Topic Author
Posts: 344
Joined: Tue Sep 16, 2008 9:40 pm

### How Is Aircraft Range Determined?

I know there is probably some einstein formula that manufacturers use to calculate it, but can someone "dumb" it down for me? Is it calculated based on no wind, perfect weather, average payload? Obviously, different conditions will affect an aircraft's range, but when we read say, the 77L's range is 8,865nm, what is that based on?
"But this airplane has 4 engines, it's an entirely different kind of flying! Altogether"

timz
Posts: 6233
Joined: Fri Sep 17, 1999 7:43 am

### RE: How Is Aircraft Range Determined?

There's no one formula. "Range" depends first of all on the assumed payload-- you could assume full seats and baggage but no cargo, or you could assume full payload. Once you've decided what payload to assume, range will still depend on how much reserve fuel you need.

Any "range" figure you read probably assumes the aircraft is taking off at it's maximum allowed weight. At many airports on many days it can't do that-- so that's a further complication.

But yes, if you assume the aircraft is at maximum ZFW and MTOW, and you assume a standard day and no wind, and you assume some sort of standard reserve fuel, then you ought to be able to pin down a fair value for "range". But most figures you see published haven't been done that carefully.

[Edited 2010-09-03 16:23:10]

tdscanuck
Posts: 8572
Joined: Wed Jan 11, 2006 7:25 am

### RE: How Is Aircraft Range Determined?

 Quoting c5load (Thread starter):I know there is probably some einstein formula that manufacturers use to calculate it

It's not actually a formula, it's a giant lookup table. You start with the airplane state (weight & fuel load), weather (mostly winds), and flight profile (which determines reserves), then calculate the fuel burned for each stage of flight for steadily increasing ranges until you're landing with just reserves.

The trick is in the calculation of fuel burn for each stage...there's no good theoretical way to do that; the FMC just looks it up from giant tables derived during flight test.

Typically yes, although they include a reserve that covers up non-perfect weather. For example, the payload range curves on pg 3 here: http://www.boeing.com/commercial/airports/acaps/777rsec3.pdf

Are derived using the information in the block at the top left:
Standard Day (defines the temperature & pressure)
Zero Wind (self explanatory)
Step climbs at 2000' (different intervals give different cruise fuel burn)
Normal bleed & power (different configuration will change fuel burn)
Typical mission rules (normal commercial IFR reserves)

 Quoting c5load (Thread starter):Obviously, different conditions will affect an aircraft's range, but when we read say, the 77L's range is 8,865nm, what is that based on?

It's usually the range based on the above requirements when you have full fuel tanks and then add payload until you're up to MTOW (this is usually less than max payload). For a 77L, 8865nm is roughly the full fuel/MTOW range with one auxiliary fuel tank. See the above linked document and follow the "1 Aux Fuel Tank" line up until it hits the Brake Release Gross Weight Line.

Boeing lists the maximum range for the 77L as 9395nm, which is full fuel with 3 aux tanks loaded to MTOW, which is about 409,000 lbs of payload (payload is fuel + passengers + cargo). If you take the fuel away, you find you're carrying about 49,500 lbs of cargo+passengers.

If you go full fuel and no cargo+passengers and don't carry reserves (economically useless, but the true "maximum range") the range would go up to something like 10600nm.

Tom.

[Edited 2010-09-03 17:49:57]

soon7x7
Posts: 2267
Joined: Thu May 04, 2006 10:51 am

### RE: How Is Aircraft Range Determined?

 Quoting tdscanuck (Reply 2):Step climbs at 2000' (different intervals give different cruise fuel burn)

Are step climbs considered normal operations?

Fly2HMO
Posts: 7187
Joined: Sat Jan 24, 2004 12:14 pm

### RE: How Is Aircraft Range Determined?

 Quoting c5load (Thread starter):I know there is probably some einstein formula that manufacturers use to calculate it, but can someone "dumb" it down for me?

It' really not that complicated. To get a good approximation all you need is the plane's average fuel flow, fuel on board, and average block speed (speed gate-to-gate). That's it. To get even more accurate you figure in winds, fuel burn variations per the hour, configuration (bleeds and such) etc etc

Jetlagged
Posts: 2564
Joined: Sun Jan 23, 2005 3:00 pm

### RE: How Is Aircraft Range Determined?

There is a single equation which can be used to estimate an aircraft's maximum range, the Breguet range equation.

http://web.mit.edu/16.unified/www/FA...L/thermodynamics/notes/node98.html

Range = V * (L / D) * Isp * ln (Wi / Wf)

V = TAS
L/D = lift to drag ratio
Isp is overall efficiency = thermal eff * propulsive eff * combustion eff
Wi = initial weight
Wf = final weight

[Edited 2010-09-04 11:42:24]
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tdscanuck
Posts: 8572
Joined: Wed Jan 11, 2006 7:25 am

### RE: How Is Aircraft Range Determined?

 Quoting soon7x7 (Reply 3):Are step climbs considered normal operations?

Yes. Not step-climbing at all isn't very fuel efficient, so operators do it when the cruise portion is of any significant length. The ideal thing is a gradual climb, but that drives ATC crazy.

 Quoting Fly2HMO (Reply 4):To get a good approximation all you need is the plane's average fuel flow, fuel on board, and average block speed (speed gate-to-gate).

The problem is that average fuel flow is very dependant on weight.

 Quoting jetlagged (Reply 5):There is a single equation which can be used to estimate an aircraft's maximum range, the Breguet range equation.

This works well for the maximum theoretical range, not the the quoted range, since it doesn't include reserves and it doesn't include the fact that L/D changes with weight (and over the course of the flight).

Tom.

Jetlagged
Posts: 2564
Joined: Sun Jan 23, 2005 3:00 pm

### RE: How Is Aircraft Range Determined?

 Quoting tdscanuck (Reply 6):This works well for the maximum theoretical range, not the the quoted range, since it doesn't include reserves and it doesn't include the fact that L/D changes with weight (and over the course of the flight).

It can include reserves if you want. Wf does not have to mean zero fuel weight, it's the landing weight. L/D does change with weight, but then again I only said it was an approximation. You could modify the equation to integrate L/D by weight, and so allow for the change, in much the same way the basic equation allows for weight changes.
The glass isn't half empty, or half full, it's twice as big as it needs to be.

Fly2HMO
Posts: 7187
Joined: Sat Jan 24, 2004 12:14 pm

### RE: How Is Aircraft Range Determined?

 Quoting tdscanuck (Reply 6): The problem is that average fuel flow is very dependant on weight.

Of course. It gets you on the ballpark though. Obviously not good enough for flight planning but good for a quick guesstimate in case of diversions and what not.

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