lecture 4 air data and airspeed measurement

8/12/2019 Lecture 4 Air Data and Airspeed Measurement

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Air Data and Airspeed Measurement 1

Air Data and Airspeed Measurement

Pitot – Static system

Pitot – Static pressure are used for:

Feedback data in control system.

Regulate the cabin pressure.

Mach No. Warning

Data for flight recorder.

Cockpit indicators

Airspeed

Altimeter.



PP

Ps

ASI M ALT

ASI = airspeed indicator

M = Mach meter

ALT = altimeter

Pp = pitot pressure

Ps = static pressure



Airspeed

dSS

PP

P

Referring to Newton’s second law

aMF

dAdSSPPPdA

dtdU)dAdS(

(7)

dS

dAdA



For each molecule, the acceleration is given by;

t

U

S

UUt

U

dt

dS

S

U

dt

dU

(8)

Substitute equation (8) into equation (7), we

have

dSdASP

tU

SUU)dAdS(

(9)

For steady state flow, 0t

equation (9) becomes,

0U

2SS

P 2

(10)



For discrete calculation,

02

02

2

2

2

121

2

)UU(PP

SU

SP

Now consider within adiabatic flow

0U

2

1dP

1 2

(11)



From Thermodynamics theory for adiabatic flow, we

have;1/

ooo T

T

P

P

Where ρ = the air density at sea level,

Po = atmospheric pressure at sea level

= 1.4 for air

Integrating equation (11) and using adiabatic equation

above gives;

2

2

1

1U

P)( Constant

(12)

(13)



From State equation, RTP

The gas constant is given by,

1CR p

(14)

(15)

Substituting forP

in equation (13) and using

equations (14) and (15) gives:

ConstU2

1TC 2

p (15b)



Equations (13) and (15) are statements of energy in an

adiabatic flow for ideal gas and can be used to

calculate atmospheric free stream velocity.Using equation (13) on an air stream within stream

tube, gives;

P1

U1, ρ1

dS

P2

U2, ρ2

22

2

221

1

1 U21P

1U

21P

1

(16)



If we choose;

Location 1 is at the free stream with;

P1 = Ps (Static Pressure)

U1 = V (Free stream Velocity)

Location 2 is at the tip of pitot tube with;

P2 = Pp (Pitot Pressure)

U2 = 0



Substitute into equation (16), we have;

2

p2

1

s P

1

V

2

1P

1

(17)

It is also known that, the local free stream sonic

velocity is given by;

Pa (18)



1

2

s

p

P

P

12

spa

V

2

11PP

From equation (12), the P – ρ relationship can be

written as;

And equation (17) can be rewritten as

(19)

1aV

211PPPP

12

ssp (20)



Equation (20) is the most accurate equation that can

be used to calculate the air speed given the value of

Pd, the pressure difference.

However, it is not practical to use it in a typical aircraft

operation due to local atmospheric values have been

used. The values for sonic velocity a and air density ρ varies with the height.

To solve this problem, ICAO has recommended using

a and ρ values within International Standard Atmosphere (ISA) and incorporating relative

atmosphere.



From equation (18), we can rewrite it as follows;

2

o

o

o

2

o

2

aV

PP

aV

aV

Where; σ = Atmospheric relative density

= Atmospheric relative pressure

Subscript o indicates at sea level.

By definition, Equivalent Airspeed, Ve is given by;

VVe(22)

(21)



With the above definition, equation (20) becomes

11aV

211PP

12

o

esd

(23)

Equation (17) is more suited for airspeed calculation

because it uses sea level sonic velocity, ao, and

other relative values that can be obtain from

meteorological data. Almost all airspeed instruments are calibrated in the

laboratory at sea level, i.e. σ = 1 and = 1



In this condition, the calculated airspeed is called

the Calibrated Airspeed, Vc , and equation (23)

becomes;

1a

V

2

11PP

12

o

csd

(24)

Equation (24) is called “Full Law Calibration

Equation of Airspeed Indicator”.

It is the most accurate calibration equation for

airspeed indicator.



Due to = 1 during calibration, a systematic error

exist between Ve and Vc as the instrument is usedat different height.

This type of error is called “Compressibility Error”or “Scale – Altitude Error”.

This error can be corrected by using "Scale –

Altitude Correction Chart".



Equation (24) can be simplified as follows;expanding the equation using Taylor series

1a

V

8a

V

21PP

4

o

c

2

o

c

sd

taken out

2

o

c

a

V

2

and dropping the third or

higher order terms, we obtained,



2

o

c2

co

2

o

cs

2

o

cd

a

V

4

11V

2

1

a

V

4

11P

a

V

2

1P

Where o

o

s

a

P

If Ps = Po during calibration

(25)

Equation (25) is called “Simple – Law CalibrationEquation of Airspeed Indicator”.

This equation can be used up to 460 kts



Airspeed indicator summary:

VI

Vi

Vc

Ve

V

Pp

Ps

Pressure system correction

Instrument correction

Scale-Altitude correction

Relative σ correction

VI = Indicator reading

Vi = Indicated A/S

Vc = Calibrated A/S

Ve = Equivalent A/S

V = True A/S

eVV



Mach Number Calculation

a

VM By definition,

a ratio of true air speed against local sonic velocity.From equation 20, the Mach No. is given by;

1M2

1

1P

P 12

s

d

(26)



Equation (26) is the Mach No. calibration equation forsubsonic airspeed. In this equation the mach no.depends on the ratio of pressure different against static

pressure. At sonic and supersonic velocity, there exist normalshock in front of pitot tube and altered Pp

M2 , Pp2 Pitot tube

M1 , Pp1

M1 > 1 M1 < 1



Pitot tube will measure PP2 that is much less than PP1

It can be shown that;

1

224

1

2

1 1

1

2

22

2

M

M M

P

P

s

d

(27)

lecture 4 air data and airspeed measurement

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