Cutting the Crown by Charles L. Moon

Faceting Hints

"Crown in Jeopardy"

A Tangent Ratio Solution, By FRED VAN SANT and Programmed Approach by Charles L. Moon
(Thanks to Fred Van Sant, Al Huebler & Dr. Dennis Anderson for suggestions.)

Submitted by Charles L. Moon (Vice President of the US Faceters Guild), July 9, 1998, © Copyright

NOT ENOUGH CROWN MATERIAL OR TOO MUCH AFTER TRANSFER?

A Tangent Ratio Solution, By FRED VAN SANT - Programmed Approach by Charles L. Moon
(Thanks to Fred Van Sant, Al Huebler & Dr. Dennis Anderson for suggestions.)
Edited for the web by Lance A. Kanaby

In the Sept. 1993 issue of United States Faceters Guild Newsletter Fred Van Sant has come up with an extension to the tangent ratio that is most valuable to amateur and professional faceters. The formula that he has discovered allows the faceter to adjust mathematically the crown angles of a computerized design so that the plan view - the arrangements of facets, points and table area - remains the same. The most important benefit of this procedure is being able to handle the most hazardous situation of not having enough crown material available for utilizing a computerized design's specifications. If there is more crown height available than what the design calls for, the faceter can either pursue the given specifications of the computerized design or he/she may arbitrarily choose a height that will add both carat weight and color intensification to a light colored stone - all without altering the plan view. The comforting reality of this tangent ratio approach is that NO more seat-of-the-pants decisions will be necessary for designs that have been CUT via the computer .

The following programmed push-button approach via the hand held scientific calculator automatically supplies the non-mathematically minded faceter with a convenient easy solution.

One needs only a simple scientific calculator ($20.00 or less) with the following functions to utilize this procedure:

Tan ÷ X M+ MR (memory recall) INVERT or SHIFT and

Tan - ( N.B. The function of Tan - , which becomes possible after pressing

INVERT or SHIFT, is activated and completed after pressing the "Tan" key.
The key names, "Invert'" or "Shift", vary with different brands of calculators.)

PLEASE NOTE: the two words "GIVEN" & "DESIRED" used throughout this paper are defined as follows: "GIVEN" refers always to C/W ratio factor taken from the computerized design sheet. "DESIRED" refers always to the C/W ratio factor, which must be determined by measuring the uncut crown.

The procedure is simple. Take the given C/W ratio formula from the computerized design and
divide it into the desired C/W ratio of the uncut crown. The quotient of this division gives an
OVERALL RATIO FACTOR necessary for all SECOND OPERATIONS.

The only thing the faceter has to do in order to determine the C/W ratio of the uncut crown is to measure(via calipers, e.g.) the height of the uncut crown(C) and divide it by the girdle width(W) of the transferred stone.

FIRST OPERATION:

l. ENTER the desired C/W ratio of the uncut crown.

2. PRESS ••••• ÷

3. ENTER the given C/ W ratio of the given design.

4. PRESS •••• =

5. PRESS M+ (The OVERALL ratio factor is now in memory.)

SECOND OPERATION: From here on take EACH crown angle from the given design and run it through the following procedure.

1. ENTER any Angle from the given design.

2. PRESS ••••••••••• Tan

3. PRESS •••• X

4. PRESS •••••••• MR (memory recall)

5. PRESS •••• =

6. PRESS •••••••• Shift or Invert

7. PRESS ••••Tan ( Tan - is realized after pressing Tan. )

The angle that appears is ONE of the to-be-determined SET of angles that will allow the faceter to cut the new
crown with absolutely no change in the plan view.

Just be sure that the OVERALL ratio factor is still in memory when continuing with the second
procedure - press MR to check and be sure to write the factor down, just in case it is accidentally erased.
If erased, ENTER the factor and PRESS M+

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AN EXAMPLE: The pavilion has been cut according to the computerized design and transferred. When comparing the uncut crown with the design crown, the uncut crown is so low, it is doubtful that the crown can be cut by using the given crown's angles. The following three paragraphs illustrate the procedure for comparing the two crowns.

The stone's width at the girdle is 10 mm wide. The given design's C/W formula gives a ratio of C/W = .1372. From this ratio a crown height of 1.37mm can be computed . If the Width = 10mm and the ratio to the Crown is .1372, multiply 10 X .1372 = 1.37mm, the height of the crown.

The measured uncut-crown-material(via calipers) is 1.2 mm.

On comparing the two crowns, the unfortunate situation is, the uncut crown's height (1.2mm) is .17mm lower than the specified height of the given crown (1.37mm.) If the cutting of the crown is continued with the angles of the given computerized design, there is NO way that the crown plan view as shown on the computerized design will be achieved.

THE SOLUTION: The following procedure will give you a set of new angles that will allow you to cut the given plan view as shown on the computerized design -- the only visual difference will be a lower crown.

You will need two different C/W ratios. From the computerized design the C/W ratio is given as C/W = .1372. You will have to compute the missing C/W ratio of the uncut crown by dividing the crown height (1.2mm) by the stone's width (10mm) to get the necessary ratio of .1200.

Utilize the desired CW ratio (.1200) and the given C/W ratio (.1372) as follows:

[ Please Note: After 'PRESS,' the numbers in the parentheses indicates a reading in the calculator's display. Compare yours as a check for accuracy.]

FIRST OPERATION

1. Enter: .1200 (desired C/W ratio- uncut crown)

2. Press: ••••••• ÷

3. Enter: .1372 (given C/W ratio)- crown as shown)

4. Press•••••••• = (.8746)

5. Press: •••• M+ (.8746 - the Overall Ratio is now in memory)

SECONDARY OPERATION -- CONTINUE with crown angles from the given design.

1. Enter: 40.5 ( crown angle for first set of cuts taken from the given design)

2. Press: Tan (.8541)

3. Press: •••••••••• X

4. Press: MR (.8746) (MR is the memory recall button.)

5. Press: ••••••••••• = (.7470)

6. Press: Invert or Shift

7. Press: ••••• Tan The angle 36.76, which appears in the display is the corresponding angle to 40.50 of the given design.

The first series of angles for cutting the uncut-crown will be at 36.8 degrees; 3.7 degrees lower than the first given crown angle of 40.5 degrees. Continue the tangent ratio procedure for all of the remaining crown angles from the given design; DO THIS BY BEGINNING WITH THE SECONDARY OPERATION.

But remember, from time to time, check the ratio factor that is kept in the Memory Recall for accuracy.

After ALL of the angles from the given design have been changed, cut the new crown. KEEP in mind that the given plan-view as shown on the computerized design will be accomplished, only the height of the crown will be lower.

That's All Folks!