Designing and Building a Cone FrustumDate: 03/24/2004 at 12:18:06 From: Lynette Subject: cone frustum question I am making a pattern for a frustum shape to protect a piece of equipment. I found your information on making a lamp shade pattern very helpful. But since this is large, I am wanting to know how to find the distance between the top arcs and bottom arcs in a straight line so when I make my compus, I know when to stop and do not have to try and measure the arc(s) (about 12') as I go. I need direction. Can I put the known information on a plane and use a distance formula? I don't seem to know where to channel my thought on getting this information. Date: 03/24/2004 at 15:28:11 From: Doctor Rick Subject: Re: cone frustum question Hi, Lynette. I believe you are referring to this: Pattern for Lampshade http://mathforum.org/library/drmath/view/55270.html Once you have calculated the radii and the central angle according to Dr. Peterson's formulas, you can find the chord lengths and heights using formulas found here: Segments of Circles http://mathforum.org/dr.math/faq/faq.circle.segment.html You'll need Case 13: known radius and central angle. The following formulas give the chord length c and the height of the arc, h: h = rad(1 - cos(theta/2)) c = 2*rad*sin(theta/2) where, from Dr. Peterson's formulas, Rs rad = S = --- for the outer curve R-r rs rad = S-s = --- for the inner curve R-r theta = 360(R/S) = 360(R-r)/s for both curves The key points of your pattern will be like this: c/2 c/2 *----------------------+---------------------* /: |h \ / : * \ / : \ s/ :s*cos(theta/2) \s / : \ / : \ / : C/2 C/2 \ *-------+----------------------+-----------------------------* |H * where I used c and h for the chord and height calculated for the inner curve, and C ahd H for the chord and height calculated for the outer curve. You'll have to connect the asterisks with arcs to complete the pattern. You may also find the following Dr. Math page useful: Formula for Laying Out an Arc http://mathforum.org/library/drmath/view/61615.html - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ Date: 03/28/2004 at 23:59:51 From: lynette Subject: Thank you (cone frustum question) Thank you for your quick response! I was at my wit's end when I found the website. Everything is so well laid out in terms I can understand. I just wanted to say I really appreciated your help. :) |
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