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elpilote
18th May 2006, 19:24
HI, i am asking myself about a quite basic question on perfo,
What does the optimum altitude according to a decrease in weight??
Is there anybody who can help me ?
I am looking for answer in my different ATLP courses but i can not find it until now.
Thanks in advance.

Mad (Flt) Scientist
18th May 2006, 19:38
Well, assuming you're talking about optimum cruise altitude for range ....

The higher you go, the more TAS you get for a given CAS, hence the more real ground you cover for a given amount of thrust. So, higher is better - ONCE you get up there.

BUT

It costs time, and fuel to get up there. And the heavier you are, the more time and fuel it takes. So eventually the penalty of climbing outweighs the gain in the cruise, and therefore the optimum altitude is lower for a heavier aircraft.

Pretty simplistic, and one of the perf experts can give you chapter and verse no doubt.

elpilote
18th May 2006, 19:45
thanks for your quick answer i am "novice " on this forum and you spoke about perfo expert , is there a specific forem where i can have more infos???

Mad (Flt) Scientist
18th May 2006, 19:48
This is pretty much the right place, as far as I can tell (sometimes people ask in the Questions forum, sometimes here - don't think it matters much)

re "perf expert" - there's a few posters here who do performance calculations for a living, and are far better qualified than me to explain it. One of them will no doubt wander by in due course. (I'm just hoping after my appalling track record of technical explanations over the last week or so that I haven't screwed this one up too)

elpilote
18th May 2006, 19:54
so to resume , you consume less fuel the higher you are but to get up there consume fuel, so what is the solution , climb to save fuel or stay a this altitude and consume more than higher but saving the fuel to get uo there???

Mad (Flt) Scientist
18th May 2006, 19:58
Correct.

And the balance between climb or not climb varies with your weight.

(Also, as a seperate issue, a heavier aircraft can't climb as high, either, so if the mission is so long that it's a case of 'get as high as you can' then again the light aircraft has a higher optimum altitude, simply because it can get to it)

wondering
18th May 2006, 22:09
Think in terms of angle of attack. In general terms, there is one optimum AoA for max range regardless of weight. That means a heavier aircraft has to fly faster than a lighter aircraft to achieve its optimum AoA. Since more of the available thrust is needed to achieve a higher TAS and to support the heavier aircraft, the optimum altitude will be lower (and TAS higher) than for a lighter aircraft.

Another factor coming into play might be Mcrit. Assuming the heavier aircraft has enough thrust to keep climbing, the corresponding TAS for its optimum AoA would keep creeping towards Mcrit. So, somewhere will be a design trade-off between thrust, drag, speed (limits), AoA etc.

mutt
18th May 2006, 22:30
Its worth noting that MFS used the term optimum cruise altitude for range, with this in mind, it is correct to say that there is a trade off between climb and cruise in order to achieve the most efficient flight profile.

MrBoeing publishes an Optimum Altitude Chart, this chart isnt based upon range, it provides the optimum altitude based upon Nautical Air Miles/Fuel Used.

Another factor coming into play might be Mcrit
In another thread, I believe that Old_smokey stated that EVERY airliner he had ever flown flew FASTER than the Mcrit, so how exactly does it come into play? I presume that you did mean Mcrit and not MMO?

Mutt

flightopsab
18th May 2006, 22:37
so to resume , you consume less fuel the higher you are but to get up there consume fuel, so what is the solution , climb to save fuel or stay a this altitude and consume more than higher but saving the fuel to get uo there???


Not necc. true... A major factor in choosing the optimum altitiude are the winds aloft. It is a common misconception that the higher you go, the less fuel you burn, but imagine this for a second.. And this is based on an actual flight recently.

A 10hr+ flight from Western Africa to the US. The flight is planned at FL320 across the pond. The crew takes off, and ask for a higher altitude when approaching the Atlantic, becuase their actual pyld was much less than planned at. The cneter offers them FL380 and they take it. Up to this point , the crew was running exactly on the dot in terms of fuel burns and time. Now cruising at a much higher altitude, the plane hit a major headwind from a pretty nasty jetstream.... To make a long story short, the flight arrived almost 35 minutes behind schedule and very close to min fuel.

The point is, while in zero wind conditions, the higher you get the less fuel you burn, in the real world, you have to consider the actual winds.

411A
18th May 2006, 23:04
If you, as the pilot flying, reach around behind and have a look at the large book(s) that say 'Aircraft Flight Manual' aka AFM, you will find, in the performance section, a series of charts/graphs that will lead you in the right direction, to provide a series of scenarios for max range, max endurance, min flight time, etc, and in addition, many modern (and a few older) FMS's also give this information, depending on aircraft weight...and the more clever ones, winds aloft, among other parameters.

I have lost count of the number of times I have referred new(er) First Officers to the AFM, and the information they gained thereby is...priceless.
In fact, several have mentioned...'gosh, there is a LOT in here, I wonder why the company didn't tell us about it?'

I wonder also, for the info is so basic that every pilot should KNOW this, from the old gray (but new to the type) Captain to the fuzzy cheeked First Officer.

In the Lockheed TriStar, it has a bright orange or yellow cover, which says 'Lockheed California Company' on the front and EVERYTHING you need to know about performance issues or indeed aircraft systems/limitations/operational procedures are included in the two volumes.
A great deal of time and expense were invested in producing these manuals, and pilots really do need to have a look, every once in awhile.

Saying it another way...RTFB.


PS: I speak here of Lockheed/Boeing/Douglas aeroplanes, perhaps Airboos machines are a tad....ah,lacking.
Dunno.:E

wondering
19th May 2006, 00:04
@411A,
no disrespect, the AFM is obviously the first resource when checking for optimum altitude. And I do check numbers in the AFM once a while :ok: However, me thinks elpilote is asking where these numbers/graphs are coming from. What´s behind them. I am sure the CAA/FAA won´t be impressed when answering that sort of question on a test with: 'Well, check the AFM'.
@mutt,
what I was trying to get at was that at one point, be it Mcrit, Mmo or some other speed in that ballpark, the increase in drag (specifically wave drag) will be prohibitive for the TAS required to maintain optimum AoA.

Old Smokey
19th May 2006, 14:17
Mutt,

I believe that Old_smokey stated that EVERY airliner he had ever flown flew FASTER than the Mcrit

I've been mis-quoted!!!!:eek:

What I said was "ALL cruise Mach Numbers are above Mcrit, even Maximum Range Cruise". I could also have said "ALL cruise at a CAS are below Mcrit, even Maximum Range Cruise".

Yep, I'll have to stick to my original quote, when at a Pressure Height where the tangent of the line drawn to the Drag Curve from the 0/0 origin is below Mcrit, then we cruise at a CAS. When at a Pressure Height where the tangent of the line drawn to the Drag Curve from the 0/0 origin is above Mcrit, then we cruise at a Mach Number. So, if I'm cruising at a Mach Number (and not a CAS), I'm above Mcrit, and this is the case 99% of the time. Once in a while we get a low and slow sector.

Regards,

Old Smokey

hawk37
20th May 2006, 11:36
Think in terms of angle of attack. In general terms, there is one optimum AoA for max range regardless of weight.
Is this really correct? Certainly one aoa for max L/D speed, reqardless of weight, as long as mach effects are not a player. But does aoa remain constant during cruise at max range speed? Neglecting wind/temp changes etc.
Hawk

wondering
20th May 2006, 13:44
I remember reading an article about a Falcon 20 with an autothrottle which was biased to hold optimum AoA. Apparently, the folks got an impressive fuel economy flying a sortie from the US East cost to the West coast which would not have been possible otherwise. I would think as the airplane got lighter speed must have decreased since they were strictly flying an AoA. I reckon fuel economy would have been even better if they had step climbed as well.
Since normal operations are usually flown at a constant Mach number, AoA will change since the airplane gets lighter. Looking at the long range cruise numbers in my AFM, speed will be higher for higher weights and lower for lower weights. There is one best range/long range Mach number for a specific weight.
Not exactly sure what a particular FMS presents as max range speed. However, I think it would not be unreasonable that it presents an 'average' best speed for a particular sector flown. Just my guess.

hawk37
21st May 2006, 13:21
Interesting thought, an autothrottle responding to aoa inputs. Can only imagine what type of human factors/mis inputs could lead to a recipe for disaster!!
I'm not convinced there is one aoa that can be maintained as weight decreases, to give maximum range. Assuming of course that pressure altitude/geometric altitude and temperature remain the same, with no wind.
While some may claim so, I've yet to see a convincing argument. Much like the "equal transit" theory of airflow over an airfoil.
My "feel" for aviation tells me that to attain maximum range, as weight decreases, one should also decrease aoa.
Hawk

Old Smokey
21st May 2006, 15:17
I have a feeling of deja vu that I'm going into the world of Mcrit and beyond again. The constant AoA theory would work just fine for an aircraft that did not operate in the transonic region, i.e. below Mcrit. For an aircraft operating in cruise above Mcrit (and that's just about all jet aircraft at NORMAL operating levels), AoA alone is not enough to consider.:*

This one requires a picture, a picture is worth a thousand words. Stand by for said picture/s with associated text within a day or so. (I need to 'borrow' my son's web site to post the pictures, and he's aviating just now).:ok:

Regards,

Old Smokey

westhawk
21st May 2006, 21:39
Interesting discussion, since I think about this from time to time. As I am by no means an expert flight planner, but rather a simple pilot who must plan his own flights, I really try to pay attention to this area. Below are a few observations I have made. Please feel free to comment on them or point out any glaring errors in my logic or understanding of the concepts involved.

I get the distinct impression that that not all airframers take the same approach to the problem of determining a maximum range flight profile for planning purposes, and may not define optimum cruise altitude according to the same parameters. This may present a problem when attempting to universally define these terms. Consequently, the advice to consult the AFM performance planning section will guarantee that one is using the performance terminology as defined for that particular airframers product.

On one of the two aircraft I fly, the maximum range cruise profile stipulates a reducing mach number increment for each reducing increment of flight weight as fuel is burned off. An optimum altitude is assumed as determined by flight weight and atmosperic SAT. The resultant percentage of decrease in TAS between hour 1 and hour 6 appears to be aproximately equal to half the percentage of flight weight decrease during the cruise. AOA appears to increase throughout the flight. Of course, fuel flow decreases with each step climb and thrust reduction until by hour 6, cruise fuel flow has reduced by 23%, TAS has reduced by 13% while flight weight has reduced by 27% from initial hour 1 cruise. Following this profile appears to add perhaps 5% to the still air range of this aircraft compared to a constant long range mach or TAS profile. It's a draggy airframe and using this profile makes the fight seem interminable when we must use it to achieve maximum range!

The other airplane I have flown maximum range profiles in calls for a constant TAS throughout the cruise phase of flight with the obligatory step climbs. Much simpler planning! In this integrated EFIS aircraft, FMS calculated optimum cruise altitude is predicated purely upon fuel burn per NM equivalent still air distance (ESAD) and as limited by weight, altitude and pre-programmed or assumed temperatures at each altitude. Interestingly, the fuel flow reduces by a similar percentage per reduction in flight weight as in the other aircraft while this profile maintains a constant TAS as opposed to decreasing with weight. AOA is ever decreasing at each altitude increment as fuel is burned off until the next climb as dictated by the FMS optimum altitude computation. Once MOA is reached, (about 1/2 way through a max range flight) thrust is continually reduced to maintain scheduled TAS. The aircraft will easily exceed it's optimum altitude at any time, but will require a greater fuel flow to do so. (sometimes done to top weather or winds.)

In both cases, the max range profiles for these aircraft are predicated upon still air distances. They are based (for these aircraft) only on aircraft performance and no consideration is given to the effect of wind on either optimum altitude or cruise speed schedule. Consequently, optimal altitude and speed schedules provided by planning providers like Universal or Jeppesen for the actual conditions of the day may vary somewhat from the "book" figures. It's no small wonder that so many sophisticated flight planning software packages and service providers abound industry wide. Complicate the matter further by adding company specific cost indexing and the matter now completely eludes the ability of the majority of ordinary line pilots I know to maintain a grasp on with so many factors to be considered. It has become a specialist area of expertise where computers spit out the end product.

I am simply interested in being capable of determining whether or not the numbers make sense, and if not, why not? It is merely my intention never to be led down a primrose path by numbers spit out of a machine which were based on spurious input or invalid assumptions.

The bottom line in all this will come down to mission profile. Actual optimum altitudes and speed schedules will vary with what cost and mission performance factors are to be optimized, and under the conditions of the day.

As the US auto manufacturers are fond of saying, "Your actual mileage may vary!"

Best regards,

Westhawk

Old Smokey
22nd May 2006, 02:55
.........the maximum range cruise profile stipulates a reducing mach number increment for each reducing increment of flight weight as fuel is burned off..........

Not always so Westhawk, but true most of the time. If we are discussing fuel related mission profiles (e.g. Maximum Range Cruise and Long Range Cruise), at the altitudes that we're flying we are slightly above Mcrit, by about .02 to .04 depending upon the aircraft. For example, if Mcrit was 0.72, we'd find MRC typically around M0.74 or so at our Optimum Altitude. Mcrit, therefore, assumes a high degree of significance in establishing the target MRC/LRC speed. Factors affecting Mcrit are therefore important.

Whilst we tend to think of Mcrit for a particular wing as constant, it does vary over a small range. Mcrit depends primarily on two important factors, i.e.

(1) The actual Mach Number (obviously), and

(2) The angle of Attack (AoA).

At light weights through to Medium to Medium + weights, Mcrit varys very little. At very high weights, AoA must be increased because of the greater weight, and with this, even at the same speed as for lower weights, greater acceleration of air over the wing occurs, leading to an earlier encounter with Mcrit. Using 'standard' Mcrit of 0.72 as an example, at the high weight it would not be surprising to encounter Mcrit as low as 0.70 to 0.71. MRC and LRC will still be higher than this 'reduced' Mcrit, but (and it's an important but), MRC/LRC will be LOWER than it would be at a reduced weight.

In summary, because of the above, it's not uncommon to see scheduled MRC/LRC speed at high weights to actually INCREASE as weight reduces due to burn-off. This increasing speed schedule continues to the point where Mcrit becomes relatively constant, after which MRC/LRC decreases with decreasing weight in the conventional sense. This 'abberation of conventionality' is usually found in the top 10% or so of the cruise weight band for the aircraft.

Regards,

Old Smokey

mutt
22nd May 2006, 05:22
the max range profiles for these aircraft are predicated upon still air distances.

In the FMS equipped aircraft, try changing the Cost Index Value to 0, also input route winds from the flight plan, then review the optimum flight level.

Mutt

westhawk
22nd May 2006, 05:37
Thanks Old Smokey, that does much to clarify the relationship between Mcrit and both the optimal speed and altitude according to weight and temperature for maximum still air range. The effect of winds aloft adds a whole new twist to the problem and is worthy of many separate discussions.

Best regards,

Westhawk

westhawk
22nd May 2006, 05:59
In the FMS equipped aircraft, try changing the Cost Index Value to 0, also input route winds from the flight plan, then review the optimum flight level.
Mutt

Thanks Mutt, I will try that at the next opportunity I get to fly this aircraft. I would always input the flight plan winds on longer sectors but never noticed a change in the optimal altitude displayed. I was working on a cost index analysis when that job ended, so one had not yet been set. Next time I will look for that. These days, I fly the older jet with Garmin 530/430 GPS/Comms. Somewhat less sophisticated to say the least. Wonderful boxes for prop airplanes, but not ideally suited for jet ops I'm afraid.

Best regards,

Westhawk

Intruder
22nd May 2006, 06:06
But does aoa remain constant during cruise at max range speed? Neglecting wind/temp changes etc.
A modern FMS attempts to do so, assuming 0 wind and calm air...

Regarding the first (wind), the airspeed for max range will have to increase in a headwind and decrease in a tailwind. The limiting speeds (or AoA) will be the speed at which the drag curve begins to rise sharply for the headwind, and max endurance speed for the tailwind.

Regarding the second (calm air), AoA will not truly remain constant in any turbulence, because different amounts of lift (and therefore AoA) are required at different load factors at a given speed. Therefore, it is better said that the average or nominal AoA will remain essentially constant.

If you set an FMS to fly at ECON Cruise at Cost Index = 0 (Max Range), the speed will decrease with decreasing weight, and adjust for winds. I assume there is also a temperature factor, but I don't know what the adjustment will be.

Also remember that we fly with the "artificial" constraint of constant altitude (or step climbs to discrete altitudes). Ideally an FMS would also adjust altitude to the current EXACT altitude for the weight and temperature, but in reality it adjusts for the current altitude and gives its best estimate of the optimum altitude. When that optimum altitude equals one to which we can be cleared, we climb/descend to it.

MasterGreen
22nd May 2006, 10:27
This started as wind trade - and I have been remiss recently for not keeping upto date on these things (here). Below is a link from a web page made up from a write up of mine (here in PPRUNE) of a few years back - it is probably still in the archive. It says most of what the original query wanted as an answer and is still as true today as it was a few years back when I wrote same. The laws of physics not having changed over much since then :)

http://www.iasa-intl.com/wtt.html

MG

Old Smokey
22nd May 2006, 22:10
To go right back to the original question, a quick 'rundown' on range profiles used by jet aircraft is warranted. It is assumed that in referring to Optimum Altitude, reference is made to Fuel related optimum altitudes, the two most important of the fuel related profiles being Maximum Range Cruise (MRC) and Long Range Cruise (LRC). Maximum Range Cruise is an aeronautical 'Absolute', it is the profile which provides, as the name suggests, the absolute maximum range possible. Long Range Cruise, however, is a convenient speed (now falling out of favour) which gives much improved speeds over MRC, but at a fuel penalty of 1% as compared to MRC, i.e. LRC provides 99% of the range possible with MRC.

By definition, maximum range occurs when the lowest amount of fuel is consumed for the distance flown, which is directly related to Fuel Flow divided by True Air Speed if considering the still air case, or Fuel Flow divided by Ground Speed if considering the effect of wind.

Fuel Flow is directly related to Thrust, and Thrust must equal Drag in a stable cruise situation.

If we examine drag curves for an aircraft, it is possible to ascertain the relationship between Speed and Drag, and therefore Speed and Fuel Flow.

Below Mcrit, drag is directly related to Equivalent Air Speed (EAS), that is, for a given weight, the EAS for MRC will be constant right up to the Pressure Height where Mcrit is encountered. If the first diagram is examined,

http://www.gunboards.com/forums/uploaded/Vulch/200652217448_DIAGRAM%201.jpg

Any line drawn from the Zero / Zero origin (0/0) to intersect the Drag curve in 2 places (e.g. the LRC example in the diagram) will have 2 intersections, with differing EAS and Drag / Fuel Flow for each intersection. The GRADIENT (Steepness) of the line drawn indicates the specific range of the aircraft. For example, a high Fuel Flow paired with a relatively low speed is indicative of poor specific range, a lower Fuel Flow at an increased speed is indicative of improving specific range. If we continue to reduce the gradient of the line from 0/0 to the point of tangency with the Drag Curve, we are at the lowest possible gradient, and it is the speed at the point of tangency that represents MRC. In the diagram (and it is a 'true' diagram, not a sketched one), for the particular weight for that drag curve, we can see that Maximum Range Speed is 248 knots EAS. For the example chosen, Mcrit for the aircraft is M0.73, so, up to 32,583 feet, where 248 KEAS = M0.73, MRC will be 248 KEAS at all altitudes for this weight. This will require a varying CAS schedule, i.e.

10,000 ft = 249.9 CAS : 20,000 ft = 252.9 CAS : 30,000 ft = 258.0 CAS : 32,583 ft = 259.8 CAS / M0.73

FLIGHT ABOVE Mcrit - With increasing Altitude (Pressure Height) beyond the point where MRC EAS passes Mcrit, additional wave drag is encountered, and drag divergence occurs, i.e. for the Pressure Height in question, there is a whole new drag curve, being the 'original' drag curve up to Mcrit, then followed by initially quite slow drag divergence with small Mcrit exceedance, but later diverging much more aggressively. If you refer to the second diagram, and it's expanded view centred on the area of interest, -

http://www.gunboards.com/forums/uploaded/Vulch/200652217510_DIAGRAM%202.jpg

EXPANDED VIEW

http://www.gunboards.com/forums/uploaded/Vulch/20065221765_DIAGRAM%203.jpg

Three 'new' drag curves will be seen for 35000, 40000, and 45000 feet. (The curves are, again, mathematically correct, not sketches). It will be seen that the point of tangency for the line drawn from the 0/0 origin tangential to the transonic drag curve results in MRC slightly above Mcrit at F/L 350, but increasing to M0.77 at 40,000 feet and M0.80 at 45,000 feet (the latter two being substantially above Mcrit). It's worth noting that, for the example given, drag at 40,000 and 45,000 feet is less than that for 35,000 feet, even though the Mach Number is high, wave drag is high, but the drag arising from the low speed polar is low. (The curve 'belongs' to a fairly high flying aircraft, most conventional airliners exhibit the same characteristics about 5,000 feet lower). Mutt, therein lies my assertion that in 99% of jet operations, we 'live' above Mcrit, weeelll, not always!

By these means, it may be seen that for a given weight, MRC speed can be established for any useable altitude. That satisfies the requirements of aerodynamic efficiency, what must now be examined is engine and Fuel Flow efficiency.

Jet engines operate at their optimum Thrust Specific Fuel Consumption (TSFC), i.e. the least amount of fuel consumed to produce each unit of thrust, at quite high engine speed. This is typically in the region 90-93% N1, any lower or higher engine speed will result in poorer TSFC, with the worst 'off-optimum' penalty being found at higher than optimum engine speeds. Although the aircraft may be flown at the appropriate MRC at a low altitude, e.g. 10,000 or 20,000 feet, the amount of thrust available will be well in excess of that required, and will have to be 'throttled' to a lower than optimum TSFC engine speed. In short, although at the aerodynamic optimum for the Weight and Altitude, the engine will be well 'off optimum' TSFC. As altitude is increased, engine speed must be increased to maintain the required thrust in the reducing density, with consequential increase in engine TSFC efficiency. When the aircraft reaches a level where optimum TSFC engine speed is required to maintain the MRC speed, the aircraft is at OPTIMUM LEVEL.

As weight burns off, the AoA required will be less due to the lower weight, and MRC speed reduces (usually, but not always). The drag curve moves down, and to the left (by a lesser amount). To maintain MRC speed, engine thrust must therefore be reduced, to below optimum TSFC engine speeds. Although range will be increasing if the level is maintained due to the lower fuel flow, we are not doing as well as we could, we are 'off optimum'. The solution, in an ideal world of no ATC constraints, would be to maintain the engines at optimum TSFC N1, and allow the aircraft to cruise climb at MRC CAS or Mach Number. In short, Optimum Level will steadily increase in still air, due to the 'need' to maintain the engines at optimum speed if we are to obtain the maximum possible range.

Similar arguments apply to other fuel related Optimum Levels, for example, LRC.

EFFECT OF WIND - Wind effect may also be seen on the same Drag Curve. The Horizontal Axis of the Graph is speed (EAS in this case), and the effect of wind component is simply to shift the 0/0 origin. The 'tricky' bit is that the graph is for EAS whereas Wind Component is a TAS effect, and a wind component must be converted to the EAS equivalent. A 100 knot wind component is equivalent to 56 knots EAS at 35,000 feet at ISA. For a Headwind, if the line of tangency is projected from 56 Kt EAS to the Drag Curve, the new MRC for Ground Miles per unit of fuel may be found (at a HIGHER Mach Number). Conversely, for a Tailwind, if the line of tangency is projected from -56 Kt EAS (Left of the origin) to the Drag Curve, the new MRC for Ground Miles per unit of fuel may be found (at a LOWER Mach Number). Modern generation FMCs do calculate this, but a risky mix of 'real world' ground data remains mixed
with still air data in most FMCs, beware!

A piece of cake!

Regards,

Old Smokey