4.0 Background Theory

4.1 Hummingbird Characteristics

4.1.1 Flight Characteristics

4.1.2 Hovering Flight Characteristic

4.2 Technology: Hardware and Software Used in the Project

4.2.1 Software

4.2.2 Hardware

4.2.3 MSC/NASTRAN How MSC/NASTRAN Works Aeroelastic Analysis Using MSC/NASTRAN Examples of Bulk Data Entries

4.2.4 CT-Scanner

4.3 MAV Technology and Science



4.0 Background Theory

This section is intended to provide the reader with necessary background information on the hummingbird characteristics, the hardware/software used in the project, and the research findings related to MAVs. The first section will introduce the hummingbird and the special characteristics it possesses. The next section will present a detailed description of those characteristics and why they are important. The last section will list software and hardware used in the research of the project and also a detailed portion on MSC/NASTRAN. Finally, MAV research will be discussed.   4.1 Hummingbird Characteristics
The hummingbird family has about 300 different species and can be found on the continents of North, Central, and South America. Figure 4.1 portrays the Phaethornis Yaruqui species. Hummingbirds are quite small with a length of only 2 ¼ in to 8 ½ in, however, they are not the smallest of all birds. They eat the nectar of flowers for survival and can consume up to half their weight in sugar daily. The reason for this enormous appetite is the hummingbird’s extraordinary flight capability. No other bird can hover as long or as steady as the hummingbird, although, a lot of energy is expended to stay aloft in this hovering attitude. The disadvantage of hovering is the excessive energy required for its success. The excessive energy requires the hummingbird to consume a lot of food. The energy output of a hummingbird in hovering flight is ten times as much as a man running nine miles an hour. Direct comparisons to a human being show that a 170-pound man would have to consume about 130 pounds of bread to keep up with a hummingbird’s energy-output [5, pp. 3-9].  
4.1.1 Flight Characteristics
As previously mentioned, the hummingbird can hover more consistently and efficiently than any bird and is the only bird that has the ability to hover with its body motionless. The hummingbird’s bone structure allows it to move its wings quite differently from "ordinary" birds. Figure 4.2 illustrates the bone composition of the wing of a hummingbird.

Ordinary birds articulate their wings at the shoulder, wrist and elbow. During each wingbeat, their elbows and wrists will fold and bend. Hummingbirds however, cannot articulate at the elbow and wrist, but the wing is free to rotate in all directions at the shoulder joint. Note in Figure 4.2, the upper set of bones is that of a hummingbird while the lower set is that of a pelican. The juxtaposition of these two bone structures exemplify the similarities and differences between ordinary birds and hummingbirds. The hummingbird’s unusual arrangement of bone composition results in notable flying characteristics. The exceptional hummingbird is able to generate thrust from both the down beat and up beat of its wings. In contrast, ordinary birds create the force needed to stay aloft only by the down beat of their wings [5, pp. 204-6].



If a plot of wing-length to weight was made of all natural flying creatures, one would get a graph as shown in Figure 4.3. The figure displays the relationship between wing and total length for the whole range of flying animals in logarithmic coordinates. The slope is approximately 3, which means that the body-weight is proportional to the cube of the wing length. Of course, it is expected that all points will not lie on the average line. In fact, the hummingbird characteristics lie close to the end of the bird region and are on the verge of the insect region. Also, Figure 4.4 shows the relation between the wing beat rate and the wing length. In this figure, we see that the insect or bird to be modeled in the appropriate size range should have a wing beat close to a hummingbird. [5, pp. 212-215]  

4.1.2 Hovering Flight Characteristic  
Figure 4.5 illustrates the figure "8" motif the wingtips of the hummingbird trace in the air while hovering, as well as the wing patterns at various positions. Notice the change in the pitch attitude of the hummingbird as the speed of the bird changes from top speed to hovering. The motion performed while hovering is illustrated in Figures 4.6 and 4.7.

As mentioned, the elbow and wrist do not move relative to each other as seen in Figures 4.5 and 4.6. This motion is a flight characteristic of the hummingbird. Also, notice the direction change of the wing as it completes its cycle. It makes two 180 ° turns in order to create the figure-8.


4.2 Technology: Hardware and Software Used in the Project

The following subsection lists the basic equipment used in our research. It will describe the functions and reasons for using the equipment. Also, a detailed discussion of the CT-Scanner and the MSC/NASTRAN software will be presented. The first list includes the software used to create the MSC/NASTRAN example. This list also contains material on how to create the space-frame and the aeroelastic model of the hummingbird. The second list presents the hardware used to film the hummingbird and the computers on which the software was run.   4.2.1 Software The following list describes the software used to create the space-frame and aerodynamic model of the hummingbird:
  Adobe Photoshop: Scanned images were corrected using Adobe Photoshop version 4.0 for better readability and clarity of pictures and plots.

Adobe Premiere: Premiere was a graphics tool utilized in creating individual pictures from a movie.

Apple Video: This software was used to capture video footage from the VCR to the computer. It was the tool used to create a computerized movie.

HpScan: Photographs and text in books were scanned with the help of HpScan.

Kinetix 3-D Studio Max: This 3-D rendering software enabled us to render the 3-D object and view it from any angle and distance.

Microsoft Word: Versions 95 and 97 were used to put together this report and other documents such as weekly memos.

MSC/NASTRAN: Version 70 of this finite-elements based modeling program will be used to perform aeroelastic analysis on a hummingbird-wing model using the doublet-lattice method as well as a space-frame model.

Omnipage: Scanned text was converted from bitmapped images onto ASCII format (text) with this optical character recognition software. Some NASTRAN code was scanned and then converted to text for comprehension of the aerodynamic segment of NASTRAN.

Omniview: The TIFF files were assembled into a 3-Dimensional object with the aid of this program.

STL_UTIL: The Original 3-Dimensional object was converted from the stereolithography to DXF format for easier manipulation with this utility.

Visualization Toolkit: This program helped us decimate the 3-Dimensional object to a smaller number of facits.

Windows 95, MacOS 8.0, Digital UNIX v 4.0: These were the different operating systems used. MSC/NASTRAN was run on the UNIX system. The MAC OS was the operating system running while the film was transferred from the VCR to digital images. Windows 95 was the base for scanning photographs and putting together the project and the report.

4.2.2 Hardware The following list describes the hardware used to perform the filming and to use the software listed in the section above:   Computers: Macintosh, PCs, Digital DECs and SGI machines were used.

Computer with Framegrabber: This computer was connected to the VCR in order to transfer the necessary film or still images from analog film format to digital format for pre-processing the outline of the bird.

CT-Scanner: Computed Tomography is a completely nondestructive technique for visualizing features in the interior of opaque solid objects, and for obtaining digital information on their 3-D geometries and properties. The scanner has not been used yet but hopefully will assist us in determining a detailed bone composition of the hummingbird. See Figure 5-13.

Digital Camera: A digital camera was used to capture some images of the hardware used in the project such as the hummingbird test setup.

High-Speed Video Camera, Tripod and Spotlights: The High-Speed Video Camera belongs to the Department of Mechanical Engineering and is under the supervision of Dr. Kenneth Ball. This camera has the ability to record at the high rate of 2000 frames per second. A high-resolution camera under the supervision of Dr. Clemens was used to conduct some filming. One of the cameras was placed on the tripod and held still while the spotlights illuminated the box and the bird.

Hummingbird Test Setup: This is where the hummingbird was kept while being filmed. The box is made out of clear plastic and it is therefore possible to film the bird through it. See Figures 5-1 and 5-3.

Mirror Assembly: The mirror assembly supported a mirror at 45 ° which enabled us to film the bird from the top. The hummingbird could then be filmed from both the side and top views simultaneously. See Figure 2-7.

Ruby Throated Hummingbird: The hummingbird is also included as hardware, since no experimental data would be available without it.

Video Recorder: The VCR was connected to the camera and registered the film onto a videotape using S-VHS recording.

4.2.3 MSC/NASTRAN MSC/NASTRAN is a finite element program developed by the MacNeal-Schwendler Corporation. MSC/NASTRAN has very powerful analytical capabilities. It is capable of analyzing stress, vibration, and heat transfer characteristics of structures and mechanical components. [6, p. xiii] Finite element modeling is a numerical method that is used for engineering analysis and can be applied to all classes of field problems including structural analysis, heat transfer, fluid flow, and electromagnetics. MSC/NASTRAN will divide the structure into small elements (usually simple shapes like triangles or rectangles), which form the model of the real structure. The stiffness matrices for the individual elements are calculated. When combined, these matrices form the stiffness matrix for the entire model. [7, p. 268] The finite elements process in MSC/NASTRAN can be summarized by the following paragraph:

The desired structure to be analyzed is input into NASTRAN as a discretized mathematical model containing finite elements, loads, constraints, and structural properties. Next, the computer running MSC/NASTRAN will output any displacements, stresses, forces, mode shapes, plots, or calculations. This data will be used to create graphs or tables depending on the needs of the user. [6, p. 4] How MSC/NASTRAN Works MSC/NASTRAN needs an input file to begin its run. The input file must contain the following in the order as presented below [6, pp. 23-4]:
      a. The Executive Control Statements
        The primary function of this section is to identify and determine the sort of analysis solution to be performed. The CEND delimiter is always needed at the end of this section to inform MSC/NASTRAN.
      b. The Case Control Commands
        The purpose of this section is to specify and determine the type of analysis output required as well as to control Bulk Data Input, and select loads and boundary conditions.
      c. The Bulk Data Entries
        This section is the last required entry and starts with the BEGIN BULK delimiter. These entries include everything about the model: size, geometry, coordinate systems, finite elements, loads, boundary conditions, material properties, and element properties. This section is ended with the ENDDATA delimiter.
 Aeroelastic Analysis Using MSC/NASTRAN
    An aerodynamic model beside the existent structural model is needed to perform aeroelastic analyses in MSC/NASTRAN. Since the structural gridpoints and the aerodynamic grid points will probably not match, some splining techniques are used for both lines and surfaces. These techniques are used to create the transformation matrix from structural grid point deflections to aerodynamic grid point deflections. The aerodynamic forces and moments at aerodynamic boxes are transferred to structural grid points via the transpose of the transformation matrix. There are three supersonic and one subsonic lifting surface aerodynamic theories. The subsonic theory is called the Doublet-Lattice method, and is an extension of the steady Vortex-Lattice method to unsteady flow. [8, p.1]

    The Doublet-Lattice method will be used to perform a number of analyses on the hummingbird-wing. All lifting surfaces are presumed to lie almost parallel to the flow. Any interfering surface can be analyzed, given that each is idealized as a set of trapezoidal planes. [8, pp. 11,13] Examples of Bulk Data Entries
    Following are some basic bulk data entries that will be used in both the space-frame and aerodynamic model of the hummingbird.
      1) GRID

      This command defines a geometric point in the coordinate system. The directions of its displacement and its permanent single-point constraints are entered. Each point is given an identification number. [6, pp. 50-51]

      2) CQUAD4

      CQUAD4 is a common element used to model structures. The model is a quadrilateral flat plate connecting four grid points. [6, pp. 74-75]

      3) PSHELL

      The Membrane, transverse shear, bending, and coupling properties of thin plate and shell elements such as CQUAD4 are entered through the PSHELL entry. [n, 79-80]

      4) CBAR

      This entry is the model for a basic beam that can support tension and compression, bending, and shear in two perpendicular planes. [6, p. 68]

      5) CAERO1

      CAERO1 is an aerodynamic entry and defines a trapezoidal wing panel for the Doublet-Lattice or ZONA51 method. This is the basic modeling tool for the aerodynamic model when using the Doublet-Lattice method. [8, pp. 89,127]

      6) PAERO1

      This entry is used to identify associated interference bodies in the subsonic case. This entry is required even if there are no bodies defined. [8, pp. 89,127]

      7) SET1

      SET1 inputs the structural grid points to be splined for the structural-aerodynamic splining. [8, pp. 104,128]

      8) SPLINE1

      This card defines a surface spline. The spline interconnects the aerodynamic boxes to the structural grid points selected by the SET1 command.
      [8, pp. 104,128]

4.2.4 CT-Scanner
    Computed X-ray Tomography makes it possible to examine the interior of an object without actually deforming or destroying it. Two-dimensional images, called slices, illustrate the inside of the object. These images are created by passing x-rays through the object at many different angles. The difference in density of the object leads to different x-ray absorption levels which create the contrast in the picture. By making extremely thin, constant-thickness slices, one can produce a detailed three-dimensional picture of the density variations of an object by placing the slices on top of each other. On the next page, Figure 4.8 illustrates a CT-Scan picture composed of several different images. These images were created depending on the preference of the user during the reconstruction process.
    Three main factors determine the resolution of the CT image. These are the type and size of the x-ray source, the geometric relations among the source, object and detectors, and the process used to reconstruct the final image. The most modern instruments can have a resolution of tens of m m (1 m m = 10-6 m) per slice. The CT-Scanner at The University of Texas at Austin has the capability to achieve such high resolutions. [9]
4.3 MAV Technology and Science
    At the sizes envisioned for these devices, normal aerodynamic rules no longer apply. Microflyers will have to operate in an environment more common to small birds and large insects than that of larger aircraft. The forces associated with air moving around the tiny devices are more pronounced than with conventional aircraft in flight, causing increased drag, reduced lift under the smaller wings at low speeds, and decreased propeller efficiency. Such aircraft, weighing only 50 grams, are more susceptible to wind gusts, updrafts, and rain.

    Other challenges include developing tiny sensors, engines, and power sources for such planes, as well as communications, control and navigation systems for the tiny robot aircraft, which would have to operate with little or no human input. Microflyers require an entirely new approach to aircraft design and miniaturization. "We are not trying to scale down conventional technology," says Robert Michelson of GTRI. "We are scaling down new and unconventional technology [10]." Designing the devices is not a simple task since making this aircraft requires considerably more work than simply scaling down existing pilotless military drones or making tinier replicas of radio-controlled model airplanes. "Nothing about making micro air vehicles is going to be easy," said Dr. William R. Davis, manager of the MAV program at the Massachusetts Institute of Technology's Lincoln Laboratory. "With planes this small, all the rules change and everything becomes challenging [2]." Building an aircraft smaller than 15cm is easy enough, however, making them do something useful is the challenge.

    The speed of the MAV is crucial so as to avoid buffeting by gusts of wind that would make the craft useless. Aerodynamics poses major problems for the MAV as well. As flying objects become smaller, the viscosity of the air becomes increasingly important because for the smallest insects, flying is more like swimming through honey. Microwings are also susceptible to boundary layer separation. Small changes in the angle of flight can result in extreme loss of lift, and in small aircraft the boundary layer does not always reattach itself when the wing returns to level flight. [11]