Best Altitude

[767bill]

Hi again,
My question is what the best altitude to fly at is assuming that its not possible to ride the Gulf Stream (or other favourable winds) and that weather at lower altitude isn't too rough. In particular how much energy (and therefore fuel) is used to get to different altitudes compared to travelling horizontally and is there any kind of formula for ideal altitude -v- length of flight?(assuming we are talking about a jet that can fly up to about 40,000 ft)
Thanks,
Bill

[Intruder]

Depends on airplane, gross weight, air temperature, winds, and a bunch of other factors. There is no single answer.

[Trentino]

gosh,maybe its the beer but I am having trouble understanding your post. Nothing against you, sometimes I cant decode what I read.....let me try to answer best I can.
I assume you are asking what are optimum altitudes to fly at and how much extra is burned if we are not at them.

I will keep this as simple as possible as what I will say applies to all aircraft piston/turbine, flying transonic-subsonic.

To operate an aircraft efficiently, all aircraft need to achieve various forms of optimums,some of these are:
1.Optimum Angle of attack
2.Optimum engine speed (optimum RPM/optimum N2)

A.If flying below optimum altitudes. The Angle of attack of the aircraft will be lower than optimum because the air is denser.
The lower angle of attack means that drag is higher than if the AOA was higher. The solution, Slow down. But if you do that,your flight time goes up and so does your fuel consumption.
If flying above optimum altitude. The angle of attack will be higher than optimum and again, drag will be higher. The solution is to speed up but then fuel burn will increase above optimum as well.
(Low AOA drag is caused by parasite drag while high AOA drag is caused by induced drag)

B. Optimum turbine speeds for jets are the low to mid 90's
If flying below optimum altitude, say FL250 on a generic jet you may only need 83-88% N1. Your turbine speed/ground speed will be low but your fuel burn will be relativly high.
If you are flying above optimum, your turbines will be straining more than necessary for thrust and therefore need more fuel
Think of it like you are driving your car. Less than 55mph(optimum)
you are going slower than optimum but not really getting much out of your gas mileage. If you go above 55mph your fuel flow will increase out of proportion with speed.

Did I confuse anyone? Im confused!
If you want to know more about this fascinating topic try and pick up 'Handling the big jets' NOT 'Flying the big jets'

[Rainboe]

You have tables that let you work out the maximum cruise altitude for the weight you are at. The most efficient cruise altitude is a bit below this. These days, computer databases maintain an updated wind pattern for pretty much the whole Earth surface (the bits that count), and this is factored in so that sometimes it is better to stay lower and in a strong tailwind or avoiding a headwind- this is common ex Bangkok/Singapore to Europe flying westwards over north India- often it's better to stay below 28 or 30,000' for many hours after take-off to avoid higher headwinds higher up. Usually now it's computer flight plans that determine optimum cruise altitudes- it's not just a question of flying as high as possible. Getting yourself into a Jet Stream is always worth while- sometimes it's worth flying further to do so, but they can be very broad and deep indeed, so it's the computer flight planning machine that works out the optimum route and altitude. It also takes into account navigation charges- it can be worth flying further to avoid expensive countries!

[767bill]

Thanks, Trentino and for reminding me of the principles of flight and mechanics. The combination might involve some mind blowing mathematics... I have Handling the Big Jets and very good IMO.
I agree that perhaps my question wasn't as succinct as it might have been.
What's been keeping me awake at nights is, assuming no wind (hypothetical I know), no air traffic restrictions etc. and lets say a jet close to maximum load, then surely there must be a distance at which it's not worth going up to 35,000 ft because of what it cost to get up there both in fuel and time. I just wondered what that distance was, approximately?...

[Trentino]

Ahh Ok 767Bill, I didnt mean to offend your intelligence.. I understand now.

Well like said before the higher the better.

There are charts out there that actually give you max altitudes for a given distance. there is a distance index and a time index etc...
by looking at the distance you want to fly you can find your optimum altitude. There are also time, fuel and distance to climb charts.. you can refer to this too for optimal altitudes..but they are not the best.

One of my old professors, total cocky jerk told me that in 'his' G5 the most efficient way to go from A to B was not in a direct line but rathar in a circumnavigational fashion, the rationale behind it was being able to climb higher into thinner air for the cruise portion.

[Intruder]

surely there must be a distance at which it's not worth going up to 35,000 ft because of what it cost to get up there both in fuel and time. I just wondered what that distance was, approximately?
Same answer as before -- it depends on the airplane. Some won't get to 35,000' at max load; some will have a higher cruise altitude.

The minimum practical distance to climb to optimum cruise altitude for a given configuration is the distance it takes to climb to that altitude on a normal climb profile (again, varies with airplane) plus the distance it takes to descend on a normal profile (commonly, distance in NM = altitude in 1,000' plus 10 NM). Again, because of engine differences, some airplanes may benefit in total burn with the climb followed immediately by the descent, while others may benefit by 10 or 20 minutes at [a slightly lower] cruise altitude.

[411A]

Yep, deck angle, which directly relates to AoA, in the cruise.

Now, for an example, let's look at the Lockheed TriStar, the standard body model, not the -500.

During flight test, it was found that at the 'best' altitude for the most efficient cruise flight, the deck angle was, 3.2 to 3.5 degrees.
In addition, for the respective optimum deck angle, the desired cruise speed was on the order of M.845.

Slower, resulted in more fuel burn, for the sector.
Faster, also higher fuel burn but not as much as flying slower.
The TriStar, you see, was designed as a high speed cruiser, from the outset. It was also the first wide-body civil jet transport with a true laminar flow wing.

The FMS fitted to the -200 TriStar (a well designed Litton unit, installed by SaudiArabian, on all their TriStar aircraft), offered LNAV, VNAV (for climb/descent, but excluding planned crossing altitudes) and thrust management, and included software to enable the pilots to determine the optimum cruise altitude, dependant on winds, temperature aloft, weight, cruise speed desired, fuel price, etc and also offered a step-climb function, which was generally disabled, when the aircraft was close(er) to the planned destination.
How close?
Usually within three hundred miles, or so, IE: the fuel used to climb 4000 feet (500KG, approximately) was more than staying at the present altitude, to the planned destination.
The formula used by the software?
I don't know, but the FMS worked to perfection.

Lockheed/Litton....way ahead of everyone else.:ok:

Having said this, on the B707, specific flight planning charts were provided, which provided the same general information in tabulated form.
These were called 300fan flight conduct charts, and worked well.

[enicalyth]

Very quick, very basic spreadsheet based on Breguet's Law and ISA conditions. All other factors such as temp, wind, nav fees etc ignored for the present (what present?). So if you want range...

A large aircraft loosely based on a B747-400 has ISA performance as shown at 300 tonnes weight and Mach 0.85 .

All else being equal fly where (V/c)*(L/D) has the greatest value, i.e. the most nautical miles per unit of fuel.

CL = lift coefft
CD = drag coefft = Cdo + Cdi + Cdcc
= 0.0145 + (((CL)^2)/20.73) + (0.0007+0.005*((CL)^2))

V = speed ktas
c = specific fuel consumption lb/lb-hr, kg/kg-hr

FL V c CL Cdtot L/D (V/c)*(L/D)
290 503 0.64 0.342 0.0214 15.981 12563
300 500 0.63 0.361 0.0222 16.261 12929
310 498 0.62 0.377 0.0228 16.535 13303
320 496 0.61 0.394 0.0235 16.766 13649
330 494 0.60 0.413 0.0243 16.996 14005
340 492 0.59 0.433 0.0251 17.251 14391
350 490 0.60 0.455 0.0262 17.366 14182
360 487 0.61 0.479 0.0274 17.482 13977
370 487 0.62 0.501 0.0286 17.517 13773
380 487 0.63 0.524 0.0298 17.584 13607
390 487 0.64 0.550 0.0313 17.572 13385

Best of luck

the "E"

[Old Smokey]

Tut tut enicalyth, didn't hand back your B747-400 manuals when you retired?

Expect a knock on the door at about 0230, barking dogs, wailing sirens, all that stuff............:O

Regards,

Old Smokey