Weather Condition Analysis During a Mission

POLITECNICO DI MILANO

Department of Aerospace Engineering

Weather Condition Analysis

During A Mission

Aircraft Systems Course

Prof. P.C. Astori

a cura di

Giorgio Montorfano

e

Riccardo Rota

A.A. 2013/2014

Wheater Condition Anlysis During A Mission G. Montorfano, R. Rota

Table of Contents

1. Introduction ................................................................................................................................... - 1 -

2. Symbols list .................................................................................................................................... - 2 -

3. Problem characterization and method of solution ........................................................................... - 3 -

3.1 Theoretical weather conditions at sea level ....................................................................................... - 3 -

3.2 QNE and QNH altitudes above Cusco .................................................................................................. - 3 -

3.3 Cockpit and flight altitudes .................................................................................................................. - 4 -

3.4 TAS and EAS speed .............................................................................................................................. - 4 -

4. Problem data ................................................................................................................................. - 5 -

4.1 A1 data ................................................................................................................................................ - 5 -

4.2 A2 data ................................................................................................................................................ - 5 -

4.3 Standard atmosphere data .................................................................................................................. - 5 -

4.4 Flight data ............................................................................................................................................ - 5 -

4.5 Other data ........................................................................................................................................... - 5 -

5. Calculus development .................................................................................................................... - 6 -

5.1 Unit of measure conversions ............................................................................................................... - 6 -

5.2 Theoretical weather conditions at sea level ....................................................................................... - 6 -

5.3 QNH and QNE altitudes above Cusco .................................................................................................. - 6 -

5.4 Cockpit and flight altitudes .................................................................................................................. - 7 -

5.5 TAS and EAS speed .............................................................................................................................. - 7 -

6. Summary of the results .................................................................................................................. - 8 -

6.1 QNH and QNE altitudes above Cusco .................................................................................................. - 8 -

6.2 Cockpit and flight altitudes .................................................................................................................. - 9 -

6.3 TAS and EAS speed diagrams ............................................................................................................... - 9 -

prof. P.C. Astori I A.A. 2013/2014

Weather Condition Analysis During A Mission G. Montorfano, R. Rota

1. Introduction

The following report deals with an hypothetical flight taking off from the airport of Lima and

landing at Cusco. Known the altitude of the two airports and their pressure and temperature

conditions (listed below), it will provide:

 the theoretical pressure and temperature conditions at sea level of the two airports;

 a chart containing QNH and QNE altitudes, based on the actual altitude above Cusco

airport up to 11000 meters;

 the sketches of flight and cockpit altitudes, assumed that the plane's assigned airway is

FL280. Moreover the weather conditions during the take-off and the landing are

considered steady, while the cruise altitude changes from A1 to A2 areas.

 TAS and EAS speeds diagrams depending on the altitude throughout the climb up to the

assigned FL, supposing a constant CAS speed equal to 280 kts.

Place Altitude Local pressure Local temperature

Departure Lima 35 1026 28

Destination Cusco 3400 664 4

Hypothetical flight

prof. P.C. Astori - 1 - A.A. 2013/2014

Weather Condition Analysis During A Mission G. Montorfano, R. Rota

2. Symbols list

Temperature

Pressure

Altitude

Density

Speed

Time

Flight level

Gravitational acceleration

Vertical thermal gradient

Adiabatic expansion coefficient

Universal gas constant

Specific gas constant

Molar Mass

Air speed

Mach number

prof. P.C. Astori - 2 - A.A. 2013/2014

Weather Condition Analysis During A Mission G. Montorfano, R. Rota

3. Problem characterization and method of solution

3.1 Theoretical weather conditions at sea level

In standard atmosphere, the temperature decreases linearly with the altitude up to 11

kilometers, according to the following equation:

where is the vertical thermal gradient. So, if and are respectively Lima and

Cusco temperatures and and their altitudes, the temperatures at sea level are:

The atmospheric pressure reduces going high, too, but not in a linear way. Effectively:

where . Making use of the previous results, the pressures at sea level are equal to:

3.2 QNE and QNH altitudes above Cusco

The measure of the altitude shown by the altimeter descends from the pressure formula,

illustrated shortly before, making the altitude symbol explicit:

QNE and QNH are two different altimeter calibrations. In the former the pressure is set on the

typical value of the standard atmosphere, in the latter the pressure corresponds to the presumed

pressure at sea level. In each case is the standard atmosphere temperature, while is the

theoretical pressure for every altitude . Thus:

In particular:

prof. P.C. Astori - 3 - A.A. 2013/2014

Weather Condition Analysis During A Mission G. Montorfano, R. Rota

3.3 Cockpit and flight altitudes

In order to ensure comfort conditions inside the cockpit, it is necessary to calculate the

equivalent flight altitude inside it, which has to remain constant during the cruise. This altitude is:

For the same reasons there is a maximum climb speed allowed, so the climbing durations from

Lima airport to the equivalent flight altitude and from this one to Cusco airport are:

The flight level pressure is:

and it must be constant during all the flight. In this way, actually, the aircraft altitude changes

during the cruise.

and are the flight altitudes considering the flight level pressure and the weather conditions

at sea level.

3.4 TAS and EAS speed

First of all, it is necessary to know the values of temperature, density, theoretical and total

pressure of the air above Lima airport to determine the True Air Speed (TAS) and the Equivalent

Air Speed (EAS) during the climbing. In fact, the TAS expression is:

but:

Moreover, the EAS expression is:

Since the flight level is at a lower altitude than the end of the troposphere, it is possible to

obtain the remaining quantities through the following formulas:

prof. P.C. Astori - 4 - A.A. 2013/2014

Weather Condition Analysis During A Mission G. Montorfano, R. Rota

4. Problem data

4.1 A1 data Altitude

Temperature

Pressure

4.2 A2 data Altitude

Temperature

Pressure

4.3 Standard atmosphere data

Temperature

Pressure

Density

Vertical thermal gradient

Adiabatic expansion coefficient

Molar mass

4.4 Flight data

Flight level

Climbing speed

Calibrated Air Speed

4.5 Other data

Gravitational acceleration

Universal gas constant

prof. P.C. Astori - 5 - A.A. 2013/2014

Weather Condition Analysis During A Mission G. Montorfano, R. Rota

5. Calculus development

5.1 Unit of measure conversions

5.2 Theoretical weather conditions at sea level

5.3 QNH and QNE altitudes above Cusco

prof. P.C. Astori - 6 - A.A. 2013/2014