Tas
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Not really sure exactly what you mean but this is what I reckon.
Under normal conditions (i.e. temperature decreasing with height) if you fly a constant CAS in a climb, your TAS will increase and your Mach number will increase faster. However, the tropopause is a layer where the temperature stops falling with height, i.e. essentially an isothermal layer. Climbing through an isothermal layer, at constant CAS the TAS will still increase, but now the Mach number will increase at the same rate as the TAS since Mach number is TAS/(speed of sound) and the speed of sound is dependent on temperature. Conversely, if you are flying at a constant Mach number in the climb then your TAS would remain constant and CAS would decrease.
I bet that doesn't answer anything!
Under normal conditions (i.e. temperature decreasing with height) if you fly a constant CAS in a climb, your TAS will increase and your Mach number will increase faster. However, the tropopause is a layer where the temperature stops falling with height, i.e. essentially an isothermal layer. Climbing through an isothermal layer, at constant CAS the TAS will still increase, but now the Mach number will increase at the same rate as the TAS since Mach number is TAS/(speed of sound) and the speed of sound is dependent on temperature. Conversely, if you are flying at a constant Mach number in the climb then your TAS would remain constant and CAS would decrease.
I bet that doesn't answer anything!
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I should have given more details. When analysing best range we use the equation:
(V/Tr) X (1/SFC) where V = TAS, Tr = thrust required and SFC= specific fuel cunsumption.
The issue in class was the following. Do we get any advantage gaining altitude (for a jet) on the airframe point of vue (V/Tr)?
We know the thrust requried curve shifts right when increasing the altitude. We want to have the max for V/Tr. Since Tr does not move and V increases with alt we have a tremendous advantage flying high from the airframe point of vue (from the engine also but this is another issue).
Now my question was: Above the trop, is the TAS varying? If not, there is no advantage nor disavantage flying within this layer.
Your thoughts?
(V/Tr) X (1/SFC) where V = TAS, Tr = thrust required and SFC= specific fuel cunsumption.
The issue in class was the following. Do we get any advantage gaining altitude (for a jet) on the airframe point of vue (V/Tr)?
We know the thrust requried curve shifts right when increasing the altitude. We want to have the max for V/Tr. Since Tr does not move and V increases with alt we have a tremendous advantage flying high from the airframe point of vue (from the engine also but this is another issue).
Now my question was: Above the trop, is the TAS varying? If not, there is no advantage nor disavantage flying within this layer.
Your thoughts?
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The short answer to your question is yes it does.
The longer answer goes something like this:
The relationship between IAS and TAS depends on air density. The ASI always gives the same indication whenever it experiences a given dynamic pressure. So climbing at constant IAS means climbing at constant dynamic pressure.
Dynamic pressure is 1/2RhoVsquared where Rho is air density and V is TAS. As altitude increases, the air density decreases. So to get the same dynamic pressure (and hence the same IAS) we must fly at a greater TAS. It is for this reason that the TAS at any given IAS increases as altitude increases.
But air density is affected by both static pressure and temperature. As altitude increases (up to the tropopause) , both the static pressure and the temperature decrease. The decreasing pressure allows the air to expand, thereby causing its density to decrease. But the decreasing temperature causes the air to contract, thereby increasing its density. In any normal atmosphere the reducing pressure is the dominant factor, so density decreases as altitude increases. The overall effect of the reducing temperature is to reduce the rate of density decrease, which in turn reduces the rate of TAS increase at any given IAS.
Above the troposphere the temperature is constant, but static pressure and hence density continue to decrease. So the TAS at any given IAS continues to increase.
The real aerodynamic advantage comes from the fact that the drag (and hence thrust required) is constant at any given IAS (if we ignore compressibility effects). So as we go higher we pay the same price in terms of thrust, but get a higher TAS for our money.
A second benefit comes from the fact that the specific fuel consumption of jet engines is lowest at low ambient temperatures and when operating between about 85% and 95% RPM. at low altitudes the high density air would produce too much thrust when operating in this optimum RPM range, so we cannot get best SFC when cruising at low altitude.
But as we climb higher, the reducing density reduces the thrust, while the drag remains constant. If we climb high enough we can reach an altitude at which the drag (and hence thrust required) at the speed giving best TAS to Drag ratio, is equal to the thrust in the 85% to 95% RPM band. At this point we are at our optimum altitude and at our maximum range speed VMRC.
The longer answer goes something like this:
The relationship between IAS and TAS depends on air density. The ASI always gives the same indication whenever it experiences a given dynamic pressure. So climbing at constant IAS means climbing at constant dynamic pressure.
Dynamic pressure is 1/2RhoVsquared where Rho is air density and V is TAS. As altitude increases, the air density decreases. So to get the same dynamic pressure (and hence the same IAS) we must fly at a greater TAS. It is for this reason that the TAS at any given IAS increases as altitude increases.
But air density is affected by both static pressure and temperature. As altitude increases (up to the tropopause) , both the static pressure and the temperature decrease. The decreasing pressure allows the air to expand, thereby causing its density to decrease. But the decreasing temperature causes the air to contract, thereby increasing its density. In any normal atmosphere the reducing pressure is the dominant factor, so density decreases as altitude increases. The overall effect of the reducing temperature is to reduce the rate of density decrease, which in turn reduces the rate of TAS increase at any given IAS.
Above the troposphere the temperature is constant, but static pressure and hence density continue to decrease. So the TAS at any given IAS continues to increase.
The real aerodynamic advantage comes from the fact that the drag (and hence thrust required) is constant at any given IAS (if we ignore compressibility effects). So as we go higher we pay the same price in terms of thrust, but get a higher TAS for our money.
A second benefit comes from the fact that the specific fuel consumption of jet engines is lowest at low ambient temperatures and when operating between about 85% and 95% RPM. at low altitudes the high density air would produce too much thrust when operating in this optimum RPM range, so we cannot get best SFC when cruising at low altitude.
But as we climb higher, the reducing density reduces the thrust, while the drag remains constant. If we climb high enough we can reach an altitude at which the drag (and hence thrust required) at the speed giving best TAS to Drag ratio, is equal to the thrust in the 85% to 95% RPM band. At this point we are at our optimum altitude and at our maximum range speed VMRC.
Last edited by Keith.Williams.; 22nd Aug 2003 at 02:00.
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Regarding Acheo last post about how Range is affected by temperature deviation. I would like to point out that ISA deviation doesnot affect specific range, if FL ,GW and wind remain constant.
Speed for LRC doesn´t depend on temperature deviation, if temperature rises TAS and FF will increase proporcionally.
The above statement might be slightly wrong for airplanes with very high BPR engines.
Speed for LRC doesn´t depend on temperature deviation, if temperature rises TAS and FF will increase proporcionally.
The above statement might be slightly wrong for airplanes with very high BPR engines.
