# What is the relation between IAS and TAS at a constant altitude?

I have noticed that when calculating True Air Speed for any given altitude, the faster the Indicated Air Speed, there seems to be a larger increase in TAS? My thinking was that at a constant altitude the relationship between IAS/TAS would be linear, e.g you double IAS, and TAS would double.. But it seems to increase more? Not sure if I'm missing something here?

For example: 5000ft at 100knts IAS = 114knts TAS , 5000ft at 110knts IAS = 126knts TAS

Only a couple Knots difference, and it seems to make sense but I can't find any answers on it to confirm it? Would appreciate anybody to shed light on it, thanks!

If you divide 114/100 and 126/110 you'll find the common factor is ~1.14.

Which means for that altitude TAS ≈ 1.14 * IAS.

1.14 is the square root of the ratio of standard sea level ISA air density ($\rho_0$) to the air density at that altitude ($\rho$). This is assuming IAS = CAS = EAS (i.e., ignoring positioning, calibration, and compressibility effects).

$$\text{TAS} = \text{EAS} \sqrt{ \frac{\rho_0}{\rho} }$$

It looks like you got the numbers from this online converter. Note its preset is not a standard ISA, as the altimeter setting reads 28.16 inHg. Instead I recommend this one, which is for standard ISA. For 5,000 ft the values are:

CAS    TAS
100    107.7
110    118.4
120    129.2


With the multiplier at 5,000 feet ISA being ~1.077, and the relation looks like this:

• Excellent that explains a lot. I first noticed it on my Flight Computer and had to justify that it wasn't miss reading! Thanks for your help. – Jesse Jun 10 '18 at 12:20