Neck band label shape?

I am trying to create a custom neck band label for my bottle of brew, and I am having difficulty determining the exact shape that will make it wrap around the neck so that the top and bottom edges are straight.

I imagine there is some sort of formula to do this, but I haven't been able to figure it out. The neck is roughly a cone, and I have determined that the arc length of the top of the label needs to be equal to the circumference of the skinny part of the neck, and the arc length of the bottom of the label ought to be equal to the circumference of the fat part of the neck. This will make the label appear to be straight when it is applied to the bottle (this is what I'm aiming for). My problem however is determining what shape to make the curve, because although I know what to make the arc lengths, the diameter of the circle which they come from can be different, and it is this shape need to know.

Sorry if this post is confusing. If there is anyone who prides themself in math or geometry, please see if you can figure something out.

Thanks,

JohnBen

How about - find a beer with a label that comes off easily with a bit of soaking (Sam Adams are pretty good), then just take it off and see?

Try wrapping a strip of hockey or similar tape loosely in position, then crimping it to fit....take it off and you have a template. Apply to paper, smooth out the arc, and Voila!

(T*d2/(pi+A)-3.792567843*k+E/32*(A+97403P)+657.2adcI) * (65812E/72C) +(E/32cO98F) / ((T98*pi)*(AP42-69E) / (A23/pi*42ND)-(M*3.14833679243A) + (KE98*AT/(775849*EM- (((P*pi/76)*L+31245)/A42+T91) + E

The values are as follows:

"use the capital letters"



























Sorry, but I'm under the influence of too much post fermented wort and couldn't resist....

The mathmatics of an ascending cone, such as on a beer bottle neck, would require that a Euclidian non-parallel trapizoid would be required. To avoid wrinkling, apply differential vector analysis. Or...easier would be to do what bird or the nurse suggested and trace it out. Good luck.

Use some duct tape and an exacto knife to carve your own on the bottle then remove the template and transfer it to paper.

homebrewer_99 said:

Use some duct tape and an exacto knife to carve your own on the bottle then remove the template and transfer it to paper.

Click to expand...

Even easier would be to peel the neck label off of one of your commercial favorites and scan or trace it.

Yuri_Rage said:

Even easier would be to peel the neck label off of one of your commercial favorites and scan or trace it.

Click to expand...

That's 'rus'lin (a stealin') and we don't take kindly to thangs like that 'round here'...