TAS change With Altitude - The "Fastest Altitude" for a Turboprop

[TNTDJ]

Hi all,

I DID read the old threads and hopefully this will add to the discussion!
By way of introduction I am a Herc driver in Canada.

This whole discussion originated with the following statement found in a manual discussing flying into a headwind:

"Under certain conditions it will be advantageous to descend to lower levels (descending increases both TAS and Fuel Flow.) Increasing TAS and decreasing headwind results in an improved SGR (Specific Ground Range.)"

I asked myself- "Really, can I descend all the way to the ground and go faster and faster?" (I have thought about this and they are referring to level flight, not just a quick dive for speed.)

So, thus began the investigation...

I have read in various threads that, relative to given IAS, TAS roughly increases 2% per 1000' of altitude (this Rule of Thumb is even on Wikipedia.) So we can say that at 10,000' for an IAS / CAS / EAS of 100kts, the TAS is (R.O.T.) 120 kts (10*2=20) (A calculator shows it's actually a few knots less. i.e. 116kts.) This deals with the relationship between indicated and true airspeed. As was stated by smarter people, this is all because there is less pitot pressure force (due to less dense air) on the aneroid capsule moving the dial at higher altitudes = relatively less IAS than TAS as you climb.

All that, however, doesn't speak at all to how fast the plane can or will fly.

The next threads I read pointed out that since the air is less dense "up high" there is less profile drag. So, for the same reason the IAS is less, the drag is less. This is good - it allows us to go faster for less profile drag. I also seem to remember from somewhere that turboprops start to encounter compressibility effects on their props, and this limits how fast the props can pull the plane. However, here is where I started to get lost…

My question became:
What is the "fastest altitude" for a turboprop - regardless of fuel consumption? What altitude offers the maximum TAS for fuel consumption? Or, what altitude can I descend to in order to get the maximum SGR / SAR (with nil winds or headwinds)? For the adventurous, feel free to answer for pistons (turbo vs non-turbo) and jet.

Here is some data from a turboprop AFM to help us out:

Vd (maximum speed (IAS) from chart; TAS calculated using calculator)
SL - 318 KIAS / 318 KTAS
5k' - 320 I / 342 T
10k' - 322 I / 370 T
14k' - 324 I / 394 T
20k' - 293 I / 391 T
25k' - 266 I / 385 T

Cruise Charts - Fastest TAS; Heaviest Weight
SL - 292 KTAS
5k' - 298 KTAS
10k' - 302.5 KTAS
15k' - 302 KTAS
20k' - 293 KTAS
25k' - Drops off dramatically ("hanging off the props")

Fuel Flow:
We know it increases linearly from high altitude to low altitude for a given ("max") power setting (in this case "max" turbine temperature). We all fly as high as we can because we get basically the same speed with much less fuel burn. (Read Checkboard's amazing post to grasp it totally. I am in awe.)

Ok so in a sense we have our answer. The fastest the (heavy) turboprop will go in level flight (TAS or GS with no winds or headwinds) is at about 10,000' to 15,000'. As it turns out a light airplane preferred 22,000 to 27,000'.

Interestingly, the dive speed maxed out at 14,000ft as well, at 394 KTAS.



So I guess I can say that:

1. To escape a strong headwind at high altitude, descending to as low as / in the range of 10,000 to 15,000ft seems to be the best bet for the heavy turboprop. A lighter turboprop will prefer to remain higher (say 22,000 to 27,000') but won't lose much TAS by descending; the biggest penalty will be increased FF. Look at the headwind gradient and choose accordingly.
2. Descending lower than 10,000ft decreases TAS slightly (but not markedly, say 1kt/1000') but raises FF much more significantly. Hopefully your "jetstream headwind" cuts off well above 10,000'!
3. The TAS dive speed of said turboprop maxes out at 14,000ft, meaning a lower max TAS whether you are above or below that in altitude.
4. Within its normal operating envelope (14,000 to 28,000ft depending on weight) said turboprop has a largely fixed max TAS (Max GS in no winds). Someone could probably say this is a limit of the props not going supersonic.
5. Below its normal operating envelope, the turboprop slows very slightly in TAS, but FF increases significantly with any decrease in altitude to maintain said speed.
6. All that to say, in the real world, decending from the cruise ceiling to escape a headwind will give you a slight increase in TAS down to about 14,000 to 22,000ft, so it's often worthwhile to descend, assuming the headwind is lighter, lower down.
   • Even if you had to descend all the way down to sea level to escape a tall jetstream in your face, it doesn't markedly affect the TAS, only the FF.
   • Assuming the headwind only decreases slightly with altitude, you'd have to find a fancy way (ideas?) of testing whether it was worthwhile at all to descend, since the TAS doesn't increase much, but the FF increases steadily. I'd love comments on this!
   • If headwind decreases steadily / markedly from cruise ceiling then I'm going to say it's likely that descending gives you a double benefit - increased TAS down to 10,000' and increased GS. The increase in FF should be well overcome if the decrease in headwind is significant.

Finally, maybe then I can say that for said turboprop, the max cruise TAS is relatively constant throughout its entire flight envelope, with mid-altitudes and light weights giving a slight edge.
So TAS does not really increase with altitude (it just bulges slightly in the middle.)! (However TAS DOES increase relative to a given IAS with altitude. The achieveable IAS is related to the achieveable TAS, which as I just said is relatively constant.) In terms of getting there, nobody cares about IAS anyway.

Whew. I am not an engineer. My brain should be starting to hurt slightly.
Mods- did I earn a sticky post?!?

Related Posts:
http://www.pprune.org/tech-log/32881...air-speed.html
http://www.pprune.org/tech-log/10655...-altitude.html
http://www.pprune.org/tech-log/46529...t-benefit.html

-TNTDJ

[aerobat77]

you can read out the highest TAS in your performance tables. on flat rated engines is mostly occours in the region of the highest altitude where the engine is able to maintain max torque and /or IAS redline is not a limitong factor. - usually in the mid tenths for turboprops.

flights are conducted usually higher than that because fuel flow in high altitudes drops more significantly than the TAS does so the overall efficency is higher.

the same applies for tubocharged pistons.

cheers