# Calibrated airspeed formula

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I seen several formulas to calculate the CAS, but they give different results.Is there any "official" calibration formula to calculate the CAS as showed in the real airspeed indicators (IAS corrected for calibration and installation error)?ThanksCristiano

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My guess is that the answer would be no.The IAS/CAS graphs shown in each aircraft's handbook are different because the position of the pitot tube will vary. This will give errors specific to that aircraft and the graph will highlight the variation. I assume that CAS/IAS conversion is aircraft type specific.

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Calibrated airspeed (CAS) is the speed theoretically shown by a simple airspeed indicator that is free from instrument error and position error.http://www.mathpages.com/home/kmath282/kmath282.htm gives a good description.I imagine these days that CAS can be calculated by the on-board air data computer system which can have other inputs such as temperature bypassing the traditional simple altimeter. I can remember when a wind-tunnel tested pitot-static probe with fins like a small missile was towed behind new aircraft types to calibrate the aircraft's ASI.

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>http://www.mathpages.com/home/kmath282/kmath282.htm gives a>good description.Those formulas seem to give strange results: EAS much bigger than TAS and the CAS seems too small.>I imagine these days that CAS can be calculated by the>on-board air data computer system [...]That is also my opinion. For that reason I think the CAS calculated in FS should be the same of the theory.FS uses something like this:CAS = conversion_factor * sqrt( impact_pressure *2/0.125)which should be good when the air is uncompressible (0.125 is the air density in MKS units).In an old book it is written that the calibration formula adopted in the NATO countries (!) is:Vcal = 2495 * sqrt((1+impact_press/2116)^0.285 -1)which clearly gives a totally different result.It seems really incredible that there are so many formulas!Cristiano

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Hello Christiano,I have a SS to compute them and the formulas may be found there:http://perso.wanadoo.fr/hsors/FS_Soft/fsdocs.htmlGet the International Standard Atmosphere.Ian

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Hello Ian,In the sheet "Speed", I seen the table KCAS(FL,MN), but, afaik, that should be KEAS(FL,MN) because you don't take into account the compressibilty.For example your KCAS(200, 0.8) = 358.9 which is very good for the equivalent airspeed but the CAS should be around 389 kts (because of compressibility).Do you have any reference for your formulas?Thank youCristiano

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>Hello Ian,>In the sheet "Speed", I seen the table KCAS(FL,MN), but,>afaik, that should be KEAS(FL,MN) because you don't take into>account the compressibilty.>For example your KCAS(200, 0.8) = 358.9 which is very good for>the equivalent airspeed but the CAS should be around 389 kts>(because of compressibility).>Do you have any reference for your formulas?>Thank you>Cristiano Herve Sors calculated CAS for AFSD, it includes compressability effects. It is displayed in one of the 'speed' Windows. And, it different from the FS 'IAS' above 340 kts or so. That's assuming the 'IAS' is calibrated with two lines in aircraft.cfg (missing in most FS9 files). This is what I set for one jet, I think all my jets use the same numbers. IAS indicates correctly and is 'CAS' for Jet Transports at normal cruise FL's (based on FM statements). It starts to deviate at lower altitudes when I fly over 340 kts.[airspeed_indicators]airspeed_indicator.0=0.9826, 0.0 //Calibrates IAS to CAS AFSD shows how FS IAS varies from CAS as AoA increases during a landing. And, how Flaps change pitch, thus IAS. At lower speeds, EAS is equal to CAS. EAS is easy to calculate if one has an accurate 'q', Dynamic Pressure. EAS = 1/2 rho * V^2. I get rho from an A: variable in my XML test gauges. However, I ended up calculating TAS (V) from Mach. Mach is a scalar, but TAS appears to be a vector relative to the AC's long axis. That made a difference when there are alpha and beta incidences. I know my 'q' is accurate; I calculate drags using q^2, and they come out very close. The formula for CAS is long and nested. However, I probably already calculate some of the factors for it in my Test Calculations. I already take some factors to the 3.5 power. I suspect adding 'impact pressure' to EAS would make it CAS. I know the FS IAS runs higher than EAS at normal cruise FL's, but it appears to be off as noted above. Ron

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> Herve Sors calculated CAS for AFSD, it includes>compressability effects. It is displayed in one of the 'speed'>Windows.Good! My speeds are equal to the Herve's speeds. :-)> And, it different from the FS 'IAS' above 340 kts or>so. That's assuming the 'IAS' is calibrated with two lines in>aircraft.cfg (missing in most FS9 files). You're right; I have 172 aircraft.cfg files and only 12 have those two lines.> This is what I set for one jet, I think all my jets use the>same numbers. IAS indicates correctly and is 'CAS' for Jet>Transports at normal cruise FL's (based on FM statements). It>starts to deviate at lower altitudes when I fly over 340 kts.>>[airspeed_indicators]>airspeed_indicator.0=0.9826, 0.0 //Calibrates IAS to CASI don't think the error is because of the missing lines.The speed showed by the airspeed indicator in FS is in very good agreement with sqrt(impact_pressure *2/0.125) which is the simplest formula, but it doesn't care about compressibility.The right CAS should be calculated as:A=661.4786*sqrt(5*( (impact_pressure/Po+1)^(1/3.5) )-1))where Po is the ambient pressure at sea level in standard atmosphere (101325 Pa).I use that formula and it seems the same formula used in AFSD (very good program! :-) ).> At lower speeds, EAS is equal to CAS. EAS is easy to>calculate if one has an accurate 'q', Dynamic Pressure. EAS =>1/2 rho * V^2. I get rho from an A: variable in my XML test>gauges.Perhaps you meant q= 1/2 rho * TAS^2or q= 1/2 * rho_0 * EAS^2?Anyway, if you have rho you could useEAS= TAS*sqrt(static_density / sea_level_std_density).> However, I ended up calculating TAS (V) from Mach. Mach is>a scalar, but TAS appears to be a vector relative to the AC's>long axis. That made a difference when there are alpha and>beta incidences.Reading the TAS with FSUIPC (at the offset 02B8 as knots * 128) it seems the "real" TAS.There are 3 offsets in FSUIPC which seem to be what you say: 3090 is the ground speed (not the TAS) relative to the longitudinal axe, 3098 is for the lateral component and 30A0 is for the vertical component.Cristiano

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>> Herve Sors calculated CAS for AFSD, it includes>>compressability effects. It is displayed in one of the>'speed' Windows.>>Good! My speeds are equal to the Herve's speeds. :-) >> And, it different from the FS 'IAS' above 340 kts or>>so. That's assuming the 'IAS' is calibrated with two lines>in aircraft.cfg (missing in most FS9 files). >>You're right; I have 172 aircraft.cfg files and only 12 have>those two lines. The values weren't imported from the top of REC 1101 in the AIR file when it is first loaded into FS9. BTW, that record uses unsigned integers, but is displayed as signed. Which was confusing for a long time. I think '32768' amounts to 1.>> This is what I set for one jet, I think all my jets use (it)>>[airspeed_indicators]>>airspeed_indicator.0=0.9826, 0.0 //Calibrates IAS to CAS>>I don't think the error is because of the missing lines. That line has less than a 2% effect on IAS. At 250 kts, FL 250, FS IAS is about 5 kts high without it.>The speed showed by the airspeed indicator in FS is in very>good agreement with sqrt(impact_pressure *2/0.125) which is>the simplest formula, but it doesn't care about>compressibility. So, we know how FS calculates another variable. >The right CAS should be calculated as:>A=661.4786*sqrt(5*( (impact_pressure/Po+1)^(1/3.5) )-1))>where Po is the ambient pressure at sea level in standard>atmosphere (101325 Pa).>I use that formula and it seems the same formula used in AFSD>(very good program! :-) ). I check my Test Gauges against AFSD. However, note anything depending on Density, etc. is only correct in AFSD if the FS Atmosphere is ISA. Herve' couldn't get the L:Variables I used.>> At lower speeds, EAS is equal to CAS. EAS is easy to>>calculate if one has an accurate 'q', Dynamic Pressure. >> EAS = 1/2 rho * V^2. I get rho from an A: variable in my XML test>>gauges.>Perhaps you meant q= 1/2 rho * TAS^2 Yes. I calculated EAS from q since I knew my q was correct.>Anyway, if you have rho you could use>EAS= TAS*sqrt(static_density / sea_level_std_density). I used L: Variable units of 'atmosphere(s)' for pressure, which made it exactly what I wanted for "Delta".>Reading the TAS with FSUIPC (at the offset 02B8 as knots *>128) it seems the "real" TAS.>There are 3 offsets in FSUIPC which seem to be what you say:>3090 is the ground speed (not the TAS) relative to the>longitudinal axe, 3098 is for the lateral component and 30A0>is for the vertical component.>Cristiano I get all the above with XML L: variables. The definitions of some 'true' speeds is confusing. Ron

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