system
November 30, 2006, 8:48pm
1
This is only slightly OT(*), I promise…
I have a function which looks like the following:
ay^2 + bxy - cy - cx + ax^2 = d
where a, b, c, and d are constants.
Is it possible to rearrange the formula to get y as a funxtion of x? Is there some simple ‘completing the square’ trick I’m missing here? I’ll happily trade beer for a solution.
The function is bicycle-related
y = (-(bx-c)-SQRT(2a(ax^2-cx-d)))/2a
y= (-(bx-c)+SQRT(2a(ax^2-cx-d)))/2a
Rhino
November 30, 2006, 9:17pm
3
This looks slightly funny…but could be due to the original formula showing some irregularities.
No idea…
I just asked a maths geek, then copied and pasted the answer.
shrugs
Rhino
November 30, 2006, 9:21pm
5
Really should stop asking TR stuff…
system
November 30, 2006, 10:03pm
6
well spotted - it should have been:
ay^2 - bxy + ax^2 = c
which is a completing the square Sorry to interrupt.
Dionysis: can you ask that guy for a proof of his result? I’m curious as to how he managed to deal so nicely with the xy term.
lats
November 30, 2006, 10:08pm
7
faaaaaaaaaaaaaaaaaaaaaaark
This looks slightly funny…but could be due to the original formula showing some irregularities.[/quote]
The signs in the numerator look odd…
This make more sense?
-(bx-c)[b]+/-[/b] SQRT (2a(ax^2-cx-d))
y= -----------------------------------------------
2a
+/- is “plus or minus”
and
SQRT = Square Root
This thread is making me queasy. I’m so close to binning it.
system
December 1, 2006, 2:16am
12
I think you should at least be revealing how is it ‘bicycle-related’ Nath…?
system
December 1, 2006, 4:24am
13
It’s the approx fixed chain length function …
chain length = chain to wrap half cog
chain to wrap half chainring
chain above chainstay
chain below chainstay
sometimes called the “rigorous equation”, which ends up for inch pitch chain something like:
cl = 0.25(F + R) + 2 sqrt( csl^2 + (p (F - R))^2 )
cl is chain length in inches
F is chainring teeth
R is cog teeth
csl is chain stay length in inches
p is a constant 1/(4*pi)
I’m probably n+1 again, and my right-handed notes are not very neat, so i probably made errors rearranging that formula. I’ll try it again.
853: I’ll bin you!