Carpentry and Woodworking - need advice about mitre angles octagon frame
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05-23-00, 09:52 PM
Constructing frame in octagon shape. What is the calculation that would be used to determine the mitre angle of each meeting piece of lumber. I know that an octagon has 1080 degrees so somone show me the math to get the mitre. Also explain how any mitre can be determined for any polygon shape such as hexagon , pentagon etc.
05-23-00, 11:05 PM
Forget the surveying! Simplify!
For regular polygons:
360 / (number of intercepts * 2)
8 sides
360 / 16 = 22.5 miter
5 sides
360 / 10 = 36 miter
For regular polygons:
360 / (number of intercepts * 2)
8 sides
360 / 16 = 22.5 miter
5 sides
360 / 10 = 36 miter
05-25-00, 11:15 PM
Hey 2000, that's a slick trick! :D
Easy to remember too.
If anyone wants to get the angles for compound miter cuts for polygons, look for a shareware program for "Mitercalc". It has formulas for various polygons with sides tilting at a range of angles that give the miter and bevel angle degrees. It would give answers to the simple polygons too but in a more cumbersome process.
Easy to remember too.
If anyone wants to get the angles for compound miter cuts for polygons, look for a shareware program for "Mitercalc". It has formulas for various polygons with sides tilting at a range of angles that give the miter and bevel angle degrees. It would give answers to the simple polygons too but in a more cumbersome process.
05-26-00, 12:26 AM
I'm glad you liked it, but maybe some clarification is in order for those who are just beginning.
<BLOCKQUOTE><font size="1" face="Verdana, Arial">code:</font><HR><pre>
board stock
_______________________
a\b
___________c\d_________
z = single radii of a pentagon (5 sides)
x = juncture point at the interior angle
y = juncture point at the exterior angle
z
\ /
\ / /
______x\/ /
________\/
y
[/code]
Angles a = d & b = c (laws of transversal lines).
Angle x = a & d
Angle y = b & c
360 / 10 = 36 = miter cut
An angle gauge set at 36' 00' 00" produces four angles across the "plane" or board, with two angles integral to each cut piece. The opposing angle is 54' 00' 00" (the true miter of the interior angle 108' 00' 00" for a pentagon). Both acute angles will equal 90' 00' 00" when summed.
Through inspection angle 'a' (36' 00' 00") is the point of intercept of the interior angle of the polygon at x and y = 54' 00' 00". To mark a 54 degree angle with an angle gauge set at 36 degrees set the angle gauge on either side of the board to represent angle 'a' or 'd'.
It is more convenient to compute miters this way and to set a miter saw or angle gauge at 34 degrees than at 54 degrees.
The long way:
360 / number of sides (5) = 72 (radii tangents).
180 - 72 = 108 (interior angle).
108 / 2 = 54 (true miter).
90 - 54 = 36 = (convenient setting for miter saw or angle gauge).
<BLOCKQUOTE><font size="1" face="Verdana, Arial">code:</font><HR><pre>
board stock
_______________________
a\b
___________c\d_________
z = single radii of a pentagon (5 sides)
x = juncture point at the interior angle
y = juncture point at the exterior angle
z
\ /
\ / /
______x\/ /
________\/
y
[/code]
Angles a = d & b = c (laws of transversal lines).
Angle x = a & d
Angle y = b & c
360 / 10 = 36 = miter cut
An angle gauge set at 36' 00' 00" produces four angles across the "plane" or board, with two angles integral to each cut piece. The opposing angle is 54' 00' 00" (the true miter of the interior angle 108' 00' 00" for a pentagon). Both acute angles will equal 90' 00' 00" when summed.
Through inspection angle 'a' (36' 00' 00") is the point of intercept of the interior angle of the polygon at x and y = 54' 00' 00". To mark a 54 degree angle with an angle gauge set at 36 degrees set the angle gauge on either side of the board to represent angle 'a' or 'd'.
It is more convenient to compute miters this way and to set a miter saw or angle gauge at 34 degrees than at 54 degrees.
The long way:
360 / number of sides (5) = 72 (radii tangents).
180 - 72 = 108 (interior angle).
108 / 2 = 54 (true miter).
90 - 54 = 36 = (convenient setting for miter saw or angle gauge).