Wind Compensation for Small Sounding Rockets

Seventh IREC, June 2012

Green River, UTC. P. Hoult & Ashlee Espinoza

CSULB

Blowing winds move allRockets too, oft way off courseScience fixes that

Topic Outline

• Wind measurement

• Launcher compensation

• Summary

Wind Measurement

Wind Power Spectral Density

1 hour100 hours 0.01 hour

turbulence

•

diurnal breezes

cyclonicweather

Isaac Van der Hoven, “Power Spectrum of Horizontal Wind Speed in the Frequency Range from 0.0007 to 900 Cycles per Hour”, Journal of Meteorology, Vol 14 (1957), pp 160-164

Space and Time Scales

• Lowest frequency peak (~100 hour period, (Bjerknes)) is associated with cyclonic (frontal) weather

• Middle frequency peak (~ 12 hour period) is associated with diurnal breezes (common in coastal locations)

• Highest frequency peak (~ 0.01 hour period) is associated with tropospheric turbulence driven by– Turbulent planetary boundary layer motions– Rising warm air cells (thermals)

• Spatial extent found from typical phenomenological velocities– Cyclonic weather: 100 * 40 km/hr = 4000 km – Diurnal breezes: 12 * 10 km/hr = 120 km– Vertical distance scale ≈ 10 km. – Gravity constrains cyclonic weather & diurnal breezes (≈ 2D

horizontal plane)– Turbulence: 0.01 * 3 km/hr = 300 m (≈ 3D isotropic)

Weather Balloons• Classical sounding rocket approach

– Release a sequence of free pilot balloons (pibals) that drift latterly with the horizontal wind field

– Track these optically with two theodolites that regularly report pibal angular positions

– Estimate three pibal coordinates using

a ”split-the-difference” algorithm– Filter the position data to obtain wind vector– Main problem is pibals ascend erratically

even in still air…more on that later• Winds so measured will reflect frontal weather and diurnal breezes

– Gusts add noise– Most recently measured winds used to predict rocket trajectory

• Major drawback is costs well beyond what we can afford

LOS 1LOS 2

Line of closest approach

Estimated position

Tethered Pilot Balloon (Pibal) Wind Sensor

DragWind

Catenary Tether

Elevation Angle

PibalLOS

Typical Data• Pibal*

• Type: Natural rubber• Diameter: 118 cm (inflated)• Weight: 200 gm• Net lift: ~800 gm• Drag coefficient**: 0.14 (Re = 106)

• Tether***• Material: braided Fins• Spectra 2000 ®• Diameter: 0.033 cm • Tensile strength: 22.7 kg• Weight: 0.083 gm/m• Altitude: 40 m

* Scientific Sales, Inc. web site** S.F.Hoerner, “Fluid-Dynamic Drag”, 1965 *** Honeywell literature

Sensor Optics

Pibal Elevation Angle, degrees

0

20

40

60

80

100

0 1 2 3

Windspeed, m/s, @ 40 m

Ele

va

tio

n A

ng

le,

de

gre

es

Drag Coefficient of a Sphere

Sphere Drag Coefficient

0

0.1

0.2

0.3

0.4

0.5

0.6

1.00E+04 1.00E+05 1.00E+06 1.00E+07

log Re

Cd

Effect of Balloon Diameter

Balloon Drag

02468

101214161820

0 5 10 15

Wind Speed, m/s

Dra

g F

orc

e, N 1 ft Diameter

2 ft Diameter

3 ft Diameter

4 ft Diameter

5 ft Diameter

Select Three Foot Balloon Diameter to Provide Good Visibility and Acceptable Response for wind speeds < 7 m/s

Three Foot Balloon Response Curve

Three Foot Diameter Balloon Sensor

0.00E+001.00E+012.00E+013.00E+01

4.00E+01

5.00E+016.00E+01

7.00E+018.00E+019.00E+01

0 2 4 6 8 10 12 14

Wind Speed, m/s

Line

of S

ight

Ele

vatio

n A

ngle

, deg

Balloon

• Inflation Techniques– Template to control diameter

• Sources

Winch & Spectra™

• Spectra™ 2000, the wonder material• Made of polyethylene• How strong it is…15x steel at same weight• Used for fishing line & bullet-proof vests• How thin ours is: 0.011” diameter!• Bias errors from sag due to gravity and aerodynamic drag

compensated in software• Winch design & operations

SkyScout™

• How it works– Accelerometers for elevation angle– Magnetometers for azimuth angle– GPS to locate Earth’s magnetic field– Computer

• How to use it…settings & which windows have our angles• Telescope & Tripod

– BTW, also good for star parties

Wind Measurement at Higher Altitudes

• Tethered Pibal wind measurement works up to about 1 km altitude– But our rockets fly much higher than that. What’s to be done?

• NOAA routinely measures winds throughout the troposphere and stratosphere– How do we get that data?– We’ve gone to the FAA in the past– Data acquisition technique is social engineering

• ESRA, as part of hosting IREC, must get FAA clearance for our launches– Could ESRA get daily winds aloft from the FAA and share with

all contestants?– Just a thought

Wind Profiles• Classical wind response calculations ingest winds from ~ 20 altitude

layers• But, the best we can hope for is winds from 2 layers (Tethered pibal &

FAA)• Oh, what’s a poor girl to do?• Why, we fit a curve to those two points & feed it into our trajectory

code• Our first thought was to use the textbook 1/7 power law profile

– The very first time we tried we encountered a low altitude jet stream. Whoops!

• Currently, we use

• where W = wind speed, m/s, and λ = 0.005 m, and C and D are chosen to match the two data points

)exp())exp(1( hDhhCW

Typical Wind Profile Curves

0

1

2

3

4

5

6

7

0 500 1000 1500

Altitude, m

6 m/s @ 250 m 4 m/s @ 1000 m4 m/s @ 250 m

6 m/s @ 1000 m

Win

d S

peed

, m

/s

Wind Compensation

Wind Impact Point Displacement Algorithm• Establish desired impact point Find

– Desired trajectory plane azimuth in Earth-fixed coordinates– Effective Quadrant Elevation Angle (QE to hit the desired impact point

absent winds) by interpolating a table of impact range vs. QE• Resolve both measured vector winds into in-plane and cross-plane

components– Fit wind profile curves to both components

• Run trajectory simulation for both in-range and cross-range components– Estimate impact point displacements separately for in-plane & cross-

plane wind components– Include parachute phases– Use QE = 90o for cross-plane simulation run– Use Effective QE for in-plane simulation run

• Use a precision trajectory code like SKYAERO– Based on Lewis* method wind response – Corrected for finite inertia near launch *J.V.Lewis, “The Effect of Wind and Rotation of the Earth on Unguided Rockets”, Ballistic

Research Laboratories Report No. 685, March, 1949

3 DOF Simulation Wind Profile

Physical & Simulation Wind Speeds

0

0.2

0.4

0.6

0.8

1

0 200 400 600

Altitude, m

Win

d S

pe

ed

, m

/s

Vphysical

Vsimulation

• Lewis method assumes the rocket instantly heads into the relative wind (zero all the way)• Finite Inertia Correction Factor

• Only applied to ascending trajectory leg• Vsimulation = Vphysical for descending trajectory leg

• 3 DOF Lewis method results using Vsimulation closely approximates 6 DOF results using Vphysical

• Initial pitch/yaw wavelength of 200 m and wind profile ≈ altitude1/7

Cross-Plane Launcher Adjustments

First, find desired impact point location

N

Az

Range

Second, resolve both measured winds into In-Plane & Cross-Plane components

+ In-P

lane

wind

+ Cross-Plane wind

Third, fit “exponential” profiles to both components

Alti

tude

In-Plane wind

Alti

tude

Cross-Plane wind

Fourth, run SKYAERO with QE = 90O and Cross-Plane winds

Run SKYAERO with various QEs and no wind

QE Impact Range

90o xxxx

88o yyyyy

86o xxzz

84o aabbb

82o

• Impact range = (±) vv feet

• + sign implies that the Cross-Plane impact is

• and vice versa for – signs

+ Cross-Plane wind

impact point shift

Fifth

• Using the Cross-Plane wind impact point shift, interpolate the no wind range vs. QE table to find that launcher tilt, QEC, that yields the same range

• The algebraic sign associated with this QEC is opposite to the Cross-Plane wind impact shift. If we started the step four SKYAERO run with QEC, there would be no Cross-Plane impact point shift

Discussion on Cross-Plane Ballistics

• Why does the Cross-Plane algorithm described on the previous chart work?

• Because both the wind and launcher tilt provide rotations at the beginning of a flight

– The actual impact point shifts are ∂ Range/∂ Angle times the rotation angles

• The idea is to select a launcher tilt that just cancels out the Cross-Plane wind induced rotation

– All that’s needed are two SKYAERO runs, one with winds and one with tilt that have the same ∂ Range/∂ Angle

– Even though ∂ Range/∂ Angle is not quite correct, upon solving for the required tilt, the erroneous vales of ∂ Range/∂ Angle cancel out.

• If sign of Cross-Plane wind is

– Sign of Cross-Plane impact point is

– Sign of corrective launcher tilt is

+ –

+ –

– + ← QEC

In-Plane Launcher AdjustmentsSixth,

• Using the In-Plane wind component, make a sequence of SKYAERO runs taking care that at least one run gives an impact range greater than that desired, and one run gives an impact range less than that desired

Seventh,

• Using the Step 6 table of impact range vs. QE, interpolate to find that QE, QEI, that yields the desired range

• Note that there are no more sign shifts as per the Cross-Plane launcher titleQE

90o xxxx

88o yyyyy

86o xxzz

84o aabbb

82o

Impact Range

Impact RangeDesired Range

Laun

cher

Tilt

Sign Convention

• If sign of In-Plane wind is

• Sign of In-Plane wind impact point is

• If Wind Impact Range (QE = 90o) ≤ Desired Impact Range, sign of QEI is +

• If Wind Impact Range (QE = 90o) ≥ Desired Impact Range, sign of QEI is –

+ –+ –

Total Launcher Adjustments

QEI

QEC

QET

QET = √ QEI2 + QEC

2,

and

AZT = AZ + tan-1(QEC/QEI)

AZ

AZT

Eighth,

• Find the total launcher tilt, QET, and azimuth, AZT

• Mind those signs

Approximate solutionNorth

Sketch for positive QEI & QEC launcher tilts

Summary

Wind compensation of sounding rocket impact point is a mature art routinely practiced over many decades