Calculation for lift-distribution uses the vortex lattice method, VLM. The inclusion of VLM has been a joint effort with John Hazel who developed the LiftRoll Spreadsheet. For more information on this technique see Applied Computational Aerodynamics by Mason, especially chapter 6. Also see "Vortex Lattice Methods" Why Should You Care? by Mike Garton.
The tool has evolved into a tool that determines the spanwise airspeed and Reynolds Numbers in banked flight to one that uses these calculations to interpolate spanwise Cd and drag values from the UIUC airfoils database. It's a tool that can get quantitative results to concepts I've only seen qualitatively discussed the literature. But the tool is not well behaved, and often craps out. I hope it's price makes up fo this.
However, the human interface has remained crude by todays expectations for user friendliness. The free-form text input method continues to allow the new parameters to be easily added, especially parameters for each panel break. Unfortunately, while the ability to validate input is possible, I have not developed sufficient proficiency with Java to provide useful error indication, and errors may require the program to be restarted, (hopefully after the current parameter specification has been copied). While I don't think human interface it is difficult to use, it is not easy. User Beware!
While I assume its useful to have such a tool so easily available on the web and through a common browser application, providing only graphical output is very limited. I use the tool from a UNIX-like shell (e.g. MKS, cygwin) and use the printFlag option to dump all the results out to the shell where they can easily be captured into a file. Various results can then be extracted from the captured data and used elsewhere.
The primary source of the wind-tunnel data is UIUC Airfoil Data Site, where data from the UIUC Low-Speed Airfoil Tests (LSATS) program is freely available under General Public License. Mike Garton provided many useful comments, and suggestions for improvements that have yet to be made. His and David Orman's Airfoil Comparison Tool is highly recommended.
Another approach, is to download the Java toolkit from http://java.sun.com/j2se, along with the source code, and run the tool directly from the command line.
It is also clear that proper design will require iteration. Iteratively changing the flight velocity is neccessary to find the velocity required to produce the lift that equals the weight of the aircraft. While this can be automated, and has been in previous releases, it may more likely be the exception, than the rule. Like any tool it may take a while to learn to use it, and to use it well.
Since the vortex lattice method is probably a fairly advanced analyse method for the typical modeler, and is typically described in advanced and expensive engineering texts, the following sections will attempt to describe the basic concepts. This method is often sited being unintuitive, but surprizingly accurate when compared to experimental results.
Each panel has a control point at which a circulation (G) value is determined. The lift can be calculated from the circulation. The circulation depends on the planform, the velocity (V) and angle-of-attack (a) at the control point, and is influenced by all other panels. In other words, it solves for G in the the following equation
where[C] G = 4 p u n a n
[C] = influence matrix G = circulation V n = freestream velocity at panel n a n = angle-of-attack at panel n
This requires the inversion of the influence matrix. In the current implentation, the influence matrix only considers the panel positions in 2-dimensions without considering the verticle dimension which would represent dihedral.
The lift is determined from the circulation
L = r V n G n
or CL can be determined
CL = 2 G / (V n c)
The following equations determine various velocities for a banked circling aircraft. They include the sink velocity used to determine the local sink rate at any position along the wing span. This in turn, is used to determine a local angle-of-decent (Aod) which can be used to adjust the local angle-of-attack (Aoa).
V = (W / (1/2 r S Cl)) 1/2 required straight and level airspeed to support aircraft LD lift-to-drag ratio Vs = V / LD straight and level sink velocity (LD = lift-to-drag ratio) q bank angle Vc = V / cos(q)0.5 required circling airspeed Vcs = Vs / cos(q)1.5 sink velocity while circling G = 9.81 m/s or 32 ft/s acceleration due to gravity R = Vc 2 / (G * tan(q)) turning radius V y = Vc (R + y cos(q)) / R local velocity at span position y Aod y = atan (Vcs / Vy) local angle-of-decent Aoa'y = Aoa + Aod locally adjusted angle-of-attack
This section is effectively the user manual. Since the tool evolves so quickly, new features are added, and some removed, and it is easy for this section to become out-of-date.
There are five buttons. Three are menu buttons resulting in additional choices. The button menu structure is as follows:
acc acceleration of gravity (9.81 m/sec^2) aileronPosL On the right wing, the leftmost span position of the aileron aileronPosR the rightmost span position of the aileron aileronAng a convenient way to set both aileronAngR and aileronAngL, the left aileron is set to the negative of the value aileronAngR aileron deflection on right wing aileronAngL aileron deflection on left wing airfoil:N airfoil by name from the available list airspeed expressed in consistent units (ft/sec) aoa expressed in degrees aseq=beg,end,step display drag curve for each AOA from begin to end incrementing AOA by step bank expressed in degrees chord:N tip-chord length of wing sub-section (N=0 indicates root) debug specified debugging level (0 is off) dihedral:N upward dihedral at tip of wing sub-section (experimental) dragToLift inverse of lift-to-drag, zero is ideal end-configuration indicates the end of the input parameters, anything after this statement will be ignored while processing a planform specification. english defines rho and acc for english units (ft/lb/s) flapAng a convenient way to set both flapAngR and flapAngL flapAngR flap deflection on right wing (positive is down) flapAngL flap deflection on left wing flapPosL On the right wing, the leftmost span position of the flap flapPosR the rightmost span position of the flap mac must be expressed as a fraction less than one. metric defines rho and acc for metric units (mks) nPanels manually define number of panels, default is 100 printFlag prints screen values when run from shell rho density (1.225 kg/m^3) (0.0023769 slugs/ft^3) show-results indicates calculated results for panel positions, gamma/lift-distribution, and Cl values will be displayed in the input specification text areas. This text can be cut and pasted, allowing the data to be used for other purposes. span:N span length of wing sub-section sweep:N rearward sweep at tip of wing sub-section twist:N twist at tip of section (washout is negative) viscosity (0.0000179 kg/m/sec) (0.000000373 slugs/ft/sec) weight experessed in the most convenient units.
The specification of parameter names is case-sensitive.
Configuration parameters are entered in the text window. The mouse can be used to select the display buttons on the left. The mouse can also be used to zoom in on some of the graphical results. The left mouse button zooms in, and the right button zooms out. The mouse position indicates the center of the region to zoom in on.
Parameters can be entered on multiple lines as name-value pairs separated with semicolons:
root=10.5;Parameters having multiple values, such as span, are entered with indices:
span:0=10; span:1=15;Corresponding values must use the same indices
span:1=10; chord:1=7;Each wing section requires three parameters: span, chord and sweep. Span is the span of the section, not the distance from the root to the end of the span. Chord respresents the tip chord of the section. Sweep is specified as the difference in distance between the tip chord of the current section and the tip chord of the previous section, or the root. Zero sweep means a straight trailing edge.
Indices start with the value of one. A rectangular wing having only a single section could be specified as:
root=10; span:1=20; chord:1=10; sweep:1=0;
Web based java applications are prevented from accessing files local PC files for security reasons. However, the configuration data can be cut and pasted to a local file through a local application such as notepad. The tutorial and sample configurations can be copied and pasted over the exiting configuration in the applet text window, and can previously saved configuration text from a local file. For now, there is no easy way to save the analysis results, either graphically or numerically, except possibly through a screen capture program.
root=10; chord:0=10; span:0=40;
A root chord value is specified, along with the tip chord and span for a single section. In this case, the tip chord is equal to the root chord. When specifying the chord and span values for each section, a section parameter is needed. This is the value specified after the colon, ':', for each section parameter, in this case, chord and span. And yes, the first section is zero.
The Structure->Draw button shows the planform's outline, and it's overall span. The Structure->MAC button displays the mean aerodynamic chord as a verticle red line, the default value of 25% of this chord as a horizontal red line, and it value relative to the leading edge of the root chord. To the right, is dispayed various planform parameters: area, wingspan, aspect ratio (A/R), and wing loading using a default weight value of 1. By default, the applet uses english units of measure so that wing-loading is specified per square-foot.
The Lift->Alpha button displays a default downwash angle of 6o across the entire trailing edge. The Lift-Dist->Lift button displays the corresponding lift-distribution, and the Structure->Shear and Structure->Bend-Moment display the corresponding shear loading and bending moments. The Lift-Dist->Cl displays the resultant lift coefficient, given the resultant lift, a default airspeed of 1, and the corresponding wing-chord.
The downwash angle is specified as the angle-of-attack. The weight, downwash angle and airspeed (ft/sec) values can be specified with the following modifications. Try changing some values to see their affect on the lift distribution.
root=10; chord:0=10; span:0=40; weight=40; aoa=4; airspeed=10;
The wing-loading will be greater with a more realistic value, but the lift-distribution will be significantly smaller at the smaller downwash angle. Now consider a two panel wing with a tapered outer section.
root=10; chord:0=10; span:0=20; chord:1=6.5; span:1=20; sweep:1=-1.5; weight=40; aoa=4; airspeed=10;
Use Structure->Draw or Structure->MAC to verify the new planform shape. The MAC display indicates the MAC for each wing section as a verticle green line. Notice that the chord and span parameters for the 2nd section are specified uniformly as ':1', and that a sweep parameter is added. The sweep parameter if only needed if it non-zero, with zero meaning no trailing-edge sweep. Also, negative sweep means toward the leading-edge.
The downwash remains the same, but the lift-distribution is different for that of the rectangular wing, with corresponding differences in shear and bending moment.
Twist can also be specified for each section. Washout is specified as a negative twist which reduces the downwash. The amount of twist is applied proportionally across the section. Use the Lift-Dist->Alpha to verify the configuration.
root=10; chord:0=10; span:0=20; chord:1=6.5; span:1=20; sweep:1=-1.5; twist:1=-1.5;
The next step will be to add ailerons. Ailerons are specified with and inner and outer span position. The sweep is also modified so that the trailing-edge is straight. An aileron deflection angle of 2o is also specified. A positive value corresponds to a downward deflection, adding to the downwash angle on the right wing, but a deflection in the opposite direction, upward on the left wing. Use the Lift-Dist->Alpha button to see the affect on downwash angle. The lift-distribution is dramatically affected. The aileron deflections can be specified separately for left and right ailerons using aileronAngL and aileronAngR.
root=10; chord:0=10; span:0=20; chord:1=6.5; span:1=20; twist:1=-1.5; weight=40; aoa=4; airspeed=10; aileronPosL=20; aileronPosR=38; aileronAng=2;
The next step is to add flaps, in a similar manner as ailerons. Flap deflections are the same for both left and right wings. Use the Lift->Alpha and Lift-Dist->Lift buttons to see the affect.
root=10; chord:0=10; span:0=20; chord:1=6.5; span:1=20; twist:1=-1.5; weight=40; aoa=4; airspeed=10; aileronPosL=20; aileronPosR=38; aileronAng=2; flapPosL=2; flapPosR=20; flapAng=3;
These examples are incomplete in terms of specifying airspeed parameters in consistent units.
root=10; chord:0=10; span:0=20; sweep:0=0; weight=50; mac=0.25;
root=15; chord:0=12; span:0=20; sweep:0=8; chord:1=8; span:1=15; sweep:1=-8; chord:2=4; span:2=10; sweep:2=8; weight=50; mac=0.25;
root=10; chord:0=9; span:0=27; chord:1=8; span:1=38; chord:2=6; span:2=15; chord:3=3; span:3=7;
root=9.875; chord:0=8.875; span:0=26.25; chord:1=5.25; span:1=28.625; chord:2=3.5; span:2=5.125; weight=74.0; mac=0.35
english;, aoa=4.0;, bank=60.0; dragToLift=0.05;, airspeed=20.0;, root=10;, chord:0=8; span:0=30; sweep:0= 0;, chord:1=6; span:1=10; sweep:1= 0; twist:1=-1;, chord:2=4; span:2=10; sweep:2= 0; twist:2=-2;, nPanels=8;
metric; weight=2.0; airspeed=20; root=0.1; chord:0=0.1; span:0=1; aoa=4.3;
The corresponding example in english units is a 4.4 lb plane, with a wing area of 2.16 sq ft, and traveling 65.7 ft/sec. For an accurate comparision, the aspect-ration of the wing must be identical.
english; weight=4.4; airspeed=65.67; root=0.328; chord:0=0.328; span:0=3.28; aoa=4.3;
english; aseq=1.0,10.0,2.0; bank=30.0; dragToLift=0.00; weight=1.35; root=8.2; airfoil:0=AG_16; chord:1=7.5; span:1=15; airfoil:1=AG_17; chord:2=5.8; span:2=16; airfoil:2=AG_18; chord:3=3.4; span:3=8.3; airfoil:3=AG_19; nPanels=32; printFlag=0; end-config;
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