User`s Manual for Genair - utoronto-comp-aero
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1. mirror scale and shear For example say crv fus and pts are a Curve a Fuselage and a list of Point objects respectively then the following commands are valid 28 Again use the tab completion feature of Python to see all available functions 29 To be precise its data points would be saved if the airfoil is not fitted This is because save_IGES only saves what would be displayed by the draw function ie what is returned by the draw method of a Part object More on this topic in Sections and 30 Use ing Python s help system to see the full inheritance tree of an object e g help SODUBISUL z 09 f WOI s qou p z fi uorgegou 97 pue s ouejsur rtour IO OJ9Z SOJOUDP TOQUI S oY 9917 JLATYRIDOSSE OY u IRUOL Jo ure orp ssep ese T AMSA KYTATYRIDOSSe a5 qosgunN 352 q013o Td SQUBILISYUL USPPTH 9TTANA oun Toda omoa 9S9PJANS SAND qurod PIJ sqinu UO0ryeyuaura dur 91NIIN1ISGUTM Juorqounr 19pTON93 TSSNH dTIBUTM xue_Ten ISpTOWNBUTITOA TTOFATY f urqeo eselesny OTTOSeN qyeroIty 10 gt gt gt draw crv fus pts gt gt gt crv elevate 1 gt gt gt fus glue fus rotate 902. reparam_arc_length_curve 4 Component Based Aircraft Design The only package in Genair that knows anything about aircraft design is geom Its main challenge is to translate the vocabulary of an aircraft designer to the classes and functions of the nurbs package Like most tools of its kind Genair takes a component based approach to aircraft design For example a wing body configuration is generated from a wing and a fuselage component In Genair each component is assigned a different class and each class is derived from the same base class Part see Figure I 4 1 Part Class The Part class is defined in the geom part module It is to the Airfoil Wing etc classes what the NURBSObject class is to the Curve Surface and Volume classes i e it implements functionality common to all aicraft components 55 The attributes of the Airfoil class are explained in Section 56 This example is for demonstration purposes only the second command is more intuitively written as af rotate 90 57 fit py defines many other useful functions related to the inter polation and approximation of curves and surfaces have a look 18 4 1 1 Common Attributes The Part class implements the following basic properties and methods bounds symmetrize colorize clamp and copy Refer to their docstring and source code for more information Analogous to the Point and NURBSObject classes
3. If everything looks fine then the last step is to save the files required to run Jetstream This can be done with the following commands gt gt gt opti axial write_axial_connectivity and gt gt gt ffds a ffd for a in axials gt gt gt gd write_patch ffds The first command saves the FFD volumes and axial curves in two separate B spline files b It also saves connectivity information in a format that is analogous to the patch con file As for the write_patch method of the Grid object it saves anew patch con file that contains additional information such as which embedded surface control point belongs to which FFD volume The above commands are decoupled i e you don t need to embed control points prior to calling write_axial_connectivity and conversely you don t need to call set_module variables prior to calling write patch In the connectivity file the type of a joint refers to 0 for a normal joint 1 for a joint that connects two or more axial curves at their common tip and 2 for a joint that attaches the tip of an axial curve anywhere along another axial curve The make_joints_from_axials utility can automatically detect Type O and 1 joints Type 2 joints must be specified manually 84 Here because wO has dihedral you must use a0 snap_ffd to snap the first row of FFD volume control points on the y 0 plane prior to embedding the surface cont
4. The coordinates of a Point object are actually stored on its xyzw at tribute 2 Do not modify this attribute directly e g use gt gt gt pt xyzw 1 0 None None None as opposed to gt gt gt pt _xyzw 0 1 0 Actually you can safely modify xyzw as long as you make the modifications in place If you do the only downside is that the position of the point will not be updated in the OpenGL window s if any 3 1 2 NURBSObject Class The NURBSObject class is defined in the nurbs nurbs module It is the base class of the Curve Surface and Volume classes see Figure I respectively de fined in the nurbs curve nurbs surface and nurbs volume modules As explained in gt gt gt nurbs nurbs NURBSObject 32 A common example is when generating a tracjectory curve for a Wing object 33 Like most classes discussed here the Point class has already been injected in your namespace i e Point is shorthand for nurbs point Point 3 4 In Python the underscore denotes a private object it is intended to discourage you from using that object 35 None tells the Point object to keep a coordinate intact 36 This is a recurring concept in Genair make sure to understand the section on Copies and Views of the Tentative NumPy Tutorial 5 12 it is fully defined by a ControlObject object storing control point coordinates degree s and knot vector s The ControlOb
5. You may notice that none of the surfaces are trimmed where components intersect This is good practice Indeed because the geometry produced by Genair is likely to be meshed in an external application anyway and because the IGES file format is ill suited to export trimmed geometry it is best to let the external application do the hard work i e clean up and trim the geometry for you You may also notice that the first wing segment of the blended wing body has a very specific and well delineated planform and that the B spline function used to achieve this nonlinear taper is different than the one used to scale the tip airfoils in the vertical direction In this case both B spline functions were created from the same BSplineFunctionCreator2 object For your convenience this object has been stored on the Sc attribute of the Aircraft object 7 so assuming that bwb is the Aicraft object you may inspect it like so gt gt gt bwb Sc design and you may retrieve the B spline functions with something like gt gt gt r n 1000 200 gt gt gt scx bwb Sc fit r n gt gt gt scz bwb Sc fit r n di 2 76 The make_ruled_surface function is part of the NURBS toolbox discussed in Section 3 4 77 In ANSYS ICEM CFD look for the Repair Geometry tab 78 BSplineFunctionCreator objects are normally saved as separate pickles 25 Finally both the blended wing body and the box wing feature corner fillets
6. gt gt gt for pt in pts pt copy O but these are not gt gt gt draw pts Not a PlotQbject gt gt gt crv glue Not a Part gt gt gt fus elevate 1 Not a NURBSObject The remainder of this manual focuses on the Point and NURBSObject classes of the nurbs package Chapter 3 and on the Part class of the geom package Chapterl4 Before that here is an overview of the file structure used in Genair main py The script used to launch Genair It imports commonly used objects such as the Airfoil and Wing classes the draw function etc and injects them directly into the IPython namespace These objects are not listed by hwhos and will not be deleted by a soft reset i e reset s doc The directory related to the documentation Includes this user s manual ffd see Figure 1 The directory related to FFD It defines the FFDVolume class which is used for example by the geom package geom see Figure 1 The directory related to aircraft design It defines the family of Part classes Implements high level utilities including the save and load functions and the glue unglue mechanism nurbs see Figure 1 The directory related to NURBS It defines the Point class and the family of NURBSObject classes Implements low level util ities including data reduction and point inversion algorithms opti The directory related to Jetstream It defines the Grid Axial and Joint
7. map fit the grid using Jetstream 4 set up the GCS using Genair and 5 optimize the geometry using Jetstream The remainder of this section addresses Step 4 A 1 Fortran Interface First off you need to compile the Fortran I O interface of the opti package Simply navigate to opti io and type make in your shell Make sure that the FC variable in the Makefile points to a valid Fortran compiler A 2 Plot3D and Connectivity Files Following Step 3 you will need these four files newgrid g typically renamed as grid g grid map grid con and patch con A good place to put these files is in a subdirectory of play and a typical usage session goes like 79 Of course you don t have to use Genair in Step 1 but doing so will greatly facilitate Step 4 80 Tip the Unix command which can help you locate the executable 81 To be precise grid g is not strictly required to set up the GCS i e you could just copy and rename grid map to grid g 27 gt gt gt gd Grid gt gt gt gd read_grid gt gt gt gd read_connectivity gt gt gt gd read_map gt gt gt gd read_patch gt gt gt save gd fn gd p The Grid class is defined in the opti grid module It can be thought of as a visual interface to the grid connectivity files of Jetstream A Grid object has five attributes blk iface bcfa
8. the Part class implements all five transformation functions translate rotate mirror scale and shear as methods For example assuming w is a Wing object one could sweep it back like so 59 gt gt gt w glue gt gt gt w shear 30 The glue and unglue methods of a Part object control which objects actually transform when the Part object is transformed In the previous ex ample these objects include the trajectory curve w T the wing surface w nurbs etc but exclude the orientation curve w Bwv More specifically the glue unglue mechanism keeps track of a list of Point and NURBSObject objects assigned to a Part object Every object in that list is also given a pointer to the list Hence transforming any object in the list either through one of the two translate modes of the OpenGL interface Section 3 2 or one of the five class methods Section 8 3 has the same effect than transforming the Part object itself For example the commands gt gt gt w glue gt gt gt w nurbs shear 30 are equivalent to the previous ones The glue unglue mechanism is also responsible for updating the family tree of a Part object In the previous example if w had a Wingtip object assigned to it then the wingtip surfaces would have also been sheared Note that gluing a component also unbinds it from its parent if any So
9. at wing wing transitions Those are actual Wing objects generated with the help of the BSplineFunctionCreator3 class 26 A Workflow with Jetstream Genair can help you set up the geometry control system GCS implemented in Jetstream There are in fact many common features between the two similar to the trajectory curve of the Wing class Section 4 1 3 the GCS uses axial curves and similar to the WingMerger class Section 4 1 4 the GCS uses joints to connect axial curves one after the other Note that despite the flexibility of the GCS it is unlikely that the default implementation will satisfy your own needs For example the use of axial curves to control FFD volumes is not necessarily recommended So as a first warning be prepared to tweak the code Also note that the material discussed in this section is for your convenience only In particular the implementation of the GCS in Jetstream is capable of more than what you can set up with the utilities provided by Genair Again be prepared to tweak the code One more note keep in mind that the GCS is ill suited to handle surface surface intersections such as wing body junctions It can however support wings of arbitrary topology including boxed and braced configurations Now that you have better idea of what you are getting into here is the recommended workflow between Genair and Jetstream 1 generate the geometry using Genair 2 generate the grid using ANSYS ICEM CFD 3
10. classes as well as utilities to help set up the geometry control system for optimization purposes play The directory that Genair puts you in upon launching Use it as a sandbox plot see F igure 1 The directory related to OpenGL It defines the Plot Object class together with the draw function Integrates the pyglet event loop with the IPython shell 3 Non Uniform Rational B Spline Library A NURBS library is a set of utilities that specializes in the generation and manipulation of NURBS In Genair it is a completely independent entity in particular it has no notion of the geom package 31 31 Hence it may as well be used by an application other than Genair 11 The goal of Genair is to automate aircraft design by making smart and efficient use of the NURBS library However for increased flexibility Genair sometimes forces you to directly interact with the library 2 It is thus helpful to know how it works and what it can and cannot do Most classes and functions discussed here are fairly well documented don t hesitate to use the and operators to learn more about them 3 1 Point and NURBSObject Classes 3 1 1 Point Class The Point class is defined in the nurbs point module As explained in gt gt gt Point it can be used either as a regular point or more commonly as a control point Example usage gt gt gt pt Point 1 2 3 gt gt gt pt xyz gt gt gt pt xyzw
11. it just so happens that the example given also uses the NACA 0012 airfoil so go ahead and follow it step by step starting with gt gt gt af Airfoil n0012 dat This commands creates an instance of the Airfoil class and assigns it to the variable af 5 Again the first command assumes that you are using the Anaconda Python distribution see Section 2 11 6 The play subdirectory is not tracked by Git so use it as you please 7 In IPython the character denotes a magic function To learn more about IPython s magic function system type magic 8 The operator is another extremely useful feature of IPython it lets you inspect an object s docstring without leaving the prompt Similarly the operator lets you inspect not only an object s docstring but also its source code Both 2 and can be used on any Python object e g try using them on the pwd magic function At this point it is worth mentioning that similar to Matlab Python can list the variables defined in your namespace by typing whos The output of the previous command will have informed you that the data file contains 132 points Indeed for this particular instance of the NACA 0012 airfoil the lower and upper halves are each defined with 66 points Type lhead n0012 dat to verify this information Note also that the first line of n0012 dat has been stored in gt gt gt af name In c
12. the WingStructure class As you can see from gt gt gt geom misc WingStructure it defines only two public methods generate_spars and generate_ribs The first extract u directional curves from the lower and upper halves of a wing 75 Tip when translating the pilot points of an FFD volume make sure to be in either one of the xy yz or zx views 24 before linearly interpolating them The second takes a similar approach but with v directional curves Note that similar to a Wingtip object a WingStructure object can be instantiated directly from a Wing object through the generate_structure method 4 2 Examples The aircraft components described in the previous section are for the most part highly flexible This section gives examples of how this flexibility can be exploited in the context of unconventional aicraft design The play examples directory of Genair contains a conventional tube wing ctw p a box wing bw p a blended wing body bwb p and a strut braced wing sbw p configuration All four configurations are saved as Aircraft objects Make sure to inspect each one of them e g gt gt gt ctw load ctw p gt gt gt ctw colorize gt gt gt draw ctw ctw symmetrize and try to pay attention to things like what trajectory curve was used for each wing segment which airfoils were used how many FFD applications did the fuselages have
13. through the cpts interface in order to correctly update the OpenGL window s if any Once a ControlObject object is defined a NURBSObject object is easily instantiated Continuing our example 8 39 gt gt gt c Curve cpol 2 The cobj p and U attributes of a NURBSObject object store the Con trolObject object degree s and knot vector s respectively A NURBSObject object can be modified by modifying cobj or U Mod ifying cobj consists of modifying Pw in place as explained above This is typically achieved through one of three interfaces 1 cpts as explained above 37 N 2 3 and 4 for the ControlPolygon ControlNet and ControlVolume classes respectively 38 The degree is specified as a 1 tuple to be consistent with the Surface and Volume classes 39 If unspecified the knot vector is assumed uniform 13 2 OpenGL as explained in Section 3 2 and 3 transforms as explained in Section 3 3 As for modifying U the recommended approach is to simply reassign the attribute e g gt gt gt c U np array 0 0 0 2 2 2 Internally the library checks whether the new knot vector s are valid 4 This won t be possible if the modifications are performed in place For example although the command gt gt gt c U 0 0 2 is technically valid the resulting knot vector is invalid Modifying p on an existing NURBSObject ob
14. valid knot vector 42 As of February 2015 the reduce method is not imple mented on the Volume class 14 The second command first instantiates a Curve object of degree 1 which is immediately used to instantiate a Curve object of degree 3 which is immediately used to instantiate a Curve object that has one extra control point toward the tip Although the same could be achieved with gt gt gt cpol ControlPolygon Point Point y 0 8 Point y 1 8 ES Point y 2 8 Point y 3 gt gt gt T Curve cpol 3 np array 0 0 0 0 0 8 1 1 1 114 9 in general it is far more difficult to obtain a good parameterization with this second more manual approach 3 2 OpenGL Interface The OpenGL interface of Genair is key to a productive design session The idea is to quickly inspect or even modify parts of your design by opening and closing OpenGL windows on the fly The OpenGL interface is not intended to replace the command line interface but rather to supplement it As such the OpenGL windows should be closed as soon as you are done working with them Besides opening too many windows at the same time will reduce the overall responsiveness of the application 3 2 1 The draw Function The draw function opens a new OpenGL window For example type gt gt gt draw T to render the Curve object defined at the end of the previous section An OpenGL window is an instance of the Figure class When
15. you open a new window Genair automatically injects the Figure object in your namespace under the variable name figN where N is the number of times you have called the draw function so far 44 That same variable is automatically deleted from your namespace when you close the window As explained in gt gt gt draw no matter what combination of PlotObject objects see Figure 1 you give to draw only Point and NURBSObject objects are actually rendered 8 All the points curves surfaces and volumes that a Figure object is aware of are stored in its pos attribute 43 The number displayed in the bottom left corner of the window is the frame per second FPS in general a window is considered responsive if its FPS is at least 60 Hz 44 The same name is given to the window s caption so it is easy to know which variable corresponds to which window 45 When a Part object is drawn draw draws the objects returned by its draw method see Section 4 1 1 46 For Volume objects only the control point lattice is rendered not the underlying NURBS representation 15 If you want to add remove any PlotObject object to from an existing OpenGL window use the inject deject method of the Figure object For example say srf wi and pts are a Surface a Wing and a list of Point objects respectively then one could do gt gt gt draw srf wi gt gt gt fig2 inj
16. NumPy Tutorial 5 Pay special attention to the section on Copies and Views Finally Genair uses IPython for its command line interface IPython can be thought of as the Command Window of Matlab but for Python I suggest you read the Introduction chapter of IPython s documentation 7 Pay special attention to the section called Enhanced interactive Python shell including the subsection called Main features of the interactive shell 2 Introduction 2 1 Installation 2 1 1 Python Distribution Before you install Genair you will need a Python 2 interpreter along with the NumPy 5 SciPy 6 IPython 7 PyOpenGL 8 pyglet 9 and PIL packages While it is possible to install all of these using the standard Distutils I highly recommend using a third party Python distribution such as Continuum Analytics Anaconda 11 Anaconda is free of charge and ships with a very handy package manager called conda The following instructions assume that you have installed Anaconda but they can be easily adapted to any Python distribution If you have not already done so start by updating conda followed by Ana conda itself conda update conda conda update anaconda Next create a new conda environment called genair and activate it in your current shell conda create n genair pip source activate genair The second command should have modified your shell path and prepended the string ge
17. User s Manual for Genair Hugo Gagnon February 1 2015 Contents 1 Preliminaries E A w 1 2 Suggested Readings a DO Ar atte 82 Ge Sy He Ge A RO ea de 2 2 Quick Start 2 3 Saving and Loading 3 Non Uniform Rational B Spline Library 3 1 Point and NURBSObject Classes o 3 2 OpenGL Interface 3 3 Transforms 34 Toolbox sac s ss e s di a A 4 Component Based Aircraft Design Al Part Glass as y z k Ce e Q T S Sad Sha a SU M S W eva QV aa 4 2 Examples Uk h woa ee ee IS aen N a sas Z ew we tos I i ad a arta B Suggested Scripts B 1 Multi Segmented Wingl o 1 Preliminaries 1 1 Scope Genair is a high fidelity conceptual aircraft design tool At the moment it is most useful to generate the outer mold line of general aircraft such as the blended wing body the box wing the truss braced wing etc It does that through a component based approach whereby wings fuselages nacelles etc can be arbitrarily assembled in three dimensional space Genair has been developed for high fidelity exploratory aerodynamic shape optimization As such it emphasizes on high quality surfaces flexible aircraft components and an interactive interface The graphical capability of the inter face has been kept to a minimum The intention was to prioritize the develop ment of an intuitive API meant to steer large scale multidisciplin
18. al gt gt gt fin glue gt gt gt fin dihedral 90 You could use a similar approach to generate the upper Wing object but in this case it is more convenient to simply copy the lower Wing object and to give to that copy a 180 degree dihedral gt gt gt upper lower copy gt gt gt upper glue gt gt gt upper dihedral 180 Now is a good time to save your work gt gt gt save lower fin upper fn lower_fin_upper p 18 This is a common example of where you are required to directly interact with the NURBS library The library is discussed in Chapter 3 for now to see other functions available in its toolbox type nurbs tb at the prompt followed by the Tab key 19 As explained in aE twist and taper are easily specified through B spline functions 20 By default the second command will show you the NURBS representation of the final Wing object In Genair keep in mind that what you see is only a triangulation of the actual NURBS curves and surfaces Type draw to find out more 21 Alternatively one could have generated a trajectory curve with the point Point x 1 73205081 y 3 z 0 before orienting and fitting the wing Try it 22 The glue unglue mechanism is explained in Section EL Basically it is necessary so that for example when sweeping a wing not only does its NURB representation shear but also its trajectory curve wing tip if any etc 23 Again this ex
19. ample reflects the fact that in Genair there are often multiple ways to arrive at the same result You may have noticed that all three wing segments are positioned relative to the global origin See it for yourself draw lower fin upper What remains to be done is to connect them one after the other and to make sure that the connections are watertight The WingMerger class does that for you gt gt gt box WingMerger lower fin upper gt gt gt box merge Finally you should save your work one last time gt gt gt save box fn box p and perhaps even export the geometry in IGES format if you intend on using it in an external application such as ANSYS ICEM CFD The next section describes how to do this 2 3 Saving and Loading The save and load functions demonstrated in the previous section are thin wrappers built around the cpickle module A pickle is a binary file typically with the extension p that stores any number of any Python objects well almost In Genair pickles are typically very small in size and are thus ideal to share work with others It is important to understand that pickles are not specific to Genair For example the snippet gt gt gt def power2 x S return x 2 gt gt gt save 0 1 np array 3 2 1 power2 works as expected You have probably figured out by now that the save function can take an arbitrary number of arguments Conve
20. aring origin is by default the root of the wing s trajectory curve Therefore if you want sweep with respect to say the trailing edge curve then you must reassign the T attribute first e g gt gt gt wO T wO TE gt gt gt wO glue wO sweep 20 At any point of the design process you may also reassign the half attribute of a Wing object For example if you are designing a vertical tail then use a value of 0 or 1 to only show the lower or upper portion of the wing surface respectively 4 4 1 4 WingMerger Class The WingMerger class is defined in the geom wing module As explained in gt gt gt WingMerger 73 Of course this step must be performed prior to fitting the wing 74 The attribute merely modifies the list returned by draw not the internal representation of the Wing object nor of its child object s if any 22 it merges wings one after the other The wings can be arbitrarily positioned and oriented in space prior to the merge process The only requirements are that the connecting tip s must share the same airfoil as well as the same chord and twist Building on the example of the previous section first generate a Wing object that is merge compatible with w0 e g gt gt gt w1 Wing al a0 gt gt gt w1 orient T Tw tw reverse show False gt gt gt wi fit scs sc reverse None sc reverse show False gt gt gt wi glue wi dihedral 45 N
21. ary optimiza tions Genair parameterizes aircraft components with non uniform rational B spli nes NURBS the same mathematical representation used in CAD Hence Genair can be thought of as a hybrid between CAD and a parametric air craft design tool The main difference with CAD is that model topology is ignored Moreover surface trimming at wing body junctions and the like is still somewhat experimental Genair uses object oriented programming in Python to encapsulate aircraft components Each component defines its own construction recipe thereby hiding most of the geometry generation process to the user Naturally a good understanding of NURBS or even Python is still required when designing custom shapes or implementing new components 1 2 Suggested Readings Genair is not your typical CAD package in that it remains a fairly low level library of classes and functions The advantage is an increase in flexibility the disadvantage is the steep learning curve Here are some topics I suggest you brush up on before you install Genair 1 2 1 Non Uniform Rational B Splines Anyone serious about aircraft design should know about NURBS The go to reference for NURBS is surprise surprise The NURBS Book 1 I suggest you read Chapters 1 to 4 and skim through Chapters 5 to 10 If you are short on time then at least read On NURBS a survey 2 By the end of your readings you should be able to answer questions such as wh
22. at is the effect of multiple knots or coincident control points on the geometric and parametric continuity of NURBS curves and surfaces 1 In practice at least in Prof David Zingg s research group these limitations are inconsequen tial since first we assume fixed topology throughout an optimization and second surface trimming is in any case best handled by the geometry kernel e g Parasolid native to the mesh generator e g ANSYS ICEM CFD used to generate a watertight grid 1 2 2 Free Form Deformation Free form deformation FFD is not only central to the geometry control system implemented in Jetstream Appendix A but is also used in Genair for the manual design of aircraft components In both cases a significant departure from standard FFD is the fact that it is the control points of the deforming objects that are manipulated as opposed to their discretization 1 2 3 Python NumPy and IPython To use Genair effectively you will need a working knowledge of Python Fortu nately Python is very easy to learn and use I suggest you read The Python Tutorial which is part of the standard documentation 4 Pay special atten tion to the chapters on Data Structures and Classes What makes Python a scientific computing language comparable to Matlab is NumPy Genair makes extensive use of NumPy s array object To learn about the array object and its use in linear algebra I suggest you read the Tentative
23. ce ptch and stch These are all Python lists that store Block Interface Boundary Patch and Stitch objects respectively 32 A sixth type of object Map objects are stored directly on the map attribute of the Block objects Note that all six object types are derived from the NURBSObject classes so they can all be for example rendered in OpenGL window s Moreover each object type im plements a print_info method which is useful to verify information such as boundary conditions and connectivity between patches 83 A 3 Geometry Control System Essentially a Grid object holds the surface control points that go inside the FFD volumes of the GCS The next step is thus to define those FFD volumes and if necessary their assigned axial curve For wings Genair can automate much of this step provided that the wings were generated by Genair in the first place as suggested in Step 1 above Take for example the wing component of the Aircraft object saved in the ctw p file of the play examples directory gt gt gt ctw load ctw p gt gt gt ctw blowup gt gt gt wO wl wing wings You may easily generate the FFD volume and axial curve for each wing with the make_axial_from_wing function of the opti axial module e g gt gt gt a0 opti axial make_axial_from_wing w0 LE 2 1 10 4 2 3 3 1 offsets 0 01 0 01 0 0 0 01 0 01 gt gt g
24. continuing the previous example the commands gt gt gt w tip glue gt gt gt w tip shear 30 shear only the wingtip Analogously the command gt gt gt w tip unglue unglues only the wingtip but the command gt gt gt w unglue 58 Again use the and operators of IPython 59 A more convenient alternative would be to use the sweep attribute of the Wing class see Section 4 1 3 60 Have a look at the _glue method of a Part object to see which objects it controls e g w _glue 61 FYI the list is a Python list called glued 19 unglues both the wing and its wingtip Finally each Part class implements its own draw method Similar to glue this method returns a list of objects the difference being that the list only contains objects that the designer is most likely to be interested in at a given stage of the design process For example once a Wing object has been fitted drawing it should no longer display its trajectory curve w T but rather its lower and upper surfaces w halves This information is used by a number of functions other than draw including those in the geom io module 4 1 2 Airfoil Class The Airfoil class is defined in the geom airfoil module As explained in gt gt gt Airfoil it creates a B spline approximation to an airfoil from a set of data points The Airfoil class is well documented please refer to th
25. e Intended section of its docstring and make sure to read the docstring of each one of its methods as well You may also want to revisit Section 2 2 When fitting an airfoil for the first time make sure to find the right selection of parameters that will give you the best possible fit Generally speaking a good fit is one that results in few control points say less than 40 and smooth curvature plots Unfortunately depending on the number and quality of the sampled data points you may need to try several combinations of parameters before you achieve a good fit For example a reasonable fit of the NASA SC 2 0614 airfoil is achieved with the parameter E set to 0 0015 4 65 66 gt gt gt a Airfoil sc20614 dat gt gt gt a fit E 0 0015 Once you have found the right selection of parameters make sure to save your airfoil to avoid repeating the same process The nurbs and halves attributes of an Airfoil object store the airfoil curve in two equivalent forms nurbs is a single curve that loops around the airfoil counterclockwise looking toward the negative y axis starting from the trailing edge It is parameterized on 0 1 where the parameter 0 5 corresponds to the leading edge halves is a list of two curves each starting at the leading edge representing the lower and upper portions of the airfoil They are also both parameterized on 0 1 The direct analogs of the nurbs and ha
26. ect pts gt gt gt fig2 deject wi A Figure object does not render the same object twice e g in the above example the fourth command gt gt gt fig2 inject srf has no effect However the same object can be rendered in two or more OpenGL windows simultaneously This is useful when modifying an object under different views For example try the following with the Curve object defined at the end of the previous section gt gt gt draw T draw T Reorient the view in each window as you please and then pick and drag individ ual control points the next section explains how The curve should be updated at the same time in both windows 3 2 2 Controller An OpenGL window is controlled via mouse and keyboard input The con trols are listed in the header of plot controller py In particular use the left middle and right buttons of your mouse to respectively rotate zoom and translate the view It is possible to pick Point and NURBSObject objects inside an OpenGL window Try picking T in one of the two windows opened in the previous example If the pick is successful the curve should turn green Next try picking its control points one by one 49 Everytime you pick something the Figure object updates three variables in your namespace gt gt gt last_picked_xyz gt gt gt last_picked_object gt gt gt last_picked_objects The first two are self explanatory the third is a Python list of the las
27. ented_wing WingMerger ws multi_segmented_wing merge 30 References N o N Q 10 L Piegl and W Tiller The NURBS Book Springer 2nd ed 1997 L Piegl On NURBS a survey Computer Graphics and Applications IEEE 11 1991 no 1 55 71 T Sederberg and S Parry Free form deformation of solid geometric mod els ACM SIGGRAPH Computer Graphics 20 1986 no 4 151 160 https www python org http www numpy org http www scipy org http ipython org http pyopengl sourceforge net http www pyglet org http www pythonware com products pil http continuum io 31
28. erate a cubic B spline curve to act as trajectory curve gt gt gt T nurbs tb make_linear_curve Point Point y 3 gt gt gt T T elevate 2 and give it some nonlinear dihedral by translating some or all of its control points in an OpenGL window Then create a linear B spline function e g gt gt gt tw BSplineFunctionCreatori end 0 30 fit that shall orient your wing with linear twist gt gt gt wO orient T Tw tw Next create another B spline function to specify taper This time since we want nonlinear taper use say a quadratic B spline function with 3 control points gt gt gt Sc BSplineFunctionCreatori end 2 1 p 2 n 3 gt gt gt Sc design gt gt gt sc Sc fit 67 See the previous section for a suggestion of parameters that will give you a reasonable fit of the NASA SC 2 0614 airfoil 68 Make sure that the transform method has been called on both Airfoil objects 59 The wing profile will be a linear interpolation of these two tip airfoils 7 Do that from a yz view to avoid giving it nonlinear sweep 7 Currently Genair defines two other BSplineFunctionCreator classes example usage for each one of them are given in Section 4 2 72 As a rule of thumb the more nonlinear the twisting function is the larger m the third argument of orient should be here the twisting function is linear so the choice of m is irrelevant 21 The second comma
29. hether pyglet supports your graphics card If it does not then you probably already know it from the error messages triggered by executing main py If there were no such messages then cross your fingers and try this one last command gt gt gt draw Point which should open a black window with a yellow point in the middle of it You can close that window by pressing the Escape key and you can exit Genair like you would exit IPython i e by typing exit at the prompt 2 2 Quick Start To give you a sense of what Genair can do I propose to go over a simple tutorial where you will generate a box wing Start by launching Genair source activate genair genair main py which will automatically put you in the play subdirectory of Genair s root directory You can see this for yourself by typing pwd at the prompt By typing fls you will also see that there is an airfoils directory in play hca into it and type Als once again As you can see the directory already contains a number of airfoil data files For this first tutorial you will fit the NACA 0012 airfoil To do so you will need the Airfoil class but first you should learn how to use it In Genair the easiest way to get information is through the operator e g gt gt gt Airfoil Notice how the docstring tells you what the Airfoil class does and in particular how it is intended to be used In this case
30. ject class is the base class for the ControlPolygon Control Net and ControlVolume classes respectively required to instantiate a Curve Surface and Volume object As explained in gt gt gt nurbs nurbs Control0bject it is fully defined by either Point objects or an object matrix Both formats are stored regardless Example usage gt gt gt pO Point 1 0 w 1 gt gt gt pl Point 1 1 w 1 gt gt gt p2 Point 0 1 w 2 gt gt gt cpol ControlPolygon p0 p1 p2 The n cpts and Pw attributes of a ControlObject object store the num ber of control points minus one the Point objects N 1 dimensional NumPy array and the object matrix N dimensional NumPy array respectively The xyzw array of the Point objects stored in the cpts array are views shallow copies of the corresponding array elements in the Pw array There fore as long as modifications are performed in place modifying either type of arrays _xyzw or Pw modifies the same data For example gt gt gt cpol cpts 2 xyzw None 2 None None is equivalent to gt gt gt cpol Pw 2 1 4 Note the 4 instead of the 2 This is because the xyzw attribute of the Point object automatically converts the coordinates in homogeneous space for you Thus cpts can be thought of as a user friendly interface to Pw Also note that analogous to the Point class you must modify Pw
31. ject does not make sense so the library won t let you What does make sense is to derive a new object that has the same geometric and parametric continuity as the original one but different NURBS degree s This is exactly what the elevate and reduce methods do e g 42 gt gt gt ce c elevate 1 The NURBSObject classes each implement many other useful methods They are as of February 2015 Curve class eval_point eval_derivatives eval_curvature insert split extend refine decompose segment remove removes elevate reduce project reverse Surface class eval_point eval_derivatives eval_curvature insert split extract extend refine decompose segment remove removes elevate reduce trim project reverse swap Volume class eval_point eval derivatives split extract extend refine ele vate project reverse swap I strongly suggest that you read about and experiment with each one of those methods Doing so will ultimately increase both your productivity and the quality of your designs For example to quickly generate a trajectory curve suitable for a blended winglet one could do gt gt gt cpol ControlPolygon Point Point y 3 gt gt gt T Curve cpol 1 elevate 2 insert 0 8 1 40 In this example the same effect can be achieved with the nurbs knot remap_knot_vec function 4 Have a look at the source code of nurbs knot check_knot_vec to see what constitutes a
32. lves attributes are implemented on the Wing class 62 See it for for yourself Wing _draw 63 The default parameters were chosen based on the NACA 0012 airfoil 64 The sc20614 dat file should be located in your airfoils directory See what happens if you set E to its default value of 0 0001 66 Note that this airfoil is a good example where you won t be able to use sharpen 20 4 1 3 Wing Class The Wing class is defined in the geom wing module As explained in gt gt gt Wing it creates a wing by sweeping an airfoil along a trajectory curve Like the Airfoil class the Wing class is fairly well documented Unlike the Airfoil class however it is fairly complex Indeed the Wing class trades a lot of user friendliness for flexibility This level of flexibility is certainly not required when generating trapezoidal wings For such wings it is in fact more convenient to automate the generation process with scripts see Appendix B 1 Rather than describing each and every properties and methods of the Wing class let us go over an example where you will generate a wing with linear twist and nonlinear taper and dihedral Start off by loading two previously fitted airfoils say the NACA 0012 and the NASA SC 2 0614 airfoils 67 68 gt gt gt a0 load n0012 p gt gt gt al load sc20614 p and use them to instantiate a Wing object gt gt gt w0 Wing a0 al Next gen
33. nair to your terminal prompt To install the packages listed above proceed with genair conda install ipython numpy scipy pil Then depending on whether conda search pyopengl returns something or not as of February 2015 it does on OS X but not on Linux use either one of genair conda install pyopengl or genair pip install pyopengl Finally install pyglet genair pip install pyglet To test IPython and NumPy try the following in a new terminal genair ipython which should put you in an IPython shell From there type gt gt gt import numpy as np gt gt gt np __version__ and see if the version string matches the one returned by conda list From time to time say every other month you may want to update the packages to their latest version genair conda update all genair pip install upgrade pyglet 2 1 2 Genair Installing Genair should be as simple as git clone nfs carv d1 people comp aero genair git To test your clone of Genair cd into genair and type source activate genair genair main py 2 By convention in this manual the default Python prompt gt gt gt is used rather than IPython s prompt In n where n Zt 3 Repeat the second command for PyOpenGL if you installed it with pip The first command assumes that you are using Anaconda see the previous section which should again put you in an IPython shell The real test however is w
34. nd will open an OpenGL window where you will be given the opportunity to reshape the default representation curve Pick and translate the middle control point to about x y 0 5 0 5 Alternatively pick the control point without translating it and type gt gt gt last_picked_object xyzw 0 5 0 5 None None at the prompt At this point you can finally fit sweep the wing likewise gt gt gt w0 fit scs sc None sc As explained in w0 fit the shape of the wing will only approximate the true design intent As a rule of thumb the more nonlinear a wing is the less acccurate the approximation will be The approximation can be improved by increasing the value of the argument K but for all intents and purposes this is seldom necessary Notice how the trajectory curve w0 T is almost the same as the quarter chord curve w0 QC This is because the quarter chord point of the airfoils stored on the Wing object each coincides with the global origin If you want the trajectory curve to match say the trailing edge curve then you must translate the airfoils accordingly gt gt gt for a in w0 airfoils xyz a nurbs eval_point 0 a glue a translate xyz You may change the sweep and dihedral of a Wing object through its sweep and dihedral attributes respectively These attributes are sim ple wrappers built around the shear method of the Part class Section 4 1 1 Note that the she
35. ontrast the issymmetric and issharp attributes are both evaluated at runtime At this point feel free to inspect the data points in an OpenGL window 9 gt gt gt draw af Press the F2 key to switch to a uz view and then zoom in using the mouse middle button When you are done close the window by pressing the Escape key 2 Next proceed with the remaining instructions of the example gt gt gt af fit gt gt gt af sharpen gt gt gt af fitQ gt gt gt af transform The last method transforms the airfoil so that its chord length becomes unity and its quarter chord point coincides with the global origin You should now save your work to avoid repeating the same steps everytime you want to use a NACA 0012 airfoil Start by making a new subdirectory in play called tutorial cd into it and then save your Airfoil object likewise 15 16 gt gt gt save af fn n0012 p For the sake of demonstration relaunch Genair navigate to tutorial and type gt gt gt af load n0012 p The Airfoil object that af now points to should be in the same exact state than before and can thus be used in the same exact way Now to the box wing We will assume that the three wing segments lower tip fin and upper meet at right angles This time you will need the Wing class so as before start by learning about it 10 The reason why this command draws points and no
36. ow use the following commands to merge w0 and w1 gt gt gt wm WingMerger w0 w1 gt gt gt wm merge and use the merged_wings attribute of wm to retrieve the new merged Wings objects 4 1 5 Wingtip Class The Wingtip class is defined in the geom wingtip module As explained in gt gt gt geom wingtip Wingtip it creates a wingtip to fill the gap located at the tip of a wing Use a Wing object to instantiate a Wingtip object Continuing the example above gt gt gt wm0 wml wm merged_wings gt gt gt tip wm1 generate_tip gt gt gt tip fi110 See the docstring of the fi11 method to learn how to control the shape and length of the wingtip extension Note a Wingtip object is stored by a Wing object on its tip attribute 4 1 6 Fuselage Class The Fuselage class is defined in the geom fuselage module As explained in gt gt gt Fuselage it creates the outer mold line of a fuselage from a bullet shaped cylinder by successively molding the latter with FFD volume s Unlike most other classes discussed in this chapter the Fuselage class heavily relies on the interactive features of the OpenGL interface Section 3 2 23 Please refer to the Intended usage section of the Fuselage class docstring to get pointers on how to use the FuselageMolder and FairingMolder classes Both of these classes are derived from the FFDVolume class see Figure so refer
37. rol points 85 A Point object is successfully embedded if it turns green except if it is a control point falling on the origin of its NURBSObject object in which case it won t turn green even though it was successfully embedded Tip use the undo mechanism Section 3 2 2 to come back to the initial state 29 B Suggested Scripts B 1 Multi Segmented Wing The following script generates and merges an arbitrary number of trapezoidal wing segments The user must provide the Airfoil objects at each break point The variable REF refers to the curve about which sweep is applied permissible values are LE QC and TE AIRFOIL a0 al a2 TWIST 0 O 0 CHORD 5 82 3 40 0 78 SPAN 4 66 8 44 DIHEDRAL 2 2 SWEEP 30 30 REF LE HHH class TrapezoidalWing Wing def __init__ self a0 al tO t1 cO cl s d p super TrapezoidalWing self __init__ a0 al tw BSplineFunctionCreatorl end t0 t1 fitO sc BSplineFunctionCreatorl end c0 c1 fit T nurbs tb make_linear_curve Point Point y s self orient T Tw tw show False self fit scs sc None sc show False if REF is not QC self T eval self REF self glue self dihedral d self sweep p ws for i in xrange len AIRFOIL 1 w TrapezoidalWing AIRFOIL i AIRFOIL i 1 TWIST i TWIST i 1 CHORD i CHORD i 1 SPAN i DIHEDRAL i SWEEP i ws append w multi_segm
38. rsely Load takes only one argument but returns a list of arbitrary length While intuitive this approach works best if you are familiar with the concept of unpacking 5 For example assuming Q a is a Python list of length 3 use gt gt gt save a instead of gt gt gt savel a 0 ali a 2 Similarly use gt gt gt a0 al a2 load instead of26 27 24 Part of the Python s standard library 4 25 This concept is also very useful when it comes to using the draw function described in Section 26 The second command is more succintly written as a0 al a2 a 27 FYI length 1 sequences can also be unpacked e g a0 a versus a0 a 0 gt gt gt a load gt gt gt a0 al0 al ali a2 a 2 The geom io module defines a few other functions related to I 0 8 Out of those you will probably find save_IGES most useful Note that ultimately save_IGES only saves points and NURBS curves and surfaces everything else gets discarded For example assuming af is an Airfoil object then gt gt gt geom io save_IGES af only saves the NURBS curves representing the lower and upper portions of the airfoil 9 2 4 Code Overview If you have read and understood Sections and 2 3 then you already know more about Genair than you think To learn about some other useful features e g geometrically nonlinear wings and automatically generated wingtip
39. s you can go ahead and jump to the relevant sections without worrying too much about the code structure If on the other hand you plan on implementing new features or even on becoming proficient with Genair I strongly suggest that you spend some time understanding the machinery behind the interface Indeed the true intent of this manual is not so much as documenting each and every aspect of Genair as to explaining its design philosophy Central to this philosophy is the notion of inheritance As seen from the class diagram of Figure 1 all classes defined in Genair at least those shown here are derived from the PlotObject class which means that an instance of any one of those classes will be recognized by the draw function This is easily remembered In general the end user you only needs to know about three fundamental classes Point NURBSObject and Part all of which are shown in Figure 1 The first is universal and easily understood The other two are specific to Genair and are based on the same general principle that a superclass inherits the properties and methods of its base class For example the FFDVolume class inherits its p attribute from the NURBSObject class and the Wing class inherits its glue method from the Part class Now even though the Point NURBSObject and Part classes are fundamentally different they still share some common methods too including copy translate rotate
40. t al opti axial make_axial_from_wing w1 LE 2 1 10 8 2 3 3 1 offsets 0 01 0 01 0 0 07 0 01 0 01 gt gt gt draw wing a0 al Next you should check if the wings fit inside the FFD volumes Normally you would do that by embedding the control points of the patches stored on a Grid object i e 82 The order of the objects stored in each list is implied from the connectivity files 83 Tip if you don t know the index of an object in a list then pick it from an OpenGL window and type last_picked_object print_info in the prompt 28 gt gt gt draw gd ptch axials gt gt gt for a in axials a ffd embed gd ptch but for this example try embedding the surface control points of the Wing objects instead Make sure that all the control points are successfully embedded including those at the tip and at the symmetry plane 84 85 Next proceed with extracting joints called points in Jetstream from the axial curves gt gt gt axials a0 al gt gt gt joints opti axial make_joints_from_axials axials after which point is it customary to check the whole setup by visualizing the effect of translating joints on the shape of the axial curves FFD volumes and 6 86 wings gt gt gt opti axial set_module_variables axials joints gt gt gt draw gd ptchtaxials joints Again to follow with this example use the Wing objects instead of the grid patches
41. t A be a 4 x 4 transformation matrix and P be a reshaped object matrix then the product A PY achieves the desired transformation The translate rotate mirror scale and shear functions defined in the nurbs transform module each performs A P relative to any arbitrary point line or plane in Euclidean space For example say c is a Curve object then the command gt gt gt nurbs transform scale c cobj Pw 2 L 1 1 0 4 scales c by a factor of 2 in the given direction All five transformation functions are implemented as methods on the Point and NURBSObject classes For example the command gt gt gt c scale 2 L 1 1 0 is equivalent to the previous one That being said using the class methods over the module functions is still preferable First they take less effort to type Second they will correctly update the OpenGL window s if any Third anal ogous to the modes of an OpenGL window they are aware of the glue unglue mechanism described in Section 4 1 So say af is an Airfoil object the com mands gt gt gt af glue gt gt gt af nurbs rotate 90 51 The translation occurs in the plane perpendicular to the view this is also true for the Translate NURBS mode 5 If the point is a control point then the ControlObject object of the NURBSObject object will be automatically updated 53 You can toggle between the two modes by simul
42. t a NURBS curve is because the airfoil has not beeen fitted yet 11 The OpenGL interface is explained in Section Meanwhile have a look at the header of plot controller py 12 As explained in El although Genair supports multiple windows running at the same time it is best to close them when not needed 1 Don t forget to use the operator to learn about the purpose and default arguments of each method These transformations matter when constructing a Wing object Section 4 1 3 15 Try the mkdir magic function 16 The next section gives an overview of the saving and loading mechanism 17 An alternative would be to generate smooth corner fillets gt gt gt Wing Unsurprisingly the docstring informs you that you need at least one Airfoil object to instantiate a Wing object So go ahead and type gt gt gt lower Wing af Next create the trajectory curve along which af will be swept 8 gt gt gt T nurbs tb make_linear_curve Point Point y 3 Assuming that you don t want any twist nor any taper you can finalize the Wing object with the following two commands 9 gt gt gt lower orient T gt gt gt lower fitQ Finally give it some sweep 22 gt gt gt lower glue gt gt gt lower sweep 30 To generate the tip fin Wing object repeat the same exact process but use Point z 1 instead of Point y 3 Also instead of sweeping it give it a 90 degree dihedr
43. t picked object s that gets reset on an unsuccessful pick In conjunction with last picked xyz it is sometimes convenient to pick one of the two four extremities of a curve surface To do so pick any point 47 In other words the pos attribute of the Figure object does not change 48 Make sure to deactivate the Num Lock key if you are on Linux 49 Tip you will need the F8 key 50 Listed by the magic function whos 16 closest to the extremity but press the right button of your mouse instead of the left one Similar to the Vi text editor an OpenGL window can be in one of several modes A window responds differently depending on which mode is active The default mode Translate Point allows you to not only pick Point objects but also to drag them around 51 52 Similarly the Translate NURBS mode allows you to translate NURBSObject objects The mode manager is aware of the glue unglue mechanism described in Section 4 1 For example while in the Translate NURBS mode try translating an Airfoil object before and after gluing it Finally the mode manager implements a very basic undo mechanism Despite its simplicity it is actually quite useful but keep in mind that closing a window loses all the undos associated with that window 3 3 Transforms A useful property of NURBS is that an affine transformation is achieved by applying the transformation to the control points Le
44. taneously pressing the Control Alt and N keys 5 Have a look at their docstring e g nurbs transform scale 17 also rotate the lower and upper halves of the airfoil af halves as well as its camber line af CL 55 56 3 4 Toolbox Section 3 1 explains how to instantiate a NURBBObject object either directly through class constructors or indirectly through class methods A third way is through the toolbox of the NURBS library The toolbox helps you generate and manipulate NURBS curves surfaces and volumes It is accessible from the nurbs tb virtual module which is a single point of access to a set of functions collected from curve py surface py volume py conics py and fit py For example the commands gt gt gt 0 X Y 0 1 0 1 0 0 O 1 0 gt gt gt a nurbs tb make_ellipse 0 X Y 3 1 0 3 np pi 2 generate three quarter of an ellipse And the commands gt gt gt al a copy al mirror gt gt gt a2 nurbs tb make_composite_curve a a1 generate a single curve out of two I suggest that you read about and experiment with the remaining tools of the toolbox Doing so will help you understand how the geom package works For example make_swept_surface is at the core of the Wing class Other utilities that you may find especially useful are arc_length_to_param param_to_arc_length and
45. to the latter for more information on how to embed and unembed Point objects including the control points of NURBSObject objects Use the nurbs attribute of a Molder object to revert a Fuselage object back to a previous state For example the commands gt gt gt m fus molders pop gt gt gt fus nurbs m nurbs discard the changes introduced by the last Molder object on a Fuselage object called fus Don t forget to call the finalize method of your Fuselage object at the end of the molding process 4 1 7 Aircraft Class The Aircraft class is defined in the geom aircraft module As explained in gt gt gt Aircraft it is a customized Python dictionary that acts as root for all the Part objects it is composed of More specifically the Aircraft class inherits the properties and methods of both the dict and Part classes Hence an Aircraft object may still be drawn transformed clamped etc However its main purpose is to store other Part objects along with their assigned name e g gt gt gt ac Aircraft wing my_wing fuselage my_fuselage gt gt gt ac items Use the blowup method to quickly resume work from a previously saved Aircraft object 4 1 8 Miscellanea Genair can help you define a few more aircraft components other than the ones presented so far For example the geom misc module defines the Nacelle and WingStructure classes Consider for example
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