This article serves as a follow-up to my previous article, Can You Cut a Gem for Tilt Brightness. Please read that article first, since I’ll make some references to it along the way.
Can an Apex Crown Help With Tilt Brightness?
The answer is a qualified yes. However, like everything else in life, you’ll have to make some trade-offs. At the top of this article, you have a Gram Wagon Wheel gem design. Basically a redo of an old design, it has appeared under many different names. This is just my version of it.
Note that the pavilion is just a straight bottom, single tier. For that matter, so is the crown. I chose this design because of its simplicity. You can make it easily in GemCad, and it’s simple to cut. The single tiers on the pavilion and crown offer the best optical performance for comparing tilt brightness that I’ve found.
41° Pavilion and 13° Crown Ray Traces
Below, top row, you have a face-up (zero tilt) 41° pavilion/13° crown. As you can see, it shows good brightness and very little hole at the crown apex. (It’s really just about covered by the center point of the crown). In the bottom row, you have the same design tilted 10° (on the y axis only). Now you can see the small hole at the apex, as well as some tilt drop-out around the edges.
Actually, this design has decent tilt brightness. Much better than the standard round brilliant cut in quartz and other low refractive index (RI) materials in the first article. However, I wouldn’t really call this good tilt brightness. Keep in mind, this is only tilted 10°. It will get worse with more tilt.
41° Pavilion and 16° Crown Ray Traces
Below, top row, you have a 41° pavilion/16° crown. As you can see, the higher crown actually gives more reflection out around the girdle. You also get a more interesting reflection on the face-up view. The hole at the apex is maybe a little larger, but not much. In the bottom row, the 10° tilt view shows the hole at the apex is slightly larger, and the half-moon fall out at the girdle is a little smaller. Basically, you have a trade-off.
42° Pavilion and 13° Crown Ray Traces
Below, top row, you have a 42° pavilion/13° crown. You have a better reflection out around the girdle as well as in the center. Now look at the bottom row. Tilted, the apex hole is similar, and the half-moon around the girdle remains about the same. However, at 12 o’clock, notice that two pavilion facets are starting to shadow and drop out, due to the tilt. If you look back closely at the previous design, you can see it just starting.
42° Pavilion and 16° Crown Ray Traces
Below, top row, you have a 42° pavilion/16° crown. The overall brightness, especially in the random light model (left, in the set of three), is getting flatter/darker. However, note that the band out around the girdle has gone. The apex hole in the center remains about the same. On the bottom row, the tilt on this one is interesting. Out along the girdle, the half-moon has become a bit smaller. The apex hole remains the same. The 12 o’clock facets, in shadow in the previous design, are no longer dark. You can really start seeing the trade-offs happening.
43° Pavilion and 13° Crown Ray Traces
Below, top row, you have a 43° pavilion/13° crown. The face-up design appears about the same as the previous one, maybe with a little less pattern. On the bottom row, the tilt is also about the same, with one notable exception. Now, two facets at 6 o’clock are dropping out. Remember, this is the same tilt on the y axis. Funny how the two facets falling out have reversed.
43° Pavilion and 16° Crown Ray Traces
Below, top row, you a 43° pavilion/16° crown. Notice that the random light ray trace is actually brighter and more interesting. The apex remains about the same. On the bottom row, four facets are dropping out at the bottom of the design with the tilt. The half-moon shape around the top of the girdle has become smaller.
Which Variation Makes the Best Compromise?
So, what does this all add up to? In physics, every action has an equal and opposite reaction. This applies just the same whenever a gem designer takes an action when creating a new design. Sometimes, experience and maybe some luck can do the trick and help you find the proper balances.
Really, some of this just boils down to personal taste. Which design do you like? Personally, I find the best compromise of all the preceding gram wagon wheel gem designs to be the 41° pavilion/16° crown. Here it is again.
I’ve tried higher crown angles, but the apex hole gets too large for me. What I find most interesting, what adds the most life to the design, are the patterns. You will see the “spokes” of the wheel in your cut stone. Personally, patterns make up a major part of what I look for in a gem design.
Of course, other people may prefer one of the other variations.
Adding a Table to a Gram Wagon Wheel Gem Design
Wondering what a table would do? Below is the same design with a 41° pavilion/16° crown and a small table to cover the apex hole. As you can see, the table takes care of the hole in the face-up brightness (top row). However, with the tilt (bottom row), you have the drop-out just as in the round brilliant design in my previous article. So, the apex crown does solve some of the drop-out, but at a price in the design’s appearance and angles. Note the table’s brightness in the face-up view. This will increase as the table’s size gets bigger. Unfortunately, the drop-out in the tilted view will also grow in size with the table.
41° Pavilion and 16° Crown Sapphire Ray Traces
Below, you have the gram wagon wheel gem design, 41° pavilion/16° crown, no table, in a RI 1.76 sapphire. Although a bit smaller, the apex hole remains. While sapphire’s higher RI helps minimize the hole, it doesn’t eliminate it. Otherwise, the higher RI doesn’t seem to make a lot of difference. (However, I think you could raise the crown a bit without much loss).
Standard Round Brilliant, 41° Pavilion and 42° Crown Sapphire Ray Traces
For comparison’s sake, below, you have the standard round brilliant, 41° pavilion/42° crown sapphire with table from my previous article.
There is no question which one I would rather cut for brilliance. The standard round brilliant leaves no hole in the center of the higher RI sapphire. Interesting, isn’t it?
Tilt Brightness and Checker Board Designs
As I’ve said before, I do consider tilt brightness when designing. However, as you can see, you’ll often find you can do little to improve it, especially for low RI gems.
Interestingly enough, I have developed some “checker board” designs that get the best of both tilt and face-up brightness. Nevertheless, for most designs, you’ll have to make some compromises.