# LitioLAB Projects - Case studies

## Check how you can draw complex engineering or architectural shapes in AutoCAD/ GStarCAD/ ZwCAD with LitioLAB

LitioLAB Project Files (.LLP) are a type of file that LitioLAB uses to store, retrieve, and share LitioLAB project information.

It stores data like input variable data, parameter range and mathematical formula contents.

We are adding information permanently. Users are also invited to share projects!

• How to draw airfoils
• How to draw a catenary curve - a hanging-cable shape
• How to draw a Wankel engine housing
• How to draw a spur (involute) gear profile
• Equation of time - How to draw a sundial correction curve;
it can be extrapolated to the design of machine CAMS
• How to draw oblique throw trajectories
• How to draw beam-deflection shapes with LitioLAB

• ## How to draw NACA (and other) airfoils

An airfoil can be defined as a pair of parametric equations for X and Y, for the formula parameter varying from 0.0 to 2*PI. Check the RATIONALE here OR here.

We can rewrite these formulas into a calculator-like form, as follows.

X = f = 0.5+0.5*(abs(cos(r2d(u))))^c1/cos(r2d(u))
Y = g = 0.1277*0.5*(abs(sin(r2d(u))))^c1/sin(r2d(u))*(1-f ^j1) + j2*sin(r2d(pi*f ^c2)) + sin(r2d(f*2*pi))*0.0

ZwCAD users need to check LitioLAB user manual to review the math functions available and how to adapt the formulas to ZwCAD.

The R2D (radians-to-degrees) conversion function is not available in ZwCAD. Use 180/PI as a multiplying factor instead.

Here, I have already replaced some of the formula coefficients and parameters, with the name of an auxiliary parameter, either constant or formula (that works as constant in this case), as shown on the video, and as follows:

B = c1
T = 0.1277 (in the formula; this value is for NACA5412 airfoil)
P = j1
C = j2
E = c2
R = 0.0 (in the formula; this value is for NACA5412 airfoil)
T and R will be included directly in the formula.

It is clear, that there will be an issue due to the dividing cos(u) and sin(u), that turn into 0 within the range of use of the formula, creating a division by zero error.

This can be easily solved, if instead of u limits being 0.0 and 2*PI, we make them a little more than 0.0 and a little less than 2*PI, AND by skipping the u = PI value, by considering an odd number of divisions of this parameter u.

So, for our first example, the NACA5412 Arfoil, after inputting all the parameters, we get its drawing.

NACA5412

c1: 1.8608
[in formula]: 0.1277
j1: 2.5536
j2: 0.05332
c2: 0.8434
[in formula]: 0.0

We repeat the process for some more examples, as follows:

Clark Y

c1: 18.761
[in formula]: 0.1138
j1: 3.041
j2: 0.03869
c2: 0.8510
[in formula]: 0.0

Ag 24

c1: 19.731
[in formula]: 0.1176
j1: 14.890
j2: 0.0277
c2: 0.6553
[in formula]: - 0.0042

flying wing profile

c1: 21.548
[in formula]: 0.2309
j1: 16.202
j2: 0.0194
c2: 0.6304
[in formula]: 0.0078