lecture 4 air data and airspeed measurement
Post on 03-Jun-2018
225 Views
Preview:
TRANSCRIPT
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 1/25
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.
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 2/25
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 3/25
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 4/25
PP
Ps
ASI M ALT
ASI = airspeed indicator
M = Mach meter
ALT = altimeter
Pp = pitot pressure
Ps = static pressure
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 5/25
Airspeed
dSS
PP
P
Referring to Newton’s second law
aMF
dAdSSPPPdA
dtdU)dAdS(
(7)
dS
dAdA
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 6/25
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)
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 7/25
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)
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 8/25
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)
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 9/25
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)
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 10/25
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)
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 11/25
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
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 12/25
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)
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 13/25
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)
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 14/25
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.
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 15/25
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)
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 16/25
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
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 17/25
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.
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 18/25
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".
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 19/25
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 20/25
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,
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 21/25
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
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 22/25
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
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 23/25
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)
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 24/25
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
8/12/2019 Lecture 4 Air Data and Airspeed Measurement
http://slidepdf.com/reader/full/lecture-4-air-data-and-airspeed-measurement 25/25
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)
top related