Relation between IAS and Mach number
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Sorry about that
I figured I would divide this problem into three categories
1. speed of sound: The value of SoS depends upon the MEDIUM, and is affected by temp. humidity and winds. its transmission rate depends upon the elasticity of the medium [the Bulk and Young's modulus] (5X faster in steel than air). because sound travels as longitudinal waves (compressions and rarefactions) if the media is dense (humidity) or warmer (there more energetic) molecules to push around and SoS increases. As you get colder SoS decreases
2.mach number/TAS/EAS/IAS: as every one has said, increases with TAS which increases with altitude for a constant EAS, and increases as SoS decreases
3. gas laws: to avoid being timed out i'll post now
I feel I've not explained well
moles are a measure of the amount of a substance. Carbon 12 weigh 12 grams for every mol (n) and one mole of carbon has 6.023*10^23 C atoms. one mole of H2 gas a molecule weighs 2g but has same number of particles(Avogadro's No [NA]).
for an ideal gas (no molecular interaction)
The number of moles is dependent on 'state variables' P,V, and T. with any of these state variables one can find another unknown varialble, so the gas laws allow one to explain how SoS depends on any thing you want because all of the knowns lets say P,V and n can be used to rewrite the expression any how you'd like the above was a little algebra to relate every thing to density instead.
with out these laws thermodyamic would be speculation-at least till I build that entropy meter
lastly. I forgot this b4 Sigma = rho/rho(msl)
I figured I would divide this problem into three categories
1. speed of sound: The value of SoS depends upon the MEDIUM, and is affected by temp. humidity and winds. its transmission rate depends upon the elasticity of the medium [the Bulk and Young's modulus] (5X faster in steel than air). because sound travels as longitudinal waves (compressions and rarefactions) if the media is dense (humidity) or warmer (there more energetic) molecules to push around and SoS increases. As you get colder SoS decreases
2.mach number/TAS/EAS/IAS: as every one has said, increases with TAS which increases with altitude for a constant EAS, and increases as SoS decreases
3. gas laws: to avoid being timed out i'll post now
I feel I've not explained well
moles are a measure of the amount of a substance. Carbon 12 weigh 12 grams for every mol (n) and one mole of carbon has 6.023*10^23 C atoms. one mole of H2 gas a molecule weighs 2g but has same number of particles(Avogadro's No [NA]).
for an ideal gas (no molecular interaction)
The number of moles is dependent on 'state variables' P,V, and T. with any of these state variables one can find another unknown varialble, so the gas laws allow one to explain how SoS depends on any thing you want because all of the knowns lets say P,V and n can be used to rewrite the expression any how you'd like the above was a little algebra to relate every thing to density instead.
with out these laws thermodyamic would be speculation-at least till I build that entropy meter
lastly. I forgot this b4 Sigma = rho/rho(msl)
Last edited by rhovsquared; 18th May 2006 at 19:43.
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We certainly have had an interesting discussion about this and probably all have learned from it. I admit I haven't studied aerodynamics for 30 years but 30 years ago I wanted all the answers and found most of them in books. Asking fellow pilots usually ended up in multiple answers, most being wrong.
Captains wanting the flight attendants to move to the front galley to save fuel because the tail was dragging enroute, etc. One chief pilot insisted you had to hold downwind rudder when enroute to keep from weather vaning into the wind. In a discussion like this everybody gets their input and usually the truth prevails benefiting everybody. Thanks to everybody for contributing.
Captains wanting the flight attendants to move to the front galley to save fuel because the tail was dragging enroute, etc. One chief pilot insisted you had to hold downwind rudder when enroute to keep from weather vaning into the wind. In a discussion like this everybody gets their input and usually the truth prevails benefiting everybody. Thanks to everybody for contributing.
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Lets get rid of these darn moles! The universal gas constant is 8.314 J/mol/K. If we multiply this by the average moles per kilogram for dry air (34.53) we get the specific gas constant for air which is 287.05 J/Kg/K. Call this R
We can now express the ideal gas law as:
P = R rho T
where P is pressure (Pa), rho is density (Kg/ m^3) and T is temperature (K). Humidity complicates matters because it changes R, so lets us stick to considering dry air.
Mad (Flt) scientist: the ideal gas law certainly DOES apply across air masses provided we are considering dry air. Furthermore aircraft can and do maintain constant FL across air mass boundries, they do not maintain geometric altitude (ATC would complain otherwise). The reason they can do so is because the temperature change is gradual, not a step change. For this discussion we need only consider the end states, i.e at one time the aircraft is flying in air at temperature T1, at a later time it is flying at the same FL and Mach number in air at temperature T2.
Now to deal with the speed of sound (SoS). This depends on the square root of the ratio P/rho. But from the gas law P/rho = R T. The exact equation also includes the ratio of specific heats (gamma) which for dry air is 1.4. So:
SoS = sqrt(1.4 R T)
= 20.05 sqrt(T) m/s
=39 sqrt (T) knots.
Now back to the original question.
At constant FL pressure is constant, so from the gas law rho T is constant. This is the important point.
If the aircraft flies from a cold air mass (T1) to a warm air mass (T2) and mach number is held constant the TAS increases by the ratio sqrt(T1/T2). But we have established that rho T is constant, so if T increases rho decreases in exact proportion.
The ratio EAS/TAS depends on sqrt(rho1/rho2). Therefore the increase in TAS is exactly cancelled by the decrease in EAS/TAS ratio and EAS remains constant.
To go from EAS to CAS we adjust for compressibility. However compressibility is a function of Mach number and FL, both of which are constant. Therefore compressibility error is constant and CAS is constant.
To go from CAS to IAS we adjust for position error. This is empirical and aircraft specific, however modern flight instrument systems have built in position error correction and for practical purposes we may assume CAS = IAS. Besides at constant FL and Mach number position error would be constant anyway.
Therefore IAS remains constant
QED
We can now express the ideal gas law as:
P = R rho T
where P is pressure (Pa), rho is density (Kg/ m^3) and T is temperature (K). Humidity complicates matters because it changes R, so lets us stick to considering dry air.
Mad (Flt) scientist: the ideal gas law certainly DOES apply across air masses provided we are considering dry air. Furthermore aircraft can and do maintain constant FL across air mass boundries, they do not maintain geometric altitude (ATC would complain otherwise). The reason they can do so is because the temperature change is gradual, not a step change. For this discussion we need only consider the end states, i.e at one time the aircraft is flying in air at temperature T1, at a later time it is flying at the same FL and Mach number in air at temperature T2.
Now to deal with the speed of sound (SoS). This depends on the square root of the ratio P/rho. But from the gas law P/rho = R T. The exact equation also includes the ratio of specific heats (gamma) which for dry air is 1.4. So:
SoS = sqrt(1.4 R T)
= 20.05 sqrt(T) m/s
=39 sqrt (T) knots.
Now back to the original question.
At constant FL pressure is constant, so from the gas law rho T is constant. This is the important point.
If the aircraft flies from a cold air mass (T1) to a warm air mass (T2) and mach number is held constant the TAS increases by the ratio sqrt(T1/T2). But we have established that rho T is constant, so if T increases rho decreases in exact proportion.
The ratio EAS/TAS depends on sqrt(rho1/rho2). Therefore the increase in TAS is exactly cancelled by the decrease in EAS/TAS ratio and EAS remains constant.
To go from EAS to CAS we adjust for compressibility. However compressibility is a function of Mach number and FL, both of which are constant. Therefore compressibility error is constant and CAS is constant.
To go from CAS to IAS we adjust for position error. This is empirical and aircraft specific, however modern flight instrument systems have built in position error correction and for practical purposes we may assume CAS = IAS. Besides at constant FL and Mach number position error would be constant anyway.
Therefore IAS remains constant
QED
Last edited by Rivet gun; 20th May 2006 at 08:28.
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TEMPERATURE HAS NO EFFECT!
One of the basic tenets of manometry is that the relationship between CAS (or EAS) and Mach Number depends only upon Static Pressure (Ps). Temperature has no effect whatsoever upon the CAS/EAS/Mach relationship, only Ps, end of story.
I believe that the original quote that spawned this thread was a mis-quote. As an aircraft passes from a cold mass of air to a warm mass of air, the CAS, EAS, and Mach Number will all initially fall due to reduced thrust. After thrust has been adjusted to regain the original target speed, whether it be a CAS or a Mach Number, both will again be in complete agreement with each other. The TAS and TAT will be higher. An example for an aircraft at 300 CAS at 30,000 feet, and ISA-25°C moving to an ISA+25°C air mass is as follows -
ISA-25°C : CAS = 300 : EAS = 285.00 : Mach = 0.7905 : TAS = 439.75 : TAT = -44.0°C
ISA+25°C : CAS = 300 : EAS = 285.00 : Mach = 0.7905 : TAS = 490.76 : TAT = +12.3°C
Now that was one HUGE longitudinal temperature gradient that I chose to prove the point, but even with this ridiculous temperature gradient, the CAS, EAS, and Mach Number have not budged by a 10,000th of a decimal place. TAS and TAT have risen very significantly.
TAS is a very significant value to aviation, it is of extreme importance in navigation, and in aerodynamics, TAS is 'the' V that we consider in the highly important 1/2 Rho V squared formulae applied to both Lift and Drag calculations. TAS is so important that it's possible to be blinded by it when considering manometry, the measurement and calibration of speed measuring instruments.
Consider this, If we measured our speed as CAS, we need Pressure Height and Temperature to calculate TAS. If we measured our speed as a Mach Number, we need only Temperature to calculate TAS. If we now put it into very simplistic terms, we would have 2 formulae, namely -
TAS = CAS X A function of Ps X A function of Temperature, and
TAS = Mach X A function of Temperature.
Now, putting the two formulae together to calculate Mach from CAS (or vice versa), and as both equal TAS, we have -
Mach X A function of Temperature = CAS X A function of Ps X A function of Temperature
Now, as "A function of Temperature" appears on both sides of the equation, it is SELF CANCELLING, leaving us with -
Mach = CAS X A function of Ps
Wot! No Temperature?
Before I'm accused of over-simplification, take a look at the formulae by which the Airspeed Indicator and the Machmeter are calibrated -
Vc = SQR((Y/(Y-1)) X Po/Qc X ((Qc/Po + 1)^((Y-1)/Y) - 1) X SQR (2 X Qc/Rho0)
M = SQR (5 X (Qc/Ps + 1)^((Y-1)/Y) - 1)
(NOTE - For flight at altitude, substitute Ps for Po in the Vc formula).
Where -
Vc = Calibrated Air Speed, ft/sec
M = Mach Number
Y = A constant, being the ratio of specific heat of air at constant pressure to the specific heat of air at constant volume = 1.4
Po = Sea Level Air Pressure
Ps = Static Pressure
Qc = Impact Pressure
Rho0 = Standard Sea level air density
Where is the temperature for either equation? It simply isn't there.
The only time that Temperature came into play was in establishng the STANDARD Sea Level Air Density (.0023769 Slugs per cubic foot), in other words, the standard temperature at Sea Level was used in establishing a CONSTANT for calibration purposes.
As a parting remark, temperature, again, has absolutely no effect upon the Change-Over height from CAS to Mach for a given speed schedule. In other words, if your Climb speed schedule was, for example, 320 CAS / M 0.84, the Change-Over height will be 30,107 feet every day of the year, Winter, Summer, Spring and Fall, over the Arctic, the Sahara Desert.........Everywhere
The FAA guy made a mis-quote..... It's been done before
Regards,
Old Smokey
One of the basic tenets of manometry is that the relationship between CAS (or EAS) and Mach Number depends only upon Static Pressure (Ps). Temperature has no effect whatsoever upon the CAS/EAS/Mach relationship, only Ps, end of story.
I believe that the original quote that spawned this thread was a mis-quote. As an aircraft passes from a cold mass of air to a warm mass of air, the CAS, EAS, and Mach Number will all initially fall due to reduced thrust. After thrust has been adjusted to regain the original target speed, whether it be a CAS or a Mach Number, both will again be in complete agreement with each other. The TAS and TAT will be higher. An example for an aircraft at 300 CAS at 30,000 feet, and ISA-25°C moving to an ISA+25°C air mass is as follows -
ISA-25°C : CAS = 300 : EAS = 285.00 : Mach = 0.7905 : TAS = 439.75 : TAT = -44.0°C
ISA+25°C : CAS = 300 : EAS = 285.00 : Mach = 0.7905 : TAS = 490.76 : TAT = +12.3°C
Now that was one HUGE longitudinal temperature gradient that I chose to prove the point, but even with this ridiculous temperature gradient, the CAS, EAS, and Mach Number have not budged by a 10,000th of a decimal place. TAS and TAT have risen very significantly.
TAS is a very significant value to aviation, it is of extreme importance in navigation, and in aerodynamics, TAS is 'the' V that we consider in the highly important 1/2 Rho V squared formulae applied to both Lift and Drag calculations. TAS is so important that it's possible to be blinded by it when considering manometry, the measurement and calibration of speed measuring instruments.
Consider this, If we measured our speed as CAS, we need Pressure Height and Temperature to calculate TAS. If we measured our speed as a Mach Number, we need only Temperature to calculate TAS. If we now put it into very simplistic terms, we would have 2 formulae, namely -
TAS = CAS X A function of Ps X A function of Temperature, and
TAS = Mach X A function of Temperature.
Now, putting the two formulae together to calculate Mach from CAS (or vice versa), and as both equal TAS, we have -
Mach X A function of Temperature = CAS X A function of Ps X A function of Temperature
Now, as "A function of Temperature" appears on both sides of the equation, it is SELF CANCELLING, leaving us with -
Mach = CAS X A function of Ps
Wot! No Temperature?
Before I'm accused of over-simplification, take a look at the formulae by which the Airspeed Indicator and the Machmeter are calibrated -
Vc = SQR((Y/(Y-1)) X Po/Qc X ((Qc/Po + 1)^((Y-1)/Y) - 1) X SQR (2 X Qc/Rho0)
M = SQR (5 X (Qc/Ps + 1)^((Y-1)/Y) - 1)
(NOTE - For flight at altitude, substitute Ps for Po in the Vc formula).
Where -
Vc = Calibrated Air Speed, ft/sec
M = Mach Number
Y = A constant, being the ratio of specific heat of air at constant pressure to the specific heat of air at constant volume = 1.4
Po = Sea Level Air Pressure
Ps = Static Pressure
Qc = Impact Pressure
Rho0 = Standard Sea level air density
Where is the temperature for either equation? It simply isn't there.
The only time that Temperature came into play was in establishng the STANDARD Sea Level Air Density (.0023769 Slugs per cubic foot), in other words, the standard temperature at Sea Level was used in establishing a CONSTANT for calibration purposes.As a parting remark, temperature, again, has absolutely no effect upon the Change-Over height from CAS to Mach for a given speed schedule. In other words, if your Climb speed schedule was, for example, 320 CAS / M 0.84, the Change-Over height will be 30,107 feet every day of the year, Winter, Summer, Spring and Fall, over the Arctic, the Sahara Desert.........Everywhere
The FAA guy made a mis-quote..... It's been done before
Regards,
Old Smokey
Last edited by Old Smokey; 20th May 2006 at 13:58.
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--------------------------------------------------------------------------------
This quote comes from the FAA's "Airplane Upset Recovery Training Aid" referring to Mach stability:
"This stability can be independent of airspeed if, for example, the airplane crosses a cold front. When the outside air temperature changes, the Mach number changes, even though the indicated airspeed may not change."
Now I thought that at a constant flight level, the relationship between IAS and Mach number is independant of temperature. So if you maintain a constant flight level and constant IAS, you also fly a constant Mach number even if the air temperature changes.
But then the source document was written by senior test pilots from Boeing and Airbus, so maybe I have got it wrong??
Going back to this original question I say mach would change because it is soley related to temperature. If temp decreased, mach would increase because TAS would be constant and the speed of sound would decrease.
This quote comes from the FAA's "Airplane Upset Recovery Training Aid" referring to Mach stability:
"This stability can be independent of airspeed if, for example, the airplane crosses a cold front. When the outside air temperature changes, the Mach number changes, even though the indicated airspeed may not change."
Now I thought that at a constant flight level, the relationship between IAS and Mach number is independant of temperature. So if you maintain a constant flight level and constant IAS, you also fly a constant Mach number even if the air temperature changes.
But then the source document was written by senior test pilots from Boeing and Airbus, so maybe I have got it wrong??
Going back to this original question I say mach would change because it is soley related to temperature. If temp decreased, mach would increase because TAS would be constant and the speed of sound would decrease.
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Old Smokey,
Thanks, It is nice to get a definitive answer from somebody who really understands this stuff.
Since you give a formula for CAS, I'll give another CAS formula for comparison.
Vc = Ao X SQRT (5 X (Qc/Po + 1)^((Y-1)/Y) - 1)
Where:
Ao = Standard speed of sound at sea level (661.5 kts)
All other terms as defined by Old Smokey
I like this one because it is simpler and it works in any units: i.e if you want CAS in knots, enter Ao in knots, if you want it in m/s enter Ao in m/s etc. Also note the formula is very similar to the formula for Mach number (spot the differnces)
(NOTE - do NOT substitute the Po term for flight at altitude. CAS is a function of Qc and all other terms are constants. CAS is not a function of Ps)
I leave it up to more mathematically inclined readers to prove that this CAS formula and Old Smokey's CAS formula are equivalent.
Thanks, It is nice to get a definitive answer from somebody who really understands this stuff.
Originally Posted by Old Smokey
Vc = SQR((Y/(Y-1)) X Po/Qc X ((Qc/Po + 1)^((Y-1)/Y) - 1) X SQR (2 X Qc/Rho0)
Vc = Ao X SQRT (5 X (Qc/Po + 1)^((Y-1)/Y) - 1)
Where:
Ao = Standard speed of sound at sea level (661.5 kts)
All other terms as defined by Old Smokey
I like this one because it is simpler and it works in any units: i.e if you want CAS in knots, enter Ao in knots, if you want it in m/s enter Ao in m/s etc. Also note the formula is very similar to the formula for Mach number (spot the differnces)
(NOTE - do NOT substitute the Po term for flight at altitude. CAS is a function of Qc and all other terms are constants. CAS is not a function of Ps)
I leave it up to more mathematically inclined readers to prove that this CAS formula and Old Smokey's CAS formula are equivalent.
Last edited by Rivet gun; 20th May 2006 at 10:52.
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Oh my Gawd!!!!
Thank you Rivet gun, for pointing out my typo. Text suitably edited and emboldened in the corrected area. That will teach me to not be a lazy typist and not use 'cut and paste' so much.
Just in case anyone was foolish enough to copy my post, the correction relates to the value of Gamma, for which I used the letter Y (Sorry, no Greek key-board). I stated -
Y = A constant, being the ratio of specific heat of air at constant pressure to the specific heat of air at constant pressure = 1.4
It should have read (as it now does) -
Y = A constant, being the ratio of specific heat of air at constant pressure to the specific heat of air at constant volume = 1.4
Thany you again Rivet Gun,
Regards,
Old Smokey
Thank you Rivet gun, for pointing out my typo. Text suitably edited and emboldened in the corrected area. That will teach me to not be a lazy typist and not use 'cut and paste' so much.
Just in case anyone was foolish enough to copy my post, the correction relates to the value of Gamma, for which I used the letter Y (Sorry, no Greek key-board). I stated -
Y = A constant, being the ratio of specific heat of air at constant pressure to the specific heat of air at constant pressure = 1.4
It should have read (as it now does) -
Y = A constant, being the ratio of specific heat of air at constant pressure to the specific heat of air at constant volume = 1.4
Thany you again Rivet Gun,
Regards,
Old Smokey
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gamma
G'Day OS!
Isn't cp/cv in dry air a variable with temperature? I know only a teensy bit.
Eg Dry air at 273K cp = 1006 joules/per kg/per K; cv = 719 ditto.
Now I'm moist! cp =? cv = ? cp/cv = ? What happens if I add lots of polyatomic atoms instead of believing air is solely a diatomic gas.
Only splitting hares because I've run out of rabbits but if it's always 1.4 why do I have to look up tables?
Anyway how the devil are you? I shall be in the UK for Farnborough and again for the Gatbash. But not Manchester!
See yuh in the Long Bar!
Rgds
Enny
Isn't cp/cv in dry air a variable with temperature? I know only a teensy bit.
Eg Dry air at 273K cp = 1006 joules/per kg/per K; cv = 719 ditto.
Now I'm moist! cp =? cv = ? cp/cv = ? What happens if I add lots of polyatomic atoms instead of believing air is solely a diatomic gas.
Only splitting hares because I've run out of rabbits but if it's always 1.4 why do I have to look up tables?
Anyway how the devil are you? I shall be in the UK for Farnborough and again for the Gatbash. But not Manchester!
See yuh in the Long Bar!
Rgds
Enny
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I think it comes down to the ideal gas assumption. In an ideal gas gamma is constant and for a diatomic ideal gas (two atom molecules) the theoretical value is 1.4.
But of course an ideal gas is just a theoretical model. It may be a close enough description of real air for many purposes, but it is not exact. To the extent that real air is not a true ideal gas gamma may vary a litttle bit with temperature.
Also as you point out air is not entirely diatomic (N2, O2). It also contains H2O, CO2 and traces of monatomic gasses which will affect the gamma value.
Nevertheless flight instrument calibration equations are based on ISA which assumes inter alia that air is a ideal gas and that gamma = 1.4.
But of course an ideal gas is just a theoretical model. It may be a close enough description of real air for many purposes, but it is not exact. To the extent that real air is not a true ideal gas gamma may vary a litttle bit with temperature.
Also as you point out air is not entirely diatomic (N2, O2). It also contains H2O, CO2 and traces of monatomic gasses which will affect the gamma value.
Nevertheless flight instrument calibration equations are based on ISA which assumes inter alia that air is a ideal gas and that gamma = 1.4.
I may be barking up the wrong tree here but are we not confusing a static situation with a dynamic one?
Practically, during a rapid transition from one airmass to another (assuming no change in wind velocity) TAS remains constant (inertia) while Mach and IAS change. If the change in temperature is more gradual, autothrottle/drag will keep Mach or IAS (whatever your reference is) constant while TAS changes... Yes?
Practically, during a rapid transition from one airmass to another (assuming no change in wind velocity) TAS remains constant (inertia) while Mach and IAS change. If the change in temperature is more gradual, autothrottle/drag will keep Mach or IAS (whatever your reference is) constant while TAS changes... Yes?
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FullWings, No you're not barking up the wrong tree, what you say is correct. The discussion here is not so much about a change in Mach and CAS following a temperature change (at a constant Pressure Height), but about the FAA reference originally provided by Rivet gun, which indicated that -
the Mach number changes, even though the indicated airspeed may not change,
which I believe to be incorrect. My assertion is that although both Mach and CAS will change with the temperature change (a thrust and an inertia effect), once stabilised again, BOTH Mach and CAS will have returned to their original values.
enicalyth (G'day Enny) raises valid points, as usual, but I think that he's set one of his cats amongst the pigeons. Gamma (may I refer to it as Y) is certainly variable, but as the radical ((Y-1)/Y) and it's inverse is used for instrument calibration purposes for both the Airspeed indication and the Mach meter, any environmental variation in gamma will affect both indications. In Rivet gun's last post he has quite rightly stated - "flight instrument calibration equations are based on ISA which assumes inter alia that air is a ideal gas and that gamma = 1.4". Thus, although both may be somewhat in error due to environmental variation from the calibration standard, the relationship between IAS and Mach will be the same. One will not change whilst the other remains unaffected.
Sorry to awaken a thread in the 11th day of it's hibernation, work, the curse of the Prooning classes, has taken me to far flung pest holes during the course of an interesting discussion.
Regards,
Old Smokey
the Mach number changes, even though the indicated airspeed may not change,
which I believe to be incorrect. My assertion is that although both Mach and CAS will change with the temperature change (a thrust and an inertia effect), once stabilised again, BOTH Mach and CAS will have returned to their original values.
enicalyth (G'day Enny) raises valid points, as usual, but I think that he's set one of his cats amongst the pigeons. Gamma (may I refer to it as Y) is certainly variable, but as the radical ((Y-1)/Y) and it's inverse is used for instrument calibration purposes for both the Airspeed indication and the Mach meter, any environmental variation in gamma will affect both indications. In Rivet gun's last post he has quite rightly stated - "flight instrument calibration equations are based on ISA which assumes inter alia that air is a ideal gas and that gamma = 1.4". Thus, although both may be somewhat in error due to environmental variation from the calibration standard, the relationship between IAS and Mach will be the same. One will not change whilst the other remains unaffected.
Sorry to awaken a thread in the 11th day of it's hibernation, work, the curse of the Prooning classes, has taken me to far flung pest holes during the course of an interesting discussion.
Regards,
Old Smokey
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This works really well on the A320 and A321.
Get airborne and at accel alt dial up 340kts.
Keep 340kts until the mach number is what you want to cruise at.
Swap to Mach on the FCU
When IAS is the same as in the climb perf page, go back to managed speed.
Reverse on descent
That's my relationship between IAS and Mach and it works just fine
Get airborne and at accel alt dial up 340kts.
Keep 340kts until the mach number is what you want to cruise at.
Swap to Mach on the FCU
When IAS is the same as in the climb perf page, go back to managed speed.
Reverse on descent
That's my relationship between IAS and Mach and it works just fine
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ohh I'm glad this is back
RivetGun Are you flying in Vacuo????
you can't take moles out of it the adiabatic gas laws don't allow that: Cp-Cv=nR, Y=Cp/Cp+nR
and I didn't say T dependent I said Rewrite as a function of T
ex: dw = -PdV and du = CvdT and dU = dw+dq adiabatically = du = dw
so I can say Cvdt=-Pdv; REWRITING P in terms of T
Cv dT/ T = -nR dV/V since Cv is a constant I can integrate then i have
<Tf/ (dT/T) / Ti> = -nR <Vf / (dV/V) /Vi > = lnTf/Ti = -nRln (Vf/Vi)
using a ln X =lnX^a
and gas laws,
I have Ti/Tf = (Vf/V1)^y
lastly, Pi Vi^y = Pf Vf^y.
applying this judiciously with the equation fo dynamic pressure you can derive the equations (corrected for adiabatic compressibility) provided by Old Smokey
with about four pages of algebra...I' m not doing it
p.s. please let me know if I made an error if anyone finds one
edited: to correct a error Cp DIFFERS from Cv by nR NOT Cp+Cv=nR
I was very wrong there!!!
RivetGun Are you flying in Vacuo????
you can't take moles out of it the adiabatic gas laws don't allow that: Cp-Cv=nR, Y=Cp/Cp+nR
and I didn't say T dependent I said Rewrite as a function of T
ex: dw = -PdV and du = CvdT and dU = dw+dq adiabatically = du = dw
so I can say Cvdt=-Pdv; REWRITING P in terms of T
Cv dT/ T = -nR dV/V since Cv is a constant I can integrate then i have
<Tf/ (dT/T) / Ti> = -nR <Vf / (dV/V) /Vi > = lnTf/Ti = -nRln (Vf/Vi)
using a ln X =lnX^a
and gas laws,
I have Ti/Tf = (Vf/V1)^y
lastly, Pi Vi^y = Pf Vf^y.
applying this judiciously with the equation fo dynamic pressure you can derive the equations (corrected for adiabatic compressibility) provided by Old Smokey
with about four pages of algebra...I' m not doing it
p.s. please let me know if I made an error if anyone finds one
edited: to correct a error Cp DIFFERS from Cv by nR NOT Cp+Cv=nR
I was very wrong there!!!
Last edited by rhovsquared; 8th Jun 2006 at 20:11.
