Accounting for padding in helms... (Math warning)
- Stacy Elliott
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Accounting for padding in helms... (Math warning)
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
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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- Sean Powell
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- Stacy Elliott
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Hmmmm Did I use an incorrect formula?
Stacy
Stacy
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- Sean Powell
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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
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
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)
-LWCM
Seriously though, that's a really neat pair of formulae (formulas? not sure)
-LWCM
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- knitebee
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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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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
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
The mark of a good person is not whether or not you make mistakes, it is how you deal with them afterwards"
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- Sean Powell
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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)
Sean
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)
Sean
- Stacy Elliott
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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
SCA helms need 1/2 inch...
So........
Stacy
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- Stacy Elliott
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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
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
The mark of a good person is not whether or not you make mistakes, it is how you deal with them afterwards"
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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
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.
John Moore
- Sean Powell
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No that is working EXACTLY right.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
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
- Stacy Elliott
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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
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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- Stacy Elliott
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Mike.. Sure!
Stacy
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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.
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.
"The Minstrel Boy to the war is gone..."
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.
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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It's up to you now.
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.
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.
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.
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.
John Moore
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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,
Christopher
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,
Christopher
War kittens?!!!
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"Born to lose. Live to win."
Historical Interpreter- Jamestown Settlement Museum
Master's Candidate, East Carolina University
Graduate of The College of William & Mary in Virginia
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.
Once you get the suspension system sewn together the rest of it is just making patterns off the helm and padding that.
It's up to you now.
- Stacy Elliott
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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.
Giles
Giles
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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
Christopher
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
Christopher
War kittens?!!!
"Born to lose. Live to win."
Historical Interpreter- Jamestown Settlement Museum
Master's Candidate, East Carolina University
Graduate of The College of William & Mary in Virginia
"Born to lose. Live to win."
Historical Interpreter- Jamestown Settlement Museum
Master's Candidate, East Carolina University
Graduate of The College of William & Mary in Virginia