### Pitot Lag and Simulation

At last I found a text where the authors integrated the Navier-Stokes equations to achieve a closed form solution, from now on I will proceed according to reference[1] [Theoretical and experimental results for the dynamic response of pressure measuring systems] .

Is very important to considerate the model assumptions, here below the list from [7] pag 7

*Length/Radius >> 1*

*Variable nominal values variations are small*

*Laminar flow inside the tubing*

To get a numeric example let’s pretend we have the following, possible, parameters values

*Internal radius R of line [1 ; 2 ; 3] mm*

*Length of pressure line L 0,6 m*

*Volume of the sensor Vu 50e-9 mm^3*

So at the end the problems that I’ve got in the past can be explained, and some times avoided, taking into account the dynamic of the pneumatic line.

### Simulation

Simulation is one of the basic tools for modern instrumentation design. Numerical simulation can be used during early design stage as well during the final integration phase. It’s a very ductile tool and due to it’s intimate mathematical nature can take different forms. Even more the same software can carry out simulation, do software in the loop and hardware in the loop tasks so development of complex systems is really speed up. Simulation is also needed, for example but not only, during system identification and data validation tasks. l will show how to make a simulation of a DIY Pitot tube with Scilab, model parameters will be setup in a mparam.sce file that must be run prior to Xcos simulation. The working hypothesis from now on is that electronics devices included in the measure chain are so fast that do not have practical impact on overall dynamicperformance, other assumptions and data come straight forward from previous pitot analysis. I will use Scilab Xcos as simulation software but everything shown here can be ported to a different simulation software. Xcos use a block paradigm, that means that every block have well defined inputs and outputs, so it’s quite natural to implement system dynamics with transfer functions. Just to mention it, a different approach is that proposed by Modelica , here the simulation models are defined directly with equations, that’s no needed anymore to decide at priori what variable will be an input or an output. It’s available a free Modelica modeling and simulation environment that’s called Openmodelica . I warmly advise you to give it a try.

*Figure PS.1 Pitot as primary sensor for longitudinal speed regulator*

*Figure PS.2 Original frequency/magnitude relationship in black superimposed with second order identified transfer function in blue*

*Figure PS.3 Open loop test bench layout*

*Figure PS.4 Pitot block detail*

*Figure PS.5 Pitot block pneumatic lag detail*

See PS.6 for the IAS pitot error, IAS is a step of 20 m/s at 0 s, after the transitory period IAS real = IAS pitot so IAS pitot error is zero.

*Figure PS.6 Input frequency 0 Hz, step 20 m/s. IAS pitot error [m/s]*

*Figure PS.7 Input frequency 250 Hz, step 20 m/s. Real IAS [m/s black] Pitot reading [m/s green]*

*References*