DerekF From United Kingdom, joined Feb 2001, 919 posts, RR: 0
Reply 1, posted (14 years 4 months 5 days 1 hour ago) and read 15489 times:

You need to know several things like altitude, temperature and aircraft pressure errors. Basically TAS = EAS divided by the square root of atmospheric density ratios (hence using temp and altitude). EAS is derived from IAS by knowing the aircraft pressure erros to arrive at CAS the CAS to EAS by the scale altitude law or compressibility correction. If you need any more info let me know.

Ralgha From United States of America, joined Nov 1999, 1614 posts, RR: 5
Reply 2, posted (14 years 4 months 4 days 23 hours ago) and read 15466 times:

Or you could just use a flight compter . Also, many airplanes have a TAS ring on their airspeed indicator that you can adjust for pressure altitude and temperature, you can then read your TAS right off the airspeed indicator.

XFSUgimpLB41X From United States of America, joined Aug 2000, 4294 posts, RR: 36
Reply 3, posted (14 years 4 months 4 days 23 hours ago) and read 15463 times:

Isn't it density altitude and not pressure altitude?

Jetpilot500 From United States of America, joined Nov 2000, 78 posts, RR: 0
Reply 9, posted (14 years 4 months 1 day 4 hours ago) and read 15411 times:

You are all providing interesting rules of thumb, but there are a lot of factors involved to come up with an accurate answer for all speeds and altitudes. As someone else mentioned, use an E6B. Here is the correct method found on this website of aviation formulas:

Mach Number (M) = TAS/CS
CS = sound speed= 38.967854*sqrt(T+273.15) where T is the OAT in celsius.
TAS is true airspeed in knots.
Because of compressibility, the measured IAT (indicated air temperature) is higher than the actual true OAT. Approximately:

IAT=OAT+K*TAS^2/7592
The recovery factor K, depends on installation, and is usually in the range 0.95 to 1.0, but can be as low as 0.7. Temperatures are Celsius, TAS in knots.

Also:

OAT = (IAT + 273.15) / (1 + 0.2*K*M^2) - 273.15
The airspeed indicator measures the differential pressure, DP, between the pitot tube and the static port, the resulting indicated airspeed (IAS), when corrected for calibration and installation error is called "calibrated airspeed" (CAS).

For low-speed (M<0.3) airplanes the true airspeed can be obtained from CAS and the density altitude, DA.

TAS = CAS*(rho_0/rho)^0.5=CAS/(1-6.8755856*10^-6 * DA)^2.127940 (DA<36,089.24ft)
Roughly, TAS increases by 1.5% per 1000ft.

When compressibility is taken into account, the calculation of the TAS is more elaborate:

DP=P_0*((1+0.2*(IAS/CS_0)^2)^3.5 -1)
M=(5*( (DP/P+1)^(2/7) -1) )^0.5
TAS= M*CS
P_0 is is (standard) sea-level pressure, CS_0 is the speed of sound at sea-level, CS is the speed of sound at altitude, and P is the pressure at altitude.

These are given by earlier formulae:

P_0= 29.92126 "Hg = 1013.25 mB = 2116.2166 lbs/ft^2
P= P_0*(1-6.8755856*10^-6*PA)^5.2558797, pressure altitude, PA<36,089.24ft
CS= 38.967854*sqrt(T+273.15) where T is the (static/true) OAT in Celsius.
CS_0=38.967854*sqrt(15+273.15)=661.4786 knots

[Example: CAS=250 knots, PA=10000ft, IAT=2C, recovery factor=0.8
DP=29.92126*((1+0.2*(250/661.4786)^2)^3.5 -1)= 3.1001 "
P=29.92126*(1-6.8755856*10^-6 *10000)^5.2558797= 20.577 "
M= (5*( (3.1001/20.577 +1)^(2/7) -1) )^0.5= 0.4523 Mach
OAT=(2+273.15)/(1 + 0.2*0.8*0.4523^2) - 273.15= -6.72C
CS= 38.967854*sqrt(-6.7+273.15)=636.08 knots
TAS=636.08*0.4523=287.7 knots]
In the reverse direction, given Mach number M and pressure altitude PA, we can find the IAS with:

Sabenapilot From Belgium, joined Feb 2000, 2743 posts, RR: 45
Reply 10, posted (14 years 4 months 1 day 1 hour ago) and read 15401 times:

All are correct (although I haven't really spend time checking them over...)
However, the question was:
how can I quickly get an idea of my TAS based on IAS?
I don't think any of these formulas are helping you any further.

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BTW, since you talked about it:
here's a quick formula to find OAT from IAT: OAT = IAT - 20 times the speed in mach
e.g.:
indicated temp = -25°C
M = .70
OAT = -25 - 14 = -39°C

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And another very usefull notion. Machnumber equals distance travelled per minute.
e.g.:
At M.70 you travel about 7NM/minute.

Ok, both might be off somewhat at extreme winds, speeds altitudes or temperatures, but they are more then accurate enough for flight follow-up and are often used in the cockpit of planes without FMS, like the B737-200. (I started on that one at Sabena...)