palgia841

Actually it's Equivalent Airspeed (EAS) that is important in aircraft dynamics.

Equivalent airspeed is simply CAS corrected for compressibility of the air at high speed/low atmospheric pressure.

Again, I hate to disagree but this is simply not true. Stall speed increases with altitude, NO MATTER WHAT. I am not talking simply about a airspeed measurement error (like the fact that at altitude your PFD shows CAS and therefore you are reading a higher value than your plane's EAS, which again is what is related to stall margin)... I am saying that aerodynamically the wing will stall at a higher airspeed, regardless of airspeed measurement errors. To put it differently, it will stall at a lower CLmax.

This change is stall speed is SIGNIFICANT. Like I wrote on my previous post, we're looking at least at a 2kt/5000ft, but likely more depending on wing design. So at 40,000' your stall speed is at least 16kt higher than what it would be at sea-level, but most likely EVEN MORE than that due to additional effects that are wing-specific.

I hate to be disagreeing with everyone, but we've had so many cases of crews flirting with the low-end of the envelope at high altitude in the last 10 yrs (some fatal) that I feel there should be no doubts about the effect that altitude has on stall speed. Like rickair said, if you stick with the HIGH ALTITUDE values on your speed cards you should be safe (not to be confused with landing V'ref speeds....those are calculated for sea level).

I will try to get exact numbers for different airplane types, but the 2kt/5000' rule of thumb should apply to all airplanes.

250 or point 65

I'd just like some sort of Works Cited list to back up your claims.

Here's one for ya, its FAA Advisory Circular 61-67B

"j. Altitude and Temperature. Altitude has little or no
effect on an airplane's indicated stall speed. Thinner air at
higher altitudes will result in decreased aircraft performance
and a higher true airspeed for a given indicated airspeed.
Higher than standard temperatures will also contribute to
increased true airspeed. However, the higher true airspeed has
no effect on indicated approach or stall speeds. The
manufacturer's recommended indicated airspeeds should therefore
be maintained during the landing approach, regardless of the
elevation or the density at the airport of landing."

I know that there are plenty of things, especially in aerodynamics, that the FAA has explained incorrectly. However, I'd like to know where your information comes from.

jungle

Interesting topic. I am not sure what type of equipment has had all of these accidents that palgia841 claims have happened due to errors in stall speed computation. Most newer jets utilize an Air Data/ Angle of attack system that presents both a minimum speed and a minimum maneuver speed that is valid for all altitudes and mach. We generally don't fly anywhere near stall and I can't really imagine why anyone would do so intentionally.


This is what you are talking about:

At sea level EAS is the same as true airspeed (TAS) and calibrated airspeed (CAS). At high altitude, EAS may be obtained from CAS by correcting for compressibility error.

Relevant for engineering purposes is the relationship between indicated airspeed and true airspeed (or Mach number) for common altitudes and airspeeds. In engineering it is useful to have a formula that is reasonably accurate and can be used with values provided in International Standard Atmosphere as function of altitude. While for subsonic speeds up to Mach 0.6 the compressibility can be neglected and IAS/CAS can be obtained from TAS using density correction, it must be incorporated above these speeds for accurate results.


Up to mach .6 it isn't a player, and it looks to be small up to .85. I can't generate the numbers, but here is the formula if you would like to.
Equivalent airspeed - Wikipedia, the free encyclopedia

Perhaps Cubdriver or someone with an aero background can provide further input.


In the course of a normal flight weight and desired buffet margin will have a much larger influence on minimum speed than the minor effects of compressibility.

palgia841

https://www.faa.gov/regulations_poli...cumentID/22881

Shows the AC was canceled back in 2000 (fortunately!).
Keep in mind from the abstract I can tell that AC was clearly meant for GA aircraft operating at very low altitudes. If you're talking sfc-5000'msl and speeds below M0.2 I agree that you can simplify things and just say that stall speed in constant.

I'll dig out some books and find you some sources.

jungle

Those books are going to tell you it is a function of Mach, not altitude.

250 or point 65

Cancelled AC...well played! I wasn't completely buying that simple of an explanation anyway.

I'm very interested in this. Pretty tough concept to get your head around.

ryan1234

I'll have to go find the Riddle AE books around here somewhere...... but....I think you're talking about Reynold's numbers and the effect on C/Lmax , critical AoA when talking of the 2kt/5000ft rule

I don't remember what exact type of airspeed the book refers to (seems to be true-airspeed), but I want to say C/Lmax was a function of Reynolds (at low speed) and mach at over .5 (assuming unaccelated flight). It was really spliting hairs and varied with the particular airfoil. The derivatives were negligible at low mach, if I'm not mistaken.

The professional analysis for the indicated stall speed increasing with altitude is here:

http://www.flightsafety.org/ap/ap_sep91.pdf

It is an interesting argument, but I'm going to have to dig into it some more.

palgia841

BINGO!
higher altitude -> lower air density + lower air viscosity (because of lower temps) -> lower Reynolds number -> less kinematic energy in the boundary layer to oppose adverse pressure gradients -> earlier flow separation -> lower CLmax and AOAcrit -> higher stall speed

Thats the 2kt/5000ft... in addition to this effect, there is also the effect of local supersonic flow on the wing upper surface that prevents you from truly reaching the sea-level-CLmax equivalent. Even at speeds below Mcrit, at high AOA the pressure distribution over the upper surface causes the boundary layer to accelerate around the leading edge, and at high enough CL (and thus large enough pressure gradients) the flow can be accelerated to locally supersonic values. Of course the magnitude of this effect will depend on wing design, in addition to Mach, altitude and temperature.

As for sources, I remember seeing the 2kt/5000ft in various books, but after looking for the last hour I can only find it in my student manual from the Naval Test Pilot School, although if you ask me, I trust this manual more than certain aero books... I found a PDF version here http://www.usntpsalumni.org/USNTPS_FTM_108.pdf (look for page 3-27)

As for the reduction of CLmax due to Mach you can see a chart here Structural loads analysis for ... - Google Books that shows a significant reduction of CLmax at Mach speeds as low as .2-.4
This book also has a chart on page 263 that shows the slows speed stall speed increasing with increasing altitude. But I hope by now everyone in happy with this concept. If you really wanted, really you could just take any BOB chart for a transport category airplane (buffet onset boundary) and you'll see the same relationship there (look for the slow-speed buffet).

Another worthwhile read is Aircraft Performance - Google Books chapter 2.6

Bottom line is that the only TRUE way to calculate stall speed at altitude for a given wing is through flight testing. And even then, as ryan's EXCELLENT FSI article pointed out, it's not as easy as it seems. There are so many dynamic factors that play in the determination of stall speed that it's not easy to isolate all the variables.

palgia841

I must have done a poor job at expressing myself. I am not blaming errors in stall speed computation for many of the stall related accidents/incidents of the past years, however I DO believe that knowledge of the simple relationship between stall speed and altitude could have given many of these crews better situational awareness.

You are correct sir. You would think it'd be common sense to stay well above those speeds... But unfortunately common sense is not all that common, as we saw on Oct 14 2004 with the Pinnacle CRJ. In addition, as you mentioned, the low speed cue comes from an AOA probe and a computer that takes several other inputs. As we all know, sensor vanes can and DO fail, as well as the computer itself. In fact, on that ill-fated Pinnacle flight a software error in the stall protection computer caused the slow-speed cue to erroneously be 10kt SLOWER than it should. In other words, the crew hit the shaker 10kts above the top of the slow speed cue.
Although I personally knew the captain of that flight, his actions that day were unjustifiable. I have no idea what he was thinking flying an RJ at 150 KCAS at 41,000- However, we can use the FDR data reported in the accident report to put what we discussed in this thread to practical use. That day his CRJ weighed approx 37,000# when he stalled it at 41,000ft. If we look at the landing flip cards for that weight, the straight-in Vref +5 CLEAN is 160KCAS. That translates in a sea-level 1G stall speed of approx 119KCAS (155/1.3 =119). So IF stall speed was constant with altitude he should have been able to fly all the way down to this speed even at 41,000ft. Unfortunately, at 150KCAS he hit the shaker. I don't recall for sure, but I believe in the CRJ the stick shaker trip point is at an AOA-derived stall margin of about 10kts (someone please correct me if I'm way off). If this is correct, that would but the stall speed at 41,000' (@ 37,000#) at around 140KCAS, which is not far off from Sea-level stall speed of 119KCAS + 2kt/5000' + further reduction in CLmax due to "Mach effects".

Or I may just be all wrong either way, I'm going to bed

GRDHound

Palgia
I'm no aero expert but from what I've read and the little I understand I would say that most of what you're saying makes sense. However, when you start talking in KCAS and KEAS from a pilots perspective unless you're just running the charts you may not be talking in the most practical terms. Depending on the age and design of the aircraft systems there are some A/C out there that display KEAS, some that display KCAS and others that just have KIAS not corrected at all.
The laws of physics remain the same of course like you say but depending on what kind of indication system an A/C has installed the KIAS/altitude relationship could vary significantly I believe.