Mathematics for Knifemaking

C_Kyle

C_Kyle

Joined
Feb 7, 2005
Messages
1,086
Makers,

I just wanted to know how many of you use geometry and triganometry when designing your knives. For instance, if you have 3/16" thick blade, and you want to do a sabre grind only to the bevel of the blade, would you use a trig formula to determine the length of the hypotenuse(sp), or would you just draw the triangle and actually measure the hypotenuse? I'm probably not being clear in my question. I can draw a knife out on paper, including the the grind, and it looks good; but when I measure the the angles and the side of the triangles formed, the edge is a different length.

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If this is the knife, you can see that from the bevel to the edge,2 right triangles are formed. If you want a 15° grind angle per side, you know that one of the angles is 90° and one of theangles is 15°, the other angle must be 75°. You also know thelength of one of the sides(half the thickness of the blade).Does anyone plug thise numbers into equations to perfectly design your blades and bevels, or do you just grind until it looksgood?

I probably didn't explain what I am thinking very well, sorry. I guess I am looking for equations used to help with symetry, blade geometry, and balance; whatever is used when designing and grinding knives.

Thanks for any info.

OK, my pic looks like crap.
 
That's exactly what I am asking, and the formula that I am talking about. The problem is that I am not doing the SIN part correctly. Man, I used to be good at this in highschool. :(
 
A: you don't even need trigonometry for simple (right-angled) triangles like those in knife profile (just perform calculations on one half of the blade to get a right-angled triangle). The thing you're looking for is elementary school Pythagoras's theorem. *edit* now that i think about it, you were probably interested in that particular angle (rather than just in outside dimensions of blade profile). Scratch this paragraph and pay attention only to B and C instead :D

B: trigonometry basics:
a = length of the side of the triangle opposite of the corner where angle (fi) is being measured
b = length of one side of the corner where angle is measured
c = length of the hypotenuse

sin (fi) = a / c
cos (fi) = b / c
tan (fi) = a / b
ctg (fi) = b / a

asin (a / c) = fi
acos (b / c) = fi
atan (a / b) = fi
actg (b / a) = fi

Turning equations around is elementary school mathemathics, you can surely handle that :)

C: further trigonometry lessons: http://aleph0.clarku.edu/~djoyce/java/trig/ Not that you need them anyway :D
 
I don't use any mathematics when designing a knife, but I've got a couple of math jokes for you...

What do you get when you cross a cat and a mouse?

- CatMouseSin(Theta) !

What's the difference between a mountain climber and an arrow?

- One's a vector and one's a scaler!


hahahahahahaha...I crack myself up! yep, I'm a physics/math nerd... I'd tell you the joke about postulating a spherically symmetric chicken....but it'd take too long to type it out...

:D :D

oops...I think I just hijacked this thread...sorry moderators, I won't do it again! :)

-Darren
 
It is too simple.
If you need a 30 degree on a 3 mm blade the bevel width will be:
R = 30
A = 15
T = 3

X = (3mm / 2) / sin (15)
X = 1.5 mm / 0.26
X = 6 mm.

Thats it...
 
Oh, I'm retarted. Once I set my calculator to 'degrees', the formula worked.

Thanks for the input everyone.

Now that the formula is working, who uses it?
 
:D I do :D .
Seriously I dont know. I am still interested in mathematics. When reedknife order I recieved (they want constant and precise angle on the edge http://www.bladeforums.com/forums/showthread.php?t=336289) it worked out suprisingly well, though I dont have any precise eqipment: just a belt grinder with a flat platen. All I did was to grind till bevel reached to the calculated width and to the half of the thickness. It was as good as it machined :cool: .
 
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