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How to deduct compressability error from pressure altitude

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  • How to deduct compressability error from pressure altitude

    Hi,

    in several questions i see the following explanation to get EAS from CAS:

    CAS - Zp - EAS - Zd - TAS

    I dont understand how the pressue altitude can give you the compressabilityfactor? I thought that depended on speed.
    many thanks for your response.

  • #2
    Have a look at https://en.wikipedia.org/wiki/Compressibility for a really clear and simple explanation. It is pressure, not speed that is important

    Comment


    • #3
      The link provided by the previous contributor gives no information about compressibility correction of the mechanical airspeed indicator so is not relevant to this question. (despite the "really clear and simple" partial differential equations)

      A mechanical airspeed indicator has a single capsule which responds to (total pressure - static pressure). Since the instrument does not know its absolute static pressure it can be calibrated to be free of comprehensibility error only at one particular pressure altitude which by convention is ISA sea level. Therefore at ISA sea level CAS is always equal to EAS. When used at high altitude the instrument calibration does not correctly compensate for compressibility and hence CAS > EAS.

      Compressibility correction (delta Vc) is the difference between EAS and CAS. Compressibility correction can be expressed as a function of CAS and pressure altitude or as a function of Mach number and pressure altitude. It is zero at ISA sea level and always a negative value at high altitude. See the attached compressibility correction chart.


      Here is an example to illustrate:

      251 KCAS, FL 400, ISA temperature.

      Go to the compressibility correction chart and and look for 251 calibrated airspeed. Now go up to the line for 40,000 ft pressure altitude, then read across to get delta Vc = -16.

      So 251 KCAS minus 16 = 235 KEAS

      Now go to the ISA table and look up the ISA density ratio at 40,000 ft. This gives 0.2462.
      With a calculator, divide 235 by the square root of 0.2462. This gives 473.6 KTAS.

      For comparison, I could use my CRP-5:

      In the Airspeed window set "40" Press Alt x 1000 against "-56.5" Cor Air Temp C. Now look for 251 KCAS on the main inner scale and read uncorrected TAS 492. Next go to the Comp Corr window and apply the formula 492/100 -3 = 1.92. In the Comp Corr window move 1.92 divisions to the left (ok, it's hard to be precise).
      Now go back to 251 on the inner scale add read about 473 KTAS.

      Note that the CRP-5 converts directly from CAS to TAS according to its own method. It does not use EAS as an intermediate step so you can't use the CRP-5 to deduce EAS directly.

      But if I have my ISA table I can calculate EAS via Mach number.

      At 40,000 ft the ISA table gives LSS = 573 (or calculate it from known temperature)
      Mach number = TAS/LSS = 473/573 = 0.8255
      Now EAS = LSS at sea level (661.5 kts) x Mach number x square root of the pressure ratio.
      At 40,000 ft the ISA table gives pressure ratio = 0.1841, so
      EAS = 661.5 x 0.8255 x sqrt(0.1841) = 235
      and hence delta Vc = 235 - 251 = -16
      Attached Files
      Last edited by Ortac; 24-05-2020, 14:33.

      Comment


      • #4
        Ortac Hi! You are absolutely right about the uselessness of the website mentioned above. As I was very close to my exam, I didnt bother explaining it to ChrisK hoe I wasted a good 10 min on trying to find the answer to my question at that website. However, eventhough I passed the subject I read your explanation with great interest. I do believe I understand the concept now. Many thanks for your elaborate response and taking the time explaining it so well. Kindest regards!

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