IAS /MACH and TAS with increasing altitude
 

Hey guys.
So I understand that with increasing altitude, Local speed of sound decreases due to lower air density, hence leading to an increase in Mach number with increasing altitude. Also is why we hit MMO before VMO when climbing in constant VMO.

TAS also increases with increasing altitude due to decreasing air density.
Can someone briefly explain to me why this is?

Finally. I can remember that IAS decreasing with unceasing altitude, however I cannot remember why.
Help? :O

Hi :)

The LSS decreases with increasing altitude not because of decreasing pressure, but because of decreasing temperature (as you may know the temperature gradient slopes towards colder temperature through the stratosphere and flips towards higher temperatures again up until the mesosphere).

You're right that we hit MMO before VMO at a constant IAS through altitude increase.

The TAS increases with increasing altitude at constant IAS because of decreasing density (roughly explained there is further between each air molecule, so for a constant IAS, dynamic air pressure, we "have" to have an increase in TAS; velocity in the particular body of air.)

So LSS is ONLY dependant on ambient temperature, thus the formula: LSS= 39 x the root of T (in kelvin).

Hope this somewhat clarifies the relationship between the different speeds.

Hi there,

Firstly local speed of sound decreases with altitude due temperature decrease with altitude. Equation reads;

LSS = sq.root(Absolute Temp)

I'm sure there may be other factors that affect LSS but for simplicity we just consider the absolute temperature as the variable.

To the second point, why does TAS increase with a constant IAS as you climb. Well the difference between IAS and TAS is a density relationship. As you climb the air becomes less dense due to the decrease in pressure. Hence the aircraft's actual speed becomes greater. Remember density is proportional to pressure and inversely proportional to temperature but the decrease in pressure is the overriding factor.

Final point, why does IAS decrease with increasing altitude? This is the case when you start climbing at a constant Mach number. You changeover to climbing at a constant Mach number at something typically like 25000ft due to reaching MMO sooner than VMO as you correctly stated. Now if you climb above 25000 temperature still decreases. Now go to the following equation;

TAS = Mach No. x LSS

Mach No. is constant, LSS decreases with altitude due temperature decrease and therefore TAS decreases. If TAS decreases do must IAS because pressure is still decreasing as you climb. This is still the case as you pass the tropopause.

Hope that makes sense!

Just spotted my mistake.

LSS = 38.95 x sq. root(abs. Temp)

Thanks Salbar!

No problem :)

This is maybe a bit off topic, but to anyone watching the Redbull jump last night, can anyone explain why the balloon suddenly increased in ascending velocity? I would have thought the speed would steadily decrease until it came to a halt, but it actually jumped up from 2,5 m/s to over 5,5 m/s. I was thinking maybe it hit a hot body of air, but I don't know how likely that is at that kind of altitud (115.000-120.000ft I think it was).

It's actually the relationship between CAS and TAS that is determined by density. The IAS/CAS discepancy is attributable to position pressure error.

z.khalid,

The subject has been brought up several times, it's much easier if you just search the forum! ;)

The basic LCC formula is

LCC=√γRT

Where γ=1.4 the adiabatic index (think of it as a constant), R=286.9 J·mol−1·K−1 specific gas constant for dry air, T= temperature (kelvin).
This is why LCC is only dependent on T change as both γ and R are constant. (Note that the outcome will be in m/sec!)

Are you sure you remember correct? How about climbing with constant EAS? :ooh:

Briefly, at low speeds EAS≈IAS. As speed is increased so is compr. error making EAS<IAS because IAS=EAS+compr.error

For ex. Climbing with constant IAS: (Assuming CAS=IAS)
As altitude is increased, the density drops. Because of IAS being a measure of pressure on the wings (pitot-tube), as altitude is increased the air gets thiner. To counteract that, the aircraft must fly faster to keep a constant Lift. Thats why TAS increases. The increasing TAS though, compresses the air in the pitot more and more, causing an increasing error in the IAS reading. So, EAS + Compr.Error = IAS. Remember, since we are keeping constant IAS and the Compr.Error increases, the EAS must decrease.

Now if you are climbing with constant EAS all other speeds will be increasing!
EAS<IAS<TAS<M

IAS & TAS for the same reason we discussed above and M because of LSS decreasing and TAS increasing as previous posters mentioned!

Are you saying that EAS takes account of compressibility?

Selfin,

I am not sure I understand your question entirely...

IAS gets its reading from the pitot tube but as TAS is increased so does the error in the IAS reading .. If you subtract that error from IAS you get EAS!

Maybe your point is about the air, thought of being incompressible at lower speeds and compressible at higher?

What about at sea level on a standard day?

What assumptions are being made about this compressibility error? Are you saying that CAS fails to properly account for the compressibility of air and that some additive term (this compressibility error), yielding EAS, provides a fix for that simplifying assumption?

I see your point! No, in that case EAS=CAS.

I based all my assumptions from theory and never checked the actual formulas to see that CAS and EAS are actually only density and pressure related.
Ok, I understand the forms but can't really figure it out.. How is it that at higher alts a so called density error is caused in the pitot tube by the increased speed and it can't be caused at Sea Level ISA conditions? (Assume again CAS=IAS for simplicity reasons). Put simply, why can't an a/c fly fast enough to create this compr.error in the pitot at SL ISA?

I think you will find that even at sea level high TAS will generate significant pressure(and therefore density) errors. And yet,if you set your wizzwheel to ISA msl values it shows CAS equal to TAS at all speeds, and the Compressibility Correction at zero. Why is this?

Well, I've been told that the ASI makes allowance for compressibility using factors at ISA msl values but can't account for errors everywhere and that what we see on the wizzwheel as the compressibility correction at, say FL200 is actually a limited correction, the difference between the full correction and the ISA msl value

Any comment?

The best answer I could come up with is that EAS is a way to measure the equivalent dynamic pressure at SL hence it is the speed aerodynamically affecting the a/c (stall, handling, etc). I think this compressibility/density/pressure error has to do only with the calibration of the ASI (being set to only measure dynamic pressure correctly at SL ISA). So it's not actually a problem in the pitot tube with the air being compressed, (that would start being a problem above supersonic speeds I think..) but rather a miscalculation of the ASI because of the different ambient conditions than it is calibrated to measure speed in.

My conclusion: EAS is the way to mathematically correct the ASI for its error at different atmospherical conditions, giving us the ''true'' dynamic pressure affecting the a/c at all times!

Please reflect, I 'm just trying to find my way through! :hmm:

In fact EAS is regarding to the "clumping up" of air molecules at speed. Try to imagine a pitot tube where at low speeds the molecules are free to exit the tube without being clumped up. As the a/c speeds up more and more molecules try to enter a rather small hole (don't you dare pprune, this is a sacred place ;) ). This clumping up in the pitot tube, which very roughly speaking is an instrument that senses pressure or number of molecules over time, makes the ASI overread. EAS is therefor a calibration from CAS. IAS can be more, less or the same as CAS. CAS is always more than EAS. EAS is always less than TAS, and TAS can be more, less or the same as GS.