Accounting for padding in helms... (Math warning)

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Stacy Elliott
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Accounting for padding in helms... (Math warning)

Post by Stacy Elliott »

Ok,

After taking a measurement around the head, how do you figure in the addtional length needed to account for the padding.

[img]http://home.att.net/~numericana/answer/ellipse.gif[/img]

Sample Measurements
23 inches around the head, (pinning the ears to the head)
.5 inch padding needed by group regulations.

Knowing that the simple formula for a ellipse is

P approx equals sqrt (2(a2+b2)) Where a = 4.025 inches and b=3 inches (I used metric and had to convert to inches since most of the board uses that antiquated system)

(http://home.att.net/~numericana/answer/ ... m#elliptic) formula #7

It would figure that the new measurement would be 24.44 inches.

This just seems small.

So, if I use .75 of an inch clearance to give .25 of *space* and .50 of padding it works out to 25.28 inches...

This also seems small.. What am I doing wrong?

Stacy
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Post by Sean Powell »

SHould come out roughly 26.141592 or 23+2*.5*pi... I'll go look up the correct formula now. I'm at the wrong computer desk.

Sean
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Post by Stacy Elliott »

Hmmmm Did I use an incorrect formula?

Stacy
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Post by Sean Powell »

OK I have 2 ellipse formulas, one simple and one complicated:
Assuming A and B are the longest and shortest distance from the center to the edge respectively:

Area=pi*A*B
Perimeter=pi*(A+B)K where K=(1 + 1/4*m^2 + 1/64*m^4 + 1/256*m^6 + …) and m=(A-B)/(A+B)

So the first equation won’t get us there and the second is a pain to use… BUT if we assume (A-B)/(A+B) ~= (A’-B’)/(A’+B’) where A’ and B’ indicate head size + 1/2" of padding then m doesn’t change and K doesn’t change.

Thus:
pi*(A’+B’)K

pi*(A+.5+B+.5)K

pi*(A+B+1)K

pi*(A+B)K + pi*1*K

old-head-perimeter + pi*1*K

Now for a head that is 8â€Â
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Post by adric »

I have only ever used the math challanged formula - wrap head in desired padding, measure, add a small bit for fudge factor, pray for good result. Pryers optional. :)
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Post by LWCM »

OW OW OW OW OW OW OW OW OW OW!!!!!!!!!!!!! Math in the morning BEFORE CAFFEINE! AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA




Seriously though, that's a really neat pair of formulae (formulas? not sure)

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Post by knitebee »

look at it from a simplier view point. In a circle the circumfrance is diameter X pi. So for every inch you add to the diameter it will add 3.14in to the circumfrance. so if you are only adding half an inch then add half of pi or a hair over an inch and a half.
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Stacy Elliott
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Post by Stacy Elliott »

Sean,

Na, that is why I asked the question here.

Got the equation from a website:

http://home.att.net/~numericana/answer/ ... m#elliptic formula #7

So what would the formula be if we want a variable padding thickness.

Stacy
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Post by Sean Powell »

Stacy,

I think I see part of your problem. You didn't include 'pi' just before the square-root. For a head 6" x 8" (aprox 150mmx200mm)

pi*(2*(A^2+B^2))^.5
pi*(2*(4^2+3^2))^.5
pi*(2*(16+9))^.5
pi*(2*25)^.5
pi*(50)^.5
22.214

pi*(2*(A'^2+B'^2))^.5
pi*(2*(4.5^2+3.5^2))^.5
pi*(2*(20.25+12.25))^.5
pi*(2*(32.5))^.5
pi*(65)^.5
25.328

Difference of 3.114

Now WHY would you want a formula for variable thickness? Do you intend to put 20mm in from and 5 on the sides? Or did you just mean a formula for circumference based on padding thickness? In that case head_circ+2*padding_thickness*pi and round up is probably your best choice.

The human head is closer to an elipse then to a circle but that isn't a perfect shape either. Find someone who has a model of a skull and remove the top. The human head is egg shaped towards the rear with flatter front and sides but rounded corners above and outside of the eyes. Aproximations are more than sufficient unless you want to start with MRI and CT data. (surprisingly, I'm enough of a geek and have access to the data that I did that once)

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Post by Stacy Elliott »

Reason for the varying thickness is Living history helms only need a little padding such as 1/4 inch.

SCA helms need 1/2 inch...

So........

Stacy
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Post by Stacy Elliott »

Sean,

First off, thanks for taking the time to hold my hand on this.

I plugged the following formulat in to Excel using these variables.

E2 Pi 3.14
E3 Padding_thickness 0.5
E4 head_circ 23

Your formula: head_circ+2*padding_thickness*pi

translated to excel =SUM(E4+2*E3*E2)

The answer was 26.14

I change the Head_circ to 24 and the answer was 27.14

Head_circ 25 answer 28.14

See the pattern?

Something is not working right.. Any ideas?

Stacy
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Post by iaenmor »

Adding only 2*padding is not going to add to the circumference properly. The padding is adding to the overall circumference making it larger. If the diameter began at 7.5 " with padding it is now 8". 7.5 x PI = 23.55, 8 x PI =25.12. See the difference.

I have always used 1/2width + padding + 1/2depth + padding*PI=. Seems to work for me, I believe it was Halberds who gave me the answer in one of his helm threads.

Corrected formula, Thanks Stacy
Last edited by iaenmor on Wed Feb 15, 2006 9:07 pm, edited 1 time in total.
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Post by Sean Powell »

Stacy Elliott wrote:Sean,

First off, thanks for taking the time to hold my hand on this.

I plugged the following formulat in to Excel using these variables.

E2 Pi 3.14
E3 Padding_thickness 0.5
E4 head_circ 23

Your formula: head_circ+2*padding_thickness*pi

translated to excel =SUM(E4+2*E3*E2)

The answer was 26.14

Head_circ 24 answer 27.14

Head_circ 25 answer 28.14

See the pattern?

Something is not working right.. Any ideas?

Stacy
No that is working EXACTLY right.

OK go back and assume that the head is a sphere. Now assume that it is 8" in diameter. The head circ would be pi*8. The head diameter plus padding on BOTH SIDES would be .5+8+.5=9. The helm size would be pi*9. The difference is pi*1. (1=.5+.5)

Now assume that the head is size X so the circumference is pi*X which we know is 23. X is 23/pi=7.3211. So now we try pi*(.5+7.3211+.5)=26.141592...

26.141592 - 23 = 3.141592
27.141592 - 24 = 3.141592
28.141592 - 25 = 3.141592
29.141592 - 26 = 3.141592

There you go. Add 3 and round up (add 75-80mm)

I hope this helps,
Sean
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Post by Stacy Elliott »

So for SCA helms just add Pi to the circ... Seems to simple.. but OK.

And for .25 inch padding I guess you would just add 1.5 inches.

Ok, so 80mm and 40 mm it is..

Thanks

aenmor, I do not follow your equation.

8 being length and 6 being width

=SUM((3.5+4.5)/2)*3.14 =12.56

do you mean

=SUM(3.5+4.5)*3.14 which equals 25.12 ?

Stacy
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Post by Mike F »

Yea, I thought the math was wrong, but it does come out to (Thickness*2*pi)

It DOES seem too simple, but I did the math, and there you go.

Do you want an actual pattern for a cloth liner?
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Post by Stacy Elliott »

Mike.. Sure!

Stacy
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Post by Tigernach »

Mike F wrote: Do you want an actual pattern for a cloth liner?
YES! YES WE DO!!!!!
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Post by Mike F »

Give me a few hours. :)
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Post by Tigernach »

Thanks, I would greatly appreciate it!
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Post by Konstantin the Red »

I keep it ultra simple to figure because I suck at math -- my math game peaked at twelfth grade high school physics class umptymumble years ago when single Windsor necktie knots were in vogue along with polyester leisure suits and has declined ever since.

For simplicity, I pretend the head is circular, for I am really paying most attention to the respective circumferences of head and helmet.

We need some additional space (radius) for padding: 1/2 to 3/4 inch either side, therefore 1/2 + 1/2 or 3/4 + 3/4. These, respectively, yield 1 and 1.5 inches added diameter. Plug Pi into that and you arrive at 3.1416" additional circumference or about 4.7", depending on which figure you use. There's nothing wrong, thinx I, with rounding upwards to gain a little more padding room to, say, a maximum of 5 inches' more circumference. So your helmet should be about 5" bigger around than your head -- 12.5 cm for our SI-based correspondents -- at the largest. You could go a little smaller.
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Post by Mike F »

Okay, this is a prototype setup I threw together in the past several minutes.

You can safely ignore R if you wish, it's mostly a placehoder for when I figure out the geometry you need to prevent gapping. This will work fairly well, so long as you reinforce the holes up top and the browband. I took the liberty of adding the information in this thread to it. I had 3 times the padding added as it would stretch from the middle (pi rounded to 3) rather than from the outside (pi times two).

Proviso: I've never made one of these. I shall add information regarding it as I recieve it or as I make one.
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Post by iaenmor »

Stacy, doh. Right idea wrong way of explaining it. The second formula was what I was trying to get at.

Use the first one if all you have are the diameters of the depth and width. Remember that you have to double the padding numbers to reflect both sides the head.

Thats what I get for posting while eating lunch and talking to my boss at the same time. Of course Math is not my worse subject, just writing out the formulas. :oops:

Now having said that for some reason, the helms that fit me the best all seem to be around 28-28.5". Guess that add 3" thing does have some validition.
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Post by RenJunkie »

Ok, so basically you add 3.25 inches to the circumference of the head? Or is the 5 inch standard better?

This is good, it's gonna save me much grief on getting my patterns right for my helm.

Do you add the extra bit onto the liner for barbutes and sallets too, or just for bascinets?

Thanks,
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Post by Mike F »

Most sallets I've seen are riveted around the browline. You can pad it in a similar fashion, but it depends on what you're doing. After all, it'd be hard to pad an articulated sallet.

Once you get the suspension system sewn together the rest of it is just making patterns off the helm and padding that.
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Post by Rainald »

Screw the math. Make a circlet to the exact shape of your noggin at it's widest level, and then figure out the size of the helm and resulting padding using the circlet as the start of your pattern. It's what I use when decide to make a new helm.
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Post by Stacy Elliott »

Ah, but my helms are made for people ranging from Finland to SouthAfrica to Greenland.... Kinda hard to have them drop by so I can do that.

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Post by RenJunkie »

Alas, I have no padding, so I have to try and anticipate the thickness.

And one day I hope to be making them for people I've never seen and to stock some.

Math is my only hope. That or the rule of 3...or Konstantin's rule of 5...lol

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