Aircraft Range

Just a quick question to all you knowladgeble types out there

where could i find information, or could you please provide me with some, regarding the equations i would need to find an aircrafts range at cruise altitude.

aircraft range is not a set figure - many factors deond on how far it can fly - how much fuel it can carry , cruise speed , and relative wind direction (you use more fuel flying into a head wind) - so whilst each aircraft might have various `ranges` combat , ferry etc local factors must be considered.

From Introduction to Flight, John D. Anderson, Jr.

Breguet range equation for a propeller-driven airplane:

R = (n/c)*(Cl/Cd)*ln(W0/W1)

n is the propeller efficiency (actually a greek eta)
c is the specific fuel consumption
Cl is the lift coefficient
Cd is the drag coefficient
W0 is the gross weight of the airplane
W1 is the weight of the airplane without fuel

Note that this is only an estimate since it assumes straight and level flight, and n, Cl/Cd, and c are constant throughout. It is generally accurate to within 10 to 20%.

For a jet it gets a little more complicated:

R = 2*sqrt(2/p/S)*(1/c)*(sqrt(Cl)/Cd)*(sqrt(W0)-sqrt(W1))

p is the ambient density of the atmosphere (actually a greek rho)
S is the wing area

Again this is an estimate since the same approximations as in the propeller-driven case are used.

You also need to factor in such things as payload, external stores (for combat aircraft) and fuel. (Some fuels have more energy in them than others. When Boeing was trying to set the record for distance flight with the 777 they tried to get fuel from a specific refinery that had more energy per pound that from other sources.

Also for propeller aircraft the age of the rotor can make a difference as well.

You also need to factor in such things as payload, external stores (for combat aircraft) and fuel. (Some fuels have more energy in them than others. When Boeing was trying to set the record for distance flight with the 777 they tried to get fuel from a specific refinery that had more energy per pound that from other sources.

Also for propeller aircraft the age of the rotor can make a difference as well.

Even taking into account the above posts, there are a huge number of other factors that determine a planes range:

- airframe efficiency
- time of day
- temperature
- angle of attack
- etc

For example, a 777-200ER dispatched at 4am with a full fuel load will fly further than a 777-200ER dispatched at 12PM with a full fuel load.

Why? Because the specific density of the fuel is different in the morning than it is in the evening - as the temperature rises, you gain less usable fuel per liter or gallon as it expands.

This is why civil airliners are dispatched with the fuel load to get from point A to point B, plus the diversion requirement, plus an extra 5% or so.

Originally posted by RichardPrice
Even taking into account the above posts, there are a huge number of other factors that determine a planes range:

- airframe efficiency
- time of day
- temperature
- angle of attack
- etc

What may be deceptive about Breguet's equation is that most of these factors are actually included. Airframe efficiency is included in Cl/Cd, temperature and time of day are included in the atmospheric density, and angle of attack would actually be determined by the weight of the aircraft, the velocity, the atmospheric conditions, the lift coefficient, and the wing area. Note that there is some optimal cruise speed that hasn't been addressed by Breguet's equation, that's a separate issue.

Things like payload would be included in the gross and dry weights, and the fuel would be factored into the specific fuel consuption. A better fuel will provide a better (lower) specific fuel consuption. Of course there are all kinds of other factors that influence it, and it's not necessarily trivial to even estimate it for a given engine.

The trick is getting a good estimate for things like Cl/Cd, specific fuel consumption, propeller efficiency, and so on. There are a number of "hidden" factors, some of them can be easy to determine, some not, but if you can come up with a good estimate of the terms in Breguet's equation, and if you can handle the assumptions made, it will give you a good estimate of the aircraft range, and I think that's all this guy needs. I'm not sure he realized the rabbit hole he was going down by asking a seemingly simple question, but that's life I guess.

reply to post by RichardPrice

Altitude is a major factor in the equation. Less air=less fuel. Jets are very inefficient at low altitude.



[edit on 8-9-2007 by Larry B.]

yes im just asking a basic question.
data i have is such this as
K
oswalds factor
Thrust specific fuel consumption
Max take off weight
fuel weights used ( eg during climb, descent, contingency fuel)
aspect ratio
wing area
parabolic drag polar


there is some equation wich has velocity optimal for range as

SQRT (2W/pS) multiplied by Fourth root (fuel weight/KCd0)

is any one familiar.

i used brugets equation and it gave an unrealisticly low value for range, although the aircraft optimal range cruiseing speed was spot on.

thnks for helping