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Which factors cause Vy to increase with Altitude

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Which factors cause Vy to increase with Altitude

Old 25th Jun 2020, 00:30
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Which factors cause Vy to increase with Altitude

Hi folks,
Does any one know what factors remain in the usual Vy with altitude equation to push Vy to a higher indicated airspeed at altitude for a turbo normalized M20J Mooney?
In other words what does having a more fixed power available curve from the Turbo Normalized, Constant Speed installation leave on the table that causes Vy to drift north.


Last edited by AC103; 25th Jun 2020 at 19:27.
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Old 25th Jun 2020, 12:10
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Don't know about this aircraft however the obvious ones that spring to mind are reduction of exhaust back pressure and reduction of throttling losses as you climb toward critical altitude. These two will tend to increase the power for the given MAP and RPM.
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Old 25th Jun 2020, 13:28
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Good question?

I cannot come up with anything, since from my understanding the aerodynamic performance is in relation to IAS/CAS....

If there anything that changes the aerodynamic shape or form of the aircraft when climbing? Something sticking out that gets larger/smaller? Radiator cowlings? Anything??

And why would you be using best rate of climb that high anyway??
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Old 25th Jun 2020, 16:17
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A complex interaction between:

1) parasite drag - air friction on the overall airframe, which decreases in thinner air for a given airframe at a given true speed.
2) induced (lift) drag - which increases in thinner air for a given airframe at a given true speed. Higher AoA required in thinner air.

Meaning that in TAS, Vy (the most efficient climb speed) increases with altitude - you can climb best at some higher TAS, as you can reduce AoA (and induced drag) without incurring as big a penalty from parasite drag.

https://www.boldmethod.com/learn-to-...ere-they-meet/

3) IAS gauge/pitot/static arrangement, which can introduce measurement errors.

While there is a defined theoretical relationship between IAS and TAS divergence as altitude increases, that relationship is only approximate when applied to a real-world aircraft: where the pitot tube is located, how well the pitot tube is aligned with the relative wind/slipstream at various pitch/climb angles, etc. etc. For a specific airframe, that can be corrected to calibrated airspeed (CAS), but that is not on "the big gauge" that pilots generally watch - one has to use tables, or look at some fine print somewhere in the cockpit. And the CAS/IAS relationship is not linear - CAS may be 2 knots slower than IAS at 140 KIAS, and 1 knot slower at 100 KIAS, and 2 knots faster at 60 KIAS.

Vy in CAS could well be identical at 0 feet and 20000 feet - but the gauge won't tell you your CAS.

4) Ultimately, what goes into the manuals is results from test flights, rather than theory. A Mooney test pilot took 'er up to 20000 feet, and experimented, and reported that up there, (s)he got the best ROC at 93 kts IAS rather than 89 kts - in that airframe design. And they put that in the book.

Outside of the fact that a turbo allows one to fly across a larger altitude and ambient density range, I'm not sure a turbo has any direct effect on rated Vy, and changes therein. One would have to experiment with a normally-aspirated version of an identical airframe for comparison.

Now, in a twin, the fact that the props "blow the wing" and add airflow and lift, might mean a noticable change in Vy with/without turbocharging (more power).
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Old 25th Jun 2020, 20:58
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It is an interesting one. I had a look at the M20K 252 factory turbo charged so not TN but same air-frame and don't see anything for CAS with altitude, plenty for altitude calibration with altitude though so not ruling that out.

I can understand why Vy IAS moves slower with altitude as power required is a function of TAS so even with a Constant Speed propeller the power available by IAS curve becomes less slanted towards higher speed and for a Normally Aspirated installation, less over all with altitude, so it distorts Vy less and lets it come back towards the un-powered (propeller zero thrust) min sink CAS (AoA) it is based on.

As to why it would increase in this case maybe the power plant is more efficient as we have dramatically reduced the OAT, added ~8psi to the pressure differential over the turbine wheel and the waste gate is now closed. With a Turbo Normalized installation with automatic waste gates you should be wide open throttle the whole way up so maybe we are seeing more power dragging Vy north, but by 5% total and maybe over 10% further stretched away from min sink? Possibly?

Does un-powered min sink CAS change with altitude? As sink rate is a TAS (vertical) I assume the rate will increase but does the min sink CAS (AoA) it occurs at change?

I would have thought Reynolds numbers would be working against us as we climb progressing the lamina to turbulent flow trip forward toward the leading edge. Airfoils for the Mooney are NACA 63-215 root and 63-412 tip.
I would also have thought propeller efficiency would be reducing as its mach number increases at the tip particularly for a prop the was originally selected for a NA IO-360.
So it is hard to see how the power available curve becomes more slanted toward a higher airspeed if that is what is causing this Vy move in the opposite direction to what we expect.

Some pretty pictures:





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Old 26th Jun 2020, 00:40
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AC103, you may have to dive into something like this to see what is happening: https://www.avweb.com/features_old/t...ler-airplanes/ the tables and diagrams have all been stripped out of it to encourage purchase of his book at https://arc.aiaa.org/doi/book/10.2514/4.103704

I have the files from the original publication of that webpage plus the spreadsheet if you want it.
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Old 26th Jun 2020, 11:45
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Originally Posted by AC103 View Post
I would also have thought propeller efficiency would be reducing as its mach number increases at the tip particularly for a prop the was originally selected for a NA IO-360.
So it is hard to see how the power available curve becomes more slanted toward a higher airspeed if that is what is causing this Vy move in the opposite direction to what we expect.
But that's the thing, as long as IAS stays the same, the aerodynamics shouldn't change. Until you reach compressibility issues.

The speed of sound at the ground is, in the ISA, 340 metre per second, or about 661 knots, and at 20000 FT, 316 metres per second, about 614 knots.
Your Mach is the relation between TAS and speed of sound, so at the ground you'll be climbing Vy, 89 knots, at Mach 0.135, where as in 20000 FT you'll be at, with the adjusted Vy at 93 knots, Mach 0.223.... I don't even think that does change anything, even with the accelerated velocity over the wings and fuselage.... but it's fun to do a little calculus from time to time.

Even the propeller is not "rotating" any faster, since the RPM is the same all the way up.... and if I read the settings correct, the power output is the same?

The propeller angle would be more coarse.... but I'm at a loss if that also means the angle of attack on the propeller is changed? The aircraft is moving through the same "amount of air" up there over time as close to the gound, so the AoA of the propeller is probably not changed.... But I could be wrong.

On the other hand, you have cowling flaps on the Mooney 20J, right? Wouldn't they need to be retracted the higher you go, since the air gets cooler? Once you retract them, less drag, more speed at the same power setting....
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Old 27th Jun 2020, 10:32
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Physically, the best rate of climb is the point on the power curve where the greatest difference between thrust horsepower required and thrust Horsepower available exist.
where thrust horsepower is equal to Thrust * Velocity (TAS) So as TAS increases and likewise CAS or IAS will have to increase in order to keep the relationship.
T*Vreq-T*Vavail a constant.

Last edited by Pugilistic Animus; 29th Jun 2020 at 05:42.
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Old 29th Jun 2020, 09:12
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Originally Posted by Pugilistic Animus View Post
Physically, the best rate of climb is the point on the power curve where the greatest difference between thrust horsepower required and thrust Horsepower available exist.
where thrust horsepower is equal to Thrust * Velocity (TAS) So as TAS increases and likewise CAS or IAS will have to increase in order to keep the relationship.
T*Vreq-T*Vavail a constant.
You're breaking my head here.... cause now I had to dive more into it.

https://people.clarkson.edu/~pmarzoc.../AE-429-10.pdf

Wouldn't the speed for best rate of climb decrease with altitude, if anything?
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Old 29th Jun 2020, 11:28
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It's on page 7, I liked that summary!
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Old 29th Jun 2020, 15:16
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Originally Posted by Pugilistic Animus View Post
It's on page 7, I liked that summary!
Yeah me too, I was referring to page 6:

There it states that the relation should give a lower speed at altitude to maintain best RoC.
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Old 30th Jun 2020, 17:16
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The top graph on page 6 looks a bit dodgy to me. First of all it's for a jet (while all/most of the discussion above is for a prop) and secondly the effect of altitude on the power required curve is to move it up and right along a tangent drawn from the origin; the power required curve in this diagram has hardly moved up at all, certainly not along a tangent. It's a problem with so many of these graphs in textbooks, they are not taken from hard data, just 'illustrative'.

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