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'[OT:] Fw: help for cutting penetrating tubes'
2004\04\29@114522 by

A friend in Germany has asked if I have a solution to this problem.
Sounds like the sort of things that metal workers will have worked out a few
centuries ago.
I imagine some playing would produce an analytical  result BUT someone may

As I read it he's trying to insert a small tube into a larger tube with
their axes at right angles. He wants a formula to make a template that will
allow him to mark the smaller tube for cutting so the smaller tube fits into
a hole in the larger and smoothly touches the outer surface with essentially
zero clearance gaps to fill. AFAIK the application is for a rocket body with
a parachute mounted in the smaller horizontal tube.

Any suggestions?

Russell McMahon

Here's a first try which may be right.
E&OE / late / excuses ...

r = radius of small tube.
s = angle around small tube from top.
B = distance small tube has to be redcued from maximum length as you
progress from 0 degrees (at top) to 90 degrees (at side)
R = radius of large tube
L = angle around large tube where small and large meet for a given s

There will be 4 quadrants which are mirror images.

****   B = R(1 - cos  (arcsin([r  sin(s) ]/R ))) ****

Inspection of a graph of this function suggests that it may be a simple
sinusoid with amplitude equal to the radius of the small tube!

E&OE (ie - may have made a mistake or two :-))

Method:

Distance out from centre of small tube as we go around small tube is
r sin(s)    1
Also =
R sin(L)    2
So
Rsin(L) = r sin(s)    3
Rearranging
L=arcsin(R/(r sin(s)))    4
Distance small tube is reduced by from maximum is
B = R(1-cos(L))            5
Substitute 4 in 5
B = R(1-cos(arcsin(r sin(s))/R))

____________________________________

Hi Russell,
...
I want to glue a smaller tube into a larger one, 90° angle beween their long
axises - (no, axes).
Think of a HDTT. If I do this, I always have to cut both the tubes by
eyesight - not very perfect, and a relative lot of glue needed to fill the
gaps.

Do you know a simple way of creating a drawing on paper that I could cut
out, apply on the smaller chute tube and cut along the paper? This should
give a perfect fit between backside of the horizontal tube and the inner
side of the larger rocket head. The papaer template edge would have a sinus
related shape (not more related than having ups and downs, and the beginning
of the line meeting the end without a sharp bend, when applied to the HD
tube).

The only variables needed would be Diameter(rocket)=Dr and Diameter(HDTT
tube)=Dt. And eventually the meeting angle, usually 90°.

A drawing for the hole to be cut into the rocket head would be nice as well.
Again, the drawing should be applied to the rocket head and the hole cut
along it's margin - result: the chute tube fits perfectly in.
An ellipse eventually, with the axes a=Dt and
b=Dr * 2 arcsin(Dt/(2*Dr))  ? I am not sure if the ellipse is "round" enough
on the b end.

Is the problem clearly stated?
Have you an idea how to solve it?
Best with a PC software that prints the templates out.
Any better ideas than that?
--
With greetings from Germany
Ulrich

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Cut it with a hole saw of the right size.
No math, no templates, fits perfectly.
What could be easier?

Ed G.
{Original Message removed}
At 10:52 AM 4/29/2004 -0500, you wrote:
>Cut it with a hole saw of the right size.
>No math, no templates, fits perfectly.
>What could be easier?

Yup. A fellow at the local (TSME) model engineering group demo'd a device
(part jig, part fixture, part tool) that used a bog-standard bimetal hole saw
to drill into the side of a tube (at right angles or, IIRC, other angles).
Basically a die-clamp and similar stuff to clamp the tube to be drilled,
and a hole saw mounted on bearings, driven by a motor.

Worked a charm, and he did quite a few metal tubes with it (to make
some kind of frames- race cars or bicycles or something like that.. I was
more interested in the tool than in his application.)

Bset regards,

Spehro Pefhany --"it's the network..."            "The Journey is the reward"
speffinterlog.com             Info for manufacturers: http://www.trexon.com
Embedded software/hardware/analog  Info for designers:  http://www.speff.com

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Don't have time at the moment, but if you can wait till this evening (6-7
hours from now) I dig out my 1930's pipefitters manual and tell you all
-Denny

A friend in Germany has asked if I have a solution to this problem.
Sounds like the sort of things that metal workers will have worked out a
few
centuries ago.
I imagine some playing would produce an analytical  result BUT someone may

As I read it he's trying to insert a small tube into a larger tube with
their axes at right angles. He wants a formula to make a template that will
allow him to mark the smaller tube for cutting so the smaller tube fits
into
a hole in the larger and smoothly touches the outer surface with
essentially
zero clearance gaps to fill. AFAIK the application is for a rocket body
with
a parachute mounted in the smaller horizontal tube.

Any suggestions?

Russell McMahon

Here's a first try which may be right.
E&OE / late / excuses ...

r = radius of small tube.
s = angle around small tube from top.
B = distance small tube has to be redcued from maximum length as you
progress from 0 degrees (at top) to 90 degrees (at side)
R = radius of large tube
L = angle around large tube where small and large meet for a given s

There will be 4 quadrants which are mirror images.

****   B = R(1 - cos  (arcsin([r  sin(s) ]/R ))) ****

Inspection of a graph of this function suggests that it may be a simple
sinusoid with amplitude equal to the radius of the small tube!

E&OE (ie - may have made a mistake or two :-))

Method:

Distance out from centre of small tube as we go around small tube is
r sin(s)    1
Also =
R sin(L)    2
So
Rsin(L) = r sin(s)    3
Rearranging
L=arcsin(R/(r sin(s)))    4
Distance small tube is reduced by from maximum is
B = R(1-cos(L))            5
Substitute 4 in 5
B = R(1-cos(arcsin(r sin(s))/R))

____________________________________

Hi Russell,
...
I want to glue a smaller tube into a larger one, 900 angle beween their
long
axises - (no, axes).
Think of a HDTT. If I do this, I always have to cut both the tubes by
eyesight - not very perfect, and a relative lot of glue needed to fill the
gaps.

Do you know a simple way of creating a drawing on paper that I could cut
out, apply on the smaller chute tube and cut along the paper? This should
give a perfect fit between backside of the horizontal tube and the inner
side of the larger rocket head. The papaer template edge would have a sinus
related shape (not more related than having ups and downs, and the
beginning
of the line meeting the end without a sharp bend, when applied to the HD
tube).

The only variables needed would be Diameter(rocket)=Dr and Diameter(HDTT
tube)=Dt. And eventually the meeting angle, usually 900.

A drawing for the hole to be cut into the rocket head would be nice as
well.
Again, the drawing should be applied to the rocket head and the hole cut
along it's margin - result: the chute tube fits perfectly in.
An ellipse eventually, with the axes a=Dt and
b=Dr * 2 arcsin(Dt/(2*Dr))  ? I am not sure if the ellipse is "round"
enough
on the b end.

Is the problem clearly stated?
Have you an idea how to solve it?
Best with a PC software that prints the templates out.
Any better ideas than that?
--
With greetings from Germany
Ulrich

--
http://www.piclist.com#nomail Going offline? Don't AutoReply us!
email listservmitvma.mit.edu with SET PICList DIGEST in the body

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email listservmitvma.mit.edu with SET PICList DIGEST in the body

Looks like you found a better source than I have, I won't bother posting
it.

-Denny

{Quote hidden}

may
> have this sorted out already.
>
> As I read it he's trying to insert a small tube into a larger tube with
> their axes at right angles. He wants a formula to make a template that
will
{Quote hidden}

the
> gaps.
>
> Do you know a simple way of creating a drawing on paper that I could cut
> out, apply on the smaller chute tube and cut along the paper? This should
> give a perfect fit between backside of the horizontal tube and the inner
> side of the larger rocket head. The papaer template edge would have a
sinus
{Quote hidden}

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