PRÁCTICA 1. ADC (2017)Pràctica Inglés
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Alba Martín, Anna Reig
AIR DATA COMPUTER
Simulation with Lab View software
Simulate and deeply analyse an Air Data Computer
Get introduced in LabView
Apply theoretical equations to simulate real devices
Compute different kind of errors
Choose the convenient pressure sensor according to the ADC analysis
The main aim of this exercise is to develop an Air Data Computer by means of LabView software, an essential
avionic component of an aircraft. The Air Data Computer can be represented as a block with inputs which
allow to get outputs through the system equations explained on theory lessons of Avionics.
So, the way the ADC is going to be build is the next one. Firstly, the equations of the ADC are going to be programmed in LabView and it is going to be check they work as expected for certain known inputs. Once this step achieved, the program will be extended so to be able to give vectorial outputs instead of scalar ones.
Finally, to know how good the ADC is performing its functions, different errors are going to be computed to then choose the appropiate pressure sensor. This sensor must have an error smaller or equal to the one obtained in order to get the best accuracy.
2. How should it be done? As it was said before, the ADC has been built in three phases. The first phase consisted of figuring out inputs and outputs of the ADC and of introducing its equations in LabView Software.
The function of this ADC is to determine the altitude, Mach number and static air temperature, SAT in all the phases of a flight so to give to the cockpit systems the needed inputs which will be necessary for the pilots to control the aircraft. Consequently, these will be the outputs.
So, once known the outputs, let’s find the input variables by isolating the outputs in the characteristic equations of the system.
• Altitude, h: −𝑟·𝜆 𝑃 𝑔𝑆𝐿 𝑇𝑆𝐿 ( 𝑠 ) − 𝑇𝑆𝐿 𝑃0 ℎ= 𝐸𝑞. 1 𝜆 1 Alba Martín, Anna Reig • Mach number, M: 1 𝑃𝑇 3.5 √( 𝑃𝑆 ) − 1 𝑀= 𝐸𝑞. 2 0.2 • Static air temperature, SAT: 𝑆𝐴𝑇 = 𝑇𝐴𝑇 𝐸𝑞. 3 1 + 0.2𝑀2 Where: 𝜆= −6.5℃ 1000𝑚 , 𝑟 = 287 𝐽 , 𝑘𝑔𝐾 𝑚 𝑔𝑆𝐿 = 9.81 , 𝑠 𝑇𝑆𝐿 = 288𝐾, 𝑃0 = 1013.25 ℎ𝑃𝑎 Looking to these equations and the constants already defined, the inputs can be find. For these three equations, the needed variables are the static pressure (Ps), the total pressure (Pt) and the True Airspeed Temperature (TAT).
Once all the values are defined, inside LabView, a Matlab program has been developed based on the previous equations to do so. The idea explained before can be summarized in the figure below.
P0 Ps PT ADC H M Matlab program inside LabView SAT TAT Figure 1 ADC input/output diagram To close this first phase, it is going to be checked that for certain inputs, it is got the desired output. To do so, it is needed to determine the input variables by means of the standard atmosphere and isentropic functions tables shown in Annex 1 where the following values are obtained: ℎ = 11000 𝑚, 𝑃𝑠 = 226.3 𝑚𝑏𝑎𝑟, 𝑃𝑇 = 339.42 𝑚𝑏𝑎𝑟, 𝑇𝐴𝑇 = −56.5℃ Introducing these values, the ADC should display a height of 11000m, a Mach number of 0.78 and a SAT of -50.37ºC. The displayed values are the ones appreciated in the figure 2. As it can be seen, the theoretical values match with the real ones validating the first phase of the ADC.
Figure 2 Given inputs obtained outputs for ADC 2 and Alba Martín, Anna Reig The second phase consists of transforming the program to give vectorial outputs instead of scalar ones. This leads to transform the first program by the use of a while command and the use of arrays. To be sure that the ADC works properly for this second phase, a flight that increases its altitude from 20000 ft to 30000 ft, has been simulated. To validate it, first it is needed to determine the input variables by means of the standard atmosphere and isentropic functions tables shown in Annex 1 where the following values are obtained: ℎ = 20000 𝑓𝑡, 𝑃𝑠 = 465.6 𝑚𝑏𝑎𝑟, 𝑃𝑇 = 311.53 𝑚𝑏𝑎𝑟, 𝑇𝐴𝑇 = −24.62℃ For the previous computations, it is also necessary to determine the tolerance for pressure altitude of an ADC as a system will never give the exact altitude. To consider a real value for this tolerance, the one taken was the from the model ADC 2000 of Shadin Avionics. Looking at the table 1, for 20000 ft, the tolerance corresponds to 50ft and for 30000 ft, to 75 ft. The chosen value was the one for 20000 ft as the tolerance is smaller which means making the system more accurate.
Introducing this values on the ADC it should be obtained a height of 30000ft, a Mach number of 0.78 and a SAT of -21.95ºC. As it can be appreciated in the figure 3, the values displayed by the ADC match with the expected ones which approves the second phase.
The third and last phase considers the errors of the ADC system. The type of errors can be divided in three: Table 1 Pressure Altitude Tolerance for the ADC 2000 (Shadin Avionics) • Absolute error 𝐸𝑎𝑏𝑠 : The absolute error of each measure will be the difference between each of the measures and that value taken as being exact (the arithmetic mean).
∆𝑃𝑠 • Relative error 𝐸𝑟𝑒𝑙 : The relative error of each measurement will be the absolute error of the same divided by the value taken as the exact one (the arithmetic mean).
∆𝑃𝑠 · 100% 𝑃𝑠 • Full-scale error 𝐸𝑓𝑢𝑙𝑙𝑠𝑐𝑎𝑙𝑒 : The relative error of the measurement divided by the maximum value of the range. This type of error is used when it is wanted to show a smaller error but it actually increases when the maximum measurement has a very small value. If this maximum is set to zero, this error value goes to infinite.
∆𝑃𝑠 · 100% 𝑃𝑠𝑀𝐴𝑋 These errors have to be considered in the altitude equation to get the height error. To obtain it, it is needed to derivate the height equation (Eq. 1) in function of the static pressure 𝑃𝑠 and finally clear the variation of height in function of all the variables together with the variation of the pressure as shown below.
𝑟·𝜆 𝑟·𝜆 −𝑟 · 𝑇𝑆𝐿 𝑔𝑆𝐿 𝑔𝑆𝐿 −1 Δℎ = · 𝑃0 · 𝑃𝑠 · Δ𝑃𝑠 𝑔𝑆𝐿 3 Alba Martín, Anna Reig For each set of input data, it is got an absolute, a relative and a full-scale error. So, for a bench of input data, these three kind of errors can be shown in three different plots as a function of the height. For the built ADC, the corresponding absolute, relative and full-scale errors follow the behaviour appreciated in the figure 3 (right side).
Analysing these results, the greatest absolute error is below 1mbar which corresponds to the lowest relative error (0.210%) and to the greatest full-scale error (0.096%FS). Concerning the lowest absolute error, the value is below 0.7 mbar which corresponds the greatest relative error (0.227%) and the lowest full-scale error (0.067%FS). The real error is the one given by the absolute error, so as the minimum error is wanted, the minimum absolute error and the relative and full-scale errors associated to it are going to be considered when choosing the pressure sensor which will give the inputs to the ADC.
Figure 3 Air Data Computer results from 20000 ft to 30000 ft 3. Chosen sensor To finish with the project, it has been carried out the search of a pressure sensor adapted to the ADC restrictions. Those necessities involve a wide range of temperature (thus the aircraft will be affected by both, positive and negative values), a minimum full-scale error of 0.0676 FS% and the most important, it has to measure absolute or differential pressure values.
4 Alba Martín, Anna Reig Honeywell’s next generation Precision Pressure Transducer (PPT2) was designed to meet the high-quality standards of the aerospace market and has expanded features to increase functionality and performance for a variety of applications. The PPT2 has a typical accuracy of ±0.0375% full scale, a maximum reading rate of 1000 readings per second, improved electromagnetic interference performance and an extended operating temperature option of -55 to 110°C.
Figure 4 Pressure sensor PPT2 As the full-scale error is less than the needed, the temperature range fulfills the specifications and it measures absolute pressure, it has been the chosen for the project. The most prominent features of the datasheet are shown in the following table in case it is needed to check other type of data that may be necessary in the future.
PRECISION PRESSURE TRANSDUCER 2 (PPT2) Total Error ±0.075% FS Max Long Term Stability 0.025% FS Max per year typical Communication Type RS-232, RS-485 Baud Rate 1200 to 115200 Networkable Yes Operating -40° to 85°C Temperature Range -55° to 110°C Pressure Range 10 standard ranges 1 to 500 PSI Pressure Type Absolute, Gauge, Differential Analog Output Analog Output Customizable Yes Power Supply 6 – 34 VDC, 50 mA max Weight 4.4 oz (125 g) RoHS Compliant Yes Export Classification EAR99 Table 2 PPT2 specifications 5 Alba Martín, Anna Reig Annex 1 Table 3 Standard atmosphere values 6 Alba Martín, Anna Reig Cruise Mach for a commercial aircraft, M=0.78 Extrapolating, for M=0.78, P/Po=Static Pressure/Total Pressure=0.6691 Table 4 Isentropic flow functions for different Mach number 7 ...