## Sunday, December 29, 2013

### Pitot test and calibration part 2

This is a follow up of a precedent post
Here is examined some practical aspect of the proposed test rig layout.
Refer to the following DIY calibration rig layout.
Figure P27.1 Calibration rig layout scheme

Previously we've talked about pitot test, neglecting all the practical aspects.
A brief description of operation is examined. The connections to reference instrument and to pitot are based on a wide used layout, the five ways manifold or instrumentation manifold.

A typical test operation is here examined. Is quite clear that procedure can be further automatized, here is considered the use of a basic hardware DIY setup. A basic IAS test is examined, in a quite similar manner also a TAS pitot measurement can be tested.

At the beginning of test procedure all valves are closed.
The first operation to be accomplished is the connection of the reference differential pressure manometer and the pressure ports of pitot. The total pressure port should be connected to the (+) line, the instrument high pressure port should be connected to the (+) line too.
Commonly used sensors have a very little internal volume. The connection of a pressure line, practically speaking the connection of a plastic tube to a instrument nipple, will cause a sudden rise in the internal pressure. To avoid the pressure ram rise the “bypass” valve should be left open during the whole operation. If present condensate should be removed opening valves “(+)” and” (-)”.
Then open “(+)” and “reservoir” valves and unscrew the piston knob to the full back position.
Close “(+)” valve.
Connect instruments and close the valves ”(+)””(-)” and “bypass” , open the “air” valve.
Connection of instruments shall respect
Now is time to zero your reference instrument, it is a function available on almost all digital instruments , refer to manometer manual for details. After zeroing the differential pressure reading should be exactly zero.
Turn the piston knob clockwise to reach the desired test differential pressure.

P27.2 Piston with knob

Once the test pressure have been reached close the “reservoir” valve, this operation is essential to avoid problems with piston leaks.
If your reference manometer is capable of take “average” measurements than only wait for the desired number of samples is collected and note the average value. If your reference manometer takes the pressure instant value than carefully note the desired number of samples and compute the average.
Do the same to get IAS measurements.
At this point just move to the next test pressure point, open the “reservoir” valve and turn clockwise the piston knob to increase the pressure.

As you note the procedure is quite simple, anyway some precautions should be taken during the design and use of the test rig.

Pressure lines cannot be made of flexible material, that will avoid the risk to have a pressure reading modified by the variation of line volume. A short flexible pressure line segment can be acceptable, anyway use a high thickness material. Good construction materials are metal and rigid plastics, do not use silicon tubing.

The drain lines exit must be below any other point of the pneumatic circuit. Drain lines routing should avoid any obstruction to the flow of condensate. A minimum slope of 5° is to be used.

P27.2 DIY Calibration rig

Pressure lines connections of the single instruments should lie on the same plane.

All the components for test, testing equipment and tested equipment should be placed in the test room some hours before the test.

Turn on the pitot electronics and the reference manometer at least one hour before the test measurements.

The electronic used to power and reading the pitot should be the same of those that will be used during normal operation.

Work in a room with a mild temperature, around 20 °C is a good value.

Record the room temperature during the test

As soon as the prototype is ready I will post a review and off course other information to allow the construction of your own DIY pitot test rig.

Next part post

## Season's greetings and thank you!

Pitot test and calibration rig under construction

## Thursday, December 19, 2013

### Linear sensors measurement introduction, static measurements

Within this document a general model for linearized sensors is examined. After a general introduction, a numeric example will be introduced. Instrument-specific calibration and test procedures, can be found on the instrument test section of the site, where available.

A sensor responds to a physical stimuli and transmits a corresponding electrical signal.
For a wide range of sensors, the relationship between input $$x$$ and output $$y$$ can be approximated as linear. There are cases, however, where the relation cannot be linearized.
The linearized sensor input-output characteristic is assumed to be a straight-line and towards that goal, the purpose of the calibration procedure is to find the straight-line that fits best the real sensor characteristic.

Digital sensors can be modelled in the same manner of the analog ones. The better the resolution (in bits) of the sensor output, better model accuracy is achieved.

Defining the sensor sensitivity or slope $$m$$, the offset $$o$$ and $$\epsilon$$ as a random, normally distributed error variable $$N(0,\sigma^2)$$, the linear input-output measurement model is

Equation ILS.1
$$y(t)=x(t)m(t,T,x_n)+o(t,T,x_n)+\epsilon$$

Refer to figure ILS.1 for a graphical representation.

Figure ILS.1 Ideal linear sensor input-output characteristic

The last equation explicitly accounts for the time $$t$$ and temperature $$T$$ impact on the output. Any other negligible or uncompensated for deviation sources are formally represented by $$x_n$$. For example, in the case of a ratio-metric sensor, $$x_n$$ can be the power voltage value. In general $$x_n$$ should account for every environmental factor such as vibrations, humidity and acoustic noise level. Sensor datasheets are commonly available on the internet and publish the upper-bound of the main error sources. $$x_n$$ can be incorporated in Eq. ILS.1 with a corresponding increase in the $$\sigma$$ deviation value of $$\epsilon$$ error variable.

Equation ILS.2
$$y(t)=x(t)m(t,T)+o(t,T)+\epsilon$$

The slope and offset values are time dependent. The variation with time of this parameters have two different time scales. The long scale variation is reported on data-sheets as “long term drift”, “aging” or with similar terms. That accounts for the fact that even a stored sensor is subject to aging and consequently the input-output relationship is time dependent.

For calibration and test purposes, aging related effects can be neglected. If a reliable sensor is required then the calibration of the sensor itself should be periodically retested.
Refer to the following figure to visualize the impact of slope and offset variation.

Figure ILS.2 Variation of slope, left. Variation of offset, right

The following equation will be used during linear sensor calibration.

Equation ILS.3
$$y(t)=x(t)m(T)+o(T)+\epsilon$$

Generally, $$m$$ and $$o$$ are affected by two main thermal related issues, the initial warm up of the sensor and the operating environmental temperature.
$$o$$ drift is reported in data-sheets as '”offset thermal drift” or with similar terms under the thermal characteristics section. Τhe indicated drift is the total variation inside the sensor operating temperature range. The drift of the offset value after an initial power up period is called “power up offset drift”, “warm up thermal shift” or with similar terms.

We define $$y_{span}$$ as the output span or range and $$x_{span}$$ as the input span or range, hence

Equation ILS.4
$$m=\frac {y_{span}} {x_{span}}$$

It is uncommon to find in data-sheets explicit descriptions on slope/sensitivity variation with temperature. Instead, it is quite common to have indications about input and output span deviations; usually in the thermal effects section.

Another useful piece of data reported in data-sheets is the “linearity error”. The general concept is that linearity error accounts for the differences between the sensors measurements and a best fit straight-line.

Figure ILS.3 Sensor deviation from linearized characteristic.
Linearized characteristic in black and real sensor characteristic in blue.
$$\epsilon$$ error band not shown

To operate in a static or quasistatic condition, it is necessary to check the response time of the sensor. Generally this value is reported as the time to reach a certain percent of the true output value.
To be sure you are operating at low frequencies check that your sample time is at least six times the time required by the sensor to reach 68% of output value. For the majority of sensors this will be an overly conservative value.

In the next post a numeric example will be introduced.

## Sunday, December 15, 2013

### Pitot test and calibration

This is the first part of a mini-series. The aim is to provide an introduction to the pitot test topic and to present a DIY oriented free calibration rig.

If a basic air data system is used then calibration and test of pitot tube is a routine operation, nevertheless is a compulsory procedure if a third party pitot is used.

Also for small RC/FPV/UAS test and calibration is fundamental, in this post we will examine general preliminary requirements for test equipment.

Figure P26.1 Pitot test equipment fitted on a plane, http://www.dfwinstruments.com

During test pitot static and total pressure ports are pneumatically connected to a test instrument and then a sequence of pressures are applied, at the same time the pitot speed readings are recorded.

Video P26.1 Video shot of static and airspeed test with an analog portable device 2:30

The IAS speed is defined

Equation 26.1
$$IAS=\sqrt{\frac{2q_c}{\rho_{base}}}$$
with $$\rho_{base}=1,225 kg/m^3$$ hence it is indipendent of current air density

After a period of time from initial calibration it is necessary to ensure that our sensor is reading the correct pressure value over the full operative range. Is to be noted that to test the pitot under true operating condition is necessary to mimic the static pressure and air temperature variations with altitude. To minimize test equipment cost and complexity, in a DIY vision, only the really basic tests will be considered.

To focus on the topic we examine a pitot test that uses a differential sensor with a pressure $$q_c$$ range of 12,5 mBar or 1250 Pa.
Table P26.1 Ideal, no uncertainty, input-output characteristic of a Pitot

If the sensor input range is divided into five parts we obtain the following input-output correspondence. To personalize that table you can use the provided “experimental.ods” spreadsheet.

To increase test accuracy we record $$n$$ multiple samples of input differential pressure and pitot IAS . Mean of pressure measurement and IAS measurements will be reported on a table and used during the acceptance test.
After a complete test run we get a table similar to the following.

Table P26.2 Example measurements results and IAS calculated values

The uncertainty calculation must be carried out and recorded, details will be shown in a dedicated post.
The proposed test allow to evaluate, at the same time, the correct functionality of the software and of the hardware

An important part of testing is to dispose of a stable platform that allows us to work in a comfortable way.

At this stage is possible to define some requirements for the hardware that will be used during tests.

Calibration rig general requirements :
-DIY technology and cost compatible
-Portable
-Variable calibration range
-Pitot and altimeter test capable
-Usable on the field and in laboratory
-Reduced maintenance
Based on precedent test and calibration experience the followings technical requirements have been individuated.

- Manual operated, to reduce overall cost.
- Static pressure range 130 000 Pa to 90 000 Pa.
-Differential pressure range 5000 Pa
-Pneumatic connections should avoid condensate to reach reference manometer/s
-The rig should allow the operator to :
Connect static with total port
Insulate pressure ports
Drain condensate
- Reference manometer/manometers requirements are linked to pitot ranges and required accuracy, more detailed description in a successive post

Refer to the following scheme to visualize a preliminary layout.
Figure P26.2 Calibration rig layout scheme

Figure P26.3 Picture of piston prototype

All the coments are welcome, prototype is under building an testing.