The secrets of aligned edgespots-

palmimports · #1 (**permalink**) 02-09-2007, 07:19 AM

The key to perfect aligned edgespots on ceramics

This will be the first of several articles on ceramic edgespot design.

The key to perfect alignment is math. Pure and simple.
The face edge must be the same length as the side edge- if it is- everything matches perfectly. But it's not quite that simple.......

Lets start out with a chip with a diameter of 1.550 inches. The radius will be 1/2 the diameter or .775 inches. Draw a line from the center of the chip to the edge and this is your radius. Now, for edgespots to align perfectly- when we draw an edgespot on the face of the chip, each side is tapered- and this taper has an angle to it on each side... and an angle from the center of the chip where both of the lines we draw on each side of the edgespot meets the center of the chip. This center angle is what we will work with today.

If we draw a line across the bottom of this edgespot from where the left and right point meets the edge of the chip- we will see there is an arc remaining under the line-this arc length MUST be computed as the length of this arc will be needed to figure out the length of the edgespot on the side of the chip. THese MUST be the same length if perfect alignment is to be achieved.

We can go nuts doing complex math- or there's a simple way of doing it.

So we have our tapered edgespot drawn, and we draw a line from the center of the chip to the left side of the edge- and another to the right side. We now have an angle in the center of the chip- once we connect the bottom left and bottom right side of the edgespot where it meets the edge of the chip we just made a triangle.

Keeping things simple- math tells us that IF the angle we use is 57.295 degrees ( which is the same as ONE radian) then the length of the arc will be identical to the radius of the chip. So, we make a HUGE edgespot with an angle of 57.295 degrees in the center and we take our radius of .775 inches- we now know that our arc length is also .775 inches long. So when we design the side edges- we make our side edge .775 inches long and.. it will be identical to our face edge.

The problem is- 57.295 degrees is one HUGE edgespot. We need smaller edges.

No problem.

Two ways of doing this- the first way is using whatever size you want for the edges, figure out your angles, and do a ton of math to figure out the arc length...

or... keep everything a ratio of the above.

So- if we make our face edgespot 1/2 of 57.295 degrees,or 28.65 degrees then our arc length will be 1/2 of the radius... or .3875 inches long. Simple.

Next article we will discuss the math involved for those wanting to design their own edges using a different angle then as stated above.

This is alot to digest, but its not as bad as it sounds
Joe

kmalsom · #2 (**permalink**) 02-09-2007, 08:22 AM

Great information Joe

Thanks for helping everyone out with it.

99%evil · #3 (**permalink**) 02-09-2007, 08:41 AM

Cool...now I'm going ot buy clay without edge spots...I can leave my math for calculating the odds of the suckout beats I receive.

Nanook · #4 (**permalink**) 02-09-2007, 09:51 AM

Thanks Joe,

Good info. It made perfect sense to me. I do have an Engineering degree though so the math part comes easy.

Nanook

OnTheButton · #5 (**permalink**) 02-09-2007, 10:09 AM

A sharp pain just shot through my temples while trying to read that.

Buy then again, I don't even have my 'times tables' memorized.

Can someone that 'gets this' possibly this put up an illustrated version for those of us that are mathematically challenged? I'll +10 rep ya if you do, because I'd like to be able to do this accurately.

jmc · #6 (**permalink**) 02-09-2007, 11:09 AM

In a nutshell:

We want our edge stripes to match up.

x = length of our desired edge spot, in inches

57.295 degrees = .775 inches
Therefore,

Edge spot arc length (on the face) = 57.295 / .775 * x (degrees)

In the above example, we've picked our edge spot arc length to be 45 degrees.

45 *.775 / 57.295 = Our edge stripe (on the side of the chip) is .6087"

palmimports · #7 (**permalink**) 02-09-2007, 11:45 AM

Quote:

Originally Posted by jmc

In a nutshell:

We want our edge stripes to match up.

x = length of our desired edge spot, in inches

57.295 degrees = .775 inches
Therefore,

Edge spot arc length (on the face) = 57.295 / .775 * x (degrees)

In the above example, we've picked our edge spot arc length to be 45 degrees.

45 *.775 / 57.295 = Our edge stripe (on the side of the chip) is .6087"

this is even easier then the way I waas learning it--makes perfect sense.

We used the 57.295 degree only because this equates to the same as one radian... and when the radian =1 then the arc and radius are identical.

Thanks for this info- hopefully it will aid many in designing custom edges outside the 57.295 degree arena

[IMG]file:///C:/DOCUME%7E1/OWNER%7E1.WAR/LOCALS%7E1/Temp/moz-screenshot.jpg[/IMG][IMG]file:///C:/DOCUME%7E1/OWNER%7E1.WAR/LOCALS%7E1/Temp/moz-screenshot-1.jpg[/IMG]

cowboys · #8 (**permalink**) 02-09-2007, 11:53 AM

Can't you just take diameter X 3.1416... to find the length of the edge? What am i missing here?

cowboys

edit: OK, after rereading, you're trying to find the lenth of just the edgespots, right?

wijwij · #9 (**permalink**) 02-09-2007, 12:48 PM

I posted this elsewhere but I think it got lost.

The math is much simpler. No need to use radians. Just use a proportion.

Let a = central angle of edge spot on face (in degrees)
Let r = radius of chip (in mm or whatever)
Let s = desired edgespot arc length (what you want to find)

Ratio of central angle / full circle = Ratio of edgespot length / full circumference

a / 360 = s / (2 x pi x r)

If you know r and a, then you just solve that proportion for s.

s = (2 x pi x r) x a / 360

If you measure r in mm then s will be in mm.

In addition, you can use the same proportion to find what central angle to use if you know the arc length of your desired edgespots. (Say, if someone wanted their edgespots to be 10 mm long and needed to find what central angle to use on the face.)

a = (360 x s) / (2 x pi x r)

Since illustration programs use degrees for angle measures, it seems to me you would want to be measuring your angles in degrees, not radians.

OnTheButton · #10 (**permalink**) 02-09-2007, 12:55 PM

Quote:

Originally Posted by wijwij

I posted this elsewhere but I think it got lost.

The math is much simpler. No need to use radians. Just use a proportion.

Let a = central angle of edge spot on face (in degrees)
Let r = radius of chip (in mm or whatever)
Let s = desired edgespot arc length (what you want to find)

Ratio of central angle / full circle = Ratio of edgespot length / full circumference

a / 360 = s / (2 x pi x r)

If you know r and a, then you just solve that proportion for s.

s = (2 x pi x r) x a / 360

If you measure r in mm then s will be in mm.

In addition, you can use the same proportion to find what central angle to use if you know the arc length of your desired edgespots. (Say, if someone wanted their edgespots to be 10 mm long and needed to find what central angle to use on the face.)

a = (360 x s) / (2 x pi x r)

Since illustration programs use degrees for angle measures, it seems to me you would want to be measuring your angles in degrees, not radians.