effect of weight and cruise level on performance

[JulieFlyGal]

I'm studying for my atpl aerodynamics exam and am confused about a few things.

1. As weight reduces due to fuel burn off, the aircraft can be flown at a slower mach no. to preserve the angle of attack that gives 1.32 Vimd (for max range cruise). True or False?

2. As weight reduces due to fuel burn off, the aircraft can climb to higher altitude and cruise at the same (constant) mach no. as before. True or False?

3. If 2 above is true, then will the aircraft be cruising at the optimum angle of attack that gives 1.32 Vimd for max range? Yes or No?

4. How does the higher altitude affect fuel flow (and thus SFC) when cruising at 1.32 Vimd? Increase or decrease?

The ATPL text I have waffles on too much in a confusing manner. Hope someone can give me a "keep it simple" answer. Thanks.

[Intruder]

1. True.

2. True.

3. Yes, assuming that is the company policy.

4. Decrease.

[dream747]

What is Vimd? I see Vimd and Vmd being used interchangeably, is Vimd = Vmd?

Also is there any particular reason for the jet's best range AOA to be at 1.32 Vimd and the props to be at Vimd only?

Thanks for any clarification!

[hawk37]

Vmd is velocity for minimum drag. I know not of Vimd, perhaps a typo.

An jet/turboprop best range is theoretically approximately 1.32 * Vmd (actually the fourth root of 3, then multiply by Vmd, if I remember correctly). This assumes a constant fuel flow and thrust as speed changes, which may be close for jet engines, less so though for turboprops.
Further, this assumes zero compressibility drag, so for jets at mid to high altitudes, this can be wildly inaccurate. Take for example an 777 at cruise altitude, I'm guessing Vmd to be .75 to .80 depending on weight. Multiply by 1.32 and you get best range to be M1.0 or greater, clearly impossible. But low altitude for jets and turboprops, I expect 1.32 * Vmd to be fairly accurate.

Intruder, I'm wrestling with whether your answer to question #4 is correct, that Thrust SFC ** AND ** fuel flow will both decrease. I'm taking TSFC as lbs of fuel consumed, per lb of thrust produced, per hour of flight (or metric equivalent). Higher altitudes should increase TSFC, as a jet engines has it's lowest (or best) TSFC at sea level. The question is not that clear on specifics which makes it difficult to answer too. Of course, I could be wrong...

Hawk

[dream747]

Hawk, how does a jet engine have the best or lowest TSFC at sea level? SFC varies with altitude and RPM for the jet engine which is the lowest at high altitude because of increasing engine efficiency and decreasing drag (up to the optimum altitude).

From this I can assume SFC would be higher at sea level and thrust would be high as well given the denser air, higher atmospheric pressure?

[hawk37]

Dream747,

When you say SFC, I'm not sure what you're referring to, and what units you are using. If you mean TSFC, which I described in my previous post, then yes, TSFC varies with altitude and mach. But if you look at graphs of such (often kept secret), you would see indeed that the lowest (best) values are at the lower altitudes, other factors constant. I can't really explain why, as I don't know. Perhaps because the air is denser, so there is less energy required to compress it up to the optimal value for the conditions.
As an aside, the "efficiency" of a jet engine is not defined as it's TSFC, but on some ratio of pressures within the engine, if I recall correctly. So don't use TSFC and efficiency interchangeably.

But don't confuse TSFC with the aircraft's performance. While indeed the engine generally puts out less thrust with the same amount of fuel as the altitude increases, there is less drag on the aircraft for the same true airspeed as altitude increases (for normal flights), and hence the SR (specific range, nautical miles per lb of fuel burned) will usually be higher at higher altitudes for the jet aircraft, up to a limit. And this is why I think it is said that jet aircraft are more "efficient" at higher altitudes.

[Fullblast]

SFC (specific fuel consumption) is less at higher altitude than at sea level because the ratio between air and fuel is in weight, that means that less denser air, less fuel required (true for all endothermic engines).

Hawk37, 1.32 is Best range speed only for jet a/c not for turboprop (turboprop best range and best endurance coincide with Vimd), because the difference is in the curve of power/thrust required, in jet engine tangent to the total drag curve at 1.32 Vimd.
The example you give is totally wrong, Vimd is a KIAS speed, nothing to do with Mno, (we use Mn at high altitudes for Mcrit limits) and doesn't change with altitude (effects of compressibility starts at speed above 300 IAS, so can be trascurable on this matter). Obviously the Mno counts, but only if it is limiting, pretty much impossible, maximum Mno have always a sensible margin above maximum range, that is even lower than long range speed.

Vmd and Vimd are both correct terms.

FB

[enicalyth]

..But please remember that TSFC does not get smaller and smaller indefinitely the higher you go. If a manufacturer shows you a graph suggesting that this is true, ask to see the plot of installed TSFC against thrust, ML/D, L/D, even God Forbid CL by itself. The curve starts with relatively high values, not unsurprisingly, and curvilinearly falls to a nadir where it stays for a bit then with a waywardness of all mechanical devices starts to climb again. And just to heighten the fun, if you pardon the unintended pun, the nested curves for various flight levels are skewed and minimum TSFC rarely coincides with maximum L/D or the flight level you'd really like.

Other than that I'll get my coat and sit in pedants corner.

The "E"

[hawk37]

Full Blast,

If I knew what exactly you mean by SFC I could comment. I dealt with TSFC, which I explained clearly. The S is for specific, ie in relation to something. One puts the T in front, so that it is known to be thrust (a force). It could be power, if one was to define it that way. That is why I asked Dream 747 what he meant as well, because it matters in the discussions.

you say "turboprop best range and best endurance coincide with Vimd)". I will have to check my books then when I return.

you say "The example you give is totally wrong" What was wrong?

you say "effects of compressibility starts at speed above 300 IAS". Well, certainly not true in my example, which was at mach .75 and above. Sure, maybe at 300 KIAS at low level there is little/no compressibility effects, but I said a 777 at cruise altitude, at .75 which is not low level normally.

you say "Vimd is a KIAS speed, nothing to do with Mno". Of course you're right, and I said nothing to the contrary.

Mr E,
I'd like to follow what you say, but a picture would be worth a thousand words. But are you suggesting that if one was to take a 777 engine at cruise thrust, and take it up continuously in altitude at a constant mach .85 until it flamed out, that the TSFC would not continuously increase?

[Fullblast]

From Cathay Pacific notes:

Specific Fuel Consumption
Specific Fuel Consumption is a measure of the fuel consumed by an engine. There are two types of specific fuel consumption:

1.Thrust Specific Fuel Consumption [TSFC]
2.Power Specific Fuel Consumption [SFC]

TSFC is defined as fuel-flow per pound of thrust produced [FF/Thrust]

SFC is defined as fuel-flow per horsepower produced [FF/HP]

Fuel-flow should be measured in units of pounds of fuel per hour, rather than gallons per hour. This is because the chemical energy in the fuel is a function of the mass of the fuel. A gallon of fuel expands or contracts with temperature. Therefore, a gallon of cold fuel contains more energy than a gallon of warm fuel.

The units of TSFC and SFC will be:
TSFC = lb per hr/thrust lb
SFC = lb per hr/HP

Converting the Drag vs. Velocity Curve
A perfectly accurate conversion of the drag curve into a Fuel-flow vs. Velocity graph must take variations in engine and propeller efficiency into account. However, we will find it easier to break the process into two steps. We will therefore conduct a simple aerodynamic analysis first, in which we will assume that:

§ TSFC is constant for a jet
§ SFC is constant for piston and turbo-prop engines.

FF vs. Velocity for a Jet
We will start by converting a Drag vs. Velocity curve into a Fuel-flow vs. Velocity curve for a jet aircraft. This will be very easy because the TSFC is a constant.

Remember the definition of TSFC:
TSFC = FF/Thrust

We will assume that:
TSFC = FF/Drag (i.e. we assume thrust = drag)

Therefore:
FF = TSFC x Drag


Hope it helps a bit.

FB

[JulieFlyGal]

Thanks all, it's now starting to make some sense. I have the exam this week so will let you know how I go. :)

[JulieFlyGal]

I passed my ATPL Aerodynamics and Systems exam today so thank you all for your help. It's much appreciated. 6 down and 1 to go. :)