Friday, April 24, 2015

Pitot-Static Calibrator requirements Part 3

Figure 1. Central-southern Italy, with lakes Trasimeno and Bolsena to the right. The view faces South. Panorama created with StratoSpera 3 photos by Francesco Bonomi

The precedent article on this theme can be found here.

After our discussion on the static and total pressure ports calibration ranges, we turn our attention to the leak test. A leak test ensures that a pneumatic connection is airtight, or if leakage is present it verifies that it is within acceptable margins. We are interested in finding a robust procedure to define equipment requirements. The values mentioned here should be treated as coarse reference and customized for each particular case.

For a baseline case we will refer to Federal Aviation Regulations.  In 23.1325 (i), a test procedure for unpressurized cabin planes in presented in short.
Assuming that the test is carried out in ISA standard day conditions at 0 m MSL, 15°C and 101325 Pa, the procedure is as follows:
  • Pressurize the static port to a pressure equivalent to 1000 feet (304.8m). In the ISA atmosphere this is equivalent to a pressure of 97716 Pa.
  • Wait one minute and measure the altitude again.
  • If the indicated altitude decreases by less than 100 feet (30.48m) the test is successful, otherwise it is considered a failure. The ISA atmosphere pressure at 900 feet is 98072 Pa.

In other words, the test requires that pressure variation is less than 356 Pa per minute or 5.93 Pa per second.
A leak test is also carried out on military equipment. You find a complete description of dedicated hardware in "TESTER PITOT AND STATIC SYSTEMS, PART NO.REIC 340000,NSN 4920-00-475-7161,US Army".

Calibration procedures may require the calculation of the average pressure value over \(n\) multiple measurements. Under these requirements, it is advisable to use pressure sensors that can handle medium to high sampling rates, at least 50 Hz, for example. The higher the sampling rate \(SR\) the lower the impact of the air leakage on the measurements. If the leakage characteristics are known it's also possible to remove the pressure trend from the samples.

Let's add a new requirement to our equipment: we require that the average pressure measurement \(p\) uncertainty value \(u_{\bar{p}}\) is under 75 Pa. Using ISA atmosphere the atmospheric pressure variation between an altitude of 304.8 m (1000 feet) and 298.4 m (979 feet) is about 75 Pa (-6.4 m). Assume that we use a pressure sensor characterized by a Gaussian uncertainty distribution with standard deviation \(s=400\ Pa\). The average measurement uncertainty is \(u_{\bar{p}}=\frac{s}{\sqrt{n}}\). To get \(u_{\bar{p}}=75\ Pa\) we should have \(n \geq 29\).The total measurement time is \(t_m=\frac{n}{SR}=0.58\ s\).

In an ideal leak scenario for a good and trend free measurement the pressure should be stable for at least \(t_m\).
Defining \(l_{rate}\) as the leak rate in \(Pa/s\), we will get a measurement error of \(\epsilon_l=t_m\cdot l_{rate}\ Pa\). If we assume \(\epsilon_l=u_{bar{p}}/10\), then we should have \(l_{rate}=\frac{7.5 \ Pa}{t_m}=13\ Pa/s\). The resulting overall measurement uncertainty is bounded to \((1+\frac{1}{10})\cdot u_{\bar{p}}=82.5 Pa\). This exceeds our accuracy limits and to attain the original 75 Pa desired uncertainty value, it is necessary to reiterate the design process. 
For instance, we can set either a higher \(n \) or a smaller \(s\), and in each case, after substitution we get \(n \geq 35\) or  \(s \leq 366\ Pa \). With \(n=35\) we have \(l_{rate}=6.8/0.7=9.7\ Pa/s\). This value is greater than the value based on the FAR regulations of 5.93 Pa/s. Both approaches are equally valid, but comparing both results helps to understand the level of required accuracy in the two different cases.

During measurements we should pay special attention to the thermal issues. If the pressurized fluid is not in thermal equilibrium the pressure inside the pneumatic circuit will change over time. The calibration equipment should be put inside the test room for a long period of time before the calibration begins. When the pressure is expected to change during normal calibration operations, a small settle time should be allowed before the measurements are taken. Temperature inside the test room should be as stable as possible during the measurements. Sampling at 50Hz for less than one second mitigates the high order temperature fluctuation effects.

In this article we have outlined a procedure to evaluate the leak impact on the measurements. The performance of the pressure sensor has been correlated with the measurement uncertainty. The procedure is accurate enough to allow a quick component selection. Up to now, the sensors which will be installed inside the BasicAirData calibrator have not been selected yet. Regarding static pressure sensing, following the trend of the commercially available telemetry equipment, we will report absolute pressures uncertainties in the range of (400[1], 2000) Pa. It seems prudent to have a reference measurement at least six to ten times better than those values, so broadly in the range (70,200) Pa.

[1] Some quick references from the net:

In page 5 of the datasheet, accuracy is stated as (-1500,1500) Pa. Is commonly used across the DIYers

Used on various flying platforms ranging from the most expensive to the cheapest. Bosch site gives the pressure accuracy as (-400, +200) Pa. Breakout boards with this sensor are quite common and are also shipped by SparkFun.

APM 2.6 Autopilot uses MS5611, MEAS High Resolution Altimeter.  Page 3 states that total worst case error band with no autozero is restricted in the -600 Pa to 600 Pa range
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