Hornady4DegreeofFreedom(4DOF)TrajectoryProgram

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TableofContents

Introduction…………………………………………………………………………………………………….………………2

GyroscopicStability………………………………………….………………………………………………….6

ZeroAngle…..…….………..……….……………………………………………………………………………….7

MuzzlevelocityCorrection…………………………………………………………………………………….7

SpinDrift……………………………………………………………………………………………………………..9

AerodynamicJump……………….………………………………………………………………………..……9

EarthBasedEffects………………………………………………………………………………………………..10

DragFormFactor………………………………………………………………………………………………….10

ImportantFactorsandTips………………………………………………………………………………………….…..13

AdditionalInformation…………………………………………………………………………………………………..…16

RecommendedZeroingProcedures………………………………………………………………………16

UnderstandingAerodynamicJump.………………………………………………………………………20

CalculatingMuzzleVelocityfromChronograph/Radar…………………………………….…..25

Uphill/DownhillShootAngles...………………………………………………………………..…………..27

ApplyingSpinDriftandAerodynamicJump……….………..……………………………..…………..28

Index…………………………………………………………………………………….…………………………………….…….30

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This document includesmultiple sections to provide information and background on the use of theHornady4DegreeofFreedom(DOF)TrajectoryProgram.TheUsermanualexplainsthebackgroundandcapabilityoftheHornady4DOF.TheImportantFactorsandTipsprovidesinformationregardingtheuseof theprogram.TheAdditional Information section containsdetailed informationon various subjectspertainingtotheunderstandingandapplicationoftheHornady4DOFoutputs.WesincerelyhopeyoufindthenewHornady4DOFTrajectoryProgramaccurateanduseful.

Introduction

The Hornady 4 DOF trajectory program is a state of the art trajectory engine that utilizes amodifiedpointmasssolutiontoprovideincrediblyaccuratetrajectoriesforlistedprojectilestoextremelylongranges.TraditionalSiaccibasedBCcodesdonotconsiderprojectiledynamicflightcharacteristicsandtheircontributionstothefinaltrajectorysolution.TheHornady4DOFaccuratelymodelsthedynamiccharacteristicswhichcaneffectandmodifytheprojectile’strajectory.ThesoftwaredoesnotuseBallisticCoefficient(BC),butinsteadutilizesDragCoefficient(Cd)versusMachnumberforeachprojectile.TousetheprogramyouwillselectaspecificprojectilefromapulldownmenuinsteadofinputtingaBC.Whenaprojectile is selected, the program inputs projectile mass properties, aerodynamic moments, andcoefficientstoincludeDopplerradardetermineddragcoefficientsspecifictoeachprojectile.Thesoftwareaccuratelypredictsdrop,winddrift,projectileGyroscopicStabilityFactor(Sg)asafunctionofrange,yawofreposeandcorrespondingpredictionofspindrift,aerodynamicjumpduetoacrosswind,andlimitcycleyawatextendedrangesduetoMagnuseffects.

All listedprojectileshavebeenextensivelytestedwithDopplerradarduringdevelopmentandanalysisoftheprogramaccuracy.OutputvalueshavebeencomparedtoDopplerradardataatrangesasfaras2,000yardswithpredictederrorsbeingwithinsingledigitsofradardataforretainedvelocity.Itisnotpossibletoobtainthisleveloffidelitytoactualrealworlddataanyotherway.TheuseofBCisagoodapproximationoftrajectories,butbecomesincreasinglyinaccurateatvariouspointsduringthetrajectory.ForthisreasontruingtheBCtoreflectactualretainedvelocityordropdatahasbeenthecommonmethodusedtoaddresstheerrorsinpredictionwhenusingBC.TheinaccuraciesseenwhenusingBC,evenG7,areduetothemismatchbetweentheactualdragoftheprojectilebeingfiredandthedragofthestandardprojectilebeingusedtomodelit.Asprojectilesareshottolongerandlongerranges,trajectorypredictionsbasedonBCbecomeincreasinglyinaccurateinelevation,becomesubstantiallyinaccurateinwindandspindrift,andoffernopredictionforaerodynamicjumpduetocrosswind.

ThesuperiorityofCdoverG7canbeshowninacomparisonoftheCdversusMachnumberoftheG7standardprojectiletothatofseveralcurrentlyproducedprojectilesFigure1.Ascanbeseen,otherthanthe220grELD-X™noneoftheotherprojectilesmatchupwiththeG7dragcurveinbothCdvalueandcurveshape.Thiswillinevitablyleadtoerrorsintrajectorypredictionsatlongerrangesandespecially

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atcertainpointsinthetrajectorywheredragcurvesdonotmatchup.Theonlywaytotrulyandaccuratelymodelthetrajectoryofaprojectileiswithspecificmassandaerodynamicmodels,specificdragdataandmodelingofthedynamicbehavioroftheprojectile.

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Figure1:Cdvs.MachnumberForVariousProjectiles

TheG7Ballisticcoefficientdoesabetterjobofpredictingthetrajectoryofmodernlongogive,boattailbulletstolongerrangesthantheG1standard,however,itisstillnotmodelingtheexactCdvalueorshapeandwillresult inerrors.Utilizingthepopularandwell-designedJBMballisticscode,Table1.showsacomparisonofdownrangepredictionsbetweenG7andHornady4DOF.AHornady6.5mm140ELD-Matchprojectile iscompared for retainedvelocity,drop,andspindrift.Table2.shows thesamecomparisonofwinddriftanddropvalueswithaerodynamicjumpduetoacrosswind.

Table1.TrajectoryPredictionsforHornady6.5mm140grELD™Match

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Table2.TrajectoryPredictionsforHornady6.5mm140grELD™Match

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GyroscopicStability

Gyroscopicstability(Sg)ismerelyameasureoftheprojectile’sabilitytomaintainpointforwardflightandnotassumealargeandvariableangleofattack.Aminimumgyroscopicstabilityfactoratthemuzzleof1.0isrequiredforabullettoflypointfirst.Sgdependsontheprojectile’smass,momentsofinertia,spinrate,airdensity,pitchingmomentandvelocity.Existingstabilitycalculatorsavailabletodaybasedoffbullet lengthareagoodruleof thumbestimate,but theyareexactly that,approximations.Withoutproperlymodelingmassdistributioninsidetheprojectileaswellastheeffectitsuniqueshapehas on the location of the Normal Force Center of Pressure location, accurate gyroscopic stabilitycalculations using the Greenhill or Miller stability calculations are estimates. The Hornady 4 DOFaccurately calculates Sg based on each projectiles mass, aerodynamic properties, and atmosphericconditions.Itmustbepointedoutthataprojectilegetsrapidlymorestablegyroscopicallyasitfliesdownrange.Thespinofaprojectiledecaysatamuchslowerratethanitsaxialvelocitydoes.Thechangingaerodynamicpropertiesastheprojectileslows,withoutthespinappreciablychanging,resultsinamoreandmorestableprojectileasitfliesdownrange.

Ingeneral,aprojectilewithSgvaluesatthemuzzle,inambientatmosphericconditions,ofaround1.4isconsideredthelowerlimit.ThisallowsforsomeerrorinthecalculationofthePitchingMomentandforincreasedairdensitywhentheprojectileisfiredundercoldconditionsatlowaltitudes.Hornady4DOFwilldisplaytheSgofthebulletasitfliesdownrange.IfyouhaveanSgoflessthan1.4atthemuzzleunderambientconditionswewouldrecommendyoumodelafastertwistrate,andconsiderusingafastertwistbarrel.ExtensiveDopplerradartestinghasshownthatforsupersonicMachnumbersabove1.7-1.8thatthedragofaprojectilereachesaminimumatanSgofabout2.0.ThetransonicdragonaprojectilewillcontinuetodecreaseasthespinrateandSgisincreased.Therearepracticallimitsofthisasyoucanspinaprojectiletothepointthatitwillmechanicallyfailinflightfromexcessivecentrifugalforce.Excessivelyspinninganon-expandingbulletwillhavedetrimentaleffectsonitsterminalperformance.

Afterrunningatrajectory,thefirstcheckshouldbethehighlighted“Gyro”columnoftheoutputstable,seeFigure2.TheHornady4DOFwillnotproduceanerrorif theSgisbelow1.0atthemuzzle.Instead,the4DOFwillmodeltheprojectileasunstableuntilithaslostenoughvelocitytoclimbbacktoaSgof1.0.WhenlaunchedwithaSgoflessthan1.0,velocitylossoccursextremelyrapidlyandshouldappear abnormal. Figure 3. is an example output table showing the highlighted area that should becheckedbytheusertoensureaproperlystabilizedbullet.Thisvalueshouldbecheckedforeachtrajectoryran.

Figure2.SampleOutput

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ZeroAngle

VersionIIof4DOF™hasauniqueandveryusefulfeatureaddedcalledZeroAngle.ZeroAngleistheangleoftheboreoftheriflerelativetotheLineofSight(LOS)oftheoptic.Itisdependentonthegeometryofthescopemountingrelativetotherifleboreandthescopeadjustmentsettingorzero.Anychangesinenvironmentalconditionsfromzeroingtoactualfieldshootingcanhaveaneffectontheactualzerorangecrossingoftheprojectileandthelineofsight.Thisincludeschangesintemperature,pressure/altitude,humidity,windspeed,andwindangle.Ifthechangestheseenvironmentaleffectshaveontheactualzerorangearenotaccountedfor,missestovaryingdegreesarelikely.

ZeroAngledoesnotchangewithdrasticchangesinatmosphericconditionslikeaZeroRangecan.Aslongasthescopezeroisnotchangedthemechanicalrelationshipbetweentheboreangleandlineofsightwillremainthesame.OncetheZeroAngleisdeterminedforagivenload,atmosphericconditionandZeroRangeitcanbeconsideredafixedvalue.TheprogramnowallowstheusertoenteraZeroRange,whichcanbedependentonatmosphericconditions,ortheZeroAnglewhichisindependentofatmosphericconditions.ThisallowstheusertoutilizeaZeroAngleinsteadofZeroRangeandeliminateanyerrorsassociatedwithachangeinatmosphericconditionseffectingtheactualZeroRangeandcorrespondingtrajectory.UsingZeroAngleallowstheusertogotoanyatmosphericcondition,nomatterhowdifferentfromtheirzeroingconditions,andthe4DOF™willoutputthecorrectzerodistanceandtrajectorywithouthavingtore-zerotherifletothosespecificconditions.

TodeterminetheZeroAnglespecifictoyourrifleandload,followtherecommendedzeroingproceduresdescribedlaterinthisdocument,orinvideoformontheHornadyYoutubepage.The4DOFwilloutputbothaZeroRangeandZeroAngleforeverytrajectorythatisranintheYourInputVariablesportionoftheTrajectoryResultsTable.Afterfollowingtherecommendedzeroingprocedures,theusershouldnotetheZeroAngleforfutureuse.Forallfollowingtrajectorycalculations,theusercanselectZeroAngleontheinputpageinsteadofusingatraditionalZeroRange.UsingZeroAngleensuresthatanyvarianceinatmosphericconditionswillnotinadvertentlyeffecttrajectorycalculationsusingthe4DOF.

MuzzleVelocityCorrection

Forpreciseshooting,muzzlevelocityneedstobeveryaccuratelyknown.Allpropellantschangeperformanceasafunctionoftemperatureandthusthepressureandmuzzlevelocitychangeaswell.Somepropellantschangemuchlessthanothers.Typicallysinglebase,noNitroglycerin(NG),propellantschangetheleastfollowedbydoublebasepropellants,whichincorporateNGandthebiggestvariationisusuallyfoundwithBALL™propellants.Dependingoncaliber,primer,andespeciallythepropellant,loadscanchangebyaslittleas30-50feetpersecond(fps)overa150degreesFtemperaturedifferentialtoasmuchashundredsoffps.Tomakealongstoryshort,themosttemperaturestablepropellantsasofthewritingofthispaper,November2016,aretheHodgdonExtremeSeriesandthenewIMREnduron™

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propellants.ToaccountforthesepossiblechangesinmuzzlevelocityduetotemperatureVersionIIof4DOFincorporatesaTemperatureSensitivityCoefficient(TSC)feature.

CustomTemperatureSensitivityCoefficient

Toachievethemostaccuratemuzzlevelocityprediction,theusershouldtesttheirloadattwowidelydifferenttemperaturesaswellasabaselinetemperatureandaccuratelyrecordthevelocities.Anexampletemperaturerangewouldbe20degforbelowbaseline,70degforbaseline,and100degforabovebaseline.Thetemperaturerangeoftheenvironmentyouwillbeshootinginshoulddictateyourtestedtemperatures.Whenconductingtesting,itisimportanttomakesuretheammunitionhasenoughsoaktimetoreachtheactualtemperaturebeingtested.VelocityandtemperaturerecordingscanbeenteredintoTheTemperatureSensitivityCoefficientCalculatortodeterminethecustomTSC’sthatwillbeenteredintothe4DOF.Manualcalculationcanbeconductedbydividingthedifferenceinvelocitybythedifferenceintemperaturebetweentwotesttemperatures.

OncetheTSC’sarecalculatedandenteredintothe4DOFthebaselinetemperatureandatmospherictemperaturesmustbeinputandwillbeusedtocalculatethechangeinvelocity.TheinputmuzzlevelocityatthebaselinetemperaturewillbeautomaticallyalteredbasedontheTSC,thebaselinetemperature,andtheatmospherictemperatureoncethetrajectoryiscalculated.Thealteredvelocitycanbeviewedintheupperleftportionofthe“YourInputVariables”ofthe“TrajectoryResults”page.

Mostpropellantsshowalowermuzzlevelocityatcoldtemperaturesandahighervelocityathottemperatureswhencomparedtothebaselinetemperaturevelocity.TheamountofchangeinvelocityperdegreechangeintemperatureusuallyisnotexactlythesameforabovebaselinetemperaturesvsbelowbaselinetemperaturesandthereforewillresultinauniqueTSCfortemperaturesaboveandbelowthebaseline.InthiscasetheuserwillneedtoenterthecorrectTSCbasedontheatmospherictemperaturebeingaboveorbelowtheirbaselinetemperature.Intherarecasethatvelocitiesriseattemperaturesbelowbaselineorvelocitydropsattemperaturesabovebaseline,anegativeTSCvalueshouldbeentered.

GeneralTemperatureSensitivityCoefficient

Iftheuserisunabletoconducttheirowntesting,VersionIIof4DOFalsoallowstheusertochooseapropellantandassociatedTSCfromapulldownmenu.Thebaselinetemperaturewhenrecordingmuzzlevelocityisstillrequiredtoaccuratelycalculatechangesinvelocity.Afterinputtingthebaselinetemperature,thepowderbeingusedshouldbeselectedfromthedropdownmenu.AgeneralTSCwillautomaticallybeusedbasedontheselectedpowder,baselinetemperature,andatmospherictemperaturetoalterthemuzzlevelocity.

TheuserdeterminedTSCwillprovidemoreaccurateresultsthanthetable,whichisanaverageTSCoftheselectedpropellanttestedbyHornadyinanumberofdifferentloadsandwithdifferentcomponents.IfthecustomTSCisnotavailable,utilizingtheprovidedtableofTSC’swillprovidemoreaccurateresultsthannotaccountingfortemperatureeffectsonmuzzlevelocityatall.

IftheuserdoesnotwanttousetheTSCfeatureofthe4DOF,simplyleavetheTemperatureSensitivityCoefficientboxuncheckedandthe4DOFwilloperatebasedonasimplemuzzlevelocity.

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Note:WehavenotincludedanyBALL™propellantsintheTSCtablebecausetheytypicallyhavemuchgreatertemperaturesensitivityascomparedtomostotherpropellants.Becauseofthiswedonotconsiderthemappropriateforuseinlongrange,highprecisionshootingapplications.IfyouareusingBALLPropellantswehighlyrecommendyouusetheCustomTSCapplicationin4DOFanddeterminetheTSCforyourload.

SpinDrift,DriftDuetotheYawofRepose

Asaprojectile fliesdownrange, thetrajectory iscurved in theverticalplanebytheactionofgravity.Thetrajectorycurvatureintheverticalplane,combinedwiththegyroscopicmomentarisingfromtheprojectilespinandinertia,maketheprojectilenosepointslightlyuprelativetothevelocityvectorofthebullet.Theprojectilenosepointinguprelativetoitsvelocityvector,combinedwiththetrajectorycurvatureinducesanangularrateontheprojectile.Ifthebulletspinisinthe“righthand”sense(spinaxisaligned with your thumb, the direction of rotation aligned with your fingers), the projectile angularmomentummakesthebulletpointnoserightrelativetoitsvelocityvector.Theprojectilenosepointingslightlytotherightcauseshigherpressureontheleftsideoftheprojectile.Thispressuredifferentiallefttorightmakesthebullet“drift”totherightforrighthandtwistbarrels.Thedriftisknownasthe“driftduetotheyawofrepose”or“spindrift”.Thedriftduetoyawofreposedependsontheballisticdropofthebullet,thetwistofthebarrel,andtheinertialandaerodynamiccharacteristicsoftheprojectile.

TheHornady4DOFtrajectorycodecorrectlycalculatesthedriftduetoyawofreposeforeachbullet/twist/velocitycombination,somethingthat theold“Siacci”basedtrajectoryprogramscanonlyestimate.

AerodynamicJump

Aerodynamicjumpisaninterestingaerodynamicphenomenonthatoccurswhenspinstabilizedprojectilesarefiredintocrosswinds.Thegyroscopicspinmomentoftheprojectilecausesthebulletnosetosuddenlypointupordowndependingonthecrosswinddirection,makingtheprojectilejumpinthevertical direction. This phenomenon is known as “aerodynamic jump” and arises because of theinteractionofgyroscopicmomentoftheprojectileandangularrateinducedwhentheprojectilesuddenlyentersacrossflowfromwindsactingperpendiculartothemuzzlevelocityvector.Ifthewindisblowingfromrighttoleft,theaerodynamicjumpis“up”intheverticaldirection.Whenfiringincrosswindsfromtheleft,theverticaljumpisdown.Theaerodynamicjumpisafixedanglethatdependsonthemagnitudeofthewind,thetwistofthebarrel,andtheinertialandaerodynamiccharacteristicsoftheprojectile.AmoredetailedexplanationofaerodynamicjumpcanbefoundintheAdditionalInformationsectionbelow.

The Hornady 4 DOF trajectory code correctly calculates the aerodynamic jump for eachbullet/twist/velocitycombination,somethingthattheold“Siacci”basedtrajectoryprogramscan’tdo.

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EarthBasedEffects

Earthbasedeffectsarecommonlyreferredtoas“CoriolisEffect”.TheeffectisactuallywhatisknownastheEotvosEffectforthosewhowishtodofurtherresearch.Forourpurposesherewewilluse“EarthBasedEffects”(EBE)asacatchall.InVersionIIof4DOFwhenEBEeffectsareturnedontheprogramiscalculatingthetrajectoryoftheprojectileincludingbothelevationanddriftcomponentscausedbytheprojectilevelocityvectorrelativetotheearthaswellascurvedeartheffects.

ManyassumethattheEBEisduetotheearthrotatingundertheprojectile.Thisisinfactnottrue.

Forallpracticalpurposes,insmallcaliberballistics,theprojectileremainsattachedtothereferenceframeoftheearth.Simplyput,theprojectilestartsoutwiththerotationalvelocityoftheearthatthepointitisfired and keeps that velocity component throughout its flight. What is actually happening is theprojectile’svelocityiscreatinganincreaseordecreaseininertia,oracentrifugalforce,whichforaverybrieftimeistryingtopushtheprojectileeitherfurtherawayorclosertotheearth.

OnewaytopicturetheEBEistopictureanearthsatellite.Thefasterthesatellitetravelsthehigheritorbitsrelativetothecenteroftheearth.Ifitattains17,000mph,relativetotheearth,itwillleaveearthorbit.Rocketsaretypicallyfiredfromwesttoeasttotakeadvantageof theapproximately1,000mphrotationalvelocityattheequator,soastocarrylessfuelandmorepayload.Ifarocketisfiredfromeasttowesttherocketisnowworkingagainstthe1,000mphrotationalvelocityanditmustcarrymorefuelandlesspayload,inordertoovercomethe1,000mphinthewrongdirection,toachievethesameorbitalheight.Inthesameway,ifaprojectileisfiredwesttoeast,forabriefperiodithasavelocityaddingtotheearth’srotationalvelocityandwillwanttobeatagreaterdistancefromthecenteroftheearth,higherthanitstartedoutat.Andconversely,ifitisfiredfromeasttowestitisnowworkingagainsttheearth’srotationalvelocityandwantstobeclosertothecenteroftheearth,lowerthanitstartedoutat.BearinmindthisisaVERYsimplifiedexplanationofwhatishappening,buthopefullyhelpstoexplainahardtovisualizephysicalconcept.

Whenfiringatanynorthorsouthazimuthsthisaddsahorizontaldriftcomponenttotheprojectile

trajectory.Rememberfromabove,theprojectilehasthesamereferenceframeasthepointonearthitwasfiredfrom.Theprojectilewillhavetherotationalvelocityvectoratthepointitwaslaunchedfrom.Theearthhasthehighestsurfacerotationalvelocityattheequator.Becauseitisasphericalsurface,asyoumoveawayfromtheequator,northorsouth,therotationalspeedatthesurfaceisslowerbecauseofthesmallerradius.Inthenorthernhemisphereifyoufirenorththeprojectilewillhaveawesttoeastvelocitycomponentgreaterthantheimpactpointbecauseyouarefiringtoasmallerradiuspointontheearth.Theprojectilewilldriftslightlytotheright.Inthenorthernhemisphereifyoufiresouthyouarefiringtoapointthatismovingfasterthanthepointthebulletleftfromandagaintheprojectilewilldrifttotherightofthetarget.Inthesouthernhemisphereeverythingistheopposite,theprojectilewilldrifttotheleftofthetarget.Bearinmindthatattypicalsmallarmsrangesthisdriftisprettysmall.

Toaccuratelypredicttheearthbasedeffectsontheprojectileyoumustknowrelativelyaccurately

whatlatitudeyouarefiringfromandwhatazimuth(compassangle)youarefiringto.Earthbasedeffectscanessentiallybeignoredouttorangesof1,000yardsastheyareverysmall.Wehavedoneextensivetestingat1,500yardsandhave foundtheearthbasedeffects tobeequal toor less thanthenormalvariationsofmuzzlevelocity,dragvariationfrombullettobulletandtailorheadwindeffects.

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Notesontheuseofthe“AxialForceFormFactor”InputtotheHornady4DoFTrajectoryEngine

TheHornady4DOFisonlyasaccurateasthedatafeedingit,andHornadyhastakengreatpainstoensurethedragvs.Machnumberdataforeachprojectilemodelusedinthenewtrajectoryengineisbasedonanaverageofaverylargedatasample.Hornadyhasfiredeachoftheprojectilesinthisdatabasefromseveralriflesandwehaveoccasionallynoticedsomeminorshiftsinthedragvs.Machnumbercurvesfrombarrel-to-barrelwithinthesamesampleofbullets.Anyactualdragshiftforagivenbarreldependsonthebarrelgeometry,twistrate,andqualityofmanufacture(internalroughness,straightness,etc.).Figure3.showsanextremeexampleofobserveddragvariabilityofalargenumberofidenticalprojectilesfiredfromdifferentbarrelswithdifferenttwistsanddifferentriflinggeometries.Dopplerradarhasalsoshownsignificantchangesintheprojectiledragasafunctionofthetypeofpropellantusedandthemuzzlebraketype.

Figure3.Dragvs.MachNumberforIdenticalProjectilesandDifferentBarrels

Generally,theaveragedragvs.Machnumberprofileforastandardprojectilefiredfromagivenbarrelwilldifferonlybyasmallamount(a“bias”fromnominal),usuallyafixedpercentshiftfromthebaseline.

Hornadyhas firedeachof theprojectiles in thedatabasethroughseveralbarrels,and it’souropinionthatwhenusingthe4DOF,youshoulduseadefaultdragformfactorof1.00toinitiallysimulatetheflightpathofprojectiles.Thiswillprovidetheexpectedbulletpathofthe“average”bulletfiredfroman“average”barrel.Dependingonthedetailsofthebarrel,loadandmuzzlebrakeyouareusing,bulletsfiredfromyourgunmayhavedragvs.Machnumberbehaviorthatisasmallpercentagehigherorlowerthanthedatawehaveprovided.Whiletherearerandomdragvariationsshot-to-shotontheorderof2%,

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theaverageverticalimpactpointatextendedrangesisstronglyinfluencedbythingsliketheairdensity,averagemuzzlevelocity,averageprojectileweight,aswellastheaveragedragvs.Machnumberprofile.

Ifyouhavesimulatedtheflightpathofourprojectiles,andcloselymonitoredthemeanpointofimpactatzerorangealongwithmuzzlevelocityviaanaccuratechronograph,butfindyourimpactpointsaredifferentthantheHornady4DOFpredicts,youcanmakeaminorshift(a“bias”)intheimpactpointintheverticalplanebymakingaminoradjustmenttotheprojectiledragformfactor.Iftheactualmeanpointofimpactoftheprojectilesfiredatextendedrangesishighrelativetothepredictedimpactpoint(drag is lower thanwhat is being used and it is causing the program to predict toomuch elevationadjustment), incrementally reduce the drag form factor in the Hornady 4 DOF until the simulatedtrajectorypathmatchesyourverticalimpactpointtestingatextendedrange.Conversely,iftheaverageimpactpointofyourgroupsisbelowtheimpactpointpredictedbytheHornadytrajectoryengine(dragis higher than what is being used and the program is under predicting elevation adjustment),incrementallyincreasethedragformfactoruntilyouhavematchedtheobservedverticalimpact.

The use of the axial force form factor to true your specific rifle should only be used aftereliminatingotherpossiblevariablesthatcanaccountforanerrorinpointofimpact.TheusershouldcheckthelistinTable3.toensurenoneofthelistedvariablesarecontributingtoanobservedverticalpointofimpactdifferencebetweenlivefiredataand4DOFprediction.

IncorrectMuzzleVelocityErrorinZeroRangeErrorinSightHeight

AccountedforAimingErroratRangeErrorinParallaxSetting

UncalibratedTurretAdjustmentsUnaccountedforWindSpeedandDirection

InaccurateAtmosphericDataTable3.PointofImpactErrorAccountabilityChecklist

Theuseofsecondaryinstrumentationsuchasanadditionalchronograph,rangefinder,orweatherstationmaybeneededtovalidateaccuracyofinputs.Onceyouhaveadjustedthedragvs.Machprofileto your specific rifle based off of a repeatablemean point of impact at distance, you should find itaccuratelypredictsthebulletpathallalongthetrajectoryandinenvironmentalconditionsotherthanthosetestedin.Therewillbenoneedtoadjustthingsforotherconditions,4DOFwillautomaticallydothis.

Thedataexaminedonprojectilesfiredfromvariousbarrelsindicatesthataccuratesimulationofthebulletpathisusuallywithinadragformfactorbetween0.95and1.05forjustbarreldifferences.Formaximumflexibilityandtoaccountfordifferentloadsandmuzzledevices,theprogramallowsforaxialforceformfactoradjustmentsfrom.90-1.10.Ifyoufindthatisnotthecase,besuretocheckthefactorsintable3.

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Thismethodoftweakingoradjustingtheprojectiledragisdifferentthanandmuchmoreaccuratethanthemethodof“truing”aBC.WhenaBCistrued,notonlyisittryingtoaccountfordragvariancefrombarreltobarrel,butalsoforthemismatchinshapeofthedragcurveofthestandardprojectileandtheactualprojectilebeingfired.InextremecasesthismethodoftruingcanproduceCdvsMachvaluesthatmatchwellatonespeedofsound,butcanproduceerrorswhenusedinadrasticallydifferentspeedofsound.Inotherwords,thetruedBCthatgavegooddropvaluesat80degreesmaynotproducethesameaccuracyofoutputsat20degreesduetothechangeinMachnumberandcorrespondingCdvalue.

Hornady4DegreeofFreedom(4DOF)ImportantFactorsandTips

Thefollowinginformationisaguidelineaddressinginputtermsandimportantdetailsandprocedurestoprovidethemostaccuratetrajectorypredictionspossible.

Selectionofprojectilefromdropdownmenuautomaticallyloadsmass,aerodynamic,anddraginformationspecifictoeachprojectile.

Itisextremelyimportanttohaveasaccuratemuzzlevelocitydataaspossible.TheHornady4DOFdragpredictionsarebasedonCdvsMachvaluesofeachprojectile.BallisticCoefficientbasedcalculatorsarebasedonCdvsMachvaluesofastandardprojectile. Inbothcases,Machnumberaccounts foravelocityvalueanditsrelationshiptothespeedofsound.Ifaninaccuratemuzzlevelocityisinput,boththeHornady4DOFandBCbasedcodeswillusedragvaluesforanerroneousMachnumber.Althoughthiserrormaybeverysmall(2600fps=Mach2.33vs2650=Mach2.37),itcanhaveameasurableeffectonpointof impactatlongerrangeswhencombinedwiththerawerrorinvelocityalone.Muzzlevelocityshouldbeused,notinstrumentalvelocityfromachronographplaced10-20ft. infrontofthemuzzle.Generally, a projectile will lose 10-15 fps in the first 15 feet. See “CalculatingMuzzle Velocity fromChronographorRadar”onpage21.

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Zerorangeshouldbebasedonaveryaccuratedistancetothezerotargetaswellasaveryprecisemeasurementof theaverageelevationofagroup,at thegivendistance, relative to thepointofaim.Simplyshootinga3shotgroupat100or200yards,roughlymeasuringthingsandcallingitgoodenoughcanproducelargepredictionerrorsinpointofimpactatlongranges.Table4.representserrorsinmeanpointofimpactat100yardsandthecorrespondingerrorsinpointofimpactwithatrajectoryranforatrue 100 yards zero. These values are not absolute andwill vary in severitywith projectile, velocity,atmospherics,andzerorange.

MeanPointofImpactat100YDS Errorat1000YDS.1”highorlow 1”.2”highorlow 2”.3”highorlow 3”.4”highorlow 4”.5”highorlow 5”.6”highorlow 6”.7”highorlow 7”Table4.ImpactPointErrors

Itdoesn’tmattermuchwheretheactualimpactsarerelativetothepointofaimintheverticalplane,onlythatitbeaveryaccuratemeasurementoftheaverageelevationpointofimpactrelativetothepointofaim.Thisprovidestheprogramwithaprecisepointthatallotherresultswillbebasedon.Thisallowsfortheadjustmentofthedragcurveviatheaxialforceformfactortotheactualfirearm/loadforprecisetrajectorypredictionsatlongranges.DetailsofrecommendedzeroingpracticecanbefoundintheAdditionalInformationsectionbelowonpage14.

Most ballistic programs available today compute an air density value based on the inputatmosphericconditions.Thisairdensityisthenassumedforallpredictionsoftheprojectile’sflight.TheHornady4DOFcreatesaninternalaltitudebasedatmospherictableofconditionsbasedontheprovidedinputsandaccountsfor theairdensitychangesattheprojectile’saltitudeduringflight.Changesinair

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densityduringthebullet’sflightcanbecomeimportantiflongrangehighangleshootingisconducted.A1000yardshotata30degreeangleresultsina1,500footchangeinaltitudefromlaunchtotarget.Itisvery important to know or have a very good estimate of the firing altitude in combination withatmosphericconditions.

Barreltwistinputscanbemarkedonthebarrelorprovidedbythemanufacturer.Correctbarreltwistiscriticalforaccurategyroscopicstability(Sg),spindrift,andaerodynamicjumpvalues.Alwayscheckthe“Gyro”columnoftheoutputstablefirsttoensuretheprojectileisstableatthemuzzle,Sggreaterthan1.4.

Boredimensionsarestandardizedandcanbeselectedfromthepulldownmenubasedonbulletcaliber.Fornon-standardboredimensions,selectthe“other”optionandmanuallyinputborediameter.

Theaxialforceformfactoroptionallowsforafixedpercentageincreaseordecreaseindrag(Cdvalue). This is not the same method employed when truing a BC on traditional ballistic programs.Variancesindraghavebeenrecordedbetweendifferentguns,barrelsandloads.Byselectinga.95AxialForceFormFactortheprojectiledragvalueswillbereducedby5%.Selectinga1.06%AxialForceFormFactorthedragwillbeincreasedby5%.Thisinputallowstheusertotweakthespecificimpactthebarrel,load,etc.hasonthedragoftheprojectiletoprovidethemostaccurateresultspossible.

WhenusingtheAxialForceFormFactoritisimperativethatmuzzlevelocity,andzerorangeinputsareasaccurate as possible. The axial force form factor should be changed from 1.00 as a last option aftercorrectlymeasuringmuzzlevelocityandpointofimpactatzerorange.Truingthemuzzlevelocityshouldbeavoidedand instead shouldbemeasured to avoid the useof erroneousMachvaluesduringdragcomputations.FormoredetailedinformationpleaserefertotheHornady4DOFUserManualonpage1and2.

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Windangleinputseffectnotonlythevaluesofwinddriftbutalsothevalueanddirectionofaerodynamicjump.0headwind,90fromtheright,180tailwind,270fromtheleft.

AdditionalInformation

RecommendedZeroingProcedures

Theimportanceofhavingaverydetailedmeasurementoftherelationshipbetweenpointofimpact(POI)andpointofaim(POA)isdescribedintheImportantFactorsandTipssection.Smallerrorsinzeroingatrelativelycloseranges(100,200yards)canproducelargeerrorsbetweenactualPOIandpredictedPOIatlongerranges.Measurementsduringzeroingtowithinaminimumofatenthofanincharenecessaryandareeasilyachievedbytheuseofdialcalipers.Arulerorothermeasurementmethodcanbeusedwithcloseattentiontodetail.

A limiting factor in achieving the perfect zero is the unit value of the sight adjustment. A .25MOAadjustmentoptichasaunitvalueof.26”@100yards,.52”@200yards,and.79”at300yardfor1click.A1/10MRADadjustmentoptichasaunitvalueof.36”@100yards,.72”@200yards,and1.1”@300yardsfor1click.Thecoarsenessoftheseadjustmentvaluesallowforpossibleerrorsofonehalfoftheinchvalueattheirrespectiveranges.Example:Ifthecenterofa100yardgroupis.13”aboveorbelowthepointofaim,applyingoneclickwill result in thesameerror in theotherdirection fora .25MOAadjustment.Thispossiblepreventionoftheperfectzeroisaddressedintheproceduresbelow.

Procedures

1:Withanaccuratelymeasureddistancetothetarget,firea5shotgroupwithoutadjustingPOAviaturretadjustmentsorholdingoff.

2a:Ifindividualbulletholescanbeidentified,measuretheverticaldistancebetweenPOAandthecenterofthePOIofeachshot.AverageallofthevaluestofindtheverticalpointofimpactoffsetfromthePOA.SeeFigure5.

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Figure5:VerticalImpactPointMeasurement,IndividualHolesVisible

2b:Ifindividualbulletholescannotbeidentifiedduetooverlappingholes,measuretheverticalsizeofthegroupanddivideby2tofindthecenter.MarkthelocationofthecenterofthegroupandmeasuretheverticallocationofthecenterfromthePOI.SeeFigure6.

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Figure6:VerticalImpactPointMeasurement,IndividualHolesNotVisible

Figure7:Close-upofFigure6.

3:IftheverticaldistancebetweenthePOAandthePOIisgreaterthantheunitvalueofthesightbeingused, adjustments canbemade tobring thedifference closer to zero if desired,however this is notnecessaryforaccurateoutputs.Example:IfthemeanPOIofthegroupis.6”highat100yards,everything

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canbeleftaloneifdesiredortheopticcanbeadjustedtobringthePOItowithinaminimumofahalfofaclickvalueasdescribedintheintroduction.TheoffsetbetweenPOAandmeanPOIwillbeaccountedforregardlessofitsvalue.

4:WithameanPOIoffsetmeasureddowntothenearesttenthofaninch,theHornady4DOFshouldbeprovidedwithinputswithallinformationandconditionspresentduringfiringofthezerogroup.

5:IfthemeanPOIisabovethePOA,setthezerorangeslightlybeyondthezerotargetdistance.Example:meanPOIis.6”highat100yds.Setzerodistanceof4DOFto120yds.IfthemeanPOIisbelowthePOA,setthezerorangeslightlycloserthanthezerotargetdistance.Example:meanPOI-.4”at200yds.Setzerodistanceof4DOFto180yds.

6:Runatrajectoryandlocatethedropcolumnininches.Findyourzerorangeandnotetheheightofthetrajectoryatyourzerorange.SeeTable5.

Table5:ReferenceTrajectory

7:Adjustzerodistanceof4DOFzeroinputandre-runthetrajectoryuntiltheinchvalueatzerorangematchesmeanPOImeasuredatzerorange.

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Table6:AdjustedTrajectory

ThismethodofzeroingproperlyaccountsforseeminglysmalldifferencesinPOIandPOAduringtrajectorycalculations.Theseseeminglysmallerrorsatzerorangecancauselargeerrorsatlongerrangesandshouldbeaccountedfortowithinatenthofaninchminimumresolution.ThismethodalsoallowsthezerorangetobepreciselydialedinformeanPOIthatiswithintheadjustmentvalueoftheopticofferingtheuseronemorelevelofprecisioncomputation.

Ifmultipledifferentloadswillbeusedinasingleriflethissamemethodcanbeusedtocomputezero’sforeachdifferentloadeventhoughitmayhaveadifferenceinPOIintheverticalplane.

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Understanding Aerodynamic Jump

Aerodynamic jump can be a difficult concept to understand, but is an important factor of projectiletrajectorytoaccountforwhenattemptingtomakefirstroundhitsatlongrangeinwindyconditions.Thisexplanationwill provide visual and textual descriptionsof aerodynamic jump toassist the shooter inunderstandingandutilizetheconceptscausingaerodynamicjump.

Figure8.isarepresentationofthepatternoftheprojectile’snoseafterexitingthemuzzleunderanowindconditionviewedfromthebaseofthebulletasittravelsdownrange,Alphaispitchupordown,Beta to the right. Thepitchandyaw resulting frommuzzleexit and thegyroscopicpropertiesof thespinningprojectilecause it toprecessaroundthe flightpathorvelocityvector inaneverdiminishingpattern.Thepitchandyawangleiscontinuallygettingsmallerbecausethebulletisdynamicallystable.Astheprojectilemovesdownrange, theyawof reposecauses thenosetopointslightly to therightandslightlyupascanbeseenbythediminishingangles.Theaverageyaxisorientationoftheprojectile’snoseis.000133degreesabove0andtheaveragexpositionof.003354degreesrightof0.Thisistheprocessoftenreferredtoas“goingtosleep”.

Figure8.ProjectilePitch&YawAnglesNoCrosswind

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Figure9.showsthesameconditionsasFigure8.butwiththeadditionofa1MPHwindat90*(righttoleft).Theintroductionofacrosswindcausesadramaticallydifferentresponsefromtheprojectile.Thepresenceofacrosswindcausestheprecessioncyclestohaveamuchlargerinitialangleaswellasanincreasedfrequencyofnutation.Theaverageyaxisorientationoftheprojectile’snosebeing.000361degreesabove0andtheaveragexaxispositionof.00334degreesrightof0.The1MPH90*windhasresulted in theprojectilenosetopointslightlyhigher thanthenowindcondition.Thissmallangleofupwardorientationoftheprojectileinrelationtothevelocityvectorcausestheupwardjumpseenwhenshootingina90*wind.

Figure9.ProjectilePitchandYawFiredina1MPHCrossWind

Figure10.isacombinationofFigure8,Figure9.andaplotrepresentinga10MPH,90degreecrosswind.ThesmallredareaattheverycenterisaplotofFigure6toscale,fornowind.TheareainsidethegreenboxisplotofFigure7Toscale,fora1MPHcrosswind.Thelargeplotistheprojectileresponseforthe10mph crosswind. The influence of wind velocity is a large player in the projectile’s behavior and theresultingaerodynamicjumpvalues.

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Figure10.CombinationofFigure8.andFigure9.

Table 7 is a comparison of average projectile Y axis nose position at different wind velocities anddirections.The90degreewindcausesthebullet’snosetopointslightlyabovethevelocityvectorashasbeenseeninFigure8andFigure9.A270degreewind(lefttoright)hastheoppositeeffectandcausesthebulletnosetopointdownward,resultinginthedownwardjumpanglewhenshootingina270degreewind.

Table7:AverageNosePositionvs.WindSpeed&Direction

WindVelocity Direction YAxis WindVelocity Direction YAxis0MPH 0* 0.000133 0 0 0.000133

1MPH 90* 0.000361 1MPH 90* 0.0003611MPH 270* -0.000100 5MPH 90* 0.001318

10MPH 90* 0.0024925MPH 90* 0.0013185MPH 270* -0.001069 1MPH 270* -0.000100

5MPH 270* -0.00106910MPH 90* 0.002492 10MPH 270* -0.00217410MPH 270* -0.002174

ProjectileNosePosition(Degrees) ProjectileNosePosition(Degrees)

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Varyingwinddirectionhasarelativelysmalleffectonaerodynamicjumpvaluesandthecorrespondingadditionorsubtraction frombulletdropvaluesout to1000yds. Figure11.showsaerodynamic jumpvaluesfora10mphheadwind,tailwind,bothfullvaluewinddirections,aswellasthe4halfvaluewinddirections. The positive values of the right to left direction winds are due to the bullet’s nose uporientationduetothewinddirection.Thenegativevaluesforthelefttorightwinddirectionsareduetothebullet'snosedownorientation.Headandtailwindshavetheleasteffectonverticalpointofimpact,andhavelongbeenknowntobeoflittlevalueoutto1000yds.Halfvaluewindshaveagreatereffectthanheadortailwinds,butnottothefullmagnitudeofafullvaluecrosswind.

Figure11.AerodynamicJumpvs.Range&WindDirection,100-1000Yards

Atverylongranges,thefullvaluewinddirections(90and270degrees)remainfairlylinearintheirvalues.Asthewindbeginstoapproachthebulletatnon-fullvalueangles,inthisexamplehalfvaluedirections,theearlylinearbehaviorquicklyacceleratesinvalue.Asthebulletcontinuallybleedsvelocitytravelingdownrange,thevelocityoftheassumedconstantwindactingonthebulletbecomesagrowingpercentageoftheprojectile’svelocity.Thisistrueforbothhalfvaluewinddirectionsaswellasheadandtailwindsinthis example. Due to the wind vector’s alignment with the velocity vector for half value, head, andtailwinds,anaxialcomponentaswellasajumpcomponentareactingontheprojectile.

The225degreewinddirectioncomingfromthelefttorightcausesthebullettonosedownslightlygivingitadownwardaerodynamicjumpthatisseeninFigure12.However,thedramaticlossofforwardvelocity

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duetoaxialdragmakesthevelocityofthetailwindahigherpercentageoftheprojectile’sretainedvelocityonceitisbeyond1000yds.Thetailwindactstoreducetheaxialdragactingontheprojectilecomparedtoflightinstillair.Athighvelocity,the14.7fps(10MPH)windhasverylittleeffectonreducingtheaxialdrag.Oncevelocityhasbledfrom2700to950though,thatsame14.7fpswindvelocityisofmuchgreatervalue,percentagewise,whencomparedtoforwardbulletvelocity.Theeffectofdecreasedaxialdragfromthetailwindisnowgreaterthantheaerodynamicjumpcomponentandoverridingitenoughtogivetheprojectileanimpactpointabovethe0linebeyond1500yards,asshowninFigure8andFigure9.

Theheadandtailwind(0and180degrees)thatwereoflittlevalueto1000yardshavenowbecomethehighestvaluesat2000yards.Theheadand tailwindshavenoaerodynamic jumpvalueas there isnocrosswindcomponentactingontheprojectile.Theincreaseanddecreaseinaxialdragvaluesofheadandtailwindsbecomeaveryimportantconsiderationatextendedranges.

Figure2:VerticalAerodynamicJumpvs.WindDirection,1000-2000Yards

Uphillordownhillangleshootingwithaheadortailwindcomponentintroducesanotherinterestingresponsefromtheprojectile.Duringangleshooting,thevelocityvectorofthebulletisnolongerparallelornearparalleltotheheadortailwindwindvelocityvector.Instead,astheangleoftheshotisincreasedthevelocityvectorofthebulletbecomesmoreperpendiculartothewindvelocityvectorwithincreasedangle.Thisrelationshipcanbeviewedinthesamewayasaflatfireshotwithacrosswindwherethewindisactingatsomedegreeofperpendicularitytothebulletsvelocityvector.Intheexampleoftheangleshotwiththeheadandtailwinditisthesameeffect,butintheverticalplaneinsteadofthehorizontal.Thecorrespondingaerodynamicjumpvaluefromtheheadortailwindduringanangleduphillordownhillshotwillcauseaerodynamicjumpinthehorizontaldirection.

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CalculatingMuzzleVelocityfromChronographorRadar

TheHornady4DOFrequirestheinputoftruemuzzlevelocities.Ifinstrumentalvelocitiesaremistakenlyusedasmuzzlevelocities,errorswillresult.Instrumentalvelocitiesaregatheredfromachronographplacedacertaindistanceinfrontofthemuzzle,orfromaRadarplacedbesidethebarrel.Ineachcasecorrectionsneedtobemadetocalculatetruemuzzlevelocity.

Chronograph

Chronographsaretypicallyplaced5-20feetinfrontofthemuzzlewhenmeasuringvelocity.Theseparationdistancehelpspreventmuzzleblastfromfalselytriggeringthechronographsensorsandprovidingbadreadings.Ifachronographisusedtogathervelocitydata,adetailedmeasurementshouldbetakenfrommuzzletothecenterpointbetweenthetwosensors.Everyattemptshouldbemadetoplacethecenterofthechronographatawholeyardageormetervalueformthemuzzlesuchas3,4,5,6yardsor3,4,5,or6meters.Fractionaldistancessuchas3.6yardsor4.8meterswillmakeitmuchmoredifficulttocalculateaccuratemuzzlevelocities.

Procedures

1:Placethecenterofthechronographatawholenumberyardageormetervaluewithenoughseparationbetweenthemuzzleandstartsensortonotinducefalsetriggersfrommuzzleblast.

2:Firedesirednumberofshotstorecordvelocity.

3:Averagerecordedvelocities.

4:Inputallvaluespresentduringtherecordingofvelocitiesintothe4DOFinputspage.Settheoutputintervaldistanceto1.Inputamuzzlevelocitythatisslightlyfasterthantheaverageinstrumentalvelocity.Muzzlevelocitieswilltypicallybe10-20fpshigherthanthemeasuredaverageinstrumentalvelocity.GeneralvelocitylossguidelinescanbefoundbasedontheBCrangeintable8.Calculatethetrajectory.

BulletG1BC AverageFPSLostat15Feet.400-.449 11.450-.500 10.501-.550 9.551-.600 8.601-.650 8.651-.700+ 7

Table8.GeneralVelocityLossat15Feet

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5:Intheoutputtable,locatethedistancefromthemuzzletothecenterofthechronograph.Ifvelocityatthisdistanceisbelowtherecordedaveragevelocityfromthechronograph,thetrajectorywillneedtobere-runwithahighermuzzlevelocity.Ifthevelocityatthedistanceisabovetherecordedaveragevelocityfromthechronograph,thetrajectorywillneedtobereranwithalowermuzzlevelocitynumber.

6:Oncetheoutputtablevelocityatthechronographdistancematchestherecordedaverageinstrumentalvelocityfromthechronograph,themuzzlevelocityhasbeencorrectlycalculatedandshouldbeusedforfurthertrajectorycalculations.

Radar

Radaristypicallyplacedtothesideofthebarrelwhenmeasuringvelocity.Thislateraloffsetbetweenthebarrelandradarcreatearadialvelocityearlyinthemeasurementthatmustbeaccountedfortodetermineaccuratemuzzlevelocities.Theprojectilehasto“flyintothebeam”.Thiswillresultininaccuratevelocityvaluesearlyinthemeasurementifnotaccountedfor.Thisistypicallyachievedbyprecisemeasurementsbetweentheradarheadandbarrel.Ifthereisanydoubttothecorrectionaccuracyofradialvelocity,thesamemethodusedforcalculatingamuzzlevelocityviaachronographcanbeusedwitharadar.Ifthismethodischosen,adistanceshouldbepickedfartherdownrangetominimizetheeffectsofradialvelocity.Thisdistancewillbedictatedbytheoffsetbetweentheradarheadandbarrel,butingeneralby30-50yardsradialvelocityeffectshavebeenmitigated.

Procedures

1:Firedesirednumberofshotstorecordvelocity.

2:Averagerecordedvelocities.

3:Inputallvaluespresentduringtherecordingofvelocitiesintothe4DOFinputspage.Settheoutputintervaldistanceto1.Inputamuzzlevelocitythatisreasonableforloadandbarrellengthbeingused.Calculatethetrajectory.

5:Intheoutputtable,locatethedistancewhichhasbeenchosentoremovepossibleradialvelocity(30+yds).Ifvelocityatthisdistanceisbelowtherecordedaveragevelocityfromtheradar,thetrajectorywillneedtobereranwithahighermuzzlevelocity.Ifthevelocityatthedistanceisabovetherecordedaveragevelocityfromtheradar,thetrajectorywillneedtobereranwithalowermuzzlevelocitynumber.

6:Oncetheoutputtablevelocityatthechronographdistancematchestherecordedaverageinstrumentalvelocityfromthechronograph,themuzzlevelocityhasbeencorrectlycalculatedandshouldbeusedforfurthertrajectorycalculations.

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UphillandDownhillShootAngles

Traditionalballisticcalculatorsofferrelativelyaccuratepredictionsatshootanglesbelow15degreesatmoderatedistances.Atanglesgreaterthan15degrees,orincreaseddistances,errorsfromtheflatfirecalculationswillbecomemorepronounced.TheHornady4DOFcorrectlyaccountsforangledshootingbasedonamultitudeoffactorstoincludevelocityvectoralignmentwithgravity,changesinairdensitywithincreasingordecreasingprojectileelevation,andtherelationshipbetweenprojectileelevation,lineofsightangle,andtarget.

Itiscommonpracticetocorrectforanangledshotinthefieldbymultiplyingtherangetotargetorthedropvalueatagivenrangebythecosinevalueoftheanglebeingfired.Atangleslessthan10degreesthismethodisrelativelyaccurate,butwillresultinmuchlargererrorsastheangleandrangeincrease.ActualdropvaluesfromtheHornady4DOFcomparedtocosinecorrectedvaluescanbeseeninTable9.

RANGE ANGLE4DOFDROPINCHES

COSINECORRECTEDDROP

INCHES500 10 -43.6 -45.2500 -10 -43.4 -45.2500 15 -40.7 -44.3500 -15 -40.6 -44.3500 20 -37.1 -43.1500 -20 -36.8 -43.1500 30 -27.9 -39.8500 -30 -27.7 -39.8

RANGE ANGLE4DOFDROPINCHES

COSINECORRECTEDDROP

INCHES1000 10 -275.7 -284.31000 -10 -274.3 -284.31000 15 -259.6 -278.91000 -15 -257.7 -278.91000 20 -238.2 -271.31000 -20 -235.9 -271.31000 30 -184.2 -250.01000 -30 -181.7 -250.0

Table9.4DOFvsCosineCorrectionMethod

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ApplyingSpinDriftandAerodynamicJump

TheHornady4DOFoutputtableprovidesvaluesforspindriftthatareindependentofwinddriftandaerodynamicjumpindependentoftrajectory.Duetothechangingnatureofwinddirectionandspeed,thevaluesforspindriftandaerodynamicjumpwillneedtobeappliedbasedonthejudgementoftheshooter.Iftheshootingconditionsareconsistentwiththeinputwindspeedanddirection,theshootersolutionlocatedinthegreyedTotalComeUpandTotalWindagecolumnsdothecalculationsdescribedbelowautomatically.Ifwindconditionschangefromtheinputvaluesandtheshooterdoesn’thavetimeorabilitytoaccountforthembychanginginputs,theindividualvariablescanbeappliedattheshootersdiscretionbasedonthechange.

SpinDrift

Spindriftfromarighthandtwistbarrelwillalwayscausethebullettodrifttotherightwhenviewedfrombehindtherifle.Valuesofspindriftareconstantifvelocity,twistrate,andatmosphericconditionsarethesame.Table10showsthe1000yardspindriftvaluehighlightedingreenandthe10mphwindvalueinred.Ifarighttoleft(90degree)10mphwindispresent,thespindriftvalueshouldbesubtractedfromtheoverallwinddriftvalue.Ifa10mphlefttoright(270degree)windispresentthespindriftvalueshouldbeaddedtothewinddriftvalue.Thecalculatedvaluehighlightedinbluecanbeseenautomaticallycalculatedintheshootersolution.TheexampleoutputinTable10iscalculatedwitha90degreewinddirection.

Table10:ApplyingSpinDrift

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AerodynamicJump

Aerodynamicjumpisappliedinaverysimilarwayasspindrift,justintheverticaldirection.Aerodynamicjump,likewinddrift,hasadirectcorrelationtowindspeed.A10mphwindwillproducedoubletheaerodynamicjumpofa5mphwindofthesamedirection.Theshootermustdetermineifthejumpisintheupordowndirection.Awindblowingrighttoleft(90degrees)willcausethejumptobeintheupdirectionandthereforedecreasetheamountofTotalComeUp,andalefttoright(270degrees)willcausethebullettojumpinthedownwarddirectionincreasingtheTotalComeUp.TheexampleoutputinTable11iscalculatedwitha90degreewindandillustratestheapplicationofaerodynamicjump.

Table11:ApplyingAerodynamicJump

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Index

ChooseBullet:Apulldownmenuallowingyoutoselecttheprojectilefortrajectoryanalysis.Onceaprojectileisselected,itsuniquemassandaerodynamiccharacteristicsareselectedwithinthetrajectoryengine.

Units:Apulldownmenuofferingselectionbetweenstandardandmetricunits.Onceselectedallinputvaluesandoutputvalueswillbeintheunitsystemselected.

Velocity:Muzzlevelocityinput.

MaxRange:Inputvalueformaximumrange4DOFwillcalculateto.

Interval:Definesatwhatdistanceoutputswillbecalculated.Example:25ydintervalwilloutputtrajectorydataevery25ydstothemaxrange.

ZeroRange:Rangeatwhichthebulletcrossesthelineofsight.Alsocalledsightinrange.

SightHeight:Distancefromcenterlineofboretocenterlineofsight.Forscopedriflesthisisthedistancefromthecenteroftheboretothecenterofthescopemaintube.

ShootingAngle:Angularinputforuphillordownhillshooting.–isdownhill,+isuphill.

WindSpeed:Windspeedinputusedtocomputewinddeflectionandaerodynamicjumpfromcrosswind.

WindAngle:Windangleinrelationtothebullet.0*headwind,90*fromtheright,180*tailwind,270*fromtheleft.

Altitude:Heightabovesealevel.Unlikeotherballisticsprograms,altitudeandpressuremustbothbeinputintothe4DOF.Basedonaltitudeandpressurevalue,acustomtableisbuiltwithintheprogramtoproperlymodelatmospherics.

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Pressure:Uncorrectedatmosphericpressure.Typicallygatheredfromhandheldweatherstationorpressureataltitudetable.Donotusecorrectedpressurecommonlyusedinweatherforecasts.PressureandaltitudemustbothbeinputintotheHTEtobuildthecustomatmosphericmodelduringcalculations.

Temperature:Ambientairtemperature.

Humidity:Relativehumiditypercentage.

BarrelTwist:Distanceininchesorcmrequiredforriflingtomakeonecompleterevolutioninbarrel.Canbefoundonbarrelorfrommanufacturer.Criticalinputforgyroscopicstability,spindrift,andaerodynamicjumpoutputs.

BoreDiameter:Diameterofboredimensionofbarrel.Groovedimensioniscommonlyusedasthereferencetobulletcaliber.Example:.308diameterbulletsaredesignedforbarrelswith.308groovedimension.Borediametersarestandardforcaliberandcanbefoundintablebelow.Customborediametersshouldbeinputifknown,otherwiseautomaticstandarddimensionwillbeloadeduponbulletselection.Borediameterinputiscriticalforgyroscopicstability,spindrift,andaerodynamicjumpoutputs.

CALIBER

STANDARDBOREDIMENSION

22Cal,.223,5.56mm .2196mm,.243 .2376.5mm,.264 .2567mm,.284 .27730Cal,.308 .300

.338 .33050Cal .500