## Q: finding radius, finding angle

### Q: finding radius, finding angle

Here's one, boys & girls:  I have to duplicate a piece for a
friend.  It's as if you'd taken a lengthwise section from a
hollowed-out cylinder -- like a short section of rain gutter, I
guess, if that makes sense.  Is there some simple way to find out
the radius of curvature of this thing?  I can eyeball it and get
close, but how would I get an exact figure?

That's question one.  The second is like unto it, sort of.
Picture a collet, tubular for most of its length and then flared
at the end.  Assuming that the flared part is too short for me to
get a bevel in there (I'm thinking like a carpneter's bevel and
assuming that machinists use a similar kind of thing), how would
you measure the included angle?  Once again, I can get close
without doing anything unusual; but how would I find the exact
angle?

--
Bucky Goldstein

I lost a button hole.

### Q: finding radius, finding angle

Radius: use a geometric property that says if you have a diameter of a circle,
intersected at some point by a chord at a right angle, the product of the two
half-chords is equal to the product of the two segments (short and long) of the
diameter.

Kind of hard to explain. But very easy to get the diameter if you measure
across your curve (divide measurement by two to give you the two half-chords)
and measure the sagitta, which is the "gap" between your line across the curve
and the bottom (the short part of your diameter). Arithmetic will get you the
"long" part of the diameter, add that to the measured short part, and you've
got the diameter.

[Short half chord x short half chord]/sagitta = long part of diameter.

Sagitta + long part of diameter = total diameter.

Think of it this way. If you have a circle, cut exactly into quarters, this is
true; half of one diameter times the other half of that diameter is equal to
the other diameter times its other half. Now slide one of these two diameters
up until it's just a chord, not a full diameter. The relation is still true,
although the numbers will be different.

Pete

### Q: finding radius, finding angle

Quote:

> Here's one, boys & girls:  I have to duplicate a piece for a
> friend.  It's as if you'd taken a lengthwise section from a
> hollowed-out cylinder -- like a short section of rain gutter, I
> guess, if that makes sense.  Is there some simple way to find out
> the radius of curvature of this thing?  I can eyeball it and get
> close, but how would I get an exact figure?

It depends on how exact you need to get.  If the section is truly part
of a circle, you can measure the depth at the center, and the breadth,
edge to edge, and determine the radius with the help of a little bit of
trig, as accurately as your measurements.

Quote:

> That's question one.  The second is like unto it, sort of.
> Picture a collet, tubular for most of its length and then flared
> at the end.  Assuming that the flared part is too short for me to
> get a bevel in there (I'm thinking like a carpneter's bevel and
> assuming that machinists use a similar kind of thing), how would
> you measure the included angle?  Once again, I can get close
> without doing anything unusual; but how would I find the exact
> angle?

Once again, measure the things you can measure, minimum diameter,
maximum diameter, distance from one to the other, and compute.

Al Moore

### Q: finding radius, finding angle

On 12 Sep 2000 15:32:19 GMT, Bucky Goldstein

Cylindrical section:   bridge it with a straight piece of
known length L.   Measure the gap between the bridge piece
and the cylinder wall at the greatest gap.  Call that y.

R= (1/2y) * ( (L^2)/4  + y^2)

Tapered thing:   measure large diameter d1 and small
diameter d2  an axial distance x apart from one another.

The half-angle will be arctan( (d2-d1)/2 ) / x)

### Q: finding radius, finding angle

Quote:
>If the section is truly part
>of a circle, you can measure the depth at the center, and the breadth,
>edge to edge, and determine the radius with the help of a little bit of
>trig, as accurately as your measurements.

No, not trig. Way too complicated and invites errors. It's simple
multiplication and division.

I didn't find a diagram of exactly what I want, but this will do too.

http://neuronio.mat.uc.pt/crcmath/math/math/c/c279.htm

the (chord^2) / 4 = (s) (r + a)

You measure chord and s. You solve for (r + a) which is the distance along a
diameter, from your chord across the center to the other side of the circle (in
other words r+a is the diameter minus s).

Now you have r+a, and you measured s, so s + r + a is the diameter whichis what
you were looking for.

Example. You have a surface which is a very shallow bowl. You want to figure
out the diameter of its curvature.

You rest a 6" steel rule or steel parallel across it, like a beam, and measure
the "daylight" under it with a feeler gauge. Say you measure .025 inches.

Now the chord is 6" and s = .025.

(6^2)/4 = (.025) (r+a)

36/4 = .025 (r+a)

9 = .025 (r+a)

360 = r+a

diameter = r + a + s = 360.025

(call it 360).

===================

Another example with a less shallow curve.
Same 6" beam, but you measure 1 inch below the beam.

6x6/4 = 1 x (r+a)
9 = (r+a)

diameter = r + a + s = 10 inches.

Pete

### Q: finding radius, finding angle

Quote:

> Here's one, boys & girls:  I have to duplicate a piece for a
> friend.  It's as if you'd taken a lengthwise section from a
> hollowed-out cylinder -- like a short section of rain gutter, I
> guess, if that makes sense.  Is there some simple way to find out
> the radius of curvature of this thing?  I can eyeball it and get
> close, but how would I get an exact figure?

Use a radius gage?  I bought another set on Sunday from 1/64 to 1/2 by
64th.  The old gentleman from whom I bought it had another set from 1/2 to
3" by 16ths -- so they exist.

Quote:

> That's question one.  The second is like unto it, sort of.
> Picture a collet, tubular for most of its length and then flared
> at the end.  Assuming that the flared part is too short for me to
> get a bevel in there (I'm thinking like a carpneter's bevel and
> assuming that machinists use a similar kind of thing), how would
> you measure the included angle

Cast something into it -- like a quick-set epoxy -- with appropriate mold
release?

Boris

--

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TEL: 215-572-5580
FAX: 215-886-0144

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### Q: finding radius, finding angle

Quote:

> > the radius of curvature of this thing?  I can eyeball it and get
> > close, but how would I get an exact figure?

This is of course the way to go.  Use a compass to draw the circle,
cut on the line, and trim away part of it.

This will get one to within 1/64 or so, which sounds like it should
be exact enough.  Given that no tolerance on the measurement was
mentioned, one might make an educated guess.

Jim

Sent via Deja.com http://www.deja.com/

### Q: finding radius, finding angle

Quote:
>>hollowed-out cylinder -- like a short section of rain gutter, I

Quote:
>>at the end.  Assuming that the flared part is too short for me to

Use trig. Subtract diameters at each end (a) and halve the result,
then measure the distance between them (b).

tan of Angle = a/b (opposite over adjascent)

--

Grumpy, the Third Dwarf
(Dave Johnson)

*****************************************
If I were taller, I wouldn't be so short!
Dyslexics of the world, untie
*****************************************

### Q: finding radius, finding angle

Hey Bucky,

Well Pete lost ME in his first sentence.  And the last was worse.  I'm
sure what he says will work 'cause he says it will, but me????...  I'd
just draw what you have up in CAD and ask it to give you the
dimensions you want.

As to the other thing, if you can mount it in your lathe chuck or
between centres, clamp a DTI to the compound and swing the compound
until when you advance and retract it with the DTI against the
compound.  I've done that with "chamfers" as small as about 1/8"
'long' which were not located where I could mike the large versus the
small diameter or measure the length of the taper.

Let us know how you make out.

Brian Lawson
Windsor, Ontario.
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

Quote:

>Here's one, boys & girls:  I have to duplicate a piece for a
>friend.  It's as if you'd taken a lengthwise section from a
>hollowed-out cylinder -- like a short section of rain gutter, I
>guess, if that makes sense.  Is there some simple way to find out
>the radius of curvature of this thing?  I can eyeball it and get
>close, but how would I get an exact figure?

>That's question one.  The second is like unto it, sort of.
>Picture a collet, tubular for most of its length and then flared
>at the end.  Assuming that the flared part is too short for me to
>get a bevel in there (I'm thinking like a carpneter's bevel and
>assuming that machinists use a similar kind of thing), how would
>you measure the included angle?  Once again, I can get close
>without doing anything unusual; but how would I find the exact
>angle?

### Q: finding radius, finding angle

Quote:
>Here's one, boys & girls:  I have to duplicate a piece for a
>friend.  It's as if you'd taken a lengthwise section from a
>hollowed-out cylinder -- like a short section of rain gutter, I
>guess, if that makes sense.  Is there some simple way to find out
>the radius of curvature of this thing?  I can eyeball it and get
>close, but how would I get an exact figure?

Personally, I'd turn a short chunk to fit in it really nicely then measure
it.

Quote:
>That's question one.  The second is like unto it, sort of.
>Picture a collet, tubular for most of its length and then flared
>at the end.  Assuming that the flared part is too short for me to
>get a bevel in there (I'm thinking like a carpneter's bevel and
>assuming that machinists use a similar kind of thing), how would
>you measure the included angle?  Once again, I can get close
>without doing anything unusual; but how would I find the exact
>angle?

This answer is like unto the previous.  I'd turn a cone to fit nicely, and
measure it.  8-)

--
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
Mike Graham                 | Metalworker by trade
mikegraham at sprint dot ca | Weld to live, like to weld.
Caledon, Ontario, Canada    | Weird by nature
<http://metalmangler.homepage.com>
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
"By Fire and Iron doth he make Bread."

### Q: finding radius, finding angle

Quote:

> [Short half chord x short half chord]/sagitta = long part of diameter.

> Sagitta + long part of diameter = total diameter.

Excellent.  Thanks, Pete, that's what I needed for the radius
problem.

--
Bucky Goldstein

I lost a button hole.

### Q: finding radius, finding angle

Quote:

> Tapered thing:   measure large diameter d1 and small diameter
> d2  an axial distance x apart from one another.

> The half-angle will be arctan( (d2-d1)/2 ) / x)  Regards from

Don, the problem is measuring the axial distance.  I can do it
accurately if I hold the collet in a chuck, then use the travel
on the compound to measure with; but I have (or rather I had)
something in the chuck and I didn't want to disturb it.  Poor
planning.  So I measured the length with a caliper and got an
almost close enough result.  Not quite, but almost.

Sigh.

--
Bucky Goldstein

I lost a button hole.