High Altitude Minimum Airspeed

[profsx]

Havent flown one of em big shiny jets yet, but have been reading about them.

A situation in a climb of say a 737 (Most modern jets actually), on the PFD; the red & black boxes push upwards on the speed tape from the bottom, and the red & black boxes drop down on the tape from the top, I understand the lowering of Vmo with altitude, but INDICATED stall speed stays constant with altitude, so why do the red & black boxes shift upwards from the bottom.

Noteworthy-Indicated stall speed is constant with altitude, Stall TAS increases with altitude, but the speed tape is IAS/CAS.

This has been with screwing with my head for a while now.HELP!

[oxenos]

Although stall IAS should remain constant with increasing altitude, in fact compressibility causes it to increase slightly.

[sevenstrokeroll]

two good books:

"Fly the Wing"


"Handling the Big Jets"

sometimes hard to find.

[mattpilot]

From 'handling the big jets' (pg 127):

It increases for 2 reasons - compressibility effects and the higher mach number effect on the wing (disturbed pressure patterns).

[sevenstrokeroll]

mattpilot has my respect...he actually owns the book!

I was too lazy to unpack it.

two fine books! I understand Cathay pacific asks you questions based on reading ''handling''

[profsx]

Thank you, I actually did have the book, until someone nicked it off me.....

[welliewanger]

As mentioned in previous posts, compressibility has a part to play in this equation. Therefore it is not indicated air speed (IAS) but equivalent air speed (EAS) which determines when the aircraft stalls.

[Rivet gun]

This relates directly to a previous thread:

http://www.pprune.org/tech-log/443766-affects-critical-alpha-mach-number.html

PPL students are taught that indicated stalling speed remains constant with altitude, but some things they teach PPL students don't hold good at high altitudes and Mach numbers.

So why don't we calibrate our EFIS speed tapes to EAS? It would just be a software mod. There was an argument that mechanical standby airspeed indicators were calibrated CAS so the PFD tape had to read the same as the standby. Nowadays even standby instruments are EFIS so there is no reason why we should not switch to EAS displays.

There would still be a slight increase in stalling speed due to the Mach effect on CLmax, but at least the compressibility error could be eliminated.

CAS was invented as a calibration standard for the mechanical airspeed indicator. As the mechanical ASI is consigned to history, so should be CAS.

[HazelNuts39]

There would still be a slight increase in stalling speed due to the Mach effect on CLmax, but at least the compressibility error could be eliminated.Jet transport stall speed at high altitude is defined by buffet that becomes so intense as to be an effective deterrent to further speed reduction. For a typical widebody, the stall EAS at M=0.82 is 1.35 times that at sealevel.

regards,
HN39

[Rivet gun]

Ok, so it looks like the Mach effect on stall speed is rather greater than the compressiblity error.

Nevertheless I still think CAS should become obsolete. Why build in compressibility error into a EFIS display when there is no longer a good reason for doing so?

[HazelNuts39]

Rivet gun;

Compressibility is not an error, but a physical characteristic of air. It affects the dynamic pressure in the pitot tube that drives a pneumatic ASI. Therefore airworthiness regulations require operational speeds such as V2 and Vref to be specified in CAS (at all altitudes). What would be the benefit of displaying EAS?

regards,
HN39

[selfin]

Rivet gun,

CAS was invented as a calibration standard for the mechanical airspeed indicator. As the mechanical ASI is consigned to history, so should be CAS.

CAS is determined by taking the compressibility of air into consideration. Until the physical properties of air change there's absolutely no reason to discard the present calibration law. EAS on the other hand is not a physically meaningful quantity. EAS tells you absolutely nothing about compressibility. It is a fictitious speed resulting from the setting of rho to its ISA MSL value in the dynamic pressure equation. The equation for dynamic pressure is a solution to Euler's equation (which is a reduced form of the Navier-Stokes equation which itself is a reduced form of the Burnett equation, etc) where density along a streamline is regarded as staying constant.

CAS on the other hand is developed from a solution (the Barré de Saint-Venant equation for the subsonic regime) which treats density along a streamline as varying according to an isentropic law. CAS does not tell you anything about dynamic pressure.

[CliveL]

CAS is determined by taking the compressibility of air into consideration. Until the physical properties of air change there's absolutely no reason to discard the present calibration law. EAS on the other hand is not a physically meaningful quantity. EAS tells you absolutely nothing about compressibility. It is a fictitious speed resulting from the setting of rho to its ISA MSL value in the dynamic pressure equation.Let's get it right shall we.

The equations used to calibrate airspeed indicators are intended to account for compressibility when calculating EAS from measured total and static pressures. This involves a Mach Number correction. The relationship between EAS and Mach Number varies with pressure altitude. To permit a standard calibration all airspeed indicators are calibrated using the EAS/Mach relationship that exists at sea level. At any other altitude the airspeed (CAS) indicated by the instrument is not a true indication of the speed that governs aircraft forces (EAS). To calculate forces on the aircraft the meaningful quantity for me is EAS not CAS, and it has served me well for over half a century now.http://images.ibsrv.net/ibsrv/res/src:www.pprune.org/get/images/smilies/wink2.gif

The speed read by a perfect airspeed system (zero instrument and static error) with the Mach Number correction based on a standard day sea level relationship between EAS and Mach Number is the calibrated airspeed. At sea level the correction is exact, but not at any other altitude.

Note the emphasis - CAS is intended to give a correct value of EAS, which is the only relevant quantity for any calculation of aerodynamic forces. As noted, CAS tells you nothing about dynamic pressure which is the standard non-dimensionalising pressure when calculating and using aerodynamic coefficients.

Logically I'm with Rivet-gun in that we now have the computing ability to present the more meaningful EAS, but I shudder to think of the confusions and possible risks associated with any change!

[selfin]

Clive,

Which would better represent the aerodynamic forces in an ideal world? Impact pressure (as defined in NACA Report 837 (http://naca.central.cranfield.ac.uk/reports/1946/naca-report-837.pdf)) or dynamic pressure?

[CliveL]

Selfin

Depends what you are doing - NACA Report 837 points out that you must use dynamic pressure for reducing flight test (and wind tunnel data) into coefficient form and when working with structural loads (and aerodynamic forces generally). Impact pressure (total pressure) is used by the engine designers as their non-dimensionalising parameter. Pilots generally couldn't care less about either when they are actually flying - they must see and fly to CAS, because that is all they can be given.

It would be perfectly possible with today's technology to insert altitude compensation into the ASI's laws so that the indicated CAS was more nearly equal to EAS at all altitudes. That would still meet the airworthiness requirements that the instrument shall indicate the correct speed(s) at ISA sea level, and the change would be transparent to pilots because they would still fly to CAS limits. The only difference would be the underlying EAS value at any given CAS.

[Rivet gun]

CAS exists only because the mechanical ASI does not know its own altitude and can therefore only be calibrated to read EAS correctly at one particular altitude. By convention this particular altitude is sea level. In theory you could calibrate a mechanical ASI to read EAS correctly at any chosen altitude, but such an instrument would not read EAS correctly if used at any other altitude for which it was not calibrated.

An EFIS however knows its altitude and can therefore display EAS correctly at all altitudes, just as it can display Mach number at all altitudes.

Aircraft such as the SR71 and space shuttle used displays of EAS (presumably) because they operated at very high altitudes at which the compressibility error of a conventional ASI would have been too great to tolerate.

The Eclipse light jet was also designed with a EAS display. You can read a position paper here setting out the arguments in favour.

http://rgl.faa.gov/Regulatory_and_Guidance_Library/rgELOS.nsf/0/46282217e067ba2c86257567006f6a5e/$FILE/ACE-05-32.pdf

Unfortunatly this article also has (at appendix B) a copy and paste from wikipedia which in this instance is rather misleading.

From an educational point of view EAS has the advantage that EAS, TAS and Mach number are linked by some simple equations which could be taught to student pilots and are easy to remember. By contrast the proper equation expressing CAS as a function of Mach number and static pressure is a horrendous affair with multiple nested exponents. It is not surprising that we don't teach the CAS equations to student pilots.

However as a consequence, many new first officers misunderstand the relationship between CAS and Mach number. It seems to be a common belief that the relation between CAS and Mach number depends on air temperature.

[Rivet gun]

On the original subject, I did a little data gathering at work today.

Unfortunatly the red / black boxes are not always visible, being off the bottom of the scale in the cruise. I could however record the position of the yellow band which represents a 1.3 g manoeuver capability:

Fl 380 yellow band at 226 KCAS = 215 KEAS = M 0.72

FL 80 yellow band at 178 KCAS = 177 KEAS = M 0.31

I know weight effects it, but there was only 0.8% weight difference between the two readings.

So in EAS terms there was a about a 21% difference in the position of the yellow band between FL80 and FL 380.

In CAS terms the difference was about 27%

[PBL]

It seems to be a common belief that the relation between CAS and Mach number depends on air temperature.

Maybe because it does?

PBL

[HazelNuts39]

The red line on this graph (https://docs.google.com/leaf?id=0B0CqniOzW0rjNTk4MzAyZWQtMzFkMi00Mzg3LWJlOTItMWU2MDd iNDFhNDU1&hl=en_GB&authkey=CKiTsYMC) shows qc/q, the ratio between impact pressure and dynamic pressure (as defined in NACA Report 837 (http://naca.central.cranfield.ac.uk/reports/1946/naca-report-837.pdf)) as a function of Mach number. Also shown is cL/cL0, the ratio of lift coefficient at a Mach number to liftcoefficient at M=0 for a range of AoA's of a large transport airplane.

regards,
HN39

[selfin]

Clive,

The report states that, as you earlier mentioned, the practice has long been to use dynamic pressure in structural load calculations. I have no problem accepting that that is the convention.

What I do not understand is why an incompressible solution is used when dealing with ‘speeds’ above Mach 0.3. The idea of basing any calculations on an incompressible formula in the transonic regime is simply baffling to me.

In my foregoing comment I meant for ‘impact pressure’ to be read as ‘total pressure minus static pressure’ (accounting for density varying along the streamline – cf eq 2 in the report and eq 32b in NACA Report 1135.)

Rivet,

No static port on your aeroplane? It’s the static temperature which has traditionally been difficult to measure. The Wiki article Eclipse attached to their application to the FAA would be amusing if it weren’t frightening.

[CliveL]

PBL
Maybe because it does? Sorry PBL - Rivet-gun is correct - it doesn't.
CAS relates to EAS; the speed of sound expressed in EAS is independent of temperature as discussed on another thread. Ergo Mach Number as a ratio between EAS/CAS and the speed of sound is also independent of temperature.

Selfin
What I do not understand is why an incompressible solution is used when dealing with ‘speeds’ above Mach 0.3. The idea of basing any calculations on an incompressible formula in the transonic regime is simply baffling to me.I see where you are coming from, but the answer is probably historic. There is an ENORMOUS amount of data kicking about which has been calculated using dynamic pressure as usually defined and to shift now would make that useless. Presumably if one changed to your 'impact pressure' as a basis for reducing measured data one would hope to eliminate compressibiity effects from the coefficients i.e. they might then be independent of Mach No, but looking at the other curves in Hazelnuts 39's chart I don't think that would be so, so to paraphrase his remark re change from CAS to EAS in an earlier posting - what would be the point of changing now to impact pressure rather than dynamic pressure?

Hazelnuts 39

Your graphs of Cl/Clo look a lot like those of a large transport aircraft with which I am very familiar, and seeing your location is France (mostly) I am wondering if we have worked together????

[CliveL]

Rivet Gun

So in EAS terms there was a about a 21% difference in the position of the yellow band between FL80 and FL 380.

In CAS terms the difference was about 27%

Like you I refreshed my memory on the magnitude of the effect. In my case I took the data from my 'bible' - Dick Shevell's Fundamentals of Flight.

For subsonic aircraft the differences aren't too large - at 250 kts CAS/FL350 for example the difference is 12 kts, but if you have a supersonic aircraft and high altitude it becomes more important - at M 2.0/FL500 it is about 80 kts. If anyone is sufficiently interested Shevell gives his source as USAF Series T.O. 1F-5a-1 Flight Manual

[HazelNuts39]

Clive;

It is possible we have met sometime. In my working life I had frequent contacts with Toulouse, but never worked there. France became my part-time home only after I retired.

regards,
HN39

[Rivet gun]

The red line on this graph shows qc/q, the ratio between impact pressure and dynamic pressure (as defined in NACA Report 837) as a function of Mach number. Also shown is cL/cL0, the ratio of lift coefficient at a Mach number to liftcoefficient at M=0 for a range of AoA's of a large transport airplane.



Thanks, that's interesting. I suppose if you re defined CL as lift/(qc*S) the variation of CL with Mach number would be less than it is using the conventional definition of CL as lift/(q*S).

But I think this is not an arguement for CAS because qc/q does not equal CAS/EAS. qc/q = 1 + M^2/4 + M^4/40 (+ futher binomial terms if you want). However CAS/EAS = 1 at sea level for all subsonic speeds. CAS is a function of qc, but it is a fucntion designed to reduce qc to TAS (and EAS) at sea level. So if we really wanted to place qc center stage how would we calibrate the airspeed indicator? I'm not sure.

And why do very high altitude aircraft have EAS indicators? Does anybody know what the Virgin spaceship uses?

I suppose if we broadened the debate we could ask why we display airspeed on the PFD at all. Perhaps we could display some other paremeter for aircraft control such as manoeuver margin or angle of attack, but given the ability of modern EFIS to display stall speed, manoeuver margin etc on the speed tape such a change would be hard to justify.

Given then, that we are going to use "airspeed" as a control parameter we need to choose an airspeed which is closely related to the aerodynamic forces. But pilots also need to know TAS and Mach number. Therefore it makes sense to choose an airspeed for contol which also has a simple mathematical relationship with TAS and Mach number. I think EAS best fits these criteria.