Archive for August, 2017

## Motivation

In more than one episode of “The Woodwright’s Shop” Roy uses a gauge he calls an “Octoganizer”.  See this recent show at about 23 minutes in. He can mark a piece of square stock with the layout lines needed to plane off the four corners, creating an octagon. The tool has a pair of locating posts that straddle the work piece, and two scratch pins to mark the face.

These screen shots from the Woodwright’s 3613 episode show the antique Octagonizer and also Roy marking a stool leg blank. He made a point that the tool can follow a tapered leg blank.

Bottom side of the Octagonizer

Using the Octagonizer

Searching the internet reveals this is a common tool in the boat building business called a “Spar Gauge”. I don’t know what “Spar” is on a boat.  I thought it was something Texans carried in the back of their pickup. Many internet pages discuss methods of making this tool, here is one that uses a graphical method to locate the marking pins.

I decided to explore the concept and make one. Or two. Or three. It turns out one size doesn’t fit all.

## The Method

So exactly where do you drill for the scratch pins?

This is the necessary derivation:
In the following W = Width of stock, F = Width of a full facet, X = Width of an angled facet (to be removed).

Square stock layout

The full width W contains one full sized facet and two angled facets
$W = F + 2 * X$

Angled facets measure full width times the cosine of 45 degrees, which is $\frac{1}{\sqrt 2}$
$W = F + 2 * (F * \frac{1}{\sqrt 2})$
$W = F * (1 + \frac{2}{\sqrt 2})$
$W = F * (1 + \sqrt 2)$

Rearrange the last to solve for the full facet width:
$F = \frac {W}{1 + \sqrt 2}$
Plugging in the numbers and calculating gives:
$F = W * 0.4142$

But we really need to know X, the width of the angled facet, so we can mark the stock by measuring from an edge.
$X = F cos 45$
$X = \frac {W}{1 + \sqrt 2} * \frac {1}{\sqrt 2}$
$X = W * \frac {1}{\sqrt 2 + 2}$
Running that through my calculator gives:
$X = W * 0.2929$

So 0.2929 is the Magic Number!

Just to verify:
$0.2929 + 0.4142 + 0.2929 = 1$
Yes!

## Implementation

Locating posts on either side of the tool are a source of error because of their thickness. If the tool has to be skewed to a really steep angle, like using a four inch long Octagonizer to mark a half inch stick, the marks will be too close to the edge. In this exaggerated example with posts an inch in diameter, the scratch pins miss the thin board completely.

Error caused by post diameter

If the locating posts were infinitely thin this would not happen and the tool could always lay out an accurate octagon. Therefore we need to keep posts as small a diameter as practical and avoid steep skew angles. I’m going to use six penny nails for posts and eventually make several Octagonizers to accommodate projects of different widths. Practically though, for many uses octagon shapes don’t have to be perfect.

The Octagonizer I made doubles up on a 4 1/2″ piece of Osage Orange. The wide side will mark stock up to 3 3/4″ wide. I let the wide side scratch pins stick out on the side opposite the points, these form the locating posts for marking narrower stock up to 1 3/8″.

Dual Octagonizer front

Dual Octagonizer wide side

Dual Octagonizer narrow side

This photo shows the wide side marking a piece of 2 inch stock. I’ve enhanced the scratch marks with pencil for the photo.

Marking a blank with the Octagonizer wide side

I had a piece of Poplar about 1 1/4″ square, I marked it out with the Octagonizer’s narrow side. Here it is clamped corner to corner in the vise.

Planing a 1 1/4″ Poplar square into an octagon

The Poplar works down quickly. I left one facet uncut just to show how it works.

The first try, three facets planed

While working through the arithmetic to locate the six holes in this double sided tool, I had to carefully account for the radius of the nails. Six penny nails measured 0.116″ in diameter, not accounting for this would throw the accuracy off a lot. I sharpened the points before assembly by chucking the cut off nails in a battery powered drill, then gently spinning them against a grinding wheel. The points were tempered by heating them red hot, quenching in water, then cooking in a toaster oven for 20 minutes at 425 degrees. I used a machinists vise to press the nails through pre-drilled holes in the Osage Orange.

## Usage

In many cases you can set a marking gauge to Width times the Magic 0.2929, and just mark all eight lines with that.  If I had to make only one octagon I would use a marking gauge. If I had to make more than four, I might make an Octagonizer. A marking gauge will not encounter the error discussed in the previous section and you can lay out an octagon on a piece of stock any length, any width. It would not work though on tapered stock.

I plan to Octagonize a treated 4×4 for a porch support post.

Roy showed using the Octagonizer to lay out a tapered stool leg but laying out a short tapered octagon like a chisel handle, can also be done by marking both ends of a tapered blank, then using a straight edge to connect the dots. This is also a good method if you don’t want to see evidence of scratch marks.

## Viewing Methods

A few weeks ago I started thinking about what to do with materials I have on hand for the August 21 Solar Eclipse. This area of Illinois (just West of Chicago) will see about an 88 percent occlusion, per this calculator, starts at 11:53, peaks at 1:19PM and ends at 2:42. Weather permitting of course – what are the odds?  This post is written six days before the event. I will update if the viewing is successful.

Pinhole projection seemed like a good traditional method, but Google research indicated the image would only be about 3/4″ diameter. One of the pinhole discussions also talked about using one side of binoculars to focus the Sun’s image. I do own a medium quality 7×30 pair with zoom so decided to try them. This is one of the first images obtained.

Close up of projected sun image

I was very pleased with this, if you look just below center slightly to the left, there is a genuine sunspot clearly visible. The image is about 3 inches across at minimum zoom.

Now to make a two hour viewing interval practical I explored mounting the binoculars to a good camera tripod. This tripod has the pan and tilt head on a tall crank up rod and a mechanism to tilt that rod at it’s base up to 90 degrees (parallel to the ground). Long ago I owned a telescope with an equatorial mount and I thought maybe laying the central rod down at the proper angle would enable that function.

The advantage of an equatorial mount is you can track a star, or the Sun, by adjusting only one of the two axes of the telescope mount. Having to manhandle both the azimuth (pan) and elevation (tilt) to track is a real PITA. You don’t realize how fast the Sun moves across the sky until you magnify it 7 times. The sky moves 360degrees/24hours = 15 degrees every hour. The way the mount works is, you align the primary axis of the scope, in this case the tiltable rod, with the earth’s rotational axis. Then the stars rotating around the earth’s axis also rotate around the telescope’s axis and you can keep the scope pointed at the same spot in the sky by adjusting only the azimuth. Ideally with a powered clock mechanism.

Of course it’s you that’s moving, not the Sun but the result is the same. Thank you,

First, my binoculars had to be firmly attached to the tripod. The dozen or so rubber bands I used for initial testing just didn’t work out. I drilled a block of hard wood to fit the round central spine of the binoculars. All binoculars I have seen are made like this, it is part of the mechanism that allows the two eyepieces to separate or close to match your eye spacing. Then I sawed through the drilled block and installed a couple of screws to clamp the block on the spine. Then I drilled and tapped a 1/4-20 hole in the bottom of the block to mate with the tripod screw.

You need a large shade so the projected image is in shadow. This was easily made from cardboard.

Binocular clamped to tripod

This photo shows the tripod tilt mechanism with the riser set to equatorial position.

Tripod extended in equatorial position

I made a box to further keep out stray light. It’s about ten inches square, painted flat black with a sheet of white paper at the bottom. The string you see in the photo above helps align the shadow box axis with the binoculars. I mounted the cardboard box on a 1×6 with a hinge and a sliding prop arrangement so the box can easily be tilted to align with the projected image.  The box must be moved and realigned every now and then as the Sun moves across the sky.

Sun image projected into shadow box

If I was observing stars at night, I could align the scope by looking at the north star. But during the day the procedure for equatorial alignment is:

1. Align the riser rod exactly North by positioning the whole tripod.
2. Raise the central rod to the exact latitude of the location. About 42 degrees here.
3. Uncover one side of the binoculars
4. Hold a sheet of paper below the eyepiece and move the tripod pan and tilt until you see the Sun image. Try to center the image in the binocular field by exploring the edges.
5. Remove temporary paper, set and align the shadow box with the projected image. Stretching the string back to the box will show you the axis.
6. Tighten the tripod tilt but leave pan axis loosen enough to move with the Sun.

Here is the assembled Helioscope. You can see the projected image in the bottom of the box.

Binoculars with shade projecting sun image

So far my only expenses are a spray can of flat black paint and new batteries for the camera.

## Camera Modification:

Hand holding a camera on the image is awkward. I decided to mount a camera directly on the box so it would always see the same image field. To enable this and not block the projecting beam, I bumped out one side of the box 2 1/2 inches. Hot glue is wonderful stuff. It took some fussing with a tapered shim to get the camera pointed at the image correctly.

Camera mounted inside box

It’s very hard to read this Canon A530 screen in the sun so I connected a small television which has a composite video input to remote the display. This works well. You can see the 2 1/2 inch bumpout in this photo.

Camera in box and composite monitor

The best images are shot with the camera zoomed in a bit. I’ve worked out how to crop the pictures consistently with GIMP. A stretch goal is to make a video of the whole occlusion. I’ll need a photo every 30 seconds, two hours and 45 minutes should fit on a 2 gig camera card.  But I worry about having to change camera batteries in the middle of the sequence.

I worked up a BASIC script with the Canon Hack Development Kit. It is based on a Wiki post by Keoeeit, his version 3. It should solve the setting consistency problem if I have to change the batteries and fires the camera at a set interval.

It has the following parameters to set:

• Initial Zoom amount, a number 0-8 for the A530
• Delay before first shot Min, Sec, Allows time to reposition the camera after a disturbance
• Number of shots to take, zero runs forever
• Time between shots, Min, Sec.

I run the camera in Manual mode with shutter about 1/80 sec at F4.5 (the small Canon cameras don’t really have an iris). I don’t want the exposure to change any time during the run. I put a magazine page in the box so the lens has something busy to focus on then put the camera in CHDK mode and start the script, .

The following happens:

1. The lens zooms out to the fixed setting supplied.
2. There is a delay countdown so you can tweak the camera position
3. The lens focuses and then locks the focus
4. A ten second delay to allow removing a focus target.
5. The camera begins taking pictures at the specified interval.

This is the BASIC script

rem Author – Keoeeit
rem Time accuracy and shutdown for a710is by Viktoras Stanaitis
rem h-accuracy for delay, j-accuracy for interval
rem Reset zoom added to restore the same picture
rem in case batterys have to be changed during a long session

h=-1
j=-1755

@title Eclipse Intervalometer

rem number of zoom steps to execute at beginning of script
rem A530 has steps 0 – 8
@param i Initial Zoom
@default i 3

rem the delay is after zooming so camera positon can be tweaked
@param a Delay 1st Shot (Mins)
@default a 0
@param b Delay 1st Shot (Secs)
@default b 0

@param c Numb. of Shots (0 inf)
@default c 0

rem interval is the time between shots
@param d Interval (Minutes)
@default d 0
@param e Interval (Seconds)
@default e 10

print”DISABLE THE FLASH!”

rem Move the zoom to a consistent setting
set_zoom 0
for s=1 to i
print “step”,s
set_zoom_rel 1
next s

n=0
t=d*60000+e*1000
if c<1 then let c=0
if t<1000 then let t=1000
g=(a*60)+b+h
if g<=0 then goto “focus”

rem count down seconds until begin shooting
for m=1 to g
print “Intvl Begins:”, (g-m)/60; “min”, (g-m)%60; “sec”
sleep 930
next m

rem set and lock focus
:focus
set_aflock(0)
press “shoot_half”
sleep 2500
release “shoot_half”
set_aflock(1)
print “Remove Focus Target”
sleep 10000

:interval
n=n+1
if c=0 then print “Shot”, n else print “Shot”, n, “of”, c
shoot
if n=c then goto “quit”
sleep t
goto “interval”

:quit
set_aflock(0)
shut_down
end

:restore
set_aflock(0)
exit_alt
end