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ha = absolute altitude

hG

= geometric altitude

r = radius of Earth

g varies with altitude g = g0

r

ha

2= g0

r

hG + r

2

1.2 Hydrostatic Equation

This describes the force balance of an element of fluid at rest.

dp = gdhG integrate to get p = p(hG) and assume g = constant = g0 at sea level.

Then dp =

g0dh

The Geopotential Altitude is given by h =

r

hG + r

hG

There is little difference between Geopotential and Geometric Altitude forlow altitudes.

If hG

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2 Chapter 3

2.1 Basic Aerodynamics

We need to get

flow properties: pressure

velocity

temperature density

This will get us lift

drag

There are 3 important equation:

Continuity Equation Momentum Equation Energy Equation

The Continuity Equation = Continuity of Mass.

In a time interval dt, the mass going through A1 is given by dm =1(A1V1dt)

Then, the mass flow is given by m1 =

dm1

dt= 1A1V1.

Since mass cant be created or destroyed m1 = m2 which gives us the Continuity Equation for steady fluid flow. It is

for compressible flow, i.e., for high speeds, such as in rockets. As thepressure changes, he volume changes, and with it the density, thus 1 = 2.1A1V1 = 2A2V2

For incompressible flow, the density does not change, and 1 = 2.Thus, A1V1 = A2V2.

This is an assumption, but a good one for liquids and air up to about 100m/s.

The Momentum Equation = Continuity of Momentum based onF = m a

Bernoullis Equation for incompressible flow is given by:p2 +

V22

2

= p1 +

V21

2

or p + V2/2 = constant along a stream line.

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For compressible flow, is a variable, and Bernoulli cannot be used.

The Energy Equation is for frictionless adiabatic (isentropic) compress-ible flow in a stream tube, we have with as the ratio of specific heats

=cPcT

p2p1

=

21

and

p2p1

=

T2T1

1

We also can derive for isentropic flow with h as the enthalpy

h1 + V2

1

2= h2 +

V22

2or h +

V2

2= constant.

Or with h = cpT we can get cpT1+

V21

2

= cpT2+V22

2

or h+V2

2

= constant.

These two equations combined with the continuity equation and theequation of state to solve for compressible flow conditions

2.2 Airspeed indicator

If we put a hollow tube (Pitot tube) far enough out into the undisturbed airflow, and cap the tube off at the rear end, there will be a stagnation point atthe opening of the tube, and the pressure measured at the capped end will bethe total pressure: static pressure + dynamic pressure or P0 = P +

1

2V2

If we then measure the static pressure P on the side of the tube with pres-sure ports, we can solve the above equation for the true airspeed V to get

V =

2(P0 P)

We can use a water column to measure the differnece in pressureP0 P = g(h0 h)

2.3 ICeT

Indicated Airspeed versus Calibrated Airspeed versus equivalent Air-speed versus True Airspeed

Indicated Airspeed Vi is the speed shown on the airspeed indicatorin the cockpit. This has to be corrected for location of the static pres-

sure ports and the associated quality of the static pressure measurements,sometimes even of the total pressure measurements. This position orinstallation error Vp is corrected via a table or graph, showing theerror with configuration and airspeed, to yield Calibrated Airspeed Vc:

Vc = Vi + Vp

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Then, the calibrated airspeed has to be corrected for compressibilityeffects at a given altitude and calibrated airspeed using the f-factor from

a table to yield the (usually lower) equivalent Airspeed Ve:

Ve = fVc

The last correction comes from adjusting the equivalent airspeed to thestandard sea level density to obtain the True Airspeed V:

V = Ve

SL

V is normally larger than Ve since the density ration is normally largerthan 1. With q as the dynamic pressure we get:

q =1

2V2

=1

2(VeSL

)2

=

1

2 SLV2

e

For high subsonic compressible flow, we use the Energy Equationto obtain airspeed from a Mach meter. This gives us the Mach numberM directly from (p0/p):

M =

2

1

p0p

1

1

The speed of sound is given by a = RT Which tells us that the speedof sound only depends on temperature.

M < 1 is subsonic M = 1 is sonic 0.75 < M < 1.2 is transonic M > 1 is supersonic M > 5 is hypersonic

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