A Question of Perception

LH - Radii 1:2:3, areas 1:4:9

RH - Radii 1:2.236:3, areas 1:5:9

I prefer LH.

I was just mucking about with the numbers, thinking along the lines of "bet it would look better with a Golden Ratio in there somewhere", when I noticed that, in the equal-area-increment case, the radius of the middle circle divides the radii if the inner and outer circles in (a number very close to) the Golden Ratio! Whoda thunk it?

2/1.236 ≈ 1.236/0.764 ≈ 1.618

There's prob'ly a reason for that, but I cba to work it out atm.

Bingo!

OK, lunchtime ...

R1 = 1

R2 = √5

R3 = 3

Let a = √5 -1 , b = 3-√5,

Then (a+b)/a = 2/(√5 -1)

Which can be shown to be = (1+√5)/2 = φ (the golden ratio).

Also φ = 2 x cos 72°

Codey

Maybe make your circles proportional to the circles on the targets that are typically used for archery.

The dots won't be concentric they will be along a curved line getting larger towards the tip of the nock (which will have a hole in it, allowing for a thin thong used to retain the string when the bow isn't strung... we all love a good thing thong).
Of course this then raises the Q of the ideal spacing between dots.
Del
_{(Golden ratio my arse)}

I think equal spacing would be visually effective; the curved line will be nice.

I admit I never use actual math for design. But it is interesting to think about it. I just did a freehand sketch and they came out equally spaced.

... and the ideal curvature of the locus of the centres.

_{(... and what's your arse got to do with it, anyway?)}

_{(... and what's your arse got to do with it, anyway?)}

He did mention a thong didn't he?

"...of the nock (which will have a hole in it, allowing for a thin thong used to retain the string when the bow isn't strung."

So the nock has a nick in it, right?

OH NO! Not a nicked nock.

The sum of infinite series from a graphical perspective, defined quite nicely here… check out the "Doodling in Math Class: Infinity Elephants"

So, strike the curve you want, your desired start and stop point and desired size of your base dot, and even your desired end dot, then strike your tangent curves and that will give you a nice pattern to work within. Obviously your dots wont be tanget, but that's solveable through a proportianal increase in center distance along the arc at a value that fits well on your piece and with your materials.

JavaHead

I'm sure the most pleasing appearance for archers would be to have the inner circle proportionally much larger.

You're on page 1 !

I'd make them proportional to the amount of background each will be placed upon.

This might mean that they are all about the same size, which may not be the desired result, aesthetically.

Make up two or three sets of drawings and let the lady decide.

Nice work, by the way.

Your picture doesn't really do justice to your idea. It kind of looks like an index finger that's succumbed to severe frost bite.

Yeah, but wait until it's polished and the silver inserted, I've just ordered it online.
I went for 2, 2.5 and 3mm dia, I really wanted 2.5, 3, 3.5 but they didn't have 3.5, anyhow I just order 50mm of each and it was only about £7.
That should keep me going for ages.
Del

Good deal! Your bows are already one of a kind. A little extra bling can't hurt.

Post pics of your finished product. Always a pleasure to see!

I think two sets of concentric circles give a very pleasing appearance:

First thongs; now this.

Is this a bow, or a whip?

I've always been mesmerized by that particular pattern.

Ahh, symmetry!

Bilateral symmetry at its finest.

Milo

(4/3)Π a²b in toto

And that is all I have to say about that!

We won't think it too cheeky of you to post some pix. It's great craftsmanship after all.

Hell, if we can't show off and brag here, where else is there?

True craftsmen are a dying breed. I would encourage anyone here to show off their talents. At least it will be appreciated.

I would also encourage any craftsmen among us, or anyone with knowledge of anything, to pass it on.

More than anything else, these kids need something to be proud of..............let's help them if we can.

o o o o o o o o

I like dots with spacing increased by +1 between each.

Are you going to thing a thong for us now?

...but I don;t know how to get it to display here!

I think I would do this;

But curve it to the horn 'centerline' form.

Which I see a bit like this;

And make the dimension between 5^th dot and biggest dot, about .25 mm more 'negative space' (distance).

It's just a tiny bit 'compressed' (wrong/jarring/odd) in 'visual acceleration'.

There are a lot of responses I don"t seem to be able to see, so this may be a duplicate response.

The equal radii increase will be percieved by many people as a target. The equal area increase will have a 3D aspect of a hill or a bowl to many people. The equal radii is a Harder hit. the equal area is softer. Do you want to get people's "attention?" (radii) or "attraction?" (area).

We went wrong at #1 with the assumption that they were concentric rings when the OP says dots, anyhow the aim is to look attractive yet clean and stylish, not ostentatious. It's just a whimsical question really, I shall let my eye do the real work and post the result in a day or so, I've alread made the nock a tad smaller and polished it, the silver wire might arrive today.
Del

And, the OP clearly corrected it in #4 which appears to have been ignored by almost every one.

Del, that depends on the person looking at the circles - I can almost guarantee that Salvador Dali and Pablo Picasso would not agree with your concept of pleasing nor would they agree with each other.

Indeed, they prob wouldn't even agree on what constituted a circle.
Anyhow my silver has arrived... off to my secret workshop...ok, it's in the garage.
Del

Got home, silver was there...dived into garage...no trial piece...realised that I couldn't get 3 dots in as I'd smallimicated the lobey bit.
Bish bash bosh jobs a good 'un. Gotta drill the hole for the thong in the tip, and it's not all finall polished yet, but you get the idea.

Del (impatient? Moi?)

Niiiiiice

My, what nice nocks you have.

Looks great. Did you glue the silver wire into the horn, or, cut the wire a little long then hammer it so it swelled a little in the hole, or, .........?

Ha, wellll, of course you can't get 2mm wire into a 2mm hole, and to try to drill straight through a courved surface mounted on a long curved bow when you're an impatient git is fraught with probs.
So I enlarged/trued up the hole with a needle file (I started with what was originally intended to be the middle hole). I opened up either end slightly with the pointy lead in spike of a flat wood boring bit so that the silver would spread out into it.
It's the first time I've used silver and I'm quite impressed with the stuff (so is Mrs Cat, but that's another story).
Soooo the 2mm dot ended up much bigger than 2mm, couple that with the fact that I'd reduced the size of the lobe (having excess mass at the tip of the bow offends my engineering sensibilities) and I didn't have room for 3 dots without jeopardizing the structural integrity capt'n.
It leaves plenty of room for the thong hole, (I may use a KrisDell^TM press in hole for this exacting application, I have a packet of them somewhere).
Anyhow, I'm V pleased for a first attempt at the whole process.
Del

Looks good! I imagine you could do the same with brass or copper. Truly customizable to the customers taste. I was gonna say gold, but that would get pricey.

Nice indeed. milo

Hi Del

From my initial drawing I came up with 3 circles that looked good and 3 that were geometric in radii 5, 10, 15 mm to see what the difference was. This was my first and only spontaneous attempt. As you can see I was able to draw a line through the outsides of the circles I chose suggesting it may be a factor whereas with the geometric circles at the same centres I couldn`t. I would say your eye is tuned in to perspective. Drawings done in CAD.

I've put the hole in!

It does give the 3 dot effect. I couldn't get the hole as shiny as the silver
Del

Nice job.

That's a very nice effect! Handy, using the hole to make the third dot.

If I understood your explanation correctly, the silver dots are true rivets, with the 'head' spread a bit larger than the hole diameter, no glue required. Silver is nice to work with eh, so malleable.

And a brilliant polish on the black horn nock - t's stunning. The lady will be swep off her feet.

Remind me sometime to give you the link to Hole Polishing 101.

Impressive result so far - you may get credits for this, and not have to do the full 36 x 1hr classes.

I tried to explain this thread on "spotted nocks" to my wife...

Her comment...."Engineers..."

Outstanding work, as usual .

Niice

No laptop or flatscreen is safe :D

That's a beauty Del! And the pix.. very nicely done indeed.

Indeed... quite nice!

WOW! A spectacular work of ART and CRAFTSMANSHIP.

Thank you for sharing this with us!

Thanks guys.
Del