technical questions
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Regarding Stall Speed at high altitude: The formula for stall speed is given by Vs (ktas) = Sqrt (295 L/qSClmax) where q is the density ratio. However since the speed is given in Vs (ktas), this part of the formula can be rewritten as Vs(ktas) = (SMOE)*(EAS) where SMOE = 1/sqrt(density ratio). When both equations are simplified the density ratios at altitude cancel out leaving only EAS. Position error also cancel each other. Refer to Classnotes for Basic Aerodynamics by Norbert R. Kluga 1991 page 124 from Embry-Riddle Aeronautical University and Flight Technique Analysis for Professional Pilots by Les Kumpula page 30 also from Embry-Riddle Aeronautical University.
Just to be pedantic, the above is essentially wrong because you've made an incompressible flow assumption to ascertain the second flow equation (and forgotten about the compressibility correction), which will obviously not show a Mach number depedence!
Its fine for M<=0.3.
A better idea of the aerofoil C_p valid up to M~=0.7 would be to apply a Prandtl Glauert correction, whereupon
C_p = C_p(INC)/sqrt(1-M^2)
where
C_p(INC) is the incompressible flow pressure coefficient.
Above that, there are other pressure coefficient corrections, such as those given by von Karman & Tsien.
Bear in mind that the aerofoil lift is merely the integral of the pressure over the geometry.
The Mach number dependence in C_L(max) is obviously related to the, initially, advantageous presence of shock waves in the flow, which increase C_L(max) until the point of drag divergence, whereupon shock induced flow seperation means you suffer a collapse of lift.
So true stall speed is obviously a function of altitude i.e., density, (or alternatively remember that CAS is EAS plus a compressibility correction), but perhaps less/more intuitively (depending on how your mind works), a function of the similarity parameters, Mach Number and Reynolds Number.
Reynolds number is essentially a ratio expressing the relative importance of the inertial and viscous forces of a flow.
As Reynolds number tends to infinity, the viscous effects, become less and less important to consider.
Whereupon, one may conclude that stall being a viscous phenomenon, will display some dependence on Reynolds number. A good illustration of this dependence can be found in Fundamentals of Flight by Richard Shevell, Pg 248. As it suggests, in flight tests, Reynolds numbers are often far higher than those found in tunnel testing, whereupon the demonstrated C_L(max)'s are somewhat higher.
The simple expanation for this is that the inertial effects in the flow are better able to combat the adverse pressure gradient and further delay separation at a given constant angle of attack.
For those interested, Fundamentals of Flight by Richard Shevell also gives some graphs of the compressibility correction factor, F, on Pg 106/107 used in determining EAS's.
My $0.02
Last edited by SR71; 14th Oct 2004 at 06:34.
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rjer,
You might like to check the following thread:
V_mca versus V_mcg Discussion
can someone clarify exactly why Vmca is lower than Vmcg in the 747?
V_mca versus V_mcg Discussion
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VMCG vs VMCA
in regards to VMCG vs VMCA on the B744, here is the way it was explained to me during an interview prep course: (i am in no way and aerodynamics expert, but it made sense to me)
VMCG on the 744 (and some other A/C) is higher than VMCA because:
VMCG has to do with controllability on the ground - therefore the effective rudder moment is between the tail and the main gear.
VMCA = in the air, so you have an effective rudder moment between the tail and your CofG.
because the rudder moment between the tail and CofG is longer than that between the tail and the main gear on the ground, your rudder will be more effective in the air, therefore VMCA will be lower than VMCG.
does that sounds right?
VMCG on the 744 (and some other A/C) is higher than VMCA because:
VMCG has to do with controllability on the ground - therefore the effective rudder moment is between the tail and the main gear.
VMCA = in the air, so you have an effective rudder moment between the tail and your CofG.
because the rudder moment between the tail and CofG is longer than that between the tail and the main gear on the ground, your rudder will be more effective in the air, therefore VMCA will be lower than VMCG.
does that sounds right?
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Remember that for the VMCA you have the ability to bank the aircraft to aid recovering control.
AFAIK there isnt a relationship between VMCG and VMCA, so you really cant compare them.
Mutt.
AFAIK there isnt a relationship between VMCG and VMCA, so you really cant compare them.
Mutt.
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Vmca and Vmcg
There is no fixed and direct relationship between these because they occur under different aerodynamic conditions with no single, simple, factor dominating. The only true answer to your question, without delving into the minatuae of Boeing's aerodynamic and systems data, is "because it is".
What some airlines like to use as interview questions, they are welcome to use. But the fact that the interviewer expects you to say the moon is made of blue cheese, and everyone is therefore coached to say the moon is made of blue cheese, in no way relates to the composition of lunar rocks. For that I'd want to talk to one (or several) lunar "geologists".
EAS is "Equivalent Air Speed" and is commonly used for e.g. loads calculations, where the fact that the kinetic pressure is the same at all altitudes for the same EAS is very convenient.
There is no fixed and direct relationship between these because they occur under different aerodynamic conditions with no single, simple, factor dominating. The only true answer to your question, without delving into the minatuae of Boeing's aerodynamic and systems data, is "because it is".
What some airlines like to use as interview questions, they are welcome to use. But the fact that the interviewer expects you to say the moon is made of blue cheese, and everyone is therefore coached to say the moon is made of blue cheese, in no way relates to the composition of lunar rocks. For that I'd want to talk to one (or several) lunar "geologists".
EAS is "Equivalent Air Speed" and is commonly used for e.g. loads calculations, where the fact that the kinetic pressure is the same at all altitudes for the same EAS is very convenient.
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A question for this learned thread and an observation.
Squalo,
If the Cof G were closer than the main gear would the a/c not fall on it's tail? Or is this what you were trying to imply was the reason for VMCG being higher than VMCA? I have always understood (mainly from what I have learned in these Tech Log threads!) that the two values are essentially totally different.
I was under the impression that JAR had harmonised with FAA on the X-wind value for VMCG on modern a/c ie: A320 onwards. I was aware that the L1011 was certified by the CAA with 7 knots across but that the FAA used 0 knts. Can someone clarify this please?
Thanks idg.
Squalo,
If the Cof G were closer than the main gear would the a/c not fall on it's tail? Or is this what you were trying to imply was the reason for VMCG being higher than VMCA? I have always understood (mainly from what I have learned in these Tech Log threads!) that the two values are essentially totally different.
I was under the impression that JAR had harmonised with FAA on the X-wind value for VMCG on modern a/c ie: A320 onwards. I was aware that the L1011 was certified by the CAA with 7 knots across but that the FAA used 0 knts. Can someone clarify this please?
Thanks idg.
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Tonic Please,
You asked " What is EAS ?. Mad (Flt) Scientist addressed it correctly but rather fleetingly. One of my pet "hobbyhorses" is that most pilots don't have a real appreciation of the importance of EAS, due to no fault of their own.
EAS = Equivalent Air Speed, Ve. It is the speed that pilots want to see, and need to see, but cannot because CAS, which pilots do see, is affected by compressibility. CAS is corrected for compressibility at ISA Sea Level, where CAS = EAS. At higher levels, relative to the increasing Mach Number, Indicated Airspeed lies to the pilot indicating more than he/she really has, and airspeed is "money in the bank".The higher you fly, the greater becomes the error.
EAS, as Mad (Flt) Scientist stated, is the kinetic value of the airstream expressed in knots. That's what we want to see in flight, but don't. At low altitudes, it really doesn't matter a great deal, e.g. even at 400 Kt CAS at 10,000 feet, the EAS is 393 Kt. If, however, minimum manoeuvre for an aircraft at a particular weight is 250 KIAS at low level, the aircraft would need to be flown at 266 KIAS at 37000 feet to have the same stall protection, as 250 KIAS equates to only 236 Kt EAS at that level - stick shaker time!
For a given weight, the CAS for all of the following situations increases with increasing altitude, whilst EAS remains constant - Stall speed, Holding speed, Best Angle of Climb speed, Maximum Range Cruise Speed, Vmo, Minimum manoeuvre speed, and even V1, Vr, and V2 at relatively low altitudes. All of this, of course, applies in the regimes of flight where airspeed is the primary performance management parameter, above Mcrit, at high altitudes where the effects of Reynolds number and kinematic viscosity come into play, Mach No. or a mix of EAS and Mach No. become more important.
Private Pilots please note - It's been EAS you've been assuming that you have when you calculated TAS using CAS and Density Height, actually this is DAS but carries little error at low speeds and altitudes - horrendous errors at jet type speeds and altitudes prevail, but they could do it with EAS also.
If EAS were introduced as standard cockpit equipment tomorrow, the bulk of Aircraft performance manuals would be significantly reduced. It beats me why "they" didn't introduce it years ago. I'd be genuinely interested to hear if anyone can think of ANY advantage of retaining CAS with all of it's attendant errors.
Vive la revolution!
Old Smokey (aka Old Grumpey)
You asked " What is EAS ?. Mad (Flt) Scientist addressed it correctly but rather fleetingly. One of my pet "hobbyhorses" is that most pilots don't have a real appreciation of the importance of EAS, due to no fault of their own.
EAS = Equivalent Air Speed, Ve. It is the speed that pilots want to see, and need to see, but cannot because CAS, which pilots do see, is affected by compressibility. CAS is corrected for compressibility at ISA Sea Level, where CAS = EAS. At higher levels, relative to the increasing Mach Number, Indicated Airspeed lies to the pilot indicating more than he/she really has, and airspeed is "money in the bank".The higher you fly, the greater becomes the error.
EAS, as Mad (Flt) Scientist stated, is the kinetic value of the airstream expressed in knots. That's what we want to see in flight, but don't. At low altitudes, it really doesn't matter a great deal, e.g. even at 400 Kt CAS at 10,000 feet, the EAS is 393 Kt. If, however, minimum manoeuvre for an aircraft at a particular weight is 250 KIAS at low level, the aircraft would need to be flown at 266 KIAS at 37000 feet to have the same stall protection, as 250 KIAS equates to only 236 Kt EAS at that level - stick shaker time!
For a given weight, the CAS for all of the following situations increases with increasing altitude, whilst EAS remains constant - Stall speed, Holding speed, Best Angle of Climb speed, Maximum Range Cruise Speed, Vmo, Minimum manoeuvre speed, and even V1, Vr, and V2 at relatively low altitudes. All of this, of course, applies in the regimes of flight where airspeed is the primary performance management parameter, above Mcrit, at high altitudes where the effects of Reynolds number and kinematic viscosity come into play, Mach No. or a mix of EAS and Mach No. become more important.
Private Pilots please note - It's been EAS you've been assuming that you have when you calculated TAS using CAS and Density Height, actually this is DAS but carries little error at low speeds and altitudes - horrendous errors at jet type speeds and altitudes prevail, but they could do it with EAS also.
If EAS were introduced as standard cockpit equipment tomorrow, the bulk of Aircraft performance manuals would be significantly reduced. It beats me why "they" didn't introduce it years ago. I'd be genuinely interested to hear if anyone can think of ANY advantage of retaining CAS with all of it's attendant errors.
Vive la revolution!
Old Smokey (aka Old Grumpey)
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To add to the debate, I remember the relationships between the speeds via the following:
IAS = Indicated Airspeed
CAS = Calibrated Airspeed = IAS +/- Instrument & Position Error
EAS = CAS - Compressibility Correction
TAS = EAS * Density Correction
EAS is defined as:
V_e = V_0*\sqrt(\rho/\rho_s)
where
V_0 = TAS
\rho = ambient density
\rho_s = sea level density
As one may infer from Old Smokey's post the compressibility correction (typically known as the F factor) that one may apply to CAS to acquire EAS may be thought of as a function of two variables, namely, CAS and altitude.
The derivation is relatively simple and starts from the isentropic flow relationship for pressure:
p_0/p = (1+(\gamma-1)/2*M^2)^(\gamma/(\gamma-1))
If we solve for TAS, V, in terms of the difference between p_0 and p, and substitute for M, bearing in mind we know that:
M = V/(\sqrt(\gamma*p)/\rho))
we find that:
V = a complicated expression
which may be subsequently re-arranged, using the fomula for EAS, to give V_e.
The unknowns in this equation are the static pressure and the difference between the static and total pressure, which is exactly what a pitot-static system measures.
As Old Smokey alludes to, it is standard practise to calibrate the instrument at sea level, whereupon, the complicated expression above is evaluated in terms of sea-level standard pressure. The speed given by such a calculation is the CAS.
It is now clear that, to evaluate the EAS at other altitudes, a correction must be made, and that this correction is the ratio between the equation for V above, evaluated using the actual pressures at the altitude you are interested in and sea level values:
V_e=F*V_cal
where
V_cal = CAS
F = Compressibility Correction factor
I certainly agree that in the days of EADI's and ADC's, whereupon I suppose that at some stage during the path from sensing airspeed to displaying it, a pressure transducer is involved, it would not be hard to apply the relevant correction to the signal.
Maybe there are certification issues involved here involving the nature of standby instrumentation?
If one retains traditional standby instruments, one would have to remember, in the event of a failure of all primary instruments that one was working with CAS again rather than EAS.
But, of course, we seem to work with CAS successfully at the moment...
IAS = Indicated Airspeed
CAS = Calibrated Airspeed = IAS +/- Instrument & Position Error
EAS = CAS - Compressibility Correction
TAS = EAS * Density Correction
EAS is defined as:
V_e = V_0*\sqrt(\rho/\rho_s)
where
V_0 = TAS
\rho = ambient density
\rho_s = sea level density
As one may infer from Old Smokey's post the compressibility correction (typically known as the F factor) that one may apply to CAS to acquire EAS may be thought of as a function of two variables, namely, CAS and altitude.
The derivation is relatively simple and starts from the isentropic flow relationship for pressure:
p_0/p = (1+(\gamma-1)/2*M^2)^(\gamma/(\gamma-1))
If we solve for TAS, V, in terms of the difference between p_0 and p, and substitute for M, bearing in mind we know that:
M = V/(\sqrt(\gamma*p)/\rho))
we find that:
V = a complicated expression
which may be subsequently re-arranged, using the fomula for EAS, to give V_e.
The unknowns in this equation are the static pressure and the difference between the static and total pressure, which is exactly what a pitot-static system measures.
As Old Smokey alludes to, it is standard practise to calibrate the instrument at sea level, whereupon, the complicated expression above is evaluated in terms of sea-level standard pressure. The speed given by such a calculation is the CAS.
It is now clear that, to evaluate the EAS at other altitudes, a correction must be made, and that this correction is the ratio between the equation for V above, evaluated using the actual pressures at the altitude you are interested in and sea level values:
V_e=F*V_cal
where
V_cal = CAS
F = Compressibility Correction factor
I certainly agree that in the days of EADI's and ADC's, whereupon I suppose that at some stage during the path from sensing airspeed to displaying it, a pressure transducer is involved, it would not be hard to apply the relevant correction to the signal.
Maybe there are certification issues involved here involving the nature of standby instrumentation?
If one retains traditional standby instruments, one would have to remember, in the event of a failure of all primary instruments that one was working with CAS again rather than EAS.
But, of course, we seem to work with CAS successfully at the moment...
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I could never understand the logic of flight testing VMCG with zero crosswind and then approving the aircraft for operation with a 30 kt crosswind.
Can anyone explain this to me?
Mutt.
Can anyone explain this to me?
Mutt.
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Mutt,
The logic you may never find.
The rationale, as I accept it, is that the VMCG is determined at the performance testing stage to meet FAR25 requirements with Nosewheel steering made inoperative in zero (or up to 7 Kt) Xwind and an engine failed.
The crosswind capability is determined at a different (handling qualities) phase of testing with Nosewheel steering operative, also with an engine failed, different FAR (not one that I use regularly, don't have the number, sorry).
Just take a look at the Xwind limit plummet towards zero when Nosewheel Steering Inop is considered from the 'handling qualities' perspective in other 'Non-Normal Procedures'.
The very significant determinant, VMCG, is evaluated with Nosewheel Steering Inop AND an engine failure, but the on-going assumption for day to day operations (at least at the Takeoff phase) does not consider multiple failures, in this case both an engine AND Nosewheel steering, thus allowing normal steering capability to be factored into Xwind limit evaluation.
Good to see you're back from the Emerald Isle Mutt, it was becoming quite boring without you.
The logic you may never find.
The rationale, as I accept it, is that the VMCG is determined at the performance testing stage to meet FAR25 requirements with Nosewheel steering made inoperative in zero (or up to 7 Kt) Xwind and an engine failed.
The crosswind capability is determined at a different (handling qualities) phase of testing with Nosewheel steering operative, also with an engine failed, different FAR (not one that I use regularly, don't have the number, sorry).
Just take a look at the Xwind limit plummet towards zero when Nosewheel Steering Inop is considered from the 'handling qualities' perspective in other 'Non-Normal Procedures'.
The very significant determinant, VMCG, is evaluated with Nosewheel Steering Inop AND an engine failure, but the on-going assumption for day to day operations (at least at the Takeoff phase) does not consider multiple failures, in this case both an engine AND Nosewheel steering, thus allowing normal steering capability to be factored into Xwind limit evaluation.
Good to see you're back from the Emerald Isle Mutt, it was becoming quite boring without you.
Moderator
.. also, consider that Vmcg is for fairly critical conditions .. aft CG, no NWS, rated thrust, min weight (generally at very low fuel with min yawing inertia).
In the normal operational environment, we don't go anywhere near the actual Vmcg for the day. Given that the onset of controllability problems generally is quite rapid (in terms of speed deltas), we don't normally need to worry too much.
However, several of us restate the hobby horse, regularly, that one needs to be cautious if the actual conditions tend toward the certification configuration, especially if there is an option to use a higher speed schedule to avoid the problem region. This crops up in the ferry/positioning scenario from a non-critical runway ... if the crosswind is significant, consider using a higher speed schedule (but still within the RTOW data for the runway).
In the normal operational environment, we don't go anywhere near the actual Vmcg for the day. Given that the onset of controllability problems generally is quite rapid (in terms of speed deltas), we don't normally need to worry too much.
However, several of us restate the hobby horse, regularly, that one needs to be cautious if the actual conditions tend toward the certification configuration, especially if there is an option to use a higher speed schedule to avoid the problem region. This crops up in the ferry/positioning scenario from a non-critical runway ... if the crosswind is significant, consider using a higher speed schedule (but still within the RTOW data for the runway).
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The only "logic" is that we don't have large numbers of aircraft running off the sides of runways when an engine fails; the conditions for Vmcg are arbitrary, and they way we apply that restriction to the performance data is arbitrary. But the end result is an acceptable "level of safety".
It's the same as trying to find an academic reason for using 1.2Vs or 1.13Vsr; there isn't one. It just happens to work out ok most of the time. If we had 12 fingers we might still be using 1.2Vs, just because we'd have picked the digit "2" for the first "decimal" (twelvical??) place; but it's be the equivalent of 1.167Vs in decimal notation. If it works....don't amend it.
It's the same as trying to find an academic reason for using 1.2Vs or 1.13Vsr; there isn't one. It just happens to work out ok most of the time. If we had 12 fingers we might still be using 1.2Vs, just because we'd have picked the digit "2" for the first "decimal" (twelvical??) place; but it's be the equivalent of 1.167Vs in decimal notation. If it works....don't amend it.
Moderator
.. and, following on from MFS ..
For certification exercises, one needs a boundary condition ("rule") against which to measure compliance.
Many of the "rules" originated in "finger-in-the-wind" professional assessments by the chaps who ran the show in the early days of commercial aviation.
So, for example,
(a) the initial screen height of 50 ft dates back to a demonstration of an early aircraft to the US military. Apparently, the parade ground from which the demonstration flights were conducted was surrounded by a tree line of such approximate height ... seemed a good idea so the FAA ancestor adopted it.
(b) the 70 mph stall speed limit (dutifully carried across to the modern era as 60.8 kt - rounded to 61 kt - in FAR 23.49(c) ) originated in an early engineer's need to have a figure .. consideration of motor vehicles apparently led to the 70 mph figure's being thought to be a reasonable place to start from ....
Vmcg, being an extreme certification boundary, is not often encountered in routine operations, but we need a "rule" against which to show compliance .. the accident record's having shown the definition to be reasonable, it hasn't altered materially.
For certification exercises, one needs a boundary condition ("rule") against which to measure compliance.
Many of the "rules" originated in "finger-in-the-wind" professional assessments by the chaps who ran the show in the early days of commercial aviation.
So, for example,
(a) the initial screen height of 50 ft dates back to a demonstration of an early aircraft to the US military. Apparently, the parade ground from which the demonstration flights were conducted was surrounded by a tree line of such approximate height ... seemed a good idea so the FAA ancestor adopted it.
(b) the 70 mph stall speed limit (dutifully carried across to the modern era as 60.8 kt - rounded to 61 kt - in FAR 23.49(c) ) originated in an early engineer's need to have a figure .. consideration of motor vehicles apparently led to the 70 mph figure's being thought to be a reasonable place to start from ....
Vmcg, being an extreme certification boundary, is not often encountered in routine operations, but we need a "rule" against which to show compliance .. the accident record's having shown the definition to be reasonable, it hasn't altered materially.
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The only "logic" is that we don't have large numbers of aircraft running off the sides of runways when an engine fails
Mutt.
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Mutt, John_T,
Please feel free to harp on, and harp on, and then when you retire, leave a computer virus that keeps on harping on about VMCG. Some things cannot be over-emphasised.
SR71,
You make a good point about standby instruments if we were to introduce EAS as standard. It wouldn't take much of a notice to crews if reverting to CAS on standby instruments. High speed limits would need no notification, CAS is more conservative, for low speed operations a simple "Add 20 Kt to CAS indications above F/L 250 (or something similar) would suffice.
Regards,
Smokey
Please feel free to harp on, and harp on, and then when you retire, leave a computer virus that keeps on harping on about VMCG. Some things cannot be over-emphasised.
SR71,
You make a good point about standby instruments if we were to introduce EAS as standard. It wouldn't take much of a notice to crews if reverting to CAS on standby instruments. High speed limits would need no notification, CAS is more conservative, for low speed operations a simple "Add 20 Kt to CAS indications above F/L 250 (or something similar) would suffice.
Regards,
Smokey
