IronRainForge
I’m going to forge a pair of half penny scrolls from square stock as mounts for a gnomonless sundial. These scrolls typically involve a taper from the stub end that transitions to the final square stock. 

Q: is there a rule of thumb for the length of the taper from the stub to the square stock? I was at a workshop recently where the Golden Ratio was mentioned as a general rule for forged tapers of all kinds, but that didn’t make sense to me. 

I realize that this is subjective, relating to ‘visually appealing’, but I thought I’d ask. Obviously I’ll be forging a test article or two, but as some of you know I’m a lazy sod and would like to at least get close the first time.
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anvil
Actually you are limited only by your imagination and skills.

I "evolved" from just that twards the golden mean. From there i came up with my own variation of that and all that preceeded. I can see this progression in mysamples and portfolio pics.

I would do a scale drawing on paper until you get what you like. Then do a full siz3d drawing in chalk on your table, or something similar. Do all your lines a bit oversized. Then use that great eraser, your wet finger, and fine tune your drawing.

ANext make a test piece so you can learn how to make it.  😉  and, actually see it in iron. Keep good notes, and be especially aware of all transitions. These are the detail points that catch the eye.
Easy peasy.

Lol, now you are ready to start.

When done, hang your sample on the wall for all future clients to be amazed by! 
With your notes and sample you should, if needed, be able to recreate this scroll whenever you want.
And, sometime in the future, you too can see tour acroll progression!

And, by the way, the golden mean is a good place to start if you are looking for a short cut.
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IronRainForge
@anvil Feel a bit stupid, didn’t even think of doing a template to figure out what taper works for me. Duh. I’ve done it a number of times on other projects, and have a number of metal templates hanging in the forge; it didn’t seem to occur to me for this.

... and thanks for the soft tone in the response.
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anvil
dear God I can't even begin to see how you got thru all my typos!  🙂

I have a few templates, but not many. 

As far as templates go, I have a few. We architectural Smith's  are stuck, sorta, by code. The space on railings we get to design in is set at 4" I'd. A template or a jig will lock you into a production roll and remove you from the design process. It's too easy to design a particular scroll or jig that fits that 36"x 4" space no matter what and always use that single pattern or jig. If you follow my procedure above, then you are always creating a variation on a theme to fit that opening and your clients dream.  One is craftsman work, the other is tradesman work. Both have their benefits and drawbacks. Neither is an indication of your skill level. They are just indicators of which path you wish to follow.
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Mike Westbrook
Chalk a large surface and a sewing tape the flexible one in your better halfs sewing kit help me alot to bring a shape I like to actual metal I still get amazed that a scroll let's say 2- 1/2 turns with a diameter of 6 inches takes 16-18 inches or more material 
Facebook (South mountain metal works)
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IronRainForge
Thanks to all for the suggestions. Before things get too confused, my question relates to the length of taper relative to the size of the square stock. Not necessarily to the shape of the scroll. I’ve got the scroll thing down (mostly) and have made a scroll jig. The question would apply even without the scroll application. 
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Mike Westbrook
Alot depends on the length of the taper it will lengthen by about a quarter in the first half and double in the last measure and chisel stamp every inch make one then you will know how far the metal will move approximately I make tons of little marks that guide me on the real ones or if I'm doing a double ended scroll hope that makes some sense 
Facebook (South mountain metal works)
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