TAS and Altitude
 

I've been reading about why Jets climb as high as possible, I'm quite comfortable with the changes to SFC and also minimum cruise drag on the airframe. However I'm struggling to get my head around why there is an increase in the TAS.

As far as I'm aware, above a certain altitude the mode of speed management is in relation to the MN. Therefore this would result in a decreasing TAS as you climb at a constant MN, however it seems that the TAS increases from what I've been reading, which has confused me a bit.

I'm just looking for an explanation of why this is the case.

Thanks

I'll leave it for the Tech log experts to voice their opinions but from an En-route ATC perspective, I can tell you we do notice a drop off in the radar groundspeed readout (and hence TAS in nil wind gradient conditions) as aircraft pass about F280, transition to MN and continue to climb. Probably only in the order of 10-15 kts or so.
Of course their speed picks up a little again when they level off and accelerate to cruise MN. A/C like the A330 climbs at about M.80 and cruises at about .83, which equals about a 15-18 kt increase.
So, I think your first statement is true assuming all other things are equal from my observation over many years.
Standing-by to be shot down if what I've said is incorrect.

If they climb at constant IAS first, and then constant Mach number, the highest TAS will be at the altitude where they change over from IAS to Mach climb.

They climb higher for better fuel flow.

There is a graph that shows Mach, TAS versus altitude, but cannot find it on the net.

In std conditions at SL IAS and TAS are the same. As the airplane flies higher there's less air impacting the pitot tube and thus less total pressure for the same speed.
With less density, IAS decreases. To determine the TAS we have to corrected the IAS for air density, which is a function of altitude and temperature... :)

At sea level IAS=TAS

At 40000ft IAS is roughly half the TAS.

Drag depends on IAS

TAS gets you places

TAS only increases up to cross-over altitude, then drops off again. The rest of the climb sorts out SFC. How high you go depends on your optimum level for the winds, actual mass and cost index you operate at.

If you increase the mass, increase the headwind and increase the cost index, optimum level drops considerably....

Speeds, Mach, Altitude, and Temp
 

I agree with everything stated in the posts above. Let me add a little more prespective.

The relationship between TAS and Vcas (or IAS) is a function of air density. As altitude increases, air density decreases and thus the TAS for a given Vcas goes up. If your airplane is Vcas limited (in the absense of winds) flying higher will result in covering more ground per hour.

The relationship between TAS and Mach Number is a function of temperature. The colder the air, the slower the speed of sound. For a standard atmosphere profile, Mach 1 at sea level is about 660 knots TAS. At 35K feet, Mach 1 has dropped to about 575 knots TAS. The standard atmosphere profile has temperature constant above 35K feet (up beyond altitudes for all commercial aircraft). If your airplane is Mach Number limited (again in the absense of winds) ground speed will decrease as altitude increases until reaching the iso-thermal rejoin starting at about 35K feet.

The fastest ground speed for an airplane's normal operating envelope is usually found at the Vmo/Mmo corner. For lower altitudes, the max velocity is Vcas limited. For higher altitudes, the max velocity is Mach Number limited. Depending on the aircraft, the altitude of the Vmo/Mmo corner will vary. Most commercial aircraft have a Vmo/Mmo altitude of between 25K and 31K feet.

Flip the question around. If you climbed at a constant TAS, your indicated airspeed (IAS) would be decreasing as you climb. Because the air is getting thinner and fewer molecules are ramming into the pitot tube.

Eventually you'll stall, or at least run out of lift to climb further. Because the wings are dependent on the same airflow as the pitot.

Conversely, climbing at a constant IAS means you have to fly faster (in true speed), in order to shove enough air into the pitot to keep the IAS constant.

At the same time, the thinner air makes it easier to fly faster, since there is less air to push out of the way (drag). Up to a point (air-breathing jets lose power as their air intake drops).

So it is kind of a carrot and stick reason - you NEED more TAS to maintain safe/efficient IAS as you get higher - and there is the obvious benefit of getting there faster (since you can).

Right - Once you shift to a fixed Mach as your target speed, TAS decreases with altitude. If you happened to have a plane that had no (or a very high) Mach limit, then TAS could increase all the way to cruise altitude. E.G. the Concorde, which flew Mach targets, but constantly increasing ones, flew increasing TAS to well above normal airline cruise altitudes.

Simply because of the MACH formula.

MACH = TAS/ LSS

Tas increases with altitude
LLS ( local speed of sound) decreases with falling temp. And temp usally falls with inceasing altitude.

Cheers.

One other reason to climb into cooler air is engine efficiency, where the engines can produce higher thrust as there is a higher internal temp margin. This is benefitial up to the tropopause where the temperature flattens out.

It seems cleared up now, thanks for the input.

Also, when constant mach climb is selected at the crossover point the vertical speed will increase, because from there on the aircraft is actually converting speed to height gain.
Not that I ever saw this in real life, they told me in a class room. :rolleyes:

Atmosperic pressure at 43000' is 160mb.

So why is IAS is about half TAS? Surely IAS should be 16% of TAS here?

You might be looking at the wrong numbers and sums. Density is the go rather than pressure ..

It's pretty hard not to get involved with compressible flight at those sorts of levels but, for a first cut, let's just ignore that and treat EAS to be similar to IAS in value.

TAS = IAS/SQRT(sigma) where sigma is the ratio of the actual to SL density.

See, for instance, here.

If you take the sigma value for a level, as can be found here and do the odd sum, you'll see that root sigma (using John's example at FL400)) comes out pretty close to 0.5, hence TAS is around twice EAS (or IAS if we don't get too fussed about compressible niceties).

At FL430, root sigma is a bit less at 0.463 and TAS will be a bit more than twice IAS.

Because density is tied up with pressure and temperature, you can run the equations using pressure but sigma is far easier.

A slightly off topic but related thread

Thanks.

The sums make sense but the logic doesn't!

Rather than the term "higher thrust", I would put it as greater jet velocity from the exhaust, the lower temperature at altitude provides a relatively greater combustion gas energy. Thrust reduces with altitude, at 35,000 = 39.2% of sea level, 50,000 = 18% for a tubojet. Don't know how the addition of a fan, where it can produce some 75% of the total thrust, would be influenced.

I get it... basically what you are saying is that all Air speed Indicators ( ASIs.) are faulty, as they do NOT measure Air Speed.
So we have to use these inaccurate Instruments, and apply 'Fiddle Factors' until someone creates a true Air-Speed reading Instrument.


I think someone will maybe come up with a frictionless Wind-Mill driven device, in the near future. This could revolutionise air transport, and herald a new era in aviation.
.
Didn't the Wright Flyer have something similar...?

Not pressure. The air's half as dense at 400, so

an aeroplane flying at the same indicated airspeed ie molecules per second into pitot hole will be going twice as fast over the ground, which is True Air Speed when there's no wind component.

The pressure has dropped, but so has the temperature, which also affects the density.

The term "Air Speed" is meaningless without qualifying whether it's IAS, TAS, etc.

An instrument that displayed TAS wouldn't be particularly useful as few, if any, of the aircraft's flight characteristics are TAS-dependent.