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 http://www.michiganshipwrecks.org/piper.htm

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 http://en.wikipedia.org/wiki/File:Airfoil.svg

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 http://www.worldofkrauss.com/foils/showplot/1545

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, http://www.grasshopper3d.com/profiles/blogs/evolutionary-principles.
  3. Grasshopper Primer, Second Edition, for Version 0.6.0007, Andrew Payne and Rajaa Issa, 2009.
  4. Airfoil Investigation Database: http://www.worldofkrauss.com/


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

Code: WingDesignCode

PowerPoint: Subsonic Fixed Wing Design

p3.0_David Friedlander_#001

After giving Project 3 some thought, I developed two potential project ideas: one in the aerospace field and one in the naval field.  Below is a summery of each project idea.

Finite Wing Design

Background:  There are many parameters in a finite 3D wing that can be manipulated to optimize its Lift/Drag (L/D).  These include airfoil (wing cross-section) geometries, planform (“shadow”) geometry, geometric twist, and sweep.  Such complexity yields an endless number of wing configurations

Concept:  I am thinking of using grasshopper to manipulate the wing parameters to come up a subsonic wing design.  The parameters will include all of the above plus their subset parameters, such as span, aspect ratio, and number of ribs.  For simplicity I will assume incompressible flow, which would allow the script to use a numerical lifting line method to calculate the coefficients of lift and drag (and thus L/D).  This information would then be fed to galapagos to find the configuration that yields the highest L/D.


Figure 1: Airfoil/Wing, from “Numerical Lifting Line Theory Applied to Drooped Leading-Edge Wings Below and Above Stall”


Submarine Design

Background:  Submarines come in many shapes and sizes, depending on their purpose.  There are many parameters that dictate the submarine’s overall design, including propulsion system, payload, single/double hull, ballast tank arrangements, and control surfaces.

Concept:  I have been playing around with designing my own “mini” submarine, something around the size of the HL Hunley or “USS” Alligator.  I would design a script in grasshopper that would take in parameters such as number of ballast tanks (and size of each tank), hull geometries, payload, operation time, and propulsion configurations.  Galapagos would then be used to optimize the design to minimize weight.

Figure 2: Drawing of the CSS HL Hunley

p2_David Friedlander_#001

Below are tentative renderings in Maya for Project 2.

Figure 1: Top view, all three panels together.

Figure 2: Parametric view, all three panels with box like structure.

Figure 3: Top view, each panel individual.

Design Concept: The basic concept was to use a pseudo recursive/quadsectional scheme in which a base design was created.  This was done by starting with a 1×1 grid and then bisecting it in the X and Y directions.  This was recursively repeated for each new 1×1 grid, however some bisections would be diagonal in nature and not all new 1×1 grids were bisected. This allowed for a combination of order and randomness to exist.  Although each panel has the same base design, the thickness of each panel is different.  This was done using a bisection relation on the second derivative of the thickness during the superextrude process.  Finally, each panel was oriented 90 degrees out of phase relative to the adjacent panel to complete the perceived quadrilaterals.

Below are pictures of the final project 2 box.

Figure 4: Parametric view of final box.

Figure 5: Top view of final box.

p1_David Friedlander_#001

An Automated Vehicle Conceptual Design Utility (AVCDU) was developed at Lockheed Martin MS2 to aid in the parametric design of unmanned underwater vehicles (UUV’s).  The AVCDU is a tool that takes mission descriptions and configuration options and outputs UUV specs (size, wet and dry weights) as well as subsystem specs.  Figure 1, from Ref.1, shows a schematic of this automated parametric design process.

The main benefit of using the AVCDU is that it allows the user to define parametric specs of the UUV with great ease and in rapid time.  Although this benefit is inherent in parametric design, it is amplified by the automation process.  This is crucial for UUV’s as there lacks a significant database for UUV design configurations.  A tool such as AVCDU would also allow for such a database to be created due to the benefits of automated parametric design.

The AVCDU was used to analyze a case study of a Long Range UUV (LTUUV) that had been done at Lockheed Martin in 2009.  The purpose of the case study was to analyse sizing trends for various input parameters.  Figure 9, from Ref. 1, shows some of the resulting configurations from design optimizations based on the sizing trends.

Ref. 1: Brown, C., Clark, R.P., “Using a Novel Vehicle Conceptual Design Utility to Evaluate a Long-Range, Large Payload UUV”, Lockheed Martin MS2, IEEE 978-1-4244-4333-8/10, 2010.

Link: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5664540&tag=1