TAS from IAS, PA and OAT

[mfclearner]

I used formula
TAS = IAS + (2/100) X IAS X (PA/1000)
to manually calculate value. All problems that I solved using this formula tallied with values that I get from my electronic E6B as well as Mechanical E6B except one example below

IAS = 97 Kts FL 75 OAT -75 Calculate TAS.
Now answer to this
– From mechanical E6B is 106
– From electronic E6B is 105
– Using formula above 111.5

So am I missing anything in above formula? This formula doesn’t take into account OAT is that a reason? What is the correct formula in that case? :confused:


Thanks

[Tinstaafl]

I'd say use Density Altitude instead of Pressure Altitude

[mfclearner]

Do you mean in above formula replace PA with DA to read

TAS = IAS + (2/100) X IAS X (DA/1000)

is that right?

[Chris Scott]

Do you mean:

TAS = IAS + [(IAS X 2/100) X (DA/1000)]

- where DA is in feet, and IAS/TAS are in your chosen unit.

?

Regards,
Chris

PS
At my first look, I misread it as:
TAS = (IAS + 2/100) X IAS X (DA/1000)
That's why you sometimes need to use two types of brackets, to avoid ambiguity. ;)

[FlightPathOBN]

altitude is MSL

From 8260.52

Vktas=Vkias x [1+(altitude x 0.00002)]

example Final segment CAT B, 1500 feet

Vktas= 120 x [1 + (1500 x 0.00002)] =123.6

[mfclearner]

Yes Chris I meant

TAS = IAS + [(IAS X 2/100) X (DA/1000)]

[SpanWise]

Tinstaafl,

It should be PA, because this formula is not considering the affects of Temperature, only Pressure Altitude.

If you put DA, then we have to have another formula or use the flight computer to first find Density Altitude (using Temperature) and then use that value in the formula posted by mfclearner. So you'l need 2 formulas!

This formula for TAS is a rule of thumb that considers only the affects of Pressure Altitude. It is sufficient enough because the affects of tempature on TAS is far lower than the affect of Pressure on TAS.

mfclearner,

The formula is correct. But essentially all you are doing is adding 2% of IAS per 1000 feet of pressure altitude. So, suppose you were at FL80, thats 8 * 2 = 16% correction. If your IAS is 200 knots then your TAS is simply 232 knots (16% of 200 is 32).

So its 2% correction per 1000 feet of altitude. This way of approaching it makes it very easy to do it in the air in your mind than thinking of the formula. :)

The reason why the answers are off is, as you correctly noted, the lack of use of Temparature as a variable. It is only a rule of thumb. But even 5 knots off is okay enough for mental calculations. For example, if you are using speed factors to calculate things like Top of Descent, etc (240 knots is 4 miles a minutes, 270 is 4 and half, 210 is 3 and half) you are rounding up or down by 15 knots there anyway.

If you want to be more picky, you can do a quick ISA deviation check at your altitute using the OAT. If it is a +ve deviation (the air is warmer than standard) the result of your TAS calculation is tending to under-indicate (since due to lower air density you are having to move faster to get the IAS). If it is a -ve deviation (cooler than standard atmosphere), the result of your TAS calculation is tending to over-indicate. You can then round appropriately for Speed factors. For example, on a day with -ve ISA deviation, if you found your calculated TAS to be 198 knots (more than midway between 180 and 210), when usually you would round to 210, Today you can round to 180 as you know your actual True Airspeed is closer to 180 than 210.

Note this sort of correction is in affect, making use of Density Altitude ;)

Hope that was useful info.

Regards. :)

[Lemurian]

I've used a formula that takes care of the PA / DA difference and introduces a temperature correction.
Was given to me long time ago by an old retired navigator and it's surprisingly accurate.
Here it is : TAS = IAS + 1 % per 600 ft +/- 1 % per 5°C diff with ISA
For instance : IAS = 97 kt ; OAT = 75 °F or 22° C ; FL 75.
1/- pressure correction : 7500 / 600 = 12.5 %
2/- Temp correction
At 7500 ft, ISA = 0°C --> 22/5 = 4.4
Total correction 12.5 + 4.4 ~ 17 % or ~16 kt
Therefore, TAS = 97 + 16 = 113 kt

If OAT = -75 °F or - 60°C the temp corr is -60 / 5 = -12 %, both corrections annull each other and TAS = 97 kt

Just about everybody is right, you can't have a TAS unless you specify a DA, hence a temperature.

[mfclearner]

Lemurian that is amazingly accurate formula. Using it I got answers those tally with my electronic flight computer as well as mechanical E6b. Thanks alot. Thanks to everyone else as well.

[SpanWise]

Thanks Lemurian for the forumla. Really do appreciate it! :)

[selfin]

The Lemurian approximation is a substantial improvement over the "2 per cent per thousand feet" variant. Finding a good approximation suitable over all altitudes, speeds and temperature deviations of interest (MSL to tropopause, 100 to 300 kcas, +/- 30 K) for TAS without using quadratic terms is next to impossible. Having looked at a restricted range of altitudes (MSL to 10 000 feet) it is hard to improve on Lemurian's approximation. The only value I would alter is the constant 600, which I propose be swapped for 666.67 (i.e. 3/2000). This is mentally no more difficult than dividing the altitude by 600 but the error is lower.

Here are three charts comparing the errors in KTAS across the restricted altitude range for these three approximations.

Approximation (a): TAS ≈ CAS[1+(2/100)(h_DA/1000)]
Approximation (b): TAS ≈ CAS{1+(1/100)[(h_PA/600)+(T_dev/5)]}
Approximation (c): TAS ≈ CAS{1+(1/100)[(3h_PA/2000)+(T_dev/5)]}

T_dev is temperature deviation from the standard atmosphere.
h_PA is the pressure altitude in feet.
h_DA is the density altitude in feet.

Note: Pressure altitude is used in approximations (b) and (c), but density altitude in approximation (a).

In the altitude range 0 to 10 000 feet the least square error for all CAS (100 to 300 kcas) and temperature deviation (+/- 30 K) pairs is lowest under approximation (c). The curves are plotted for Tdev=0 therefore no density altitude axis is included for charts 1 and 2. Send PM for excel file.

http://img25.imageshack.us/img25/535/ktasapproxchart1.th.png (http://img25.imageshack.us/img25/535/ktasapproxchart1.png)

Chart 1: comparison of approximations (a) and (b).

http://img94.imageshack.us/img94/8361/ktasapproxchart2.th.png (http://img94.imageshack.us/img94/8361/ktasapproxchart2.png)

Chart 2: comparison of approximations (a) and (c).

http://img641.imageshack.us/img641/7287/ktasapproxchart3.th.png (http://img641.imageshack.us/img641/7287/ktasapproxchart3.png)

Chart 3: comparison of approximations (b) and (c).

[FlightPathOBN]

Get a GPS, measure groundspeed, and forget about all of this! :)

[Lemurian]

@ Selfin,
That formula was for mental calculations for rather slower airplanes (DC-4 in particular when the ASI was in mph and at 10,000 ft, 200 mph indicated were worth 200 kt true ( you see what I mean )

For faster speeds, when one enters the Mach territory ( First plane for me was the Convair 580 /540 whoch cruised at ;55 or ;60 M )
In this case, the formula became
TAS = M x 600 . Exact at OAT = -35°C. just add - if the temp is higher - or substract - if lower - 1 kt per degree different from -35.

Ex :
M = .75
OAT = -42°c --> (-35 - 7 )
TAS = (.75 x 600 ) -7 = 450 -7 = 443 kt
The error will not exceed 1 kt !

[Oktas8]

If you find that 2% / 1000' is not sufficiently accurate, it is more accurate to say that TAS = IAS plus (IAS/60 per thousand feet). IAS/60 is of course just airspeed in nm/min.

If one thinks about it, one will see that 1% per 600 ft is almost the same as 1 in 60 per thousand feet. But I prefer to divide by 1000 than by 600!

Example: speed 180kts or 3nm/min. TAS = IAS + 3x altitude in 000's of feet.

Naturally it still doesn't take temperature into account.

Cheers,
O8

[selfin]

Lemurian,

The only way I can see a coefficient of 600 in Mach giving anything close to the correct KTAS value is by including a coefficient for the temperature term.

Regressing KTAS asgainst M and M*(T+35) values yields:

KTAS ≈ M[600+1.22(T+35)], (T in centigrade)

The error within the range I've checked (0.5 ≤ M ≤ 0.85, -75 c ≤ T ≤ + 45 c) stays reasonably small, < |2.3|. The maximum positive error (KTAS minus the approximation) won't exceed 1.44 KTAS over this range.

The +35 c tweak to the temperature was necessary to force the coefficient to a friendly 600.

Calibration and validation of model available on request.