Re: Flying High ?

Date:         19 Feb 98 01:34:26 
From:         Chris Pitzel <chris.pitzel@usask.ca>
Organization: PSINet
References:   1
Followups:    1 2 3 4
Next article
View raw article
  or MIME structure

Nathan Pusey wrote:
>         Can somebody please explain to me why planes (jet aircraft) fly
> at very high altitudes on long range flights, and how does this conserve
> fuel and get maximum distance ? How does this conserve fuel and save
> time if you can only go half the speed you normally can go at low
> altitude and you have to use twice the amount of power to get too half
> the power you get at lower altitudes ?

There are two main physical reasons this is true.  There may be others
which others can elaborate on as well (I'm not too familiar with some of
the operating characteristics modern gas turbines, so I couldn't really
comment on efficiency issues).

a)	The earth's gravitational attraction decreases as you get further
away from the earth.  When you're at sea level, the earth's acceleration
due to gravity is approximately 9.81 metres/second (or 32.2ft/sec for
the non-metric types).  As you go higher, the attractive forces between
the earth and a particle decrease (the particle being the aircraft).
This translates into less energy being needed to overcome this
gravitational attraction in order to keep an aircraft airborne.

If you were to measure your weight on an aircraft at FL400 and your
weight at sea level, you would find that you would weigh less at
altitude.  For example, I weigh roughly 130 pounds at sea level, yet I
would only weigh perhaps 110 pounds at 40k feet.  There are formulas to
determine this which can be derived from the relationship:

	F = G*m1*m2/r^2

Where F is the force between the two bodies, G is the gravitational
constant, m1 is the mass of one of the particles, m2 is the mass of the
other particle, and r is the distance between the centres of the two
particles.  Anyone who has taken an introductory physics course of any
kind will have seen these formulas.

b)	The density of air (and therefore pressure) decreases with altitude.
Air is much more dense at lower altitudes than it is at high altitudes.
If you want proof of this, just try climbing Mount Everest without
oxygen ;-).  Temperature also decreases with an increase in altitude
until you reach a certain altitude, then it levels off and (I believe)
even starts to increase.

	Since it is much easier to move an object through a very low-density
fluid than it is to move it through a higher density fluid, this means
that an aircraft will require less power in order for it to overcome
frictional forces due to wind resistance (ie: drag).  This is pretty
self-evident; take a tub of syrup and try moving your finger through
it.  Then take a tub of water and move your finger through it.  Observe
which is easier to move through.  You'll find that the water exerts much
less drag than does the water.  The resistance is proportional to the
viscosity of the fluid.  Overcoming this resistance is very costly in
terms of fuel burn, and pilots often will fly hundreds of miles out of
their way just to fly with the wind (in the jetstream) instead of
against the wind to reduce this drag and make the flight faster.  To
calculate wind resistance involves a bunch of logarithmic relationships,
but in general, to make an aircraft fly twice as fast requires 8 times
as much power (velocity cubed relationship).

In terms of fuel burn, gas turbines have certain operational power
settings at which they are most efficient.  It may be more efficient for
an operator to run an engine at 66% of full power over a period of 15
hours than it would be for an operator to run an engine at 100% of full
power for 10 hours just to achieve the same flight distance (these
numbers, are by no means, accurate or anything).  However, there are
economic reasons for not always selecting the most efficient operating
power setting on an aircraft.  For example, if you end up having to pay
for an extra crew to fly the plane because the first crew can't legally
fly a flight that long, then that adds up to some really large costs
(fuel is only ~20% of the total operating cost of a typical flight).

>                                         Thanks in advance.

I hope I've given you some answers to your questions; if I didn't, I at
least got the discussion started.