\> \-\-\-\--Original Message\-\-\-\--

\> From: Henning Leidecker \<hleideck@pop500.gsfc.nasa.gov\>

\> To: EXT-Bickel, Gary W \<Gary.Bickel@West.Boeing.com\>

\> Cc: Anna@seawire.traveller.com \<Anna@seawire.traveller.com\>;

\> carol.a.mcdonald@boeing.com \<carol.a.mcdonald@boeing.com\>;

\> Craig.T.Mueller@aero.org \<Craig.T.Mueller@aero.org\>;

\> DRothermel@BICCGeneral.com \<DRothermel@BICCGeneral.com\>;

\> elindholm@lucent.com \<elindholm@lucent.com\>; EXT-Beverly, David W

\> \<david.w.beverly1@jsc.nasa.gov\>; Gill, David
\<DAVID.GILL@West.Boeing.com\>;

\> harold.f.battaglia \<harold.f.battaglia@boeing.com\>; Jie Li

\> \<JieLi@lucent.com\>; John.S.Canham.1
\<John.S.Canham.1@gsfc.nasa.gov\>;

\> jplante@swales.com \<jplante@swales.com\>; Mitchell, Billie-Jo

\> \<BMitchell@BICCGeneral.com\>; ray.prestridge@lmco.com

\> \<ray.prestridge@lmco.com\>

\> Date: Monday, July 03, 2000 7:32 PM

\> Subject: vibrating fiber on the tower

\>

\>

\> \>Gentles,

\> \>

\> \>We are interested in imagining how latent defects (thinned regions
\-\--

\> \>sinkholes \-\-- in the polyimide, some with ten micron diameter
bubbles)

\> \>might get into FlightGuide fiber at Spectran/Lucent.

\> \>

\> \>I take it for granted that the answer will have to come from
someone at

\> \>Lucent who \"lives on the tower\".

\> \>

\> \>But I cannot help speculating while we are waiting \...

\> \>

\> \>The purpose of this email is to sketch the possibility that the
fiber is

\> \>sometimes driven into forced vibration, and that this produces the
periodic

\> \>string of latent defects. I\'ve checked with someone who is
familiar with

\> \>fiberglass draw towers, and I\'ve been assured that this sort of
thing

\> \>actually happens \-\-- the fiber \"vanishes\" from sight as it
begins to

\> \>vibrate from side to side.

\> \>

\> \>First, I compute the relation between the observed spacial
frequencies of

\> \>the latent defects (1 to 4 mm) and the vibrational frequencies that
the

\> \>fiber must have, to make these.

\> \>

\> \>Second, I sketch the allowed vibrational frequencies of a length of

\> \>FlightGuide fiber under tension.

\> \>

\> \>Third, I sketch some ways that the fiber might get excited into
vibration,

\> \>from time to time.

\> \>

\> \>Henning Leidecker

\> \>================================================

\> \>================================================

\> \>

\> \>1. What vibrational frequencies are implied by the observed latent
defects

\> \>\...

\>

\>===========================================================================

\> \>Call the fiber draw speed S_fib, and the spacial period (the
distance

\> \>between latent defects) L. Then these latent defects move past a
fixed

\> \>point with a temporal period T = L/S_fib ; the frequency is f = 1/T
=

\> \>S_fib/L .

\> \>

\> \>The typical fiber draw speed is S_fib = 20 cm/sec, so latent
defects spaced

\> \>by 1.0 mm move past a fixed point at a frequency of f = (20
cm/sec)/(0.10

\> \>cm) = 200/sec = 200 Hz. And latent defects spaced by 4.0 mm move
past a

\> \>fixed point at a frequency of 50 Hz. This sets the scale of the

\> \>vibrational frequencies that interest us: they are expected to
range

\> \>between 50 and 200 Hz.

\> \>

\> \>

\> \>

\> \>2. What are the vibrational frequencies of the natural modes of the
fiber

\> \>on the tower \...

\>

\>===========================================================================

\> =

\> \>===========

\> \>We have known for centuries that the natural modes of vibration of
the

\> \>stretched fiber are given by

\> \>

\> \> f_n = (n / 2\*L) \* sqrt\[T/mu\] ,

\> \>

\> \>where \"n\" = 1, 2, 3, is the number of loops in the fiber between
its fixed

\> \>ends, spaced a distance \"L\" apart, \"T\" is the tension of the
fiber, and

\> \>\"mu\" is the mass per length of the fiber.

\> \>

\> \>The fiber is fixed, or pinned, against transverse motion at several
places

\> \>along the draw tower. (I do not mean \"pinned in space\";
certainly, the

\> \>fiber is in motion along its z-axis. I only mean that the sideways
motion

\> \>is pinned.) I will suppose these are the places, and distances
between

\> them:

\> \>

\> \> L1 = distance between the top oven (where the draw begins)

\> \> and the 1st polymer coating \"cup\".

\> \> L2 = distance between the 1st and 2nd polymer coating \"cup\"s.

\> \> L3 = distance between the 2nd and 3rd polymer coating \"cup\"s.

\> \> L4 = distance between the 3rd and 4th polymer coating \"cup\"s.

\> \> L5 = distance between the 4th polymer coating \"cup\" and

\> \> the capstan at the bottom of the tower.

\> \>

\> \>These are might all be different lengths. I think that the order of
these

\> \>five \"L\"\'s is between 2 and 10 meters. I will suppose 5 meters
for the

\> \>following computations, until someone who actually knows the tower
will

\> \>take mercy on me, and contribute accurate values.

\> \>

\> \>The tension in the fiber is mainly set by the contest between the
viscosity

\> \>of the hot glass in the drawing furnace and the speed of the
capstan at the

\> \>bottom. But there is probably a contribution of the viscous drag of
the

\> \>fiber as it passes through each polymer coating \"cup\". All I know
about it

\> \>is that it must be substantially less than the breaking strength of
the

\> \>glass fiber, about 10 pounds. The proof test value is about 5
pounds, and

\> \>so I will suppose that the tension is 4 pounds (= 17.8 newtons);
again, I

\> \>hope someone who actually knows realistic values will contribute
here too.

\> \>

\> \>The mass per length is 0.425 mg/cm = 42.6 kg/m (if I did my
arithmetic

\> \>correctly; I\'ll weigh some).

\> \>

\> \>Therefore

\> \>

\> \> f_n = n \* (65 Hz) = 65, 130, 195, 260, \... Hz.

\> \>

\> \>These are clearly in the right ball-park to create the observed
latent

\> \>defects. This suggests to me that it is well-worth using better and
more

\> \>realistic values, to see if this plausible agreement is maintained
in the

\> \>face of better arithmetic.

\> \>

\> \>

\> \>

\> \>3. How can these vibrational defects be excited \...

\> \>===============================================

\> \>There is the possibility that an air current, or some other
excitation,

\> \>might get the fiber into a lateral (i.e., transverse) vibration, so
that it

\> \>would periodically press into the side of something (perhaps a die
at the

\> \>top or bottom of a polymer coating cup?).

\> \>

\> \>From \"A Textbook of Sound: being an account of the physics of
vibrations

\> \>with special reference to recent theoretical and technical
developments\" by

\> \>A. B. Wood (first published in 1930).

\> \>

\> \>Start of \"AELOIAN TONES\"

\> \>When a steady flow of fluid passes an obstacle with a large enough
speed,

\> \>it is usually found that eddies are formed behind the obstacle.
Such

\> \>effects are familiar in the case of a stream of water \"swirling\"
past a

\> \>rock. Similar effects are also produced in a stream of air. A

\> \>cylindrical obstacle, such as a rod or wire, in a stream of air
sets up a

\> \>double series of vortices (Mallock, Proc. Roy. Soc. vol 9, page
262, 1907).

\> \> The stream of air past the wire is thus set into transverse
vibrations, as

\> \>alternate left- and right-handed eddies are formed and detached.
This

\> \>results in alternating pressure waves, which can be audible under
certain

\> \>circumstances. An experimental investigation of these vortex
vibrations

\> \>was first undertaken by Strouhal (1878) and later by Kohlrausch
(1881).

\> \>The frequency \"f\" of the tone in the air was independent of the
length of

\> \>the wire and also the tension of the wire, and varied only with the

\> \>thickness \"d\" and the speed \"s\" of the wire through the air:

\> \>

\> \> f = 0.185 (s/d)

\> \>

\> \>The detachment of the alternating vortices, and the wavering of the
stream

\> \>of air, produces an alternating transverse force on the wire, which
set it

\> \>into forced vibration at the frequency \"f\". We have a pronounced
resonance

\> \>when this frequency coincides with one of the natural modes of
vibration of

\> \>the stretched wire,

\> \>

\> \> f_n = (n / 2\*L) \* sqrt\[T/mu\] ,

\> \>

\> \>where \"n\" = 1, 2, 3, is the number of loops in the wire between
its fixed

\> \>ends, spaced a distance \"L\" apart, \"T\" is the tension of the
wire, and \"mu\"

\> \>is the mass per length of the wire. This resonance can result in a
large

\> \>amplitude of displacement of the wire.

\> \>

\> \>The music of the Aeolian harp is produced this way. The harp
consists of a

\> \>number of wires of graduated thickness mounted on a sounding board.
The

\> \>wires are all turned to the same low fundamental note, which
consequently

\> \>has a wide range of overtones in the audible region. When a wind
moves

\> \>past these wires, and \"plays\" it, one or more of these wires will
resonate

\> \>and emit the note of the appropriate overtone. Other examples
include the

\> \>\"singing\" of overhead wires, the \"sighing\" and \"roaring\" of
wind in trees,

\> \>and the \"whistling\" of wind through tall grasses.

\> \>End of \"AELOIAN TONES\"

\> \>

\> \>We now ask what air speed might excite a transverse vibration of 50
to 200

\> \>Hz, in a fiber whose diameter is 140 microns (before the first
coating cup)

\> \>to 170 microns (after the last coating cup).

\> \>

\> \> s = 5.40 \* f \* d = 5.40 \* (50 to 200 Hz) \* (140 to 170
microns)

\> \> = 3.8 to 18 cm/sec

\> \>

\> \>So we look for \"drafts\" having an air speed of this range.
Perhaps there

\> \>is a flow of air sideways across the fiber as it moves down the
tower?

\> \>

\> \>The resonance-amplification of the fiber\'s motion could be a
factor of 50

\> \>or more! (This is the quality factor of this motion.) If the
tension in

\> \>the fiber were to vary with time, then the fiber would go into and
then out

\> \>of resonance, with a large change in the amplitude of the sideways
motion.

\> \>This is the sort of thing we see.

\> \>

\> \>Such a fiber motion would be very easy to see! We just examine the
fiber.

\> \>When we can clearly see it as it moves down the draw tower, then it
is not

\> \>in sideways motion at 50 to 200 Hz! When it vanishes, then such a
motion

\> \>has begun. We can instrument this for automatic detection very
cheaply.

\> \>

\> \>

\>

\>