Equation driven sketching with DesignSpark Mechanical

This is a tutorial to get you started with using mathematical equations to sketch curves and makes surfaces/solids using them. You will need version 5.0 or newer of DesignSpark Mechanical to access this advanced sketch mode. The video was created in partnership with ANSYS Inc.

Here is the syntax and list of pre-defined functions::

• Parameters include a name and are enclosed in square brackets [L]
• Functions include a function name followed by parenthesis containing any values as arguments
  • For example: Sine([t]-[r])
• 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)

A full list of mathematical expressions including operators & constants is given in the main help documentation: http://help.spaceclaim.com/dsm/5.0/en/Content/MathematicalExpressions.htm

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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 A380s. The leading digits '24' indicate the degree of camber.