Question about TAS

[Flysher]

I was looking through a magazine yesterday and I saw an ad for a kingair mod that was supposed to increase the maximum cruise speed of the airplane. It showed a graph demonstrating the stock speeds and then the modded speeds. The thing that struck me as odd though was they showed speeds for different altitudes and the maximum TAS actually decreased as altitude went up. I always thought you could achieve a higher TAS at a higher altitude. Would anyone care to explain this to me please? Thanks guys

 

[MidlifeFlyer]

I think you slightly misunderstood what you heard.

For a given CAS/IAS, TAS goes up as you go up in altitude. All this means is that =if= your ASI reads 100 kts, you TAS at 10,000' is higher than at 2000'. But that's a big =if=. The rule doesn't tell you that your airplane is even capable of producing 100 IAS at 10,000'

That's a separate issue. As altitude goes up, the air gets thinner and at a certain point (even with turbocharged engines) the ability of the engine to produce power, the ability of the wing to produce lift and and the efficiency of the propeller both begin to decrease with altitude (picture a screw biting into whipped cream instead of wood).

Grab a POH and look at the power settings in the performance section. You'll see the same phenomenon in fixed pitch props, constant speed props, and even turbo props. The maximum HP that can be produced with begin to go down after a certain altitude is reached. That translates into a lower indicated and true airspeed.

 

[Flysher]

Ok I was sort of thinking that after a while. Thanks for clearing it up for me.

 

[ananoman]

For a normally aspirated piston airplane, you will usually see the highest cruise TAS at around 7,000 to 9,000 feet. This is because the engine will lose about 3% of it's power output per 1,000' in altitude. Most airplanes cruise at at 75% power, so even at full throttle you can only make 75% power at these altitudes.

For a turbocharged engine, they have a 'critical altitude' which is the highest altitude they can maintian rated power. It is usually around 17,000 to 19,000 feet in many engines. Some are lower. For many of the turbo charged airplanes, their highest TAS speeds are found at their maximum operating altitude. If you are using an O2 mask in an unpressurized airplane, this is 25,000'. If you look at a Lancair turbo, this is where they reach their 240kt cruise speed.

Turboprops and jets will also lose power with altitude. However, some are 'flat rated' and can maintain rated power through a fairly wide range of altitude and temperature. For an airplane like the King Air, you really can't increase the power output of the engines. If you do, you are facing a major recertification with the FAA. If you increase power, it can affect Vmc and a host of other 'important' things. So what they have done is to install an engine that is capable of putting out quite a bit more power than what is required. Then they derate the engine, so it only makes the same horsepower as the older, less powerful engine. The advantage to doing this is that the engine will last longer, since it is not working as hard. It is also capable of making full rated power to a much higher altitude and at higher temperatures. This will greatly increase climb performance and cruise performance at altitude. But, even with a turboprop, power will still decrease at some point. When this happens, cruise TAS will start to decrease with altitude.

 

[Flysher]

Thanks for the good info Ananoman, I learned a few things there.

 

[B767Driver]

I was looking through a magazine yesterday and I saw an ad for a kingair mod that was supposed to increase the maximum cruise speed of the airplane. It showed a graph demonstrating the stock speeds and then the modded speeds. The thing that struck me as odd though was they showed speeds for different altitudes and the maximum TAS actually decreased as altitude went up. I always thought you could achieve a higher TAS at a higher altitude. Would anyone care to explain this to me please? Thanks guys

I looked into this in detail last year. I'd been flying 15 years and always thought that TAS increased as altitude increased as well. I looked at the cruise flight level performance charts and discovered the same thing that you did. Given a constant ECON power setting, The TAS is directly related to the IAS multiplied by the density ratio of the atmosphere.

Typically, you can maintain a constant IAS to approx FL270 before it begins to drop off rapidly. This will be the point of maximum TAS as well. But it's still advantageous to fly higher...because the specific fuel consumption (miles/gallon) is much more efficient (you can cover more distance with less gas, although it may take you longer).

The basic reason this occurs (TAS decreasing, given a constant mach number) is that above FL 270 the density of the air falls off much faster than the temperature decreases. So even though the MN is constant...the TAS is dropping off. (As stated above...think less thrust produced.)

Consider the space shuttle in orbit after it leaves the Earth's atmoshpere. It is travelling tens of thousands of miles per hour...but the IAS will be zero because there is no air molecules to register a speed.

Most operators will select a type of Long Range Cruise (LRC) speed...which will burn more gas...but fly at a higher TAS/Mach Number.

 

[Realms09]

Even if an aircraft is equipped with magical engines that do not lose power with altitude, your TAS would still have an adversary in the form of wave drag. As you climb, TAS will increase for a given EAS. This increases your Mach number. Also as you climb, the temperature of the air decreases. The speed of sound is a direct function of temperature, so this further increases your Mach number. Eventually you will hit a transonic regime of very high drag coefficients, and you won't be able to go any faster. Therefore, it is possible for TAS to decrease with altitude due to Mach limitations, everything else being equal. On a propeller driven aircraft this problem will probably not be present on the airframe in general but will be present on the propeller blades themselves. This is why a propeller aircraft can never break the sound barrier.

 

[Flysher]

I looked into this in detail last year. I'd been flying 15 years and always thought that TAS increased as altitude increased as well. I looked at the cruise flight level performance charts and discovered the same thing that you did. Given a constant ECON power setting, The TAS is directly related to the IAS multiplied by the density ratio of the atmosphere.

Typically, you can maintain a constant IAS to approx FL270 before it begins to drop off rapidly. This will be the point of maximum TAS as well. But it's still advantageous to fly higher...because the specific fuel consumption (miles/gallon) is much more efficient (you can cover more distance with less gas, although it may take you longer).

The basic reason this occurs (TAS decreasing, given a constant mach number) is that above FL 270 the density of the air falls off much faster than the temperature decreases. So even though the MN is constant...the TAS is dropping off. (As stated above...think less thrust produced.)

Consider the space shuttle in orbit after it leaves the Earth's atmoshpere. It is travelling tens of thousands of miles per hour...but the IAS will be zero because there is no air molecules to register a speed.

Most operators will select a type of Long Range Cruise (LRC) speed...which will burn more gas...but fly at a higher TAS/Mach Number.

So just to make sure I'm getting this correctly, an airplane at 270 can actually go faster than an airplane at 410 given the same type?

 

[ananoman]

So just to make sure I'm getting this correctly, an airplane at 270 can actually go faster than an airplane at 410 given the same type?

Yes, usually an airplane at FL270-290 can go faster (IAS and TAS) than an airplane at a higher altitude. You fuel burn will be frighteningly high and the wind noise will be pretty fierce up front, but you can go faster.

 

[meritflyer]

Yes, usually an airplane at FL270-290 can go faster (IAS and TAS) than an airplane at a higher altitude. You fuel burn will be frighteningly high and the wind noise will be pretty fierce up front, but you can go faster.

Hmm... do you have any text or references on this subject?

 

[ananoman]

The best place to look for this stuff is the performance planning section of a flight manual. I have a pile at home, but none with me at the moment, as I am on the road.

The main problem you run into is that the speed of sound is solely dependent on temperature. This is pretty constant at -55 C once you get into the stratosphere assuming ISA conditions (a big assumption!). If you are only Mmo limited, you can go faster at sea level than at high altitude, because it is warmer and you can get a faster TAS before you hit Mmo. The problem is you have Vmo to deal with and you will hit this limit at low altitude before Mmo. The high 20's seems to be the 'sweet spot' that allows the highest TAS without exceeding Vmo or Mmo.

 

[B767Driver]

So just to make sure I'm getting this correctly, an airplane at 270 can actually go faster than an airplane at 410 given the same type?

That's correct. I watched this in action last year as I was learning this stuff. During a climb, the TAS would march right up to around 475 at FL270 and fall to about 455 at FL 330.

Most of the training text books are gear to light single engine airplanes...the type we learn in. They always state that TAS increases with altitude, but they don't assume you'll be flying in the upper flight levels. A little bit of negative training, I suppose.

 

[Flysher]

Hm interesting stuff, I know most of the books I have tend to assume your flying the lower slower stuff as well. I just picked up a used copy of the turbine pilots flight manual and thats supposed to have some high altitude aerodynamics in it I think.

Thanks for the help guys.

 

[FlyChicaga]

Great thread!

A week or two ago I was explaining to and FO how FL270-FL290 was the area for the highest true airspeed, therefore the region where we could "go the fastest." We were trying to get back on schedule, and he kept asking to go to FL370 to go fast... good for fuel economy, bad for time economy. I couldn't explain the physics behind it, so I think he thought I was full of it. It did show in our FMS that we would gain five minutes by flying at FL270 compared to FL370, only expending 200-300 lbs more fuel. This is considering constant wind... the wind was lower at FL270 as well.

Now I can try to explain the physics of this so I don't get looks when I suggest we fly lower.

 

[taseal]

Most operators will select a type of Long Range Cruise (LRC) speed...which will burn more gas...but fly at a higher TAS/Mach Number.

wow really? I always thought LRC meant burn less gas by going higher and slower?

 

[taseal]

Great thread!

A week or two ago I was explaining to and FO how FL270-FL290 was the area for the highest true airspeed, therefore the region where we could "go the fastest." We were trying to get back on schedule, and he kept asking to go to FL370 to go fast... good for fuel economy, bad for time economy. I couldn't explain the physics behind it, so I think he thought I was full of it. It did show in our FMS that we would gain five minutes by flying at FL270 compared to FL370, only expending 200-300 lbs more fuel. This is considering constant wind... the wind was lower at FL270 as well.

Now I can try to explain the physics of this so I don't get looks when I suggest we fly lower.

you know, I always thought higher = faster as well...

I tell ya, I learn so much in this place, it aint even funny

 

[BeechBoy]

The basic reason this occurs (TAS decreasing, given a constant mach number) is that above FL 270 the density of the air falls off much faster than the temperature decreases. So even though the MN is constant...the TAS is dropping off. (As stated above...think less thrust produced.)

B767Driver I'm a little confused. We know that:
1. As the air thins out you get a higher TAS for any given CAS.
2. As temperature decreases your TAS decreases for any given MN.

If #1 happens to a greater degree than #2, shouldn't there be a net INCREASE in TAS if MN is held constant?

 

[Dugie8]

B767Driver I'm a little confused. We know that:
1. As the air thins out you get a higher TAS for any given CAS.
2. As temperature decreases your TAS decreases for any given MN.

If #1 happens to a greater degree than #2, shouldn't there be a net INCREASE in TAS if MN is held constant?

The speed of sound is based on density. We often refer to temp, but think about what happens to density when you raise and lower the temp (density altitude).

As the air gets thinner faster than it gets colder a constant mach will have to have a slower TAS.

 

[ananoman]

B767Driver I'm a little confused. We know that:
1. As the air thins out you get a higher TAS for any given CAS.
2. As temperature decreases your TAS decreases for any given MN.

If #1 happens to a greater degree than #2, shouldn't there be a net INCREASE in TAS if MN is held constant?

In a jet, you are usually more limited by Vmo or Mmo rather than thrust limited in cruise. Thrust does decrease considerably with altitude (75% or so from SL to cruising altitude) and this definately hurts climb, especially when it is hot. But you will probably be bouncing off the barber pole before you run out of thrust in cruise.

The main factors are Vmo and Mmo, how fast can we go before we exceed these limitations?

First lets look at the speed of sound.

Sea Level 15C 662 Kts
10,000' -5C 639 Kts
20,000' -25C 615 Kts
25,000' -35C 602 Kts
30,000' -44C 590 Kts
35,000' -54C 577 Kts
40,000' -56.5C 574 Kts
60,000' -56.5C 574 Kts

You can see that the speed of sound is highest at SL and drops off with altitude as temperature decreases. Note that the speed of sound is constant from 40,000' to 60,000' (60,000 was the highest the table in my book went). Obviously there must be air molecules to transmit soundwaves, but the speed is not really dependent on density. For sound waves to propagate, air molecules must bump into each other, so the wave can travel from molecule to molecule. If it is warm, all the air molecules are in motion and bump into each other more. The colder it gets, the less they move around and bump into their neighbors. This slows down how fast the sound wave can travel.

My airplane is Mmo limited to .80, so I should be able to cruise at 530 KTAS at SL, 472 KTAS at 30,000' and 460 KTAS at 40,000' and above.

The problem with this is that you have Vmo to deal with. In my airplane I can only go 280 below 8,000' due to a bird strike limitation (If I feel lucky I can go 335 KIAS from SL up to 12,000' decreasing to 310 at FL290).

I dug out a flight manual for the Hawker 800XP and here are some numbers for High Speed Cruise which is as fast as I can go limited by Vmo/Mmo/Maximum Cruise Thrust. All numbers are for a cruise weight of 24,000 lbs, which is 4,000 less than max gross. If I am heavier I cannot go as fast due to a lower Vmo with fuel in the ventral tank at lower altitude and I will also not be able to climb as high. Lighter weights will allow me to go a bit faster.

Note the flight manual does not concern itself with going 250 KIAS below 10,000'.

5,000' 296 KTAS 1955 lb/hr 280 KIAS (Limited by Birdstrike)
9,000' 373 KTAS 2496 lb/hr 335 KIAS (Vmo)
15,000' 402 KTAS 2374 lb/hr 331 KIAS (Vmo)
25,000' 448 KTAS 2177 lb/hr 316 KIAS (Vmo)
29,000' 463 KTAS 2387 lb/hr 307 KIAS (Vmo is 310 here and This is the highest TAS)
33,000' 454 KTAS 2102 lb/hr 280 KIAS (Mmo)
37,000' 443 KTAS 1818 lb/hr 253 KIAS (Real Close to Mmo, probably starting to get thrust limited)
41,000' 419 KTAS 1452 lb/hr 216 KIAS (This is as high as we can go and is the max wt for the altitude, probably thrust limited)

At all altitudes, if you are lighter, you can go somewhat faster.
For example:
35,000' at 24,000lbs 449 KTAS and at 18,000 lbs 454 KTAS, only a 5 kt spread.
41,000' at 24,000lbs (max wt.) 419 KTAS and at 18,000 lbs 445 KTAS, a 26 kt spread

So, in this example it does look like we are starting to be thrust limited (more drag due to higher AoA at heavier weights and a lack of power to overcome the additional drag) at our max operating altitude of FL410. In our case, we usually don't try to go this high when we are this heavy. There is not much of a fuel burn advantage and the aircraft would only climb at 200 fpm at this weight. At a more likely 22,000 lbs, we could pick up another 13 kts and cruise at 432 KTAS at FL410.

As B767 said, you usually will be wiser to pick a slightly lower cruising speed and save some gas. We usually cruise at .75 Mach and save 400-500 lbs an hour in the high 30's and only loose 20 KTAS in cruise. Even on a 3 hr flight you will probably be less than 50 or 60 miles behind someone in an identical airplane going .80 (probably less than 10-12 minutes) and will save up to 200 gallons of fuel.

 

[NJA_Capt]

...I was explaining to and FO how FL270-FL290 was the area for the highest true airspeed,

Man, that is low. We don't even start reading Mach until FL350.

For comparisons sake....
Our highest TAS is FL370-FL390 and can still manage to eek out 493 TAS at FL470. Normal cruise alt is FL410-FL430, with an occasional excursion higher.