dowels as the pivoting element since the reality is that dowels just let the top pieces rotate down due to gravitational loads. The way to combat this is to use something with threads such as a screw or bolt, which will create grooves in the acrylic and prevent the pieces from moving down unintentionally. I also only built half of the model and mirrored it so the cutting cost and fabrication time would be less.

Both projects have been useful for my education and can be utilized for an actual design project later on in my career. The sun shade can be used in virtually every project and can be an intriguing way to deal with shading without using shades or louvers to thwart the intensity of the sun at midday.  Not only will the grasshopper script be useful for other structures in the future, but the fact that I now have the knowledge of how to use Grasshopper is a very valuable tool for my future designs. I am very thankful to Ming for teaching this class because I know Grasshopper will be a tool I can utilize for many years to come and I enjoyed every minute of it.

*Render script from Giulio Piacentino on his website:

Presentation powerpoint:Final Presentation

Grasshopper Script: Calatrava Shape

p3.1_final_David Friedlander_#001

Subsonic Fixed Wing Design

Wing design is a complex process due to the many parameters that can be tinkered with to get an optimal design.  Such parameters include planform and airfoil geometry shapes, as well as the angle of attack and related parameters.  To say the least aircraft come in many different shapes and sizes, each with special needs.  For example, wing designs can be optimized for high lift if the aircraft is expected to carry a heavy payload or can be optimized for high lift over drag ratio for high endurance flights.  For my final project I decided to write a script in the Grasshopper environment to aid in the wing design process.  For numerical simplicity I restricted the wing design to low subsonic speeds, comparable to speeds reached by personal aircraft, such as the Piper Cherokee, as seen in Figure 1.  By writing the script in Grasshopper, it allows the user to be able to easily rapid prototype the wing (either in full scale, or recommended smaller scales for wind tunnel testing).

Figure 1: Piper Cherokee Arrow, image from

Figure 2 shows various wing definitions that will be used in the remainder of this paper.  The development of the WingDesign script lent itself to three major aspects: visualization, numerical, and optimization.  The purpose of the visualization (or front end) aspect is to visualize the wing within the Rhino environment.  This is done by dividing the wing into control sections across the span called rib sections.  Inputs for each rib section include angle of attack while the chord at each rib section is defined indirectly by most of the general inputs.  These include the aspect ratio, taper ratio, and airfoil type.  For simplicity the following variables are held fixed: planform geometry type (trapezoid), number of rib sections (7), and constant airfoil geometry for the wing.  Once all inputs are set, they are fed into the WingPoints block which is the heart of the script and in turn outputs a list of points that will define each rib section.  Curves are then fitted to each list of points and finally all the curves are lofted together to form the final wing.  Do note that when rapid prototyping the wing must be closed off, which can be done by using the command “cap” in Rhino on the baked model.

Figure 2: Wing definitions, note airfoil diagram is from

The purpose of the numerical (or back end) aspect was to allow for a metric for the user to determine if a wing design was a “good” design.  I decided to use a numerical lifting line method to calculate the 3D coefficients of lift and drag on the wing to be used for this metric.  The particular numerical method I am using was developed by Anderson, Corda, and Van Wie at the University of Maryland to be applied to Prandtl’s Lifting Line Theory, Ref. 1.  Prandtl’s Lifting Line Theory says one can approximate a finite wing as a series of horseshoe vortices, in which a circulation, and thus lift, distribution can be found.  The draw back to this method is that it assumes incompressible flow, so it is only good up to around Mach 0.3.  The numerical version also needs 2D coefficients of lift data to run.  Because numerical methods take time to run, there is an option to bypass running the numerical lifting line code to speed up visualization time.

To optimize, I decided to use a preexisting solver called Galapagos.  Developed by David Rutton, Galapagos uses “Evolutionary Computing” to derive an optimized solution.    Evolutionary computing works by giving each variable (called a gene) an assigned a fitness value.  The solver then iterates through different mutations of genes with the fittest solutions surviving each iteration and thus playing a role in the way the genes combine.  For more information, see Ref. 2.

For my particular wing design, I decided to use the RAF19 airfoil, as seen in Figure 3, with a 8unit span as this would fit ideally in the available 3D printer space.  Maximizing for lift over drag with 50 samples per iteration for 20 iterations, Galapagos came up with the following specs: AR=9.1629, TR=0.3671, AOA=3deg at the tips, 0deg for remaining rib sections.  However for maximum lift over drag, the wing would need to be at an angle of attack of -5deg from the base design.  The wing can be seen in Figure 4.  Below is the calculated coefficient of lift and lift over drag ratio for the optimized wing design.

At AOA 0deg: L/D=28.7223, CLw=0.8768

At AOA -5deg: L/D=56.8823, CLw=0.4300

Figure 3: RAF19 airfoil, image from

Figure 4: Optimized wing design using the RAF19 airfoil

The results for this wing design tend to agree with general theory in several ways.  First, maximum lift over drag is found at lower angles of attack as both lift and drag increase as the angle of attack increases, but drag increases by the lift squared.  Second, high lift over drag is typical of high aspect wings as lift over drag is proportional to the aspect ratio.  Third, the 3D maximum lift over drag will be lower than its 2D counterpart.  For the RAF19 the 2D maximum lift over drag is 79.949.

To conclude a Grasshopper script was developed to aid in the design of subsonic fixed wings.  With it, I was able to maximize the lift over drag for a 3D wing with RAF19 airfoil sections with a 8unit span.  This resulted in a high aspect ratio wing with slight geometric twist at the wing tips.  Although the script is in working condition, it can still be improved by adding more variablity to the wing design.  These improvements include being able to vary the planform geometry type and airfoil type for each section.  Also, the numerical scheme can be improved to allow for different ranges of speed regimes (such as higher subsonic Mach numbers, supersonic, and hypersonic) as well as to allow for user defined airfoil geometries rather than currently existing ones.


  1. Anderson, John D., Jr., Corda, Stephen, and Van Wie, David M., “Numerical Lifting Line Theory Applied to Drooped Leading-Edge Wings Below and Above Stall,” J. Aircraft, vol. 17, no. 12, December 1980, pp.898-904.
  2. Rutton, David, “Evolutionary Principles Applied to Problem Solving”, September 25, 2010,
  3. Grasshopper Primer, Second Edition, for Version 0.6.0007, Andrew Payne and Rajaa Issa, 2009.
  4. Airfoil Investigation Database:


Demos: WingDesign Code Demo, Demo Using Galapagos for Wing Optimization

Code: WingDesignCode

PowerPoint: Subsonic Fixed Wing Design

pfinal_mary jo minerich_#001

A pdf of my presentation can be viewed by following the link below.  I have video of the script being used, but it is too big to post here. Regrets.

Minerich Digital Boat Presentation