Chapter 2

Atmosphere Altitude and Airspeed Measurement

X-2 Starbuster

While the X-1’s focus was to break the sound barrier, the X-2 was to break the heat barrier

Testing started in 1946

Stainless steel and K-monel (copper nickel alloy)

Liquid fuel rocket engines to 15,000 lbs thrust

After many mishaps, powered flight took place on Jan 16, 1955

Sep 27, 1956 it reached a speed of 2094mph mach 3.196

Then crashed due to inertial coupling

Length: 37 ft 10 in (11.5 m)

Wingspan: 32 ft 3 in (9.8 m)

Height: 11 ft 10 in (3.6 m)

Wing area: 260 ft² (24.2 m²)

Airfoil: 2S-50 bicon

Empty weight: 12,375 lb (5,600 kg)

Loaded weight: 24,910 lb (11,300 kg)

Max. takeoff weight: 24,910 lb (11,300 kg)

Powerplant: 1 × Curtiss-Wright XLR25 rocket engine, 15,000 lbs

Properties of the atmosphere

by volume 78% N

21% O

1% other gases

There are 4 important properties

Static pressure

Temperature

Density

Viscosity

Static Pressure

Results from the weight per a unit of area of the air above that level.

2116 lbs per square foot or 14.7psi

At 18,000 feet the atmosphere is 50% the weight of sea level.

At 40,000 feet the atmosphere is 19% the weight of sea level.

The Pressure Ratio is

For the study of aerodynamics, a ratio is used to cancel out the units and make life easier.

The ratio is expressed in terms of

Ambient static pressure = d Standard sea level static pressure

Standard seal level static pressure is 2116 psf

So that should show up as the bottom number and the top number will be whatever the pressure is for that altitude

1455 = .6876 or about 10,000 feet

2116

check the table on page 16

Important?

Many items of gas turbine performance are directly related to some parameter of the altitude pressure ratio

The more air (the higher the pressure) the more thrust is produced.

We will cover “The rest of the story” later when we talk about jet engines.

Temperature

In order to deal with compressibility and some aspects of jet engine performance, temp must be converted to one of the two absolute scales.

F is converted into Rankine by adding 460 degrees to the F temp.

C is converted into Kelvin by adding 273 degrees.

The Temperature Ratio is

Ambient air temp = ? (theta)

Standard sea level air temp

Where Ambient air temp is the temp at the desired altitude.

Standard sea level air temp has to be converted to either:

Rankin for Fahrenheit

Kelvin for Celsius

The conversion factor for Rankin is add 460°

The conversion factor for Kelvin is add 273°

So standard day converted is:

59° F + 460° = 519° Rankin

15° C + 273° = 288° Kelvin

The reason we do this is because we need a scale that starts with absolute zero

The Temperature Ratio

Lets take an example: Find the ambient air temp for 5000′

(Use the chart on pg 20 for 5000′)

Temps converted to Rankin so 59°F + 460 = 519°R

Now get theta from the chart for 5,000 feet .9656

Solve for ambient T

Density

Density is the most important of the 4

Defined: It is the mass of air per cubic foot of volume

Density is a direct measure of the quantity of matter in each cubic foot of air.

Remember mass is measured in slugs so…

Air at sea level has a weight of .0765 lbs per cubic foot

Therefore has a density of .002377 slugs per cubic foot.

Air at 22,000 feet has a density of .001183 slugs per cubic foot.

Air density is ?(rho)

The Density Ratio is

The density ratio is s (sigma)

ambient air density/standard sea level air density = s (sigma)

Where ambient air density is the density at your altitude.

Standard sea level air density is always going to be .002377

Remember we are talking mass so the units are slugs per cubic foot.

The General or Universal Gas Law

Defines the relationship of pressure, temperature and density when there is no change of state or heat transfer.

Density varies directly with pressure, and inversely with temperature.

Viscosity

The internal friction of a fluid caused by molecular attraction that makes it resist its tendency to flow.

An increase in temp causes an increase in viscosity (in gases).

Kinematic viscosity is important in determining Reynolds numbers which relate to boundary flow study.

Standard Atmosphere

In order to level the playing field for study of all aerodynamics the ICAO standard atmosphere was developed.

The table on page 20 shows pressure altitude, density ratio, pressure, pressure ratio,temperature, temperature ratio, and the speed of sound.

For any pressure then we can extract the altitude

If we have a pressure of 1760.5 psf then 1760.5/2116 = .8320 or 5000 feet

Pressure Altitude

That altitude in the standard atmosphere corresponding to a particular pressure.

If an altimeter is set to 29.92 then the altitude indicated is pressure altitude but may not be the actual height above ground due to temp, lapse rate, atmospheric pressure, or possible errors in the instrument.

Density Altitude

The altitude in the standard atmosphere corresponding to a particular value of air density.

Pressure altitude corrected for nonstandard temp.

Usually performance charts are based on density altitude because of the profound effect on aircraft performance.

Continuity Equation

Basically explains the relationship in a Venturi between velocity and cross sectional area.

It says that a unit of air entering the venturi in a given amount of time is equal to the unit of air exiting the venturi in the same amount of time.

Constant mass flow is called steady state flow.

The continuity equation does not explain the differences in pressures related to cross sectional areas

For this we need to look at Bernoulli’s equations

Bernoulli’s Equation

Takes up where the continuity equation leaves off.

It explains the relationship of static pressure and varying cross sections of the venturi.

The conservation of energy requires PE + KE = TE

PE represents static pressure of the air flow

KE represents dynamic pressure of the air flow

So static pressure (PE) + dynamic pressure (KE) must equal the total pressure (TE) which remains constant.

H is total pressure

P is static pressure

q is dynamic pressure

H = P + q

Where:

? is density

A is area and

V is velocity

Then the continuity equation dictates:

?1A1V1= ?2A2V2= ?3A3V3

If we are subsonic then drop the rho

Bernoulli’s Equation

If total pressure remains constant when static pressure changes, dynamic pressure (q) must change correspondingly and inversely.

thus the equation can be written as (pg 22);

Dynamic pressure

One of the most important equations that will be dealt with in this course is for dynamic pressure.

The dynamic pressure of a free airstream is the one common denominator of all aerodynamic forces and moments.

Dynamic pressure

Dynamic pressure represents KE of the free stream and is a factor relating the capability for producing changes in static pressure on a surface (airfoil).

Dynamic pressure varies directly with density and the square of the velocity.

Dynamic pressure

It is this pressure we must consider in almost all airfoil study.

It is measured in pounds per square foot.

q=dynamic pressure

?=density

V=velocity

Note: in this equation V is in fps

Airspeed Measurement

When measuring airspeed remember inside the pitot head we have both static and ram pressure trapped.

We have to take the static pressure out so the reading on the A/S indicator tells just dynamic

A stagnation point develops at the mouth of the pitot tube which requires that all pressure is static pressure and must be equal to total free stream pressure.

q indicators

q indicators

The higher you go the faster your TAS

Always use TAS in the equations

Airspeed Measurement

The pitot head has no internal flow velocity and the pressure in the pitot system is equal to the free stream total pressure (ram) + static pressure.

Therefor static pressure – free stream total pressure (ram) = dynamic pressure or q.

So q is airspeed

Indicated Airspeed

Read off the airspeed indicator.

Errors inside the instrument caused by mechanical reasons leaks etc. may effect accuracy

Position error is when the static port may sense partial vacuum or some ram pressure and cause erroneous readings.

Calibrated Airspeed

IAS corrected for position and instrument error.

This may be compensated for by using many different static port locations.

An error of just .05psi at 100 kts can give a 10 kt variation.

Equivalent Airspeed

Is the result of correcting CAS for compressibility effects.

The pitot tube is not capable of collecting true free stream total pressure due to magnification by compressibility.

The compressibility produces a stagnation pressure which is greater than non-compressed air.

The pilot doesn’t usually have to worry about compressibility if flying under 10,000 feet and below 200 kts.

True Airspeed

is the result of correcting EAS for density altitude or more accurately density ratio.

The airspeed indicator is set up for standard sea level conditions so variations in density must be accounted for.

TAS is a function of EAS and density altitude.

Let’s sum up

Density is mass per unit volume (slugs per cubic foot)

Pressure is force per unit area (pounds per square foot)

To get CAS:

Correct IAS for position and installation error

To get EAS:

Correct CAS for compressibility

To get TAS

Correct EAS for density ratio (square root s)