### AIRCRAFT PERFORMANCE

### Fixed Wing Aircraft

### AIRSPEED MEASUREMENT

The speed of an aircraft relative to the surrounding air is a critical part of operation and performance analysis. No direct method is available for measurement of velocity relative to the air so instead the velocity is inferred from measurements of dynamic pressure.

Dynamic pressure is defined as $q=1/2 ρV^2$

Various forms of dynamic pressure can be obtained depending on the instruments used to measure the pressure and the flight speed range of the vehicle. A simple airspeed indicator is shown in the section on Aircraft Instruments. All instruments rely on knowledge of Standard Atmosphere properties.

The primary atmospheric properties can be expressed in the form of ratios compared to Sea Level conditions.

The approximate dynamic pressure can be measured by a Pitot-Static system,

This pressure difference is known as the **indicated
impact pressure**. For subsonic aircraft operating in a
normal angle of attack range, total pressure ( **P**_{0}_{
}) can be measured accurately. Static pressure ( **P**_{s}
) is a less accurate measure of the surrounding atmosphere
pressure ( **P**** **) and calibration factors may
need to be applied to correct for measurement errors due to
the position of the device.

where **q**_{i} is defined as the
**impact pressure.**

Applying the compressible flow Bernoulli equation gives the following expression for velocity,

where **γ = 1.4 **is the ratio of specific heats for
air.

For incompressible flow this simplifies to

As air density cannot be directly measured and static pressure measurements are subject to error, airspeed indicators use a calibrated ISA sea level pressure condition instead. The airspeed displayed on cockpit indicators is thus,

or for incompressible flow,

For transonic and supersonic vehicles additional
compressibility corrections may need to be applied. If shock
waves form in front of the pitot tube then total pressure (
**P**_{0} ) will become inaccurate due to
shock losses.

There is thus a translation sequence between the observed
speed ( **V**_{O} ) on the aircraft's
instruments and the actual airspeed of the vehicle ( V ).
For subsonic vehicles,

**V**_{O} , Observed airspeed on
instrument + **Δ V**_{IC}_{
}(instrument correction)

=> **V**_{I}
, Indicated airspeed + **Δ V**_{pos}(static
port position error)

=> **V**_{C}
, Calibrated Airspeed + **Δ V**_{C}
(compressibility correction)

=> **V**_{E}**
**, Equivalent Airspeed $×1/√{ρ} $ (Altitude
correction)

=> **V**_{T}** **,
True Airspeed = **V**

For incompressible flows a rough estimate can be made that

At high speed where compressibility correction becomes a large component then a Mach meter rather than an airspeed indicator may be used.

Indicated Mach Number would thus be,

or

For supersonic flight when a shock forms in front of the pitot tube an additional compressibility correction is required.

When

then

Based on these airspeed relationships, dynamic pressure can be formulated in several ways,