# IAS to TAS formula?

Join Date: Aug 2000

Location: California

Posts: 1,181

TAS=IAS/sqrt(delta)

where Delta=ratio of air density to ISA SL density

=288.15/(T+273.15) * (P/1013.25)

and P= Ambient pressure in HPa(mB)

T= ambient temperature in degrees celsius

This ignores the compressibility correction, which is very small at low Mach numbers up to about M0.3

The "rule of thumb" correction is actually nearer to 1.5% per 1000' at low altitudes

where Delta=ratio of air density to ISA SL density

=288.15/(T+273.15) * (P/1013.25)

and P= Ambient pressure in HPa(mB)

T= ambient temperature in degrees celsius

This ignores the compressibility correction, which is very small at low Mach numbers up to about M0.3

The "rule of thumb" correction is actually nearer to 1.5% per 1000' at low altitudes

Join Date: Aug 2003

Location: Sale, Australia

Age: 75

Posts: 3,829

From Aviation Formulary V1.43

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

[(*) If this results in M>1 - ie supersonic flight, we have to account for the shock wave ahead of the pitot tube, using Rayliegh's Supersonic Pitot equation.

Using the M from above as the first guess on the RHS, iterate:

M=0.881285 sqrt((DP/P + 1)(1 - 1/(7*M^2))^(5/2))

to convergence.]

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=2°C, 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:

x=(1-6.8755856e-6*PA)^5.2558797

ias=661.4786*(5*((1 + x*((1 + M^2/5)^3.5 - 1))^(2/7.) - 1))^0.5 (for M <=1)

Some notes on the origins of some of the "magic" number constants in the preceeding section:

6.8755856*10^-6 = T'/T_0, where T' is the standard temperature lapse rate and T_0 is the standard sea-level temperature.

5.2558797 = Mg/RT', where M is the (average) molecular weight of air, g is the acceleration of gravity and R is the gas constant.

0.2233609 = ratio of the pressure at the tropopause to sea-level pressure.

4.806346*10^-5 = Mg/RT_tr, where T_tr is the temperature at the tropopause.

4.2558797 = Mg/RT' -1

0.2970756 = ratio of the density at the tropopause to the density at SL (rho_0)

145442 = T_0/T'

38.967854 = sqrt(gamma R/M) (in knots/Kelvin^0.5), where gamma is the ratio of the specific heats of air

**Mach numbers, true vs calibrated airspeeds etc.**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

[(*) If this results in M>1 - ie supersonic flight, we have to account for the shock wave ahead of the pitot tube, using Rayliegh's Supersonic Pitot equation.

Using the M from above as the first guess on the RHS, iterate:

M=0.881285 sqrt((DP/P + 1)(1 - 1/(7*M^2))^(5/2))

to convergence.]

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=2°C, 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:

x=(1-6.8755856e-6*PA)^5.2558797

ias=661.4786*(5*((1 + x*((1 + M^2/5)^3.5 - 1))^(2/7.) - 1))^0.5 (for M <=1)

Some notes on the origins of some of the "magic" number constants in the preceeding section:

6.8755856*10^-6 = T'/T_0, where T' is the standard temperature lapse rate and T_0 is the standard sea-level temperature.

5.2558797 = Mg/RT', where M is the (average) molecular weight of air, g is the acceleration of gravity and R is the gas constant.

0.2233609 = ratio of the pressure at the tropopause to sea-level pressure.

4.806346*10^-5 = Mg/RT_tr, where T_tr is the temperature at the tropopause.

4.2558797 = Mg/RT' -1

0.2970756 = ratio of the density at the tropopause to the density at SL (rho_0)

145442 = T_0/T'

38.967854 = sqrt(gamma R/M) (in knots/Kelvin^0.5), where gamma is the ratio of the specific heats of air

Thread Starter

Join Date: Apr 2008

Location: Brisbane

Age: 34

Posts: 61

wow, thanks for the response guys

Brian Abraham that looks like a really complex way of doing it, but im sure very accurate, but i would probably be at my destination before if figured it out.

I was aware of the TAS=IASx(alt/1000)x0.2 or 0.15......

BUT is there any correction you can make to for ISA temp deviation or ISA MSL press deviation??

thanks

Brian Abraham that looks like a really complex way of doing it, but im sure very accurate, but i would probably be at my destination before if figured it out.

I was aware of the TAS=IASx(alt/1000)x0.2 or 0.15......

BUT is there any correction you can make to for ISA temp deviation or ISA MSL press deviation??

thanks

Join Date: Aug 2003

Location: Sale, Australia

Age: 75

Posts: 3,829

brns2, sorry but you did ask
Just didn't want you to say I left something out. I'm one of those nerds that wants the answer to the Nth decimal place.

411A, have yet to fly something with a TAS readout, has always been the whiz wheel. The only Lockheed (12A) was so rudimentary it had a morse key in the RHS seat, quite unlike your chariot.

Is there any formula to get TAS from a IAS with varying temp or press?

411A, have yet to fly something with a TAS readout, has always been the whiz wheel. The only Lockheed (12A) was so rudimentary it had a morse key in the RHS seat, quite unlike your chariot.

Join Date: Sep 2017

Location: USA

Posts: 2

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

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

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

Thanks.

Join Date: Mar 2014

Location: The World

Posts: 1,216

Join Date: Mar 2005

Location: N/A

Posts: 2,672

ChickenHouse, the late departed 411A knew more about the business than you are likely to learn. Flew the big pistons and was flying a 1011 till his end. Dad helped design the DC-3, and had Howard Hughes as a house guest.

chr2017, this may be of help, Chapter III.

http://www.dtic.mil/dtic/tr/fulltext/u2/a280006.pdf

Or else just use this.

TAS Calculator

411A left and right respectively.

chr2017, this may be of help, Chapter III.

http://www.dtic.mil/dtic/tr/fulltext/u2/a280006.pdf

Or else just use this.

TAS Calculator

411A left and right respectively.