# How is the equation for u_g given in MatLab's discrete Dryden Wind Turbulence Model a difference equation?

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Nicholas Herbert on 26 Sep 2016
Answered: Zhao Wang on 28 Sep 2016 Looking at MatLab's discreet Dryden Wind Turbulence Model, specifically for the longitudinal variable u_g, MatLab gives this difference equation.
The problem I'm seeing with this is that this looks in no way like a difference equation. A difference equation should have some statement equal to another statement. This is no equal sign in this equation.
Also a difference equation should be time indexed, and all I'm seeing is the index of g. How is that a time index?
MatLab also does not give an explanation for the eta either, so I'm also wondering what that is too.

#### 1 Comment

Steven Lord on 26 Sep 2016
For reference this appears to be in relation to the first row in the third table on the documentation page for the Dryden Wind Turbulence Model (Discrete) block in Aerospace Blockset.
I don't work with this blockset at all, but my guess is that this table defines a term that is used in a difference equation given in the specification "U.S. Military Specification MIL-F-8785C", the third item in the References section on that documentation page. If that guess is correct the full definition of the difference equation requires combining the information in that table and the equation from the specification.

Zhao Wang on 28 Sep 2016
I understand that you have a question about the difference equation expression in the "Dryden Wind Turbulence Model (Discrete)" block.
The difference equation in the table provides an expression that is used to update the variable for the next time step. For example, based on the current value of the longitudinal variable 'ug', its updated value can be computed from the expression.
You can also look under the mask of the "Dryden Wind Turbulence Model (Discrete)" block. In the "Filters on velocities" subsystem, you can open the "Hugw(z)" block. This subsystem realizes the expression in the table and updates value of the variable 'ug'.
From the block diagram within the "Hugw(z)" block, you can also find that 'η' is noise. The noise signal comes from a "Band-Limited White Noise" block in the "Dryden Wind Turbulence Model (Discrete)" block.
If you have any further question regarding this issue, you can contact MathWorks Technical Support for assistance.