Hey!

Just a quick question, how can I calculate my true airspeed based on IAS, winds, etc

Thanks

Speedbird092

- speedbird092
**Posts:**164**Joined:**

Hey!

Just a quick question, how can I calculate my true airspeed based on IAS, winds, etc

Thanks

Speedbird092

Just a quick question, how can I calculate my true airspeed based on IAS, winds, etc

Thanks

Speedbird092

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.

Hope this helps!

DerekF

Hope this helps!

DerekF

Whatever.......

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.

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- XFSUgimpLB41X
**Posts:**3961**Joined:**

Here's the equation I've got on my desk:

TAS= [(IAS x 2%) • (ALT/1000)] + IAS

So an example--

IAS= 300 at FL200, 300 • 0.02 • 20 + 300= 240TAS

If I'm wrong, please correct me by all means.

TAS= [(IAS x 2%) • (ALT/1000)] + IAS

So an example--

IAS= 300 at FL200, 300 • 0.02 • 20 + 300= 240TAS

If I'm wrong, please correct me by all means.

N400QX, at higher altitudes TAS is greater than IAS. But you got some of the math:

IAS decreases by 2% every 1000ft you climb.

IAS 280 at FL330

---> [280 x (33 x 0.02)] + 280 = TAS 464.8

Winds affect ground speed mostly.

-bio

IAS decreases by 2% every 1000ft you climb.

IAS 280 at FL330

---> [280 x (33 x 0.02)] + 280 = TAS 464.8

Winds affect ground speed mostly.

-bio

(2% for every 1000 feet) X CAS, then plus CAS = TAS

==EXAMPLE==

CAS: 90 kts

Altitude: 6000 ft

(6 x .02) x 90= 11

11 + 90= 101 kts TAS

And XFSUgimpLB41X, it is pressure altitude I'm pretty sure...

==EXAMPLE==

CAS: 90 kts

Altitude: 6000 ft

(6 x .02) x 90= 11

11 + 90= 101 kts TAS

And XFSUgimpLB41X, it is pressure altitude I'm pretty sure...

- sabenapilot
**Posts:**2442**Joined:**

Here's the one and only **simple thumbrule** to convert IAS into TAS.

(sadly only valid above FL100)

**TAS = IAS + half of your flight level**

To prove how accurate it is, I've used the same example as Bio15 so you can compare the results:

IAS = 280kts.

FL330

TAS = 280 + 165 = 445

(sadly only valid above FL100)

To prove how accurate it is, I've used the same example as Bio15 so you can compare the results:

IAS = 280kts.

FL330

TAS = 280 + 165 = 445

- Jetpilot500
**Posts:**78**Joined:**

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:

http://www.best.com/~williams/avform.html

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

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:

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

Have fun trying to figure this out!

JetPilot500

http://www.best.com/~williams/avform.html

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

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:

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

Have fun trying to figure this out!

JetPilot500

- sabenapilot
**Posts:**2442**Joined:**

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.

--------------------

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

---------------------

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...)

However, the question was:

how can I

I don't think any of these formulas are helping you any further.

--------------------

BTW, since you talked about it:

here's a

e.g.:

indicated temp = -25°C

M = .70

OAT = -25 - 14 = -39°C

---------------------

And another very usefull notion.

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...)

OK... I understand now.

Bio-- the reason the TAS in my math shows 240 is because of a typo... I believe I meant to put in 340. oops

Bio-- the reason the TAS in my math shows 240 is because of a typo... I believe I meant to put in 340. oops

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