Exercises Lecture 2 The Standard Atmosphere

Prof. dr. ir. Jacco Hoekstra Tim van Leeuwen

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A. Rose - CC - BY - NC - ND

AE1110x - Introduction to Aeronautical Engineering

Exercise 1What is NOT a reason for us to introduce a standard atmosphere?

We need a standard atmosphere:

A) to use as a model for simulationB) for meaningful specification of aircraft performanceC) to know what the average Earth atmosphere is likeD) to define pressure and density altitude

Exercise 2In the picture below you see the temperature profile of the International Standard Atmosphereshown in the lecture. Label the different parts of the atmosphere (shown by the gray boxes) withthe correct names.

Figure 1: The temperature profile of the International Standard Atmosphere.

Exercises Lecture 2 - The Standard Atmosphere 1

AE1110x - Introduction to Aeronautical Engineering

Exercise 3Below you see the ’block of air’ we used in the lecture to derive our hydrostatic equation.

Figure 2: The block of air used in the derivation of the hydrostatic equation.

We know that this block is in vertical equilibrium, so ΣFup = ΣFdown.1) Based on the figure above and using the quantities indicated in this figure, give the expressionsfor ΣFup and ΣFdown.2) What does the hydrostatic equation we can derive from this equilibrium look like?

Exercise 4At some point in the combustion cycle of an engine, the temperature of a combusted air-fuelmixture is 582 degrees Celsius. Given that the pressure in the mixture is 6.2 bar, determine thedensity of the mixture (in kilogram per cubic metre). Assume the gas constant R is equal to 287.00J/(kg ·K).

Exercise 5An aircraft flies at an altitude of 30,000 feet. Determine the air temperature (in [K]), air pressure(in [Pa]) and air density (in [kg/m3]) at this altitude, according to the standard atmosphere.

Figure 3: The aircraft at 30,000 feet. Image courtesy of Joe Thomissen, CC - BY - ND

2 Exercises Lecture 2 - The Standard Atmosphere

AE1110x - Introduction to Aeronautical Engineering

Exercise 6The rate of climb of an aircraft is generally computed from pressure measurements. To illustratethe principle behind this, consider the following question:

Suppose we launch a scientific rocket straight up from sea level (at standard conditions) with apressure measuring device attached to it. Given that in the first 12 seconds the rocket experiencesa 25% decrease in air pressure, what is the average speed (rate of climb) of the rocket in thesefirst 12 seconds?

A) 142.4 m/sB) 163.8 m/sC) 181.2 m/sD) 196.7 m/s

Exercise 7The hydrostatic equation holds not just for air, but for other fluids such as water (air, though it is agas, is often referred to as a ’fluid’) as well. In the case of water the equation becomes even easier,as water (as opposed to air) can be treated as incompressible, meaning the density is constant.Use a value of 1000 kilogram per cubic metre as density.

Using this information, compute the local pressure (in [Pa]) at 2.5 metres depth in a swimmingpool situated at 2400 metres altitude in the mountains. Assume a standard atmosphere.

Exercise 8As encouraged to do during the lectures, the following exercises investigate what the atmosphericproperties were like at the altitude Mr. Baumgartner went to (38,969 m).

1) What is, according to the standard atmosphere, the temperature (in Kelvin) at 38,969 metresaltitude?2) What is, according to the standard atmosphere, the air pressure (in Pascal) at 38,969 metresaltitude?3) What is, according to the standard atmosphere, the air density (in kilograms per cubic metre)at 38,969 metres altitude?

Exercise 9Which of the following statements is correct?

A) The geometric altitude hG solves the hydrostatic equation with a constant g, the geopotentialaltitude h takes the variation of g into account.

B) The geopotential altitude hG solves the hydrostatic equation with a constant g, the geometricaltitude h takes the variation of g into account.

C) The geometric altitude h solves the hydrostatic equation with a constant g, the geopotentialaltitude hG takes the variation of g into account.

D) The geopotential altitude h solves the hydrostatic equation with a constant g, the geometricaltitude hG takes the variation of g into account.

Exercises Lecture 2 - The Standard Atmosphere 3

AE1110x - Introduction to Aeronautical Engineering

Exercise 10You are given the following two statements:

1) If an aircraft flies at a geometric altitude of 10,000 metres, its geopotential altitude is 9,978metres.2) If an aircraft flies at a geopotential altitude of 12,000 metres, its geometric altitude is 12,023metres.

Which of the following is true?

A) Only statement 1 is trueB) Only statement 2 is trueC) Both statements are trueD) Both statements are false

Exercise 11A spacecraft flies over Mars at a geopotential altitude of 80 kilometres. Determine its geometricaltitude (in metres).

Figure 4: An illustration of a spacecraft over Mars.

4 Exercises Lecture 2 - The Standard Atmosphere