Re: Descent Calculator

Date:         22 Nov 97 20:41:28 
From:         "P. Wezeman" <pwezeman@blue.weeg.uiowa.edu>
Organization: The University of Iowa
References:   1
View raw article
  or MIME structure

On 21 Nov 1997, Ted Landy wrote:

> I am trying work out how to create a small program to calculate
> descent  profiles for aircraft to load into a handheld computer.
>  I want to be able to enter height, speed, wind component and weight
> to come up with a distance.
> Originally I thought I could just enter a L/D ratio and presto come
> with an answer. Unfortunately for me it is not so easy. For a given
> IAS on descent the L/D seems to constantly change (increase).
>
> Does anyone know of any useful formulas, available programs or have
> suggestions that may be of use to me?

   The behavior of airliners at changing Mach numbers is beyond my
knowledge, but basic physics suggests a possible reason for the
results that you are having.
   As the aircraft descends at constant indicated airspeed through
air that is increasing in density as altitude decreases, the true
speed will decrease. The resulting decrease in kinetic energy of the
aircraft should be reflected in a stretched out glide compared to a
calculation based only on the lift to drag ratio.
   Taking a 300,000 pound aircraft with a lift to drag ratio of 18,
descending from cruise altitude where it has a true airspeed of
500 knots to pattern altitude where it has an airspeed of 250 knots,
the kinetic energy at 500 knots would be about 3.3 billion foot pounds,
and the kinetic energy at 250 knots would be about 825 million ft lb,
for a decrease of about 2.5 billion ft lb. With the given lift to drag
ratio of 18 and weight of 300,000 lb, the aircraft would need about
100 million ft lb of energy for each nautical mile that it travels
in level flight. 2.5 billion ft lb would thus carry it an extra
25 nautical miles beyond what would be expected based on initial
altitude and L/D ratio alone. Assuming the cruising altitude is
45,000 feet, and landing is at sea level, descending 45,000 feet
at a glide ratio of 18 to one gives a glide distance of 810,000 ft
or about 134 nautical miles. Adding the 25 miles from the kinetic
energy decrease increases the glide by about 20 per cent. Is this
enough to account for the numbers that you are getting?

                        Peter Wezeman, anti-social Darwinist

                             "Carpe Cyprinidae"