## Monday, May 6, 2013

### Pneumatic lag issues

Have a look to this pitot simulation block

Some time ago at the airfield playing around with a pressure sensor  with sample rate of 50 Hz I noticed a really poor unexpected performance of my carbon fiber Pitot. You know, the measure system is quite simple, one digital pressure sensor connected to an Arduino board, two pressure lines , the static pressure port and the total pressure port. I ended the post fly analysis with a sole sure fact, I haven't a math model for the pneumatic transmission line. I needed such a model to calculate the relationship between the amplitude of the port pressure and the pressure at sensor at different frequencies, syntetically I needed the transfer function. With a transfer function it is straightforward to determinate the overall measurement system performance and even compensate for undesired transmission line behavior. Refer to the below figure 1 for the schematics of a pneumatic line.

Figure 1 Pneumatic line layout

Input pressure cannot be present at the very same time at the pressure port and at the sensor port, it take some time for the pressure wave to propagate trough the transmission line.
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 [7] that you find at this link.
Is very important to considerate the model assumptions, here below  the list from [7] pag 7

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

Let's consider now three different cases from the same base design, only variable is the line internal radius R, results plotted in the decimal scaled graphic below.

Figure 2 Frequency response of pneumatic line