This tutorial requires:
DesignSpark Mechanical V6.0This is a tutorial to get you started with using mathematical equations to sketch curves and makes surfaces/solids using them. The video was created in partnership with ANSYS Inc.
Here is the syntax and list of pre-defined functions:
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Parameters include a name and are enclosed in square brackets [L]
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Functions include a function name followed by parenthesis containing any values as arguments. For example: Sine([t]-[r])
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The table below shows common predefined intrinsic functions included
| Name | Description |
|---|---|
| Abs |
Returns the absolute value of a specified number |
| Acos |
Returns the angle whose cosine is the specified number |
| Asin |
Returns the angle whose sine is the specified number |
| Atan |
Returns the angle whose tangent is the specified number |
| Cos |
Returns the cosine of the specified angle |
| Sin |
Returns the sine of the specified angle |
| Sqrt |
Returns the square root of the specified number |
| Tan |
Returns the tangent of the specified angle |
| Exp |
Returns e raised to the power of the specified expression |
| Log |
Returns the natural logarithm of the specified expression |
| Log10 |
Returns the common base 10 logarithm of the specified expression |
| Pow |
Returns a raised to the power of b, if arguments are Pow(a,b) |
An up-to-date list of mathematical expressions including operators & constants is given in the software help documentation. This is accessible within DesignSpark Mechanical, usually via the ‘F1’ key shortcut. Search for ‘Mathematical Expressions’ in the help document.
Here's another example of a group of equations to define a symmetric airfoil using the NACA scheme. Give it a try!
This is a NACA 0015 airfoil where the trailing digits '15' means the airfoil has a 15% thickness to chord length ratio ([a] in below equations). Design units were Metric.
Upper surface of airfoil:
| x | ([t]) |
|---|---|
| y | 5*([a])*((0.2969*Sqrt([t]))-(0.1260*[t])-(0.3516*Pow(([t]),2.0))+(0.2843*Pow(([t]),3.0))-(0.1036*Pow(([t]),4.0))) |
| z | 0 |
| Interval(t) | Start:0, End:1, Scale:50 |
| a | 0.15 |
Lower surface of airfoil:
| x | ([t]) |
|---|---|
| y | -5*([a])*((0.2969*Sqrt([t]))-(0.1260*[t])-(0.3516*Pow(([t]),2.0))+(0.2843*Pow(([t]),3.0))-(0.1036*Pow(([t]),4.0))) |
| z | 0 |
| Interval(t) | Start:0, End:1, Scale:50 |
| a | 0.15 |
You could change the above equations to build a cambered airfoil, which is used in real world aircraft. Eg. a supercritical NACA 2412 used in Airbus A380s. The leading digits '24' indicate the degree of camber.
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