hi guys, im looking for some assistance with something – can someone please explain in as much detail as possible about the optimum cruising altitude of an aircraft. now obviously different aircraft will cruise at different altitudes, but using the 737-800, can someone go through the entire process of figuring out that optimum altitude. by optimum, i mean the altitude where fuel consumption is at its lowest, and most efficient.
this is part of a massive assignment that i have to do, and i cant seem to get a straight answer out of three or four hours worth of google searching.
now as aircraft weight always decreases due to fuel burn, i guess i would be looking for the optimum altitude at an instantaneous point, rather than over a span of time. i know that in level flight at a constant velocity, the weight must always equal the lift, and the thrust must always equal the drag, assuming ISA. also, i know that at higher altitudes, this always holds true, along with a constant L/D ratio, assuming that AoA is the same, which it should be if velocity is the same. however, can someone explain how and why TAS is greater, and power required is greater at higher altitudes? and what exactly is meant by ‘power required’? there is less oxygen at higher altitudes, so to maintain the same speed, the throttle must be set higher, but how does that attribute to a greater power requirement if you are merely compensating for something?
also, if someone can provide some sources, that would be great. i need to be able to write all this in easy to understand language so technical jargon for any readers is minimised.
i would greatly appreciate it if someone shed some light on all of this.
as this is my first post i guess i should have a short obligatory intro to myself – hungarian-australian living in sweden, 18 years, studying for PPL, working towards ATPL, currently in a C172, but also flown C152’s and PA28’s.
By: hiigaran - 29th November 2010 at 05:54
thanks for the replies guys. i may need some time to process this information, but im sure i might have some follow up questions.
By: Arabella-Cox - 27th November 2010 at 21:35
A few more considerations (will be taken into consideration by the FMC):
Engine efficiency
Lift/drag ratio
Try get hold of “Mechanics of Flight” by A C Kermode or “Modern Airmanship” by Van Sickle. (You might be able to “look inside” on Amazon)
By: Pacific flyer - 26th November 2010 at 07:53
There are basically 2 altitudes calculated for any aircraft type, usually by the FMC (Flight Management Computer). One is maximum altitude, and the other is optimum altitude. These altitudes can also be extracted manually from performance charts by the pilots.
Let us first look at maximum altitude. This is limited by
Generally the lighter an aircraft is, the higher it can fly, however for each aircraft type there is a maximum certified altitude (41,000 feet in the case of the B737-800, 39,000 feet in the A-320, and 37,000 feet in the B737-400). As air temperature increases above standard (standard is 15 degrees C at sea level, decreasing to -57 degrees C at 36,000 feet, the level of the tropopause), the density of the air decreases, and hence it is less able to provide lift.
Optimum altitude is limited by
To explain this in a little more detail, let us consider 2 aircraft of an identical type, both about to depart London. To keep it in perspective, let’s say they are both B737-800’s, and each is carrying 150 passengers.
The first aircraft is bound for Manchester, distance of just over 130 nautical miles, whereas the second is bound for Cairo, almost 2000 miles distant.
In the case of the Manchester flight, it will only carry enough fuel to fly to Manchester, divert to an alternate, and a certain fixed fuel reserve. Carrying fuel in addition to these requirements would entail additional cost (increased fuel burn), so unlike in a car, aircraft determine a specific fuel load for each trip. Thus the takeoff weight for this aircraft might only be 62 tonnes.
The 737-800 can climb to 39,000 feet at this weight, however the time and fuel burn required to reach 39,000 feet means that it would probably fly all the way to Manchester before reaching this altitude. Hence the FMC would calculate an optimum altitude for this comparatively short flight, and it would be in the order of perhaps 28,000 feet.
The Cairo flight on the other hand would be more likely to have a takeoff weight of 75 tonnes, due to the greater fuel load required, which would limit it to a maximum of around 35,000 feet. As the aircraft burns fuel, and thus reduces weight, it could climb higher, so about 2 hours after takeoff it could climb to 37,000 feet, and after another couple of hours to 39,000 feet. Thus optimum altitude varies as a function of aircraft weight. In order to achieve maximum efficiency, aircraft are best flown at, or as closely as possible to optimum altitude.
Another couple of variables; as our Cairo flight flies into warmer air (I.e. less dense air), optimum altitude may decrease. In practice, this may mean that having already climbed to say 37,000 feet, the flight may briefly be above optimum altitude when it flies into warmer air, however this would be only a very temporary situation, given that optimum altitude is constantly increasing as fuel is burned.
Another variable affecting optimum altitude can be wind. Whilst the benefits of a tailwind are obvious, it can sometimes be prudent to fly at a lower altitude, consuming more fuel per hour, than to climb up into a stronger headwind. This is because the time that the aircraft is in the air (and thus exposed to the headwind) is reduced at lower altitude.
I hope this helps to explain a little about optimum altitude. If my explanation seems long and complicated, you will understand why it is much easier to extract these figures from an FMC than to calculate them manually!
By: hiigaran - 25th November 2010 at 08:07
this part i knew of, which is why i need to make things as simple as possible. regarding weather, i assume standard atmosphere. as for the weight issue, i guess i would have to use some aircraft types for examples then? what are the three most popular aircraft in service?
By: Ship 741 - 24th November 2010 at 22:39
“higher is always better”
just a joke, too complex to explain in a succinct manner, but in general, most modern airliners fly most efficiently in the upper 30’s, but are sometimes too heavy to get there, or the winds are stronger than normal, in which case it is more efficient to fly lower. Most long range flights start off in the low 30’s and climb slowly (“step climb”) as they burn off fuel/weight.
By: hiigaran - 24th November 2010 at 20:30
oh man i love you already!
By: Nashio966 - 24th November 2010 at 20:29
And also a fan of the best space strategy game series “Homeworld” !!! 😀
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November 24, 2010 at 8:27 pm