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U N I V E R S I T Y O F B E R G E N

Yaw angle estimation for the measurement of turbulent fluxes from the Small Unmanned Meteorological Observer (SUMO)

Stephan T. Kral (GFI, FMI, UNIS)

Line Båserud (GFI), Joachim Reuder (GFI),

Marius O. Jonnassen (UNIS, GFI)

Geophysical Institute

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Outline

•  The SUMO system •  Background on airborne flux measurements •  Heading (yaw) measurement systems •  Yaw estimation method •  Campaigns •  Results •  Remaining Challenges

Geophysical Institute

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SUMO (Small Unmanned Meteorological Observer) Geophysical Institute

© Martin Müller

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SUMO measurement system Geophysical Institute

© Martin Müller

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Airplane coordinate system

Attitude angles (rel. to met. coord.) •  ψ = true heading (yaw) •  θ = pitch •  ϕ = roll Airstream angles (rel. to airc. coord.) •  α = attack •  β = sideslip Airstream magnitude •  Ua = air speed

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(Lenschow, 1989)

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Wind vector coordinate transformation

Transformation of wind measurements into meteorological coordinates requires knowledge of: •  air speed vector (Ua, α, β) from

5-hole probe •  ground speed vector (up, vp,

wp) from GPS •  pitch and roll (θ, ϕ) from IMU •  Heading (ψ), not measured by

SUMO

Lenschow (1989; approximated equations): assuming: •  small separation probe–IMU •  horizontal flight (small angles

of attack and sideslip)

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u = −Ua sin(ψ +β)+upv = −Ua cos(ψ +β)+ vpw = −Ua sin(θ −α)+wp

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Heading angle measurement systems and implementation in SUMO •  Gyroscope (gimbal): too large, heavy •  Gyroscope (electronic, integrated in IMU): drift problem •  Magnetic sensor: el. currents, inclination at high latitudes •  DGPS (two antennas in wing tips): small separation but

may be worth testing •  Horizontal looking camera: good visibility and clear

landmarks, complicated algorithm •  Downward looking camera/laser scanner (like an optical

computer mouse): algorithm, unclear dimensions

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Currently no reliable measurements in SUMO

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Indirect heading estimation methods

Assuming: •  constant airspeed •  straight, horizontal legs •  constant altitude •  stationarity and

homogeneity •  no rudder actions

Relative heading angles (with reference to leg direction) for two legs in opposite directions differ only in their sign

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!u2g

!u1g

u!ψ '2

ψ '1

ψ '1 = –ψ '2

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Indirect heading estimation methods (continued)

Set of equations from two consecutive flight legs: This can be solved for u and v

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!u2g

!u1g

u!ψ '2

ψ '1

21

2211

2211

'– = '

)'( v= )'(v

)'(u = )'(u

ψψ

ψψ

ψψ

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Indirect heading estimation methods (continued)

In reality (due to turbulence) the system rather looks like this: This can be solved by minimizing the root mean square differences of the two velocity components for consecutive flight legs

Geophysical Institute

!u2g

!u1g

!uaψ '2

ψ '1u1a (ψ '1 ) ≈ u2

a (ψ '2 )v1a (ψ '1 ) ≈ v2

a (ψ '2 )ψ '1 ≈ –ψ '2

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Indirect heading estimation methods (continued) Geophysical Institute

No correction Yaw correction

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Data from four campaigns

•  Adventfjorden, Svalbard (Nov 2014): Turbulence over open water during polar night/winter (13 flights; unstable/weakly stable)

•  ECN, Wieringerwerf, Netherlands (Mai 2014): Wake turbulence induced by wind turbines (5 flights; neutral; strong cross wind component)

•  Adventdalen, Svalbard (Mar 2014): Turbulence over snow covered valley during polar night/winter (24 flights; stable/very stable)

•  BLLAST, France (Summer 2011): Boundary Layer evening transition (47 flights; presented by Line Båserud)

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Results

15 16 17 18 19 20 21 22 23 24 25−2

−1.5

−1

−0.5

0

0.5

1

1.5

− 0 . 04 N m − 2

− 0 . 02 N m − 2

U = 6 . 5 m s− 1 ( 3 . 9m s− 1)

W D= 160 o ( 137 o)y a w = 17 .5 o ± 0 .7 o

τxz[N

m−2 ]

Turbulent fluxesSUMO flight: 2014−11−14 18:40 (leg: 1−6)

alt: 43.2 m ± 1.2 m

15 16 17 18 19 20 21 22 23 24 25−1500

−1000

−500

0

500

1000

1500

200070W m − 2

17W m − 2

θ = − 8 . 1 oC

T I R= − 1 . 6 oC ± 0 . 4 oC

Hs[W

m−2 ]

Ex p e rim ent tim e [min ]

instantaneous flux (max method)instantaneous flux (min method)leg averaged flux (max method)leg averaged flux (min method)flight averaged flux (max method)flight averaged flux (min method)

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900 1000 1100 1200 1300 1400 1500−4

−2

0

2

4

6

8

u, v

, w [m

s−1 ]

time [s]

rotation into earth coordinates

uvw

130 140 150 160 170130

135

140

145

150

155

160

165

170

WDFHP [deg]

WD N

FW [d

eg]

wind direction comparison

0 2 4 6 8 100

2

4

6

8

10

WSFHP [m s−1]

WS N

FW [m

s−1

]

wind speed comparison

−5 −4 −3 −2 −1 0−5

−4

−3

−2

−1

0

uFHP [m s−1]

u NFW

[m s−1

]

RMS = 0. 4

wind component u comparison

0 2 4 6 8 100

2

4

6

8

10

vFHP [m s−1]

v NFW

[m s−1

]

RMS = 3. 4

wind component v comparison

15.49 15.5 15.51 15.52 15.53 15.54 15.55 15.56 15.5778.242

78.244

78.246

78.248

78.25

78.252

78.254

78.256

Longitude

Latit

ude

SUMO flight (2014−11−14 18:40)alt: 35 m − 55 m

alt [

m]

35

40

45

50

55

Svalbard (sea) Fl 12 (14.11.2014) leg 1–6; 45 m agl

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Results

2 3 4 5 6 7 8 9 10 11 12 13−40

−20

0

20

40

60

80

0 . 02 N m − 2

− 0 . 23 N m − 2

U = 10 . 5 m s− 1 ( 11 . 7m s− 1)

W D= 221 o ( 216 o)y a w = 22 .4 o ± 2 .4 o

τxz[N

m−2 ]

Turbulent fluxesSUMO flight: 2014−05−10 14:07 (leg: 1−10)

alt: 70.3 m ± 6.7 m

instantaneous flux (max method)instantaneous flux (min method)leg averaged flux (max method)leg averaged flux (min method)flight averaged flux (max method)flight averaged flux (min method)

Geophysical Institute

100 200 300 400 500 600 700 800−10

−5

0

5

10

15

u, v

, w [m

s−1 ]

time [s]

rotation into earth coordinates

uvw

−150 −145 −140 −135 −130−150

−145

−140

−135

−130

WDFHP [deg]

WD N

FW [d

eg]

wind direction comparison

0 5 10 150

5

10

15

WSFHP [m s−1]

WS N

FW [m

s−1

]

wind speed comparison

5 6 7 8 9 105

6

7

8

9

10

uFHP [m s−1]

u NFW

[m s−1

]

RMS = 0. 7

wind component u comparison

5 10 155

10

15

vFHP [m s−1]

v NFW

[m s−1

]

RMS = 2. 2

wind component v comparison

5.08 5.082 5.084 5.086 5.088 5.09 5.092 5.094 5.096 5.09852.828

52.829

52.83

52.831

52.832

52.833

52.834

52.835

52.836

52.837

52.838

Longitude

Latit

ude

SUMO flight (2014−05−10 14:07)alt: 70 m − 90 m

alt [

m]

70

72

74

76

78

80

82

84

86

88

ECN (spring) Fl 2 (10.5.2014) leg 1–10; 80 m agl

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Remaining challenges:

•  Eliminate second solution (side wind component from opposite side)

•  Fine tune method •  Error estimation •  Find stationarity and homogeneity measures and

thresholds from flight parameters •  Impact of leg length on turbulence statistics (minimizing

random and systematic sampling errors) •  Tune autopilot: constant airspeed, altitude and direction

during flight leg •  Aerodynamic effects on true airspeed

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