Re: Fuel Weight versus Initial Cruise Altitude

From:         shevell@leland.stanford.edu (Richard Shevell)
Organization: Stanford University, Dept. of Aero/Astro
Date:         14 Oct 94 02:23:35 
References:   1
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In article <airliners.1994.1618@ohare.Chicago.COM>, lmassaro@manta.nosc.mil
(Larry Massaro) wrote:

> On a couple of transcon flights, I have noticed that that pilot has
> sometimes spoken about leveling off at an intermediate FL to burn
> off fuel.  Is it really more efficient to burn fuel first at lower
> cruise altitudes then climb to a final?  Does anyone have any
> data/equations etc. which indicate this is true.  My first impression
> would be that winds aloft would be the more probable reason 
> for flying at the lower "less eficient" altutude initially.
> 
Jet airliners are most efficient flying at a particular Mach number and
angle of attack.  The values depend upon the aerodynamic design
characteristics.  Given the desired angle of attack, which of course
corresponds to a particular lift coefficient, and the best Mach number, the
lift is determined by the ambient air pressure, i.e. the altitude.  For
steady flight the lift must equal the gross weight of the airplane. Thus
the best altitude is determined by the weight, which is constantly
decreasing as the fuel is consumed.  Ideally the best flight path is a
continual  climb.  From a traffic control standpoint that is impossible,
except in regions where the traffic is very light.  Thus the optimum
climbing flight path is approximated by a step climb where the pilot starts
at the best altitude for the initial weight and then climbs to the next
higher legal altitude for his direction of flight when the fuel is burned
down sufficently.    
    Large changes in wind velocity with altitude may modify the "best"
altitude.
Other secondary influences are the variation of specific fuel consumption 
with altitude (usually small) and the variation of the speed of sound (a
function of temperature) with altitude, usually zero above 36,150 ft.

> Lawrence Massaro
> Data Link Research
> San Diego, CA 92124
> -------

-- 
Richard Shevell
Email: shevell.leland.stanford.edu