IAS, Drag , Density, TAS

[v1_rotate]

Hello all..
I have a question regarding the relationship between IAS , Drag and Air Density (and also TAS I suppose) after reading the following statement in the JAR Oxford Performance manual...

"For given Indicated Airspeeds , the total Drag does not change with density (pressure or temperature) at a given mass"

> If an airplane (lets say a fixed pitch piston prop) at say 2300rpm gets an IAS of 90 kts. at 2000 feet , will it get the same IAS at 8000 feet. Or in order to maintain the 90 kt (IAS) at 8000 feet will a higher setting be required due to the reduced density ?

> And if the same setting is maintained at a higher altitude , wont the drag decrease due to the decreased air density ? Or does the statement mean to say that IAS will reduce at a higher altitude (drag would also reduce), and in order to get back the IAS you would increase power (& thrust) hence also increasing drag and getting it back to its original value.

>Does the statement apply to props and jets ?

..I know they may be silly questions, but ive been thinking about the statement and cant quite entirely work it out.. thanks in advance..

[Keith.Williams.]

DRAG AND IAS

The Airspeed Indicator (ASI) measures the dynamic pressure and produces an Indicated Airspeed output (IAS) that is determined by the value of that dynamic pressure. Every time the ASI senses a particular value of dynamic pressure it indicates the same IAS.

This means that if we climb at constant IAS, we must be climbing at a constant dynamic pressure.

Lift = CL 1/2ρ Vsquared S

Drag = CD 1/2ρ Vsquared S

And both CD and CL are determined by angle of attack.

If we assume that the weight of our aircraft remains constant, then as we climb at constant IAS (which also means constant dynamic pressure) we must keep the angle of attack constant to maintain constant lift to match the constant weight. This in turn means that the CD will remain constant.

So as we climb we have a situation in which CD and 1/2ρ Vsquared are both constant, so (unless our surface area (S) changes), we must have constant drag.

So climbing at constant IAS produces constant drag.



POWER REQUIRED

Dynamic pressure is equal to 1/2ρ Vsquared, where ρ is the air density and V is the TAS.

So if the IAS remains constant, then any change in air density must be balanced by an equal and opposite change in TASsquared.

If for example an aircraft climbs at constant IAS then the TAS must gradually increase so that increasing TASsquared compensates for the reducing air density to give constant dynamic pressure.

The important point here is that if IAS is constant, then as we climb, the TAS must gradually increase.

Power Required = Drag x TAS

So in our constant IAS climb we have constant drag multiplied by increasing TAS, so the power required increases with the TAS.

Note that none of the above is absolutely true. We should for example be talking about EAS not IAS and at high altitude things like compressibility effects will complicate matters a bit. But for the purposes of the early stages of the JAR ATPL POF syllabus, the above is accurate enough.

[Pugilistic Animus]

If an airplane (lets say a fixed pitch piston prop) at say 2300rpm gets an IAS of 90 kts. at 2000 feet , will it get the same IAS at 8000 feet.

well, it will need more power in order to maintain the same IAS at a higher altitude. at the same thrust setting you will slow due to using a higher aoa to maintain altitude
For given Indicated Airspeeds , the total Drag does not change with density (pressure or temperature) at a given mass"

For a decrease in density will result in a proportionate increase in [V^2] so for a given Cl at a given alpha drag remains constant, at constant [EAS], but the higher alpha required to maintain altitude at a slower airspeed [if you don't increase power to maintain that airspeed] then slower flight imparts more induced drag as Cd is increased with a higher alpha.

Does the statement apply to props and jets ?

I guess broadly it applies to both, but the difference is a little abstract....:)

[Pugilistic Animus]

Looks like Keith and I saw the thread at the same time...:)

[v1_rotate]

Keith.Williams and Pugilistic Animus... Thank you both very much , its a lot clearer now , looking at it in terms of the equations mentioned helped sort things out , just a couple of lingering queries !

> I have a couple of follow up questions regarding Density .. (these lines also from the Perf. Manual regarding factors effecting Endurance)...

"For the Jet changes of temperature do not affect the Drag at Vmd [thanks to your help this point is clear to me now!] so changes in Endurance results only from changes in sfc, which increases with temperature, giving reduced endurance"

Heres my Question...
> I understand that Endurance is greatest when FuelFlow is least and
FF = SFC x Thrust I dont understand the part where SFC increases with temperature .. SFC = FF/THRUST .. wont an increase in temperature (decrease in Density) effect both THRUST and FF(fuel flow) equally ? :confused:


"For Propeller aircraft, higher temperatures will increase the power required at Vmp increasing the FuelFlow, and reducing endurance"

...This statement i have no doubts in as the equation
POWER REQUIRED = DRAG x TAS makes it clear to me.


Thank you

[Keith.Williams.]

Heres my Question...
> I understand that Endurance is greatest when FuelFlow is least and
FF = SFC x Thrust I dont understand the part where SFC increases with temperature .. SFC = FF/THRUST .. wont an increase in temperature (decrease in Density) effect both THRUST and FF(fuel flow) equally ?


If temperature increases this will cause the air to expand. So if the engine RPM remains constant, the mass flow rate of air passing through it will decrease. This will decrease the thrust. In order to restore the thrust to balance the constant drag, we must increase the fuel flow. This will reduce endurance directly.

Another way of looking at the situation is to consider what is happening to the SFC.

SFC is the mass of fuel that is used per hour to produce each unit of thrust (for a jet engine) ot power (for a piston/prop or turboprop engine). So if SFC increases (at constant thrust or constant power output), the fuel flow will increase and the endurance will decrease.

SFC is affected by a number of factors including the following:

ENGINE RPM
For jet engines SFC is typically lowest between about 90% to 95% RPM. For pistons it is lowest when the throttle if fully open to minimise inlet restrictions.

AIR PRESSURE AND DENSITY
SFC is lowest when operating in high pressure, high density air. (You will probably find that your performance notes are wrong on this matter.)

AIR TEMPERATURE
SFC is lowest when operating in very cold air. The colder the air the lower the SFC.

So if air temperature increases the SFC increases. This means that although our required thrust (which is equal to drag) remains constant, the mass of fuel that we must burn to produce that thrust has increased. So endurance decreases as air temperature increases.

[v1_rotate]

Ah yes, its clearer now, Thank you Sir !

SFC is lowest when operating in high pressure, high density air. (You will probably find that your performance notes are wrong on this matter.)

..Now that makes sense !...

On the effect of altitude on endurance the manual says " For a Jet at Vmd increasing altitude does not effect the drag, but the engine SFC improves, giving greater endurance" (until of course you go above the Optimum Altitude and air compression becomes an issue).



>So in reality does (T)SFC increase with altitude... and would i be correct in saying that as a jet airliner cruises at a high altitude , its engine efficiency actually decreases (due increase in sfc) , but its aerodynamic efficiency increases (thrust does not get too high due to the low air density).. and Overall the aircraft is more efficient at higher altitudes ??

Thank You..

[Keith.Williams.]

>So in reality does (T)SFC increase with altitude... and would i be correct in saying that as a jet airliner cruises at a high altitude , its engine efficiency actually decreases (due increase in sfc) , but its aerodynamic efficiency increases (thrust does not get too high due to the low air density).. and Overall the aircraft is more efficient at higher altitudes ??

For maximum specific range we need to be operating our engines and our airframe at their maximum efficiencies simultaneously. This means getting minimum SFC and maximum TAS/Drag ratio.


As altitude increase we have:

For the engines:
Decreasing temperature tends to decrease SFC.
Decreasing pressure and density tends to increase SFC.
Increasing RPM (to maintain thrust to maintain Vmrc) increases the RPM, taking it closer to the optimum 90% to 95%. This tends to decrease SFC.

The overall effect is that SFC actually increase slightly with increasing altitude.

For the Airframe:
Constant IAS at Vmrc maintains constant drag.
Increasing TAS at that constant Drag increases the TAS/Drag Ratio.

The overall effect is that TAS/Drag ratio increases with increasing altitude.

Ideally we want minimum SFC and Maximum TAS/Drag ratio simultaneously. But in reallity we have to do a bit of a trade-off between the two.

We do not actually get minimum SFC at the optimum altitude, but we do get the the best balance between SFC and TAS/Drag ratio. So we get best Specific Air Range.

(You will probably also find that your perforamnce notes are wrong about the getting the minimum SFC at the optimum altitude)

[bookworm]

SFC is the mass of fuel that is used per hour to produce each unit of thrust (for a jet engine) ot power (for a piston/prop or turboprop engine). So if SFC increases (at constant thrust or constant power output), the fuel flow will increase and the endurance will decrease.

SFC is affected by a number of factors including the following:

ENGINE RPM
...
AIR PRESSURE AND DENSITY
...
AIR TEMPERATURE
...

What about speed?!

The "jet approximation" has always troubled me. The idea of using a measure such as SFC is that the ratio should be relatively unaffected by other parameters, allowing us to see the strong relationship between numerator (power or thrust) and denominator (fuel flow).

For a prop, the constant PSFC approximation is pretty good. You'd expect it to be, wouldn't you? A given mass of fuel holds a well determined chemical energy. Divide by time and it's pretty intuitive that burning a given mass per unit time transforms the chemical energy into work at well determined rate, i.e. constant power. The power should, to a good first approximation, be proportional to the rate at which we burn fuel. And it is, with a bit of an exception at speeds close to zero where the engine is doing no useful work but still needs fuel to turn. Then we look for inefficiencies, and look at the dependence of those on other parameters, like propeller efficiency and pumping losses with their dependence on throttle setting.

But what about jets? The fundamental physics doesn't change. We're still turning hydrocarbon into energy, and to a good first approximation, the power, not the thrust, should be proportional to the rate at which we burn fuel. Why should we expect to get anything like constant thrust from burning fuel at a constant rate? Of course there may be greater efficiency at high speed, but would we really expect a ton of kerosene to produce twice the power simply because we're flying twice as fast?

And if you look at a cutting-edge turbofan like the RB211 (oh well, it's only 40 years old), thrust specific fuel consumption is indeed vastly higher at higher speeds. That doesn't mean that power specific fuel consumption is constant either, it's substantially lower at higher speeds. But we're nowhere near the "ideal jet approximation" of constant TFSC.

Does it matter? Isn't TSFC just a useful ratio to measure with no real presumption that it's independent of speed? Well perhaps, but when we start suggesting e.g. that best endurance on a jet is at Vmd "because TSFC is constant", aren't we in danger of getting the real best-endurance speed quite a long way out?

(I'm not suggesting that Keith is saying anything incorrect or misleading in his post, just that the ideal jet approximation is a somewhat odd place to start when considering aircraft performance in 2010.)

[v1_rotate]

(You will probably also find that your perforamnce notes are wrong about the getting the minimum SFC at the optimum altitude)

Yes Sir, Thats exactly what they say.. Both in the Perf. Manual and the Powerplant (jet) manual which I have been going through over the last few days with the desire to learn about Jet Performance and fill in the gaps in my overall performance knowledge.

The fact that the Optimum altitude is a compromise like you mentioned makes things much more clear to me since I was pretty sure already that It was a compromise between the engine and the airframe (ie. SFC , TAS : DRAG) and something just did not quite add up from what I was reading in the Manuals.

Thanks to the replies on this thread, I now have a better understanding of the variables involved and hence a clearer view of the big picture as a whole as well.

And if you look at a cutting-edge turbofan like the RB211 (oh well, it's only 40 years old), thrust specific fuel consumption is indeed vastly higher at higher speeds. That doesn't mean that power specific fuel consumption is constant either, it's substantially lower at higher speeds. But we're nowhere near the "ideal jet approximation" of constant TFSC.

So are you saying that TSFC increase with speed because of the increases 'Power Required' to produce the same amount of 'Thrust' ( since Power is the rate of doing word and more power would be required to overcome the same amount of drag at a higher speed ) , and/or the increase in 'Induced Momentum Drag' with speed ?


Thank You...

[palou89]

DRAG AND IAS

The Airspeed Indicator (ASI) measures the dynamic pressure and produces an Indicated Airspeed output (IAS) that is determined by the value of that dynamic pressure. Every time the ASI senses a particular value of dynamic pressure it indicates the same IAS.

This means that if we climb at constant IAS, we must be climbing at a constant dynamic pressure.

Lift = CL 1/2ρ Vsquared S

Drag = CD 1/2ρ Vsquared S

And both CD and CL are determined by angle of attack.

If we assume that the weight of our aircraft remains constant, then as we climb at constant IAS (which also means constant dynamic pressure) we must keep the angle of attack constant to maintain constant lift to match the constant weight. This in turn means that the CD will remain constant.

So as we climb we have a situation in which CD and 1/2ρ Vsquared are both constant, so (unless our surface area (S) changes), we must have constant drag.

So climbing at constant IAS produces constant drag.



POWER REQUIRED

Dynamic pressure is equal to 1/2ρ Vsquared, where ρ is the air density and V is the TAS.

So if the IAS remains constant, then any change in air density must be balanced by an equal and opposite change in TASsquared.

If for example an aircraft climbs at constant IAS then the TAS must gradually increase so that increasing TASsquared compensates for the reducing air density to give constant dynamic pressure.

The important point here is that if IAS is constant, then as we climb, the TAS must gradually increase.

Power Required = Drag x TAS

So in our constant IAS climb we have constant drag multiplied by increasing TAS, so the power required increases with the TAS.

Note that none of the above is absolutely true. We should for example be talking about EAS not IAS and at high altitude things like compressibility effects will complicate matters a bit. But for the purposes of the early stages of the JAR ATPL POF syllabus, the above is accurate enough.

Hands down best explanation Ive ever seen on the topic. :D

[Keith.Williams.]

So are you saying that TSFC increase with speed because of the increases 'Power Required' to produce the same amount of 'Thrust' ( since Power is the rate of doing word and more power would be required to overcome the same amount of drag at a higher speed ) , and/or the increase in 'Induced Momentum Drag' with speed ?

It's not so much a matter of overcoming drag.

Power is the rate of doing work or the rate of expending energy.

Power = Force x Speed

In the case of an aircraft in flight this becomes

Power = Thrust x TAS

So if we accelerate in flight, as our airspeed increases, if the engine thrust remains constant while the TAS increases, the power output must be increasing.

But power is also the rate of expending energy and we do not get anything for nothing. So to maintain constant thrust with increasing power we must increase the energy input rate. This means increasing the fuel flow.

So as we accelerate, we have an increasing fuel flow for a constant thrust. This means that the Thrust SFC is increasing.

Although this is shown in many text books, the same text books then quietly assume that SFC is constant at all airspeeds, when they deal with the subject of best jet endurance.

This is fairly typical of the way that we use (and become caught out by) simplifying assumptions.

bookworm
I hadn't really thought enough about it before, but this relationship between TAS and TSFC makes it even move obvious that optimum cruise altitude is a compromise.

[v1_rotate]

This is fairly typical of the way that we use (and become caught out by) simplifying assumptions

Very true Sir..the concluding paragraphs in the text of these books seem to be accurate, but it was the explanation that was confusing me a little.
I've got things much more clear now , Thank You very much for your help.