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Greyson Brown
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 Posted: Fri 28 Jan, 2005 10:18 pm Post subject: |
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| Craig Johnson wrote: | Greyson
If you are interested in doing blades and swords the best way to start is just do it. Look at the best examples you can find and handle and try to produce something you like that is similar. There is absolutely no better teacher than experience and repetition. An old blacksmith once told me the reason most guys never produce very much is they are afraid of goofing up and that the essence of learning to smith was making mistakes. |
The blacksmith's I work with also have their own definition for an expert that kind of goes along with that. An expert is, "someone who made the same mistake you are now making in front of a different audience."
Peter,
I can make an adjustable pommel, I was just curious if you had some amazing inovation that I hadn't thought of. I had actually thought of making some kind of "test" pommel anyway; it is nice to be validated by knowing that some else has actually used one.
Thanks!
-Grey
"So long as I can keep the path of honor I am well content."
-Sir Arthur Conan Doyle, The White Company
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Angus Trim
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| Posted: Sat 29 Jan, 2005 7:21 am Post subject: Re: Computer swords |
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| Craig Johnson wrote: | Here are some more fun musings I like to add to these kind of discussions. Not trying to side track the thread but I think they are serious components to the use of the sword.
As Gus says above they are not a simple shape. I have talked to a golf club designer about some of these things and he thought the golf club was a much simpler issue. A tapering circular shaft in most cases with all the weight in one end and the need for a certain combination needed in the amount of flex and stiffness to impart. The designs are computer assisted but as he said if the computer could make a perfect club there would be only one design. I am sure swords would fall in the same category.
Each sword, as we have described above, is a slightly different taper and configuration. They were also hand made items. The result is that often you will see asymmetries in a piece. Do you factor these in? What if the guard is 1/2 inch wider on one side or the pommel is asymmetrical or one side of the blade has an extra 1/8 of width. What happens when the distal taper is on the majority of one face of the blade, does that change the dynamic balance? Almost certainly these issues have an affect.
But and this is a big "BUT" can you tell????
When the gross dynamics are being adjusted yes we can feel a difference but at a certain point and I am afraid the vast majority of us are not experienced enough to just feel the difference in the hand when the finer elements are being tweaked. As Peter said a few cms close on the pivot points is a pretty decent accuracy for the average sword user. This also does not take into account one of the most important factor for a swords effectiveness, the hand on the grip.
One wants to manage the vibration and other elements in a sword to make it as good a weapon as possible, but in all honesty the vast majority of people using swords today are unable to detect the difference on some of the fine adjustments. The hand on the tool has far more to do with how well it works than the tool itself, as an old carpenter I used to work with would say. To use the vibration while cutting issue to illustrate. If the person cutting is not meeting the target with a nice clean arc in the plan of the edges and smoothly using their strength to advantage the cut will be producing more vibration then the sword will induce working in a free environment. i.e. ideal conditions with no influence by the cutter. Even a slightly rotated cut will make the sword start vibrating more than the actual flex induced by a "perfect cut" would generate in the blade.
I am sure all of this is pretty apparent to all but I think it good to bear in mind that the best made sword is always only as good as the hand on the hilt. Helps keep me humble 
Best
Craig |
Hi Craig
You're right about tolerances, cm is fine on where various points wind up on the blade. Part of the thing though is what happens after the blade leaves the machine. For myself, I like to hold a relatively close tolerance on the machine {+ or - .002 inch} because of the things that happen after machining. Considering things like tool wear, and blank "movement" while machining {minute warpage while machining}, closer than .002 inch is impractical, and likely impossible in real world terms.
Yeah, the blade can move a bit in the machine even with the most rigid of setups. A long thin piece of stock, and the machining stresses, yeah there'll be some movement on some pieces. Can be straight to the eye, but lay out on a table, and check the surface out, and about 1/2 the blades will be a bit off from nominal.
I use a heat treat fixture to see that the blades don't warp to hell and gone, but even here, there can be some minor movement in the blade, again. Once again, you can visually check the blades "in the black", and they can appear straight and "flat". The first grinding pass will tell you if the blade moved much, as you'll have peaks and valleys that show up on that first pass {assuming you did a pefect job of keep the blade and belt in contact}.
Bottom line of this? What you have on the first side, will be mirrored on the opposite side of the blade. To "clean things up" will take more material off than a blade that didn't micro warp {either in the machine or heat treat or both}.
Then of course you have the human factor in the grinding. Its nearly impossible to do things perfect all day. This will also effect the amount of material removed, and where the material disapeared.
Once a couple of years ago, after assembling 8 Rangers for Christian Fletcher, I took a bit of time and measured the difference between them. Feeling and handling them, checking cog differences, weighing them, miking them, etc.....
All of these blades when pulled from the machine were within my machining tolerances. The finished blades were close, but one now was smaller than the other seven's average at the tip by .01 inch, and another was .22 inch thick at the base, instead of the more average .235. The "feel" of five of them was close enough that I couldn't really tell the difference. The other three had a noticeable feel difference. The cog difference? A little over 3/8 inch.
Yet the dynamic properties of all of them were excellent.
swords are fun
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Craig Johnson
Industry Professional
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| Posted: Sat 29 Jan, 2005 8:12 am Post subject: Thousandths |
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Hey Gus
The only thing I measure in thousandths is my BCC (Blood Caffein Content) 
The really cool part of this discussion is actually having it. The understanding of these issues is such an important part of really appreciating the work that was done in the past and seeing the real power of experience in their design (Peter's definition  ). I am still finding new aspects to it all the time and each blade I get to examine ends up teaching me something new. The next several years will be very interesting as this percolates through the knowledge base and the connections and discoveries begin to teach us even more.
Well I need more coffee
Craig
Last edited by Craig Johnson on Sun 30 Jan, 2005 12:19 pm; edited 3 times in total
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Angus Trim
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| Posted: Sun 30 Jan, 2005 9:28 am Post subject: Re: Thousandths |
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| Craig Johnson wrote: | Hey Gus
The only thing I measure in thousandths is my BCC (Blood Cacaffeineontent)
The really cool part of this discussion is actually having it. The understanding of these issues is such an important part of realreallyreciating the work that was done in the past and seeing the real power of experience in their design (Peter's definition ). I am still finding new aspects to it all the time and each blade I get to examine ends up teaching me something new. The next several years will be very interesting as this percpercolatesn through the knowledge base and the connections and discoveries begin to teach us even more.
Well I need more coffee
Craig |
Hi Craig
Every few months I handle, see, or do something that causes a large rethink of what I know of this game. One area or another, this is and has been an ongoing education.
One thing that really started things again, was the opportunity to handle and measure some kat antiques. Which meant reproducing the blades. Which of course drove home the realization about how different these were than the Western and Chinese stuff that I'm familiar with, and at the same time how they still follow the same rules {busted a couple of myths I'd fostered for years}.
Then I have a couple of antique sabers visiting. Sabers and kats are both curved and more or less single edged right? Two dimensionally pretty similar, right? However, once you get into the 3rd and 4th {subjective stuff like handling} dimensions things are rather different.
Still........ with the differences there's still a "character" of the handling that these two curved varieties have that you also find in antique and the best modern made double edged Western stuff that just screams "real weapon" when you dry handle one.
Its this "character" {can't think of a better term or phrase, even with more coffee} that I want to reproduce in the swords I make. As far as I'm concerned, it doesn't matter how pretty, how accurately a modern reproduction might look, if it is missing this "character", its not a sword to me. Most of the antiques I've gotten to handle freely enough have had this characteristic, and so do what I consider the best modern made swords, be they reproduction or modern.
swords are fun
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Jesse Smithers
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| Posted: Sun 30 Jan, 2005 10:36 am Post subject: Re: Thousandths |
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| Angus Trim wrote: | | One thing that really started things again, was the opportunity to handle and measure some kat antiques. Which meant reproducing the blades. Which of course drove home the realization about how different these were than the Western and Chinese stuff that I'm familiar with, and at the same time how they still follow the same rules {busted a couple of myths I'd fostered for years}. |
Which rules are different? Which are the same? What were the myths that you busted?
Thanks
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Nathan Robinson
myArmoury Admin
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Peter Johnsson
Industry Professional
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| Posted: Mon 31 Jan, 2005 6:30 am Post subject: |
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| Alexi Goranov wrote: | So I did a little test with the NG Baron and Duke trying to determine the lower ( corresponding to the point behind the guard) pivot point. What I observed is that the pivot point of the Duke is fairly close to the tip, where as, the pivot point of the Baron is somewhere midway between the start of the fuller and the tip of the sword. Are these observations accurate, or had I completely screwed up the "wiggle" experiment. the reason I am asking is because the location of these pivot points seems to be the exceptions to the rules you mentioned in your long post (The rule of the thumb being that swords with little taper have points closer to the vibrational node, and tapering swords have pivot points closer to the tip of the sword).
So first off, are my observations accurate, and if they are, why this choice. What were the properties you were shooting for with these two swords, so that you chose the respective pivot points.
Now that I have these swords I really want to appreciate them. Any comments are welcome.
Alexi |
This is correct.
The Duke is inspirted by an early 16th C warsword in Skokloster armoury. It is also a XIIIa, but slimmer (although it weighs the same). What is noteable with this sword is the forward placed pivot point that sits very close to the point.
I wanted the XIIIa blade to be balanced with a similar feel, although I let the pivot point sit a little further in on the blade.
It is still far enough out towards the point to get a very livley agility. The Duke blade can take a heavy pommel like this, and could perhaops take an even heavier pommel without becoming problematic in performance. As it is the Duke is a very agressive cutter that also have a pretty sweet and responsive balance.
When I choose the weight of the pommel for a blade, not only dynamic balance is an issue, but also precision in thrusting and performance in cutting. These three aspects has to be weighed agianst each other.
As the Duke has a distal taper that allows it to respond well even to a slight increase in pommel weight. therefore the total weight of the Duke can be kept rather low for the size and still have a forward pivot point close to the point.
The Baron is stiffer in the point section, since it needs to have more thrusting potential. The Baron blade would need to have a more dramatic profile taper to be comparable in mass distribution to the Duke, but then it would have become a type XVIa or perhaps even a big type XVII.
Again, this goes to show that there are more things coming into play than the size and mass of a blade. You cannot change the taper or shape just in any way you like without it having effects on other functional aspects. In the case of the Baron blade, it need a certain thickness in the point section for the thrust to be effective. This is not the case for the Duke. That is a dedicated cutting blade and can therefore be made as thin as ever possible.
When you compare different historical blade types you will se many examples like this in how profile taper and shape play together with distal taper and shape of cross section to emphsise different aspects of the blade.
Hope this helps explain some aspects of the blade design.
Alexi, as you own both swords you are in a unique situation to tell us about your impressions. How do you think they compare in handling? What is your impression of their character? Do you find they perform any different from each other?
What sword is your favourite, if any, and why? What other experiences of swords do you relate to in your reactions?
I am very curious to know!
Thank you.
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Chad Arnow
myArmoury Team
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| Posted: Mon 31 Jan, 2005 7:01 am Post subject: |
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| Peter Johnsson wrote: | Alexi, as you own both swords you are in a unique situation to tell us about your impressions. How do you think they compare in handling? What is your impression of their character? Do you find they perform any different from each other?
What sword is your favourite, if any, and why? What other experiences of swords do you relate to in your reactions?
I am very curious to know!
Thank you. |
Peter,
I'm not Alexi, but I've handled both. As I noted in the Duke's review (http://www.myArmoury.com/review_alb_duke.html), the two swords handle very differently. The Duke's balance makes it feel heavier, even though it is quite a bit lighter. The Baron "feels" lighter. The Duke's mass in the blade, though, makes it easy to swing. Once in motion, the blade presence creates seemingly self-sustaining motion; it pulls itself through the cut. The baron feels livelier in dry handling, and is no slouch in cutting, either.
They feel quite differently. I think you guys really nailed down the differences between the two types. I prefer the Baron, as it is more my type aesthetically and in handling. The Duke, though, is a great example of its type. If I were trying to collect one sword of each type, I'd buy the Duke as the XIIIa.
ChadA
http://chadarnow.com/
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Alexi Goranov
myArmoury Alumni
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| Posted: Mon 31 Jan, 2005 8:53 am Post subject: |
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Thanks for the explanation Peter.
I love both swords for what they are. No favorites here. I have to say that initially the Baron was better liked due to aesthetics, but now that has changed. Most pictures of the Duke just do not do it justice. These is so much subtle detail that just remains unnoticed until the sword is in your hand. I think that the Baron is a more popular sword and that is unfortunate as the Duke is a gorgeous sword in its own right.
About handling, I have a slightly different opinion than Chad's. I find the Duke to be noticeably lighter than the Baron when held in various guards. However it is a bit slower to set in motion, as Chad also noticed, but not too slow and does not feel sluggish. It is actually rather responsive. I expected a slower weapon and was pleasantly surprised to see that this monster cutter was also quite agile.
The Baron is also a much better thrusting sword in terms of dry handling. The point is easier to control and the sword in general "feels" more natural in power thrusts, and does not wobble then the trust is complete (even though that is also an indication of how well I guided the point). So I think you have successfully underlined the trusting capacity of the Baron.
I am yet to do cutting with the Duke, so until then I can only compare the two swords in dry handling. I have cut with the Baron, and I was well amazed at how effortlessly it cut through 12feet of rolled mats. With respect to cutting mats, I have only one point of reference (a cheap Valiant Armoury sword) so the comparison there is useless.
Once I get my more thrust oriented swords (Sempach and Agincourt) it will be a great exercise to compare their cross sections, mass distribution and pivot points to figure how is it that the swords gets its character. This is orders of magnitude better than looking at pictures.
Thanks again,
Alexi
Last edited by Alexi Goranov on Mon 31 Jan, 2005 1:10 pm; edited 1 time in total
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Peter Johnsson
Industry Professional
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| Posted: Mon 31 Jan, 2005 9:04 am Post subject: |
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Thanks for your feeback!
This is interesting as it illustrates that handling charactersitics is something more than point of balance and even placing of pivot points.
I think it is useful for other enthusiasts to get this kind of analyzis of swords side by side together with personal comments about what other references/experiences the writer/reviewer has in his/her background.
Thank you guys.
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Nate C.
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| Posted: Mon 31 Jan, 2005 7:29 pm Post subject: |
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Wow,
This has turned into quite an informative post. Thanks to everyone who contributed so far. I haven't gotten all the way through the ARMA article yet but it looks very interesting. I would love to try doing FEA on some accurate models. Even as I think about how to get a nice model (ILM or Weta want to scan one????  ) I start thinking which one first  ? I know some of this is definitely an art (the finishing, artistic design, research, etc...) but everything has to obey the laws of phtsics, etc. and my engineer's brain is getting very interested in this  .
So, to condense this down to a short form (if that's possible)..... One should start with a good, well balanced blade with the various points (rotation, percussion, etc) a little further towards the tip than you want it to be in the finished product to be. You then dry fit the guard/grip and tune the pommel (NOT the sword ). once this is done you finish and/or make the final piece(s) and put them together (semi) permanently. Over-simplified maybe but is that a good one paragraph synopsis up to this point?
Cheers,
Nate C.
Sapere Aude
"If you are going to kill the man, at least give him a decent salute." - A. Blansitt
If they ever come up with a Swashbuckling School, I think one of the courses should be Laughing, then Jumping Off Something. --Jack Handy
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Craig Johnson
Industry Professional
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| Posted: Mon 31 Jan, 2005 8:47 pm Post subject: Starting out |
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Hey Nate
Roughly yes. I would caution one from trying to analyse it down to a brief synopsis as there are many variations on a theme here and while the engineer part of the brain loves to calculate and codify this always involves assumptions and simplifications. I think it would be more fruitful to look at a type of sword with such formulas then just swords. Where does a thrusting sword cross over to a tuck or a cut and thrust sword vary into a pure cutter. The structure one applies to any outline on how to make the best sword would be like how do you make the best car, gun, or computer there are different purposes and that is always a series of different elements balanced to create what one is striving for, constrained by the materials and skills of the maker.
Ouch that sounds a bit philosophical doesn't it.
I think it is the interplay of the different elements that is crucial to getting a sword where you like it. This is the essence of what I think Peter described in talking about designing a sword. The node or the pivot point can be x, the weight can be y, the blade can be z type. But all these things have to work in consort for the whole to be useful. The end user also has a "feel" they like if the result is not to their liking then it is difficult to be happy with the end result.
One of the issues that arise with doing some custom pieces is the customer will say they would like a pivot point under the third finger, the balance point a .25" in front of the guard, the grip to be 6.75 inches long, the type XVIa blade to be 43.65" long .35" thick at the guard and two inches wide and have a reinforced tip for the thrust, the guard to be 8.47" wide and .75" thick and the pommel to be a 1.2" thick wheel with a center recess.3" deep, the weight to be 1.5 pounds. If one trys to make the sword they describe it will not turn out very well as the details are set but the whole has not been very well considered. Not to mention that the weight would be difficult to achieve at all. This is what I was referring to when I talked of using the pieces of the past to inform our work today. In the above case it is up to me to decipher what the client is interested in and lead them to an answer they will be happy with when it arrives new and several years later as well.
The practical knowledge of how these items were used was an empirical database that over the generations had arrived at a profound understanding of what was needed. This was used to develop the many types of swords that where made. Today we are just beginning to see into the shallows of that knowledge and using the examples of the swords they made, to be used, tells us quite a bit. That is why sometimes I am surprised when those that are studying the use of the sword will give me some new "better" design that has little or no precedent and I can see many problems in its structure but they feel it is the mousetrap no one has thought of.
Best
Craig
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Nate C.
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| Posted: Wed 02 Feb, 2005 3:28 pm Post subject: |
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Hey Craig,
I was just trying to summarize the procedure for making or cuttling a sword. I'm sorry if I was unclear. It took hundreds/thousands of years of design and experimentation to get to the originals. It would therefore be presumptuous to say that we can improve on them after only 50-100yrs of making repros.
As for creating a sword of a given type, you guys are like my grandmother when she's baking. Follow the recipe and tune it until it feels right . I guess that the bottom line is; use the science to get close and understand why the sword does what it does. And use the art of engineering to apply this info to better "design" swords that obey the rules that we discover from studying originals.
Cheers,
Nate C.
Sapere Aude
"If you are going to kill the man, at least give him a decent salute." - A. Blansitt
If they ever come up with a Swashbuckling School, I think one of the courses should be Laughing, then Jumping Off Something. --Jack Handy
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Craig Johnson
Industry Professional
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| Posted: Wed 02 Feb, 2005 6:49 pm Post subject: Evnin Nate |
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Nate
Sorry did not mean to imply that you were really off base or even slightly askew just kind of combined your top and bottom paragraphs in my mind I guess. I would have been more productive to say add to the first part of your description decide on a specific type of sword to make as the very first step. Then if one is going to use the examples of existing artifacts and research to create your sword you can be specific in your goals for the end result. Helps enormously in finding a result you are happy with and cuts down on mission creep.
Best
Craig
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Ozsváth Árpád-István
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| Posted: Mon 28 Sep, 2009 5:38 am Post subject: Determining Pommel and Guard/Grip Weights |
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I was doing some math to determine the pommel weight for setting the CoG to a certain position. I realized that it was far too complicated due to the complex shape of the blade.
I found a more simple solution:
Put the blade on a digital scale with a pencil or other narrow object under the desired CoG. Now you can zero the scale. Try to balance it by applying pressure on the tang right where the pommel should come. Now the scale will indicate the right pommel weight for this CoG.
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Vincent Le Chevalier
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| Posted: Mon 28 Sep, 2009 6:03 am Post subject: Re: Determining Pommel and Guard/Grip Weights |
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| Ozsváth Árpád-István wrote: | I was doing some math to determine the pommel weight for setting the CoG to a certain position. I realized that it was far too complicated due to the complex shape of the blade.
I found a more simple solution:
Put the blade on a digital scale with a pencil or other narrow object under the desired CoG. Now you can zero the scale. Try to balance it by applying pressure on the tang right where the pommel should come. Now the scale will indicate the right pommel weight for this CoG. |
Your solution is a very elegant and practical one indeed...
However the computation is not that complex if you take into account the center of gravity of the bare blade, which can be measured easily.
With:
mb = mass of the bare blade
gb = distance from the pommel location to the center of gravity of the bare blade
g = distance from the pommel location to desired the center of gravity of the complete sword
It's fairly easy to demonstrate that the pommel mass mp is then given by:
mp = mb (gb/g - 1)
Now, the real complicated question is finding where the center of gravity should be for a given blade I have a conjecture but the computation is considerably more involved...
Regards,
--
Vincent
Ensis Sub Caelo
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Ozsváth Árpád-István
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| Posted: Mon 28 Sep, 2009 11:02 am Post subject: |
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Thanks Vincent!
That's the "magic" formula I was looking for. I guess it's from some lever model. I'm surprised that works fine on a non-linear model, like a sword.
Here are some measurements to demonstrate the formula:
Mb = 900 g
gb = 40 cm
Mps - pommel mass measured with scale
Mpf - pommel mass with formula
g(cm) Mps(g) Mpf(g)
37.5 - 50 - 60
35 - 155 - 128
32.5 - 205 - 207
30 - 285 - 300
27.5 - 400 - 409
25 - 530 - 540
22.5 - 670 - 700
20 - 870 - 900
17.5 - 1150 - 1157
15 - 1450 - 1500
My sword will be type Xa (or something like that) with the following specs:
Material: some old spring steel
Blade length: 81 cm
Total length: 96-98cm
Blade width: 45 mm tappering to 35 mm
Blade thickness: 7 mm at guard tappering to 4 mm
Crossguard weight: 100 g
CoG: ?
Pommel weight: ?
Total weight: ?
I'm not an expert at all and I can't afford to buy a decent sword. So I grabbed my trusty angle grinder armed with sandpaper disc...
My concern is setting the "correct" CoG for a cutting sword. Leaving it far out will be like swinging a sledgehammer, bringing it too close by adding a big pommel will look like one.
My blade isn't finished yet, so it will loose about 50 grams or so and I hope the guards weight will help to bring the CoG a bit closer. I'm in good shape, but I don't want to end up with a 1.5 kg+ single handed sword.
I know it's not all about the CoG, but it has some direct connections with severe pain in the wrist.
I want to end up with something that looks like the Albion's "The Oakeshott" (from a good distance, of course )
Help please!
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Maurizio D'Angelo
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| Posted: Mon 28 Sep, 2009 2:50 pm Post subject: |
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hello Ozsváth,
your weight will be much higher than 1.5 kg.
Crossguard weight: 100 g , I make mistakes but perhaps too short?
You have a thickness exaggerated.
Oakeshott type Xa is a sword for cutting. Its thickness may be much lower.
You do not say anything about the section.
You do not say anything about Fuller, width depth and length.
So is very difficult, help you.
Ciao
Mau.
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Vincent Le Chevalier
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| Posted: Mon 28 Sep, 2009 3:31 pm Post subject: |
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| Ozsváth Árpád-István wrote: | | Thanks Vincent! |
You're welcome
| Quote: | | That's the "magic" formula I was looking for. I guess it's from some lever model. I'm surprised that works fine on a non-linear model, like a sword. |
It works because the whole complex mass distribution of the blade is taken into account when you measure its center of gravity. It's then right from the definition of the center of gravity for two objects:
mp x 0 + mb gb = (mp+mb) g
| Quote: | | My concern is setting the "correct" CoG for a cutting sword. Leaving it far out will be like swinging a sledgehammer, bringing it too close by adding a big pommel will look like one. |
And it will not handle correctly at all... Too much mass in the pommel will prevent the sword from swinging into the cut.
As you can read in this thread there are about as many ways as there are smiths to find the correct pommel weight and sword behaviour.
My opinion (and I'm not a sword maker, so take it with a grain of salt ) is that you can't do it right unless you take moment of inertia into account. And this is most easily done with pivot points. Read that post of mine and try to measure some first... This is not as easy as getting CoG, but it gives a lot more information about the mass distribution.
What you should aim for on your sword (according to my current understanding) is to have the pivot point associated to the cross about
57cm from the cross. If you do things right, on the bare blade it will be closer than that. [EDIT]If the pivot point is already there on the bare blade you do not have enough distal taper, the blade must get thinner towards the tip.[/EDIT] As you add a pommel, it moves towards the tip. If it is too far towards the tip, your pommel is too big, if it is too close to the cross, your pommel is too small. It requires some trial and error I'm afraid, there is way to compute the right pommel weight but it is really a lot more involved. Not as magical as the CoG
I'm really sorry to be unable to give you a simpler advice. Balancing a sword is really a complicated task and static behaviour (that is represented by CoG) is far from giving the whole story... If you manage to measure pivot points on the bare blade I can help you some more.
Regards,
--
Vincent
Ensis Sub Caelo
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Maurizio D'Angelo
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| Posted: Mon 28 Sep, 2009 4:09 pm Post subject: |
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I do not know if you want to bring your sword to a historical model.
If the pommel and the guard must have a size close to the historical, the weights are almost obliged.
A pommel makes too big a nasty sword.
Vincent is a great mathematician, there is other way, programs to the PC, but are not easiest of mathematical formulas ....
Mau
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