From: "Mit Microsoft Internet Explorer 7 gespeichert" Subject: stabilisation Date: Fri, 1 May 2009 08:22:49 +0200 MIME-Version: 1.0 Content-Type: multipart/related; type="text/html"; boundary="----=_NextPart_000_0000_01C9CA36.03E98490" X-MimeOLE: Produced By Microsoft MimeOLE V6.0.6001.18049 This is a multi-part message in MIME format. ------=_NextPart_000_0000_01C9CA36.03E98490 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Content-Location: http://rz-home.de/~cnentwig/stabilisation.html stabilisation

Physikalisch-Technische Aspekte des = Bogenschie=DFens

Stabilisation des Bogens

Vorbemerkung.

Hier soll nicht auf die Historie eingegangen werden, auch auf = versprochene=20 Wunderdinge der beteiligten Industrie wird keine R=FCcksicht genommen. = Es wird=20 auch vorausgesetzt, dass =FCbliche Stabilisationssysteme von Form und = Anordnung=20 bekannt sind. Hier werden nur die technisch physikalischen Gegebenheiten = von=20 vorhandenen Systemen behandelt, und angen=E4hert, aber in der = Genauigkeit weitaus=20 ausreichend, die Dinge beschrieben, die f=FCr das Treffen mit Pfeil und = Bogen=20 wichtig sind.

Dabei wird nur das physikalische System des Recurvebogens behandelt,=20 physiologische Probleme und Befindlichkeiten bleiben au=DFen vor. Z.B. = f=FChlt sich=20 ein Bogen mit Stabilisation im Auszug leichter an. Dies h=E4ngt mit der=20 Kraftrichtung der Resultierenden, gebildet aus Auszugskraft des Bogens = und=20 seiner Gewichtskraft zusammen, wird hier aber nicht weiter = behandelt.

Was ist Stabilisation?

Unter Stabilisation versteht man eine Anordnung aus = Masse- Feder-=20 und D=E4mpfungs elementen am Bogen, die am eigentlichen Schu=DFvorgang = nicht direkt=20 beteiligt ist, aber das Treffen des Zieles g=FCnstig beeinflussen = soll.

Welche Mittel stehen zur Verf=FCgung?

Jetzt mu=DF noch beschrieben = werden, wie=20 diese Elemente zusammenwirken, um die Wirkung der Stabilisation zu = verstehen=20 Dazu wird der Schu=DFvorgang in drei Teile unterteilt:
  1. Zielvorgang unmittelbar vor dem Schu=DF=20
  2. Schu=DFvorgang (Pfeil hat Kontakt mit der Sehne)=20
  3. Zeit nach dem Schu=DF (Pfeil hat den Bogen verlassen)
und = jeder=20 Zeitabschnitt gesondert behandelt.=20

Zielvorgang unmittelbar vor dem Schu=DF.

Hier hat die Stabilisation die Aufgabe, Schwingungen, die St=F6rungen = wie=20 Windst=F6=DFe, Muskelzittern oder bewu=DFte, ruckartige Korrekturen des = Visierbildes=20 hervorrufen, zu d=E4mpfen. Durch Massen, die an Stangen weit weg vom = Schwerpunkt=20 des Bogens angeordnet sind, wird die Masse des Bogens und sein = Tr=E4gheitsmoment=20 erh=F6ht.

Die Erh=F6hung der Masse bewirkt einen h=F6heren Widerstand gegen = gradlinige=20 Bewegungen des Systems, aber wenn es in Bewegung ist, dann ist die = Bewegung auch=20 genauso schwer wieder zu stoppen. Au=DFerdem kann eine hohe Masse auch = einen=20 ung=FCnstigen Einflu=DF hinsichtlich der Belastung der Gelenke usw = haben.

Die Erh=F6hung des Tr=E4gheitsmomentes bewirkt das Gleiche in bezug = auf=20 kreisf=F6rmige Bewegungen um einen Drehpunkt, nur geht hier der Abstand = der=20 wirksamen Masse vom Drehpunkt quadratisch ein. Das hei=DFt, wenn der = Abstand=20 verdoppelt wird, vervierfacht sich das von dieser Masse ausge=FCbte=20 Tr=E4gheitsmoment um die betrachtete Drehachse. Die langen Ausleger nach = allen=20 Richtungen machen also Sinn.

Gleichzeitig sind die Stabilisatorstangen Federn mit der = entsprechenden=20 Federsteife (elastischer Widerstand eines Bauteiles gegen Verformung), = die vom=20 Material der Stangen und deren Abmessungen abh=E4ngt. So hat Carbon z.B. = einen=20 sehr hohen Elastizit=E4tsmodul (Materialkennwert), der den von Stahl = weit=20 =FCbersteigt und Bauteile daraus haben eine sehr hohe Federsteife. = Deshalb werden=20 z.B. Ausleger von extrem genauen Messmaschinen aus Carbonfaser gebaut, = damit sie=20 eine sehr hohe Eigensteife bei gleichzeitig geringer Masse bekommen.

Die Federsteife und die Masse bestimmen die Eigenfrequenz des=20 Stabilisatorsystems, die angibt, wie h=E4ufig das System nach einer = Anregung pro=20 Sekunde hin und her schwingt. Man kann beobachten, da=DF nach einer = gewissen Zeit=20 jedes schwingende System zur Ruhe kommt.

Dieses Ph=E4nomen nennt man D=E4mpfung. Sie erfolgt u.a. durch den = Luftwiderstand=20 und durch die innere Reibung der Materialteilchen. Dabei wird die = Energie, die=20 in dem schwingenden System steckt, in W=E4rmeenergie umgewandelt. Beim = Schie=DFen=20 ergeben sich aus einer niedrigen D=E4mpfung, die das betrachtete System = erst in=20 einer Sekunde oder so zur Ruhe bringt, nat=FCrlich keinerlei Vorteile. = Ein schwach=20 ged=E4mpftes System mit niedriger Eigenfrequenz wird jede St=F6rung zu = einer l=E4nger=20 dauernden Bel=E4stigung machen.

Deshalb mu=DF entweder durch entsprechende Wahl des Materials und der = Konstruktion die Eigenfrequenz sehr hoch gesetzt werden, und/oder es = m=FCssen=20 brauchbare D=E4mpfungselemente benutzt werden.

Der erste Fall ist bestechend einfach. Hohe Federsteife und gro=DFe = Durchmesser=20 der Stabistangen sorgen f=FCr hohe Eigenfrequenz und vermeiden so = Aufschaukeln.=20 Der Nachteil ist, da=DF die Schwingung, die durch Muskelzittern = hervorgerufen=20 wird, halt auch nicht ged=E4mpft werden kann. Damit kommt man zu jenem = Punkt, an=20 den D=E4mpfungskonstruktionen und - materialien diskutiert werden = m=FCssen.

Elastomere, wie Gummi sind auf den ersten Blick gut geeignet, wenn = Sie eine=20 hohe Hysterese haben (Bild 1) Mit Hysterese beschreibt man die = F=E4higkeit eines=20 Materials, aufgenommene Verformungsarbeit in W=E4rme umzuwandeln.

Leider sollen die D=E4mpfungselemente bereits beim ersten Ein- bzw = Ausfedern=20 wirken, und das schaffen die verwendeten Materialien nicht. Sie = m=FC=DFten dann so=20 weich sein, da=DF Sie konstruktiv nicht verwendbar sind. Die bei B=F6gen = verwendeten=20 Gummielemente kommen aus dem normalen Maschinenbau und sind daher = hochwirksam=20 erst bei Frequenzen ab ca 200 Hz. Der Muskeltremor liegt aber eine = Gr=F6=DFenordnung=20 niedriger bei 5- 20 Hz und ist keine Schwingung im eigentlichen Sinne, = sondern=20 mit dem Begriff =93Rauschen im niederfrequenten Bereich=94 besser = beschrieben. Die=20 =FCblichen Gummielemente sind daher f=FCr diesen Zweck unbrauchbar.

Welche D=E4mpfungselemente kann man benutzen, um dieses = niederfrequentes wei=DFes=20 Rauschen zu d=E4mpfen? Erdbebenst=F6=DFe liegen in diesem Bereich und = die=20 Konstruktionen, die sich Bauingenieure ausgedacht haben, sind = verbl=FCffend=20 wirksam. Hydraulische D=E4mpfungen, wie Sie auch im Hoch- und = Fahrzeugbau als=20 Schwingungsd=E4mpfer verwendet werden, k=F6nnen ohne Probleme jedes = System=20 abgestimmt werden. Sie haben nur den Nachteil, da=DF Sie nur in einer = Achse=20 wirken, und gute Konstruktionen einen hohen konstruktiven Aufwand = erfordern. Bei=20 Sch=FCtzenb=F6gen treten Beschleunigungen bis zum 700fachen der = Erdbeschleunigung=20 auf. Da ist schon manche billige (billig ist hier nicht auf den Preis = bezogen!)=20 Konstruktion in die Knie gegangen.

Bei Hochh=E4usern in Erdbebengebieten werden Swimmingpools oder = Wassertanks in=20 den obersten Stockwerken fest mit der tragenden Konstruktion verankert.=20 Fl=FCssigkeit soll die durch Erdbebenst=F6=DFe eingekoppelten = Schwingungen d=E4mpfen,=20 d.h. die Bewegungsenergie in W=E4rme umwandeln. Hier ist die gleiche = Probleml=F6sung=20 wie beim Bogen: niederfrequent, sofortige Wirkung, = richtungsunabh=E4ngig. Der=20 Nachteil ist, da=DF Wasser nur eine geringe Dichte hat. Dies spielt bei=20 Hochh=E4usern nicht so eine gro=DFe Rolle, aber ein gro=DFer Beh=E4lter = am Stabi sieht=20 nicht besonders schick aus.

Verschiedene Hersteller bieten Stabilisatoren mit = Quecksilberf=FCllung an.=20 Technisch richtig, aber fl=FCssiges Quecksilber ist hochgiftig. Das = hei=DFt, das=20 Risiko einer Undichtigkeit ist den Vorteil nicht wert. Au=DFerdem w=E4re = eine h=F6here=20 innere D=E4mpfung als sie Wasser oder Quecksilber hat, d.h. eine = h=F6here innere=20 Reibung w=FCnschenswert (=D6le sind noch leichter als Wasser).

So kommen wir zu Spezialpulvern. Als Erstes bietet sich Sand feiner = K=F6rnung=20 an (leider niedrige Dichte). Der n=E4chste Schritt f=FChrt zu Granulaten = mit h=F6herer=20 Dichte, um D=E4mpfungswirkung bei annehmbaren Au=DFenabmessungen zu = haben. Der Autor=20 verwendet ein Stabilisationssystem mit einer F=FCllung aus = Schwermetallpulver (im=20 Extrem k=F6nnte man Goldstaub nehmen). Die Wirkung ist gut, steht aber = in keinem=20 Verh=E4ltnis zum Preis.

=DCber diesen, ohne Zweifel sehr wichtigen Teil des Schu=DFvorganges = wird=20 normalerweise kein Wort verloren. Die einzige gute Beschreibung wurde im = offiziellen Trainermanual der GNAS (Grand National Archery Society) von = England=20 gefunden. Als Zusammenfassung kann gesagt werden, da=DF au=DFer = Stabilisatoren mit=20 Sand und Schwermetallf=FCllungen kein System hier Vorteile bringt. Im = Gegenteil:=20 bei allen mit Elastomeren ausger=FCsteten Systemen ist ein Aufschaukeln = der=20 Schwingungen bei zu langem Halten zu beobachten. Da=DF Spitzensch=FCtzen = diese=20 Systeme trotzdem verwenden und keine Nachteile dadurch erlangen, liegt = daran,=20 da=DF ihre Haltezeiten deutlich k=FCrzer als die der Normalsch=FCtzen = sind, und durch=20 professionelles Training ein Muskeltremor entweder vermieden oder = minimiert=20 wird.

Schu=DFvorgang (Pfeil hat Kontakt mit der Sehne)

Dieser Zeitabschnitt, der entscheidend f=FCr das Treffen ist, kann = vom Sch=FCtzen=20 nicht beeinflu=DFt werden. Die Zeitdauer, w=E4hrend der Pfeil Kontakt = mit dem Bogen=20 hat und auf seine Abgangsgeschwindigkeit beschleunigt wird, betr=E4gt = bei einem=20 Sch=FCtzenbogen ca 13ms.

Bild 2 verdeutlicht die dabei wirkenden Kr=E4fte = und Momente.

Aus der den Pfeil beschleunigenden Kraft und der auf den Bogenarm = wirkenden=20 Gegenkraft bildet sich ein Moment, das den Bogen in die angegebene = Richtung=20 dreht. Dem wirkt das durch die Masse und durch die Massenverteilung = gegebene=20 Tr=E4gheitsmoment entgegen.

Aus dem Moment und dem einwirkenden Moment bildet sich (genau wie im = linearen=20 Fall aus Masse und einwirkender Kraft eine Beschleunigung resultiert), = eine=20 Winkelbeschleunigung, die dem System Bogen eine Winkelgeschwindigkeit um = seine=20 Drehachse gibt.

Diese Drehgeschwindigkeit bestimmt mit dem durch die Visierung = gegebenen=20 Anfangswert den Abgangswinkel des Pfeiles in der Elevation. Es ist = sofort=20 ersichtlich, da=DF durch eine =C4nderung der Handhaltung der Hebel = zwischen dem=20 Kr=E4ftepaar ge=E4ndert wird, und so eine =C4nderung der = Winkelgeschwindigkeit des=20 System, die wiederum eine H=F6henstreuung erzeugt. Eine hohe = Stabilisation (hohes=20 Tr=E4gheitsmoment) wird diese ung=FCnstige Auswirkung dadurch = verringern, da=DF das=20 hohe Tr=E4gheitsmoment eine kleinere Winkelbeschleunigung und somit eine = kleinere=20 Drehgeschwindigkeit zul=E4sst.

Das hei=DFt, ein Stabilisationssystem, dass ein hohes=20 Tr=E4gheitsmoment erzeugt, ist grunds=E4tzlich gut.

Nach dem Schu=DF (Pfeil hat die Sehne gerade = verlassen)

Das ist der Moment, den der Sch=FCtze f=FChlt. Die Reaktion des = Bogens ruft beim=20 Sch=FCtzen entweder ein angenehmes oder unangenehmes Gef=FChl hervor, = dass im=20 Wesentlichen bestimmt, ob das  Stabilisationssystem akzeptiert wird = oder=20 nicht. W=E4hrend im Schu=DF, d.h. solange der Pfeil Kontakt mit der = Sehne hat, der=20 Bogen immer so dreht, dass der obere Wurfarmnock sich vom Sch=FCtzen weg = bewegt,=20 so h=E4ngt die Bewegung des Bogens nach dem Schuss davon ab, wie hoch = die=20 Stabilisation ist und wo der Schwerpunkt des Bogens in Bezug auf den=20 Angriffspunkt der physiologischen Reaktionskraft des Bogenarmes ist. =

Unter=20 physiologischer Reaktionskraft ist die Kraft gemeint, die von der = Federspannung=20 der R=FCckenmuskeln herr=FChrt, die nat=FCrlich immer noch die Momente = aufbringen, die=20 zum Ausziehen des Bogens notwendig waren. Das zweite Bild zeigt eine wie = ich=20 glaube h=E4ufige Konstellation.

Der gr=FCne Pfeil zeigt die Drehrichtung = des=20 Momentes des Bogens mit Stabilisation, der rote den=20 gleichen Bogen ohne Stabilisation.

Diese Reaktion sp=FCrt jeder Sch=FCtze. Dieses Verhalten bestimmt = =FCber das=20 subjektive Empfinden des Sch=FCtzen, ob das Stabilisationssystem = akzeptiert wird=20 und nat=FCrlich das Treffbild verbessert oder im anderen Falle = verschlechtert,=20 obwohl objektiv keine Auswirkungen auf das Treffen oder den Pfeilflug = m=F6glich=20 ist. (au=DFer wie oben geschildert)

Zusammenfassung

Stabilisationssysteme sind grunds=E4tzlich gut. Die Verbesserung des=20 Schussbildes durch ein Stabilisationssystem wird sich aber in Grenzen = halten.=20 Ein hohes Tr=E4gheitsmoment wird die beim Schuss vorhandene zeitliche=20 Winkelgeschwindigkeit herabsetzen und damit den Fehler, der durch=20 unterschiedliche Handhaltungen hervorgerufen wird, verkleinern.

Wie sollte ein vern=FCnftiges Stabilisationssystem = aussehen?

Alle anderen Effekte sind im Bereich der Mythen, M=E4rchen, Public = Relations=20 gut aufgehoben. Wer bereit ist, daf=FCr viel Geld auszugeben, sollte es = tun. Der=20 H=E4ndler freut sich. Wer erz=E4hlt , dieses oder jenes = Stabilisationssystem h=E4tte=20 sein Trefferbild signifikant verbessert, der frage man freundlich nach=20 nachpr=FCfbaren Unterlagen (zB Treffbild vorher/nachher, wieviel Schuss, = waren die=20 Bedingungen gleich, lief die Untersuchung =FCber einen l=E4ngeren = Zeitraum, um=20 Spassigkeiten der Statistik auszugleichen).

Aus den Antworten m=F6ge sich jeder seinen eigenen Reim=20 machen.

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