[TheForge] Re: lamp shade

[Mike Spencer]

Janet> Okay, that sounds good, but what's the formula for figuring it
Janet> out?

[scribble scribble...scritch scritch scritch scribble....]


Okay, first lets get straight what goes into the formula. Here's
what one panel of the truncated cone looks like:


          ------------------------        ------
  Side   /                        \          ^
   S--->/                          \         |   Height H measured at right
       /                            \        |   angles to the upper and 
      /                              \       |   lower edges.
     /                                \      v
     ----------------------------------    ------ 


(In case your mail reader messes up the ASCII sketch: S is the length
of one of the angled sides.  H is the right-angle distance between the
two parallel sides.)


The angle we're looking for we'll call 'A'.  Then,

                    sqrt(2) S
  1/2  A = arcsin  ----------
                      2   H

That is, multiply the square root of 2 times S, divide that by 2 times
H.  Then take the inverse sine of that number.

That answer is an angle.  Multiply that by 2 to get the angle, A, at
which each pair of the the 4 panels in the truncated pyramid meet.

If this is all boogity boogity to you but yer going to try it anyhow,
note that you may have to tell your calculator to give you the answer
to the arcsin function in degrees, not in radians or grads.  Sine
tables are usually in degrees, I think.

If, on the other hand, this is all Mickey Mouse to you and I'm all
wrong, show me and I'll go do penance. :-) But I did try some numbers
and they seemed to come out about right.  As a quick check, imagine
that S and H are equal.  Then it's a square box with vertical sides
and A should be 90 deg.  That's what the formula gives.


- Mike

-- 
Michael Spencer                  Nova Scotia, Canada       .~. 
                                                           /V\ 
mspencer at tallships.ca                                     /( )\
http://home.tallships.ca/mspencer/                        ^^-^^