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**Wind Compensation for Small Sounding Rockets**

Blowing winds move all Rockets too, oft way off course Science fixes that Seventh IREC, June 2012 Green River, UT C. P. Hoult & Ashlee Espinoza CSULB

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Topic Outline Wind measurement Launcher compensation Summary

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Wind Measurement

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**Wind Power Spectral Density**

cyclonic weather turbulence diurnal breezes 100 hours 1 hour 0.01 hour Isaac Van der Hoven, “Power Spectrum of Horizontal Wind Speed in the Frequency Range from to 900 Cycles per Hour”, Journal of Meteorology, Vol 14 (1957), pp

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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)

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**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 Line of closest approach LOS 2 LOS 1 Estimated position

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**Tethered Pilot Balloon (Pibal) Wind Sensor**

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: cm Tensile strength: 22.7 kg Weight: gm/m Altitude: 40 m Wind Drag Pibal LOS Catenary Tether Elevation Angle Sensor Optics * Scientific Sales, Inc. web site ** S.F.Hoerner, “Fluid-Dynamic Drag”, 1965 *** Honeywell literature

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**Drag Coefficient of a Sphere**

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**Effect of Balloon Diameter**

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

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**Three Foot Balloon Response Curve**

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Balloon Inflation Techniques Template to control diameter Sources

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**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: ” diameter! Bias errors from sag due to gravity and aerodynamic drag compensated in software Winch design & operations

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**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

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**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

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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 = m, and C and D are chosen to match the two data points

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**Typical Wind Profile Curves**

1 2 3 4 5 6 7 500 1000 1500 Altitude, m 6 250 m m 4 250 m m Wind Speed, m/s

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Wind Compensation

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**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

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**3 DOF Simulation Wind Profile**

Lewis method assumes the rocket instantly heads into the relative wind (zero a 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

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**Cross-Plane Launcher Adjustments**

Second, resolve both measured winds into In-Plane & Cross-Plane components First, find desired impact point location Third, fit “exponential” profiles to both components N Az Altitude Altitude + In-Plane wind Range In-Plane wind Cross-Plane wind + Cross-Plane wind Run SKYAERO with various QEs and no wind 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 Fourth, run SKYAERO with QE = 90O and Cross-Plane winds Impact range = (±) vv feet + sign implies that the Cross-Plane impact is and vice versa for – signs QE Impact Range 90o xxxx 88o yyyyy 86o xxzz + Cross-Plane wind impact point shift 84o aabbb 82o

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**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

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**In-Plane Launcher Adjustments**

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 title Sixth, 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 QE Impact Range 90o xxxx Launcher Tilt 88o yyyyy 86o xxzz 84o aabbb Impact Range Desired Range 82o 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 – + – + –

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**Total Launcher Adjustments**

Eighth, Find the total launcher tilt, QET, and azimuth, AZT Mind those signs North Approximate solution AZT QEI QET = √ QEI2 + QEC2, and AZT = AZ + tan-1(QEC/QEI) AZ QET QEC Sketch for positive QEI & QEC launcher tilts

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

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