Measure out this geometry right-angle for me

I'm building a knife sharpener with a 25-deg angle out of ceramic
hollow rods. Ceramic stock: 4-1/2" long & 3/8" diameter.

Right Angle Triangle: the two sides at 90-deg, one of which will be,
of course, the base.

Figure roughly around a 10" plug-in value for an extended "sharpening
edge," which will also be the same as the 3rd side of the triangle.
(I'll rig the ceramic rods to that 10" via the hollow center, with a
steel rod, or a wooden frame that clamps down. Figure that out
later.)

Anyway, I just need the math. If the opposite, 10" side to the right
triangle forms a 25-deg. angle, (to the two other, 90-degree sides),
sic. -- a 25-deg. angle, that is, to the straight-edge of a knife
being sharpened perpendicularly to the base of the triangle -- give me
the measurements for the two remaining triangular lengths to an
approximate 10" third side I've proposed.

Avoid decimal fractions of an inch (I've a precision steel ruler
that'll go up to 64th or 128ths. Actually, I'll be doing it twice
with two ceramic rods and bringing them together for sharpening both
sides of my cutlery simultaneously.)

Hell the whole damn thing could be made adjustable, compact and
secure, for a 15- to 35-degree leeway varying from finer knives to
hatchets and cleavers. Where's all the whizbang, latenite TeeVee
copyright holders when you've got a perfectly good handle on a
copyright scheme and need them?

At Thu, 14 Nov 2013 20:18:31 -0500, Flasherly rearranged some electrons to
write:

I'm building a knife sharpener with a 25-deg angle out of ceramic hollow
rods. Ceramic stock: 4-1/2" long & 3/8" diameter.

Right Angle Triangle: the two sides at 90-deg, one of which will be, of
course, the base.

Figure roughly around a 10" plug-in value for an extended "sharpening
edge," which will also be the same as the 3rd side of the triangle.
(I'll rig the ceramic rods to that 10" via the hollow center, with a
steel rod, or a wooden frame that clamps down. Figure that out later.)

Anyway, I just need the math. If the opposite, 10" side to the right
triangle forms a 25-deg. angle, (to the two other, 90-degree sides),
sic. -- a 25-deg. angle, that is, to the straight-edge of a knife being
sharpened perpendicularly to the base of the triangle -- give me the
measurements for the two remaining triangular lengths to an approximate
10" third side I've proposed.

Avoid decimal fractions of an inch (I've a precision steel ruler that'll
go up to 64th or 128ths. Actually, I'll be doing it twice with two
ceramic rods and bringing them together for sharpening both sides of my
cutlery simultaneously.)

Hell the whole damn thing could be made adjustable, compact and secure,
for a 15- to 35-degree leeway varying from finer knives to hatchets and
cleavers. Where's all the whizbang, latenite TeeVee copyright holders
when you've got a perfectly good handle on a copyright scheme and need
them?

1) All three angles have to add up to 180 degrees
2) long side = sqrt (x*x + y*y) if x and y are the other two sides

"Flasherly" wrote in message
...
I'm building a knife sharpener with a 25-deg angle out of ceramic
hollow rods. Ceramic stock: 4-1/2" long & 3/8" diameter.

Right Angle Triangle: the two sides at 90-deg, one of which will be,
of course, the base.

Figure roughly around a 10" plug-in value for an extended "sharpening
edge," which will also be the same as the 3rd side of the triangle.
(I'll rig the ceramic rods to that 10" via the hollow center, with a
steel rod, or a wooden frame that clamps down. Figure that out
later.)

Anyway, I just need the math. If the opposite, 10" side to the right
triangle forms a 25-deg. angle, (to the two other, 90-degree sides),
sic. -- a 25-deg. angle, that is, to the straight-edge of a knife
being sharpened perpendicularly to the base of the triangle -- give me
the measurements for the two remaining triangular lengths to an
approximate 10" third side I've proposed.

Avoid decimal fractions of an inch (I've a precision steel ruler
that'll go up to 64th or 128ths. Actually, I'll be doing it twice
with two ceramic rods and bringing them together for sharpening both
sides of my cutlery simultaneously.)

Hell the whole damn thing could be made adjustable, compact and
secure, for a 15- to 35-degree leeway varying from finer knives to
hatchets and cleavers. Where's all the whizbang, latenite TeeVee
copyright holders when you've got a perfectly good handle on a
copyright scheme and need them?

I was looking for this gadget I had at work that gave the formulae for
figuring out the sides and angles, but alas, it is lost :-(

But then, I found this site:

http://www.csgnetwork.com/righttricalc.html

Just plug in the values you know, and it will show you the rest. Even
simpler than my formula wheel :-)
--
SC Tom

On Thu, 14 Nov 2013 20:18:31 -0500, Flasherly
wrote:

Thanks you guys - SC Tom and David for the formula and site link.
Saved and will be looking at both. Had hoped that information would
be fresher to someone than what I offhand remember about a compass,
straight edge, circles and angles.

"Flasherly" wrote in message
...
On Thu, 14 Nov 2013 20:18:31 -0500, Flasherly
wrote:

Thanks you guys - SC Tom and David for the formula and site link.
Saved and will be looking at both. Had hoped that information would
be fresher to someone than what I offhand remember about a compass,
straight edge, circles and angles.



When you build it, take some pix of it and post them on-line. I'm curious to
see it now :-)
--
SC Tom

On Fri, 15 Nov 2013 13:27:15 -0500, "SC Tom" wrote:

When you build it, take some pix of it and post them on-line. I'm curious to
see it now :-)
--

It's basically for average cabbage-headed functionality (I like to
cook) - here's stock (the rods, mine are hollow or roughly a sturdy
nail could be inserted.) ...

http://www.alibaba.com/showroom/cera...ning-rods.html


Simplest - would be a block of wood from a 2x4" -
with the knife coming straight down to a 22-deg. angle
(that's fine knifes, cutlery is usually 25-deg.)...

knife edge
| |

to rods (22-deg measured for knife blade perpendicular to wood at and
between the angled ceramic rod)

__\__/__
-----------
rods inserted into wood


What I'll be doing is more like an..

--X--
-/-\- (extending the X, for the rods, downward.)

moving both ceramic rods now together (touching at curved tangents, as
offset by their diameter) and somewhat past, forming that X for
bringing the knife edge through the top-V of the X, and hitting both
side edge at 25-degrees.

That's precisely what none of the commercial products offer, is being
able to slide the rods around, up and down;- once a groove is worn
into the rods at only one place it's garbage, worn out and no more
good. I guess that's what they like: keeps customers coming, in a
round about way, ass-backwardly back.

I've got a drill press and probably could rig it up for 25-deg holes
in wood. Have to see if I can keep the slop out (maybe jury-rig
something in metal or clamps on the wood...not sure), otherwise I'll
be ruining knifes with screw-ball angles.

Somebody, really, with half an ounce more brain than me could
manufacture a patent for variable angles for both diamond and ceramic
stock;- diamond to bring down various knifes to varied rough angles
and ceramic, tuned for the same angle, for polishing out a keen edge
finish;- put a leather finish on the base for a product finish and
advertise it for stropping out the likes of a folded-steel Damascus
gelding knife.

A swifty for some future entrepreneur to do all that while resisting
putting a $200 price tag on $5's materials.

"Flasherly" wrote in message
...
On Fri, 15 Nov 2013 13:27:15 -0500, "SC Tom" wrote:

When you build it, take some pix of it and post them on-line. I'm curious
to
see it now :-)
--

It's basically for average cabbage-headed functionality (I like to
cook) - here's stock (the rods, mine are hollow or roughly a sturdy
nail could be inserted.) ...

http://www.alibaba.com/showroom/cera...ning-rods.html


Simplest - would be a block of wood from a 2x4" -
with the knife coming straight down to a 22-deg. angle
(that's fine knifes, cutlery is usually 25-deg.)...

knife edge
| |

to rods (22-deg measured for knife blade perpendicular to wood at and
between the angled ceramic rod)

__\__/__
-----------
rods inserted into wood


What I'll be doing is more like an..

--X--
-/-\- (extending the X, for the rods, downward.)

moving both ceramic rods now together (touching at curved tangents, as
offset by their diameter) and somewhat past, forming that X for
bringing the knife edge through the top-V of the X, and hitting both
side edge at 25-degrees.

That's precisely what none of the commercial products offer, is being
able to slide the rods around, up and down;- once a groove is worn
into the rods at only one place it's garbage, worn out and no more
good. I guess that's what they like: keeps customers coming, in a
round about way, ass-backwardly back.

I've got a drill press and probably could rig it up for 25-deg holes
in wood. Have to see if I can keep the slop out (maybe jury-rig
something in metal or clamps on the wood...not sure), otherwise I'll
be ruining knifes with screw-ball angles.

Somebody, really, with half an ounce more brain than me could
manufacture a patent for variable angles for both diamond and ceramic
stock;- diamond to bring down various knifes to varied rough angles
and ceramic, tuned for the same angle, for polishing out a keen edge
finish;- put a leather finish on the base for a product finish and
advertise it for stropping out the likes of a folded-steel Damascus
gelding knife.

A swifty for some future entrepreneur to do all that while resisting
putting a $200 price tag on $5's materials.

So you're looking to do something similar to this:

http://www.knifehog.com/p-2396-lansky-four-rod-turn-box-lcd5d.aspx

but with the rods crossed like this one?

http://www.knifehog.com/p-2389-lansky-four-rod-gourmet-knife-sharpener-lcsgm4.aspx

I have one that's probably 25-30 years old that's similar to these. The base
is a 12x1" hardwood dowel with a 5/8" flat on the bottom to keep it from
rolling, and the holes for the (2) 9" rods. It's been used so much that you
can feel where the rod diameter is smaller above the ends where the rods
insert into the base. Works great for me; I use it for almost all of my
knives from kitchen to pocket :-)
--
SC Tom

On Sat, 16 Nov 2013 07:53:15 -0500, "SC Tom" wrote:

So you're looking to do something similar to this:

http://www.knifehog.com/p-2396-lansky-four-rod-turn-box-lcd5d.aspx

but with the rods crossed like this one?

http://www.knifehog.com/p-2389-lansky-four-rod-gourmet-knife-sharpener-lcsgm4.aspx

I have one that's probably 25-30 years old that's similar to these. The base
is a 12x1" hardwood dowel with a 5/8" flat on the bottom to keep it from
rolling, and the holes for the (2) 9" rods. It's been used so much that you
can feel where the rod diameter is smaller above the ends where the rods
insert into the base. Works great for me; I use it for almost all of my
knives from kitchen to pocket :-)
--
SC Tom

http://www.amazon.com/s/ref=nb_sb_no...rpening+system

About anything above is a tier up from below.

http://www.amazon.com/s/ref=nb_sb_no...rpening+system

Which is what I want in principle -- a mixture of the two, or as
roughly in theory applied to the top link, the model you have --
except for bigger and moveable rods that actually intersect to form
two 25-degree angles, the " X ", for sharpening both sides of the
knife simultaneously.

Just means bringing up that " X " higher to account 4-1/2" rods, I
have. Say, a 4" high piece of wood drilled for the holes at
25-degrees, so the rods intersect to form an X. Two clamp-screws
going into the wood below, to secure each ceramic rod -- well, 1)
loosen the clamps and move up/down the rods as grooves of wear form
from usage, then 2) remove and reverse a worn rod for the inserted
portion, previously clamped and in the wood, to come out and be on top
for sharpening usage.

Hadn't heard or seen of the conical effect you have from continued
wear, but I'd been given one similar made, exactly like yours. The
rods were glued and I guess I never stuck with it long enough to get
past a rough and imprecise angled-feel and into any better swing for
use. Unlike X-d rods -- for a few sharpening passes within, with
which I can bring both side to the knife edges right back into near
razor sharpness. Say in the case of slicing homemade bread, dicing
potatoes, garlic bulbs or jalapeños, it occurs a) fast from a block of
many repetitively-used knifes, apt to dull within the cooking prep and
interrupt the flow of cooking several items within heat of prep times,
and thus facilitating b) ease of quickly sharpening as safety (don't
want spurious sharpening habits to intrude into a rhythm of cooking,
or to turn into a dice off one of mine ol' fingers).