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Gah, evil maths.
I have:
L=2r*sin(l/2r) (that's a small L, not a 1)
h=r(1-cos(l/2r)) (before the cos is a 1, after is a small L)
I know L and l, and I want h in terms of these.
*mutters about nasty Engineering projects and people who are meant to be helping who don't have email at home*
I have:
L=2r*sin(l/2r) (that's a small L, not a 1)
h=r(1-cos(l/2r)) (before the cos is a 1, after is a small L)
I know L and l, and I want h in terms of these.
*mutters about nasty Engineering projects and people who are meant to be helping who don't have email at home*
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no subject
Date: 2002-03-16 04:13 am (UTC)From:no subject
Date: 2002-03-16 05:40 am (UTC)From:L/h = 2sin(l/2r)/(1-cos(l/2r)
but I can't see how to get rid of the other r...
no subject
Date: 2002-03-16 09:07 am (UTC)From:no subject
Date: 2002-03-16 09:38 am (UTC)From:Re:
Date: 2002-03-17 10:04 am (UTC)From:no subject
Date: 2002-03-17 10:20 am (UTC)From:If it was a reuslt of normal A level stuff then I suspect you've made an error in deriving these formula.
These forumula do have exact answers in the sense that "exact solutions exist" but you can't write down those answers in closed form.
The way these problems are dealt with is iteration which can achieve an arbitary degree of accuracy: adaquete for most real life purposes.
The way you'd start an interation would be to first derive the statement:
L^2+4h^2=8rh
Sub that back into the h= ... expression and then use something like the Newton Raphston (sp?) method. However, this kind of stuff was only covered at the end of my further A level so I suspect you don't know what I'm talking about at this stage.
If you want me to explain how I derived that forumla or more about iteration then just email me or ask me on a talker and I'll try and explain.
Neil
no subject
Date: 2002-03-18 05:45 am (UTC)From:I found the answer (well, the iterative formula) online, plugged that in, and it seemed to work fine.
no subject
Date: 2002-03-20 08:36 am (UTC)From:1-cos(x)=2sin^2(x/2)
=> 2sin(x)/(1-cos(x))=2cot(x/2)
I don't think this helps however ...
Neil