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This is just a helpful set of formulas for radius work. An example would be, when making arch cabinet doors, chord length and height of arc in line 11, and you get the radius, for setting up a router. No drawing in cad needed. You can calculate a dozen arcs in a minute.
16.00 22.50
12.00 37.70
11.25 22.50
Number ofsegmentsper ring
angle ofcuts on
segments
Diameter ofring
ring circumference
horizontalangle on jig
vertical angle on jig
11.25°
22.50°
sawblade
flip fo reach cut
22.50°11.25°
Tablesaw j ig
16 segment ring sample
saw blade
Tablesaw j ig
8 segm ent ring sam ple
45. 00°
22. 50°
45. 00°
22. 50°
flip fo r each cut
saw blade
Tablesaw j ig
8 segm ent ring sam ple
45. 00°
22. 50°
45. 00°
22. 50°
flip fo r each cut
11.25°
22.50°
sawblade
flip fo reach cut
22.50°11.25°
Tablesaw j ig
16 segment ring sample
saw blade
Tablesaw j ig
8 segm ent ring sam ple
45. 00°
22. 50°
45. 00°
22. 50°
flip fo r each cut
saw blade
Tablesaw j ig
8 segm ent ring sam ple
45. 00°
22. 50°
45. 00°
22. 50°
flip fo r each cut
Stair calculator
Stair height Number of treads102.90 14.00
Tread run Step rise11.00 7.35
0.59 33.75Total stair run hypotenuse
154.00 185.21
small anglein rads
small angle in degrees
154.00"
102.90"
7.35"
11.00"
33.75°
185.21"
S tair exam ple calculation11" tread
102.90"
S tair exam ple calculation10" tread
140.00"
10 .00"
7 .35"
173.75"
36 .32°
B2
The bottom landing needs to be figured as a tread for these calculations to work correctly.
154.00"
102.90"
7.35"
11.00"
33.75°
185.21"
S tair exam ple calculation11" tread
102.90"
S tair exam ple calculation10" tread
140.00"
10 .00"
7 .35"
173.75"
36 .32°
Helical handrail calculator
Stair rise Stair run
7.250 11.000 0.583
36.000 226.195 33.389
helix height hypotenuse
149.083 270.905 270.905
0.50 43.116 135.453
total cost
2.00 $2.30 $4.60
small anglein rads
cylinder radius (planview of
helix handrail radius)
cylinder circumference
small angle in degrees
handrail lengthper helix
number of helixrevolutions
radius of flattened
helix (torus)
total length ofhandrail
# of bd. feet usedper foot of handrail
Cost per bd. ft.of lumber used
1 56 .08 "2 70. 91 "
handrail begins 3' above floor
Ty pical d iam etero f helica l s ta ir case
Floor
Typica l rise and run of a stair.
Helix handrail
Circumference of 72" diam eter colum n is 226. 19"
33. 39 °
33 .39 °
7. 25 "
11. 00 "
2 26. 19 "
1 49 .09 "
36 .00 "
72. 00 "
A simple helix is the hypotenuse of a right triangle wrapped around a cylinder,where the base of the triangle is equal to the circumference of the cylinder.
1 56 .08 "2 70. 91 "
handrail begins 3' above floor
Ty pical d iam etero f helica l s ta ir case
Floor
Typica l rise and run of a stair.
Helix handrail
Circumference of 72" diam eter colum n is 226. 19"
If you know chord and radius of your arc, enter values in formula above. Then enter the number from cell E13 into cell A16.
C15
Note: height and rise of an arc, are the same thing. At this time, no actual testing has been done, this formula is just for reference, so that when an accurate springback distance is finally determined, the numbers can be recorded. If a test piece is made, then a percentage of error can be noted in column c, and kept for reference. Thereafter, that percentage of correction can be manually entered into cell B 19.
D30
Made a 3 ply curve, actual springback was .88" for a 50.5" chord curve 10.56 height program calculated a 1.3" springback. Error correction is -.36
Oak, white 0.15
Sassafras -0.24
Sycamore -0.05
Walnut, black 0.09
Poplar, yellow 0.04
cedar, incense -0.3
cedar, western -0.25
Douglas fir 0.23
Fir, white 0
Fir, mountain 0.1
Pine, white -0.16
Pine, lodgepole -0.1
Pine, ponderosa -0.14
Pine, sugar -0.21
Redwood, young -0.26
Spruce, white -0.03
Purpleheart 0.4
Rosewood 0.19
Mahogany, african -0.07
Mahogany, true 0
Balsa -0.6
Bubinga 0.5
Teak 0.03
half chord
12.4999
Chord Arc length
24.9999 25.8571
Radius Arc length
35.6102 56.1343
Half chord
25.2500 16.19992
Height Arc length
13.8001 60.0217
1.49517
45.0000 Desired chord 43.0810 half chord
61.1882 30.5941
Arc rise
12 12.7500 0.78971877222904
Right angleleg
Desired arcRadius
Make Jig Radius
Make JigArc rise
5.26" YX
Y = springbackX = riseN = num ber of plys
Y = X
N2
CLAMP FORM
PREDI CTI NG W OOD SPR I NG BACK
arc
chord
height
E16
Enter a number that is the radius you want, as well as a value in cell A16 for the arc rise. Then look into cells G16 and G19 for the values that you need to make your jig. The length of the desired chord and the length of the jig chord should remain the same.
85.6669 61.1882
936
30.3311051851758 43.0810
Hold cursor over this cell for notes
side slope degrees end slope degrees Wall angle degrees
20 0.3490658504 30 0.523599 90 1.570796
Bevel
17.495 39.856 28.481
Right triangle - angle findershort leg lengthlong leg length small angle degrees
2.45 3.76 0.5774962 33.088
Dual SlopeCompound
Miter formula
Side miterdegrees
End miterdegrees
end
side
l ines of vert ical
wal l an gle
30.00 ° 4.3 9°
14.04°
Hold cursor over this cell for notes
0.30535 17.4952 0.497091 28.4812
Bevel
20 1.22173 30 1.047198 0.695613 39.85571
side slope miter cut -
degrees
end slopemiter cut -
degrees
side slope
end slope
end
side
l ines of vert ical
wal l an gle
30.00 ° 4.3 9°
G1
This program will calculate the miter and bevel of cuts needed to make a 4 sided fixture that has a different slope on the sides then the front and back. Bevel of pieces is the same on all 4 corners, so one can index off the inside for making joint fasteners, such as biscuits or splines. I made some mockups, and the numbers seem to be fairly accurate, but I cannot garentee results.
37.629 0.914046382562 90 1.5707963267949
miter degrees bevel degrees
31.406 34.057
Right triangle - angle findershort leg length long leg length small angle degrees
This formula is great for finding compound angles for crown molding. Unconventional molding slope, no problem. It also will work for a wall angle of any degree. It will also help you calculate pieces for something like a sloped polygon planter. The other fomulas will help in finding angles, and be sure to note cell D 23 if working with polygons.
Varibles in Red Answers in Blue
Chord Rise Radius Arc length hold cursor over this
S lide router, attach ed to ba se,again st 2 p ins to cut 1/ 2 of arc
E2
This is a very nice method of making large arcs using a router, that is different from a very long router base attachment. Fasten router, so router bit is right on the edge of the base jig. Then cut 1/2 of arc, with 2 pins in place. Then cut other side. This worked very well for the beam I put in my kitchen.
hold cursor over this
10494.332641
R 327 .95"
4" rise
4 .48°
4 .48°
Pin s
Cut rou ter b ase an gle to m atch arc rise
Beam
S lide router, attach ed to ba se,again st 2 p ins to cut 1/ 2 of arc
1/ 1 6 / 20 03
1" = 1 7. 77 7 30 46 8 28 38 "
K itch en BeamD ra ftsm an - Pau l D rawin g # Rem ode l
1 38 .1 3 "
18 . 00 "
6 . 50 "
1 2.0 0"8.0 0"
8.0 0"
R 6.5 0"
6.7 2"
1 1.3 1"
10 2.1 3"
8 4.0 0"
1 0.5 0"
1 0.5 0"2.5 0"
R 3 27.9 5"Paul H unting ton
1/ 1 6 / 20 03
1" = 1 7. 77 7 30 46 8 28 38 "
K itch en BeamD ra ftsm an - Pau l D rawin g # Rem ode l
1 38 .1 3 "
18 . 00 "
6 . 50 "
1 2.0 0"8.0 0"
8.0 0"
R 6.5 0"
6.7 2"
1 1.3 1"
10 2.1 3"
8 4.0 0"
1 0.5 0"
1 0.5 0"2.5 0"
R 3 27.9 5"Paul H unting ton
Varibles in red Answers in Blue
Perimeter 1/4 ellipse arc
14 5 63.088 15.772
Area 1/4 ellipse area
219.911 54.978
ratio
2.8 to 1
string length
26.153 54.153
1/2 string length
14.866 27.077
Two axis, router and extended base method
ELLIPSE PROPERTIES
semi-major axis Semi-minor axis
Distance between Foci
Two nails,penciland string method
Hypotenuse length
Foci
String
0.50"
Router
S em i- m inor ax is
= S em i-m ajor axis (ho le center to ins ide of router bit)
3/ 8" dowel screwed to block
Router base extension
e llipse tab le template
Answers in Blue
0.2243767313
Two axis, router and extended base method
hold cursor over this cell for notes
40.00"
20.00"
hypotenuse
40.00"
20.00"
Sem i- m inor axis
S emi- m ajor axis
0.50"
Router
S em i- m inor ax is
= S em i-m ajor axis (ho le center to ins ide of router bit)
F20
This is a standard method of making ellipse templates. As in drawing below, you can make the template for table edging. This is for use on a shaper that is set up with a flush cutter and bearing. Be sure to cut rough stock within 1/8" of template for clean shaper work. If edging is of solid stock rather than laminated stock, use a setup on the shaper using 2 bearings with the flush cutter. This will allow cutter to be raised and lowered, and wood screwed to template, flipped over. This is so you can cut with the grain on the curves, rather than into it.
3/ 8" dowel screwed to block
Router base extension
e llipse tab le template
Table edge tem plate, make 4" oversize . And wood edge, about 1 1/ 2" oversize.
Table edge tem plate, make 4" oversize . And wood edge, about 1 1/ 2" oversize.