formulas spreadsheet

Answers in Blue

Arc length formula half chord

47.9966

radius height Angle rads Angle degrees Chord Arc length

131.8000 9.0500 0.74547 42.7121 95.9933 98.2526 most accurate formula

2303.6775

Arc Length formula

chord height Radius Arc length

96.0000 9.0500 0.372708098268622 122.769147387481 131.8191 98.2601 least accurate formula

Arc length formula Half chord

18.0000 18.76166

Chord Radius Angle rads angle degrees Height Arc length

36.0000 26.0000 1.52936 87.6261 7.2383 39.7635

Hold cursor overthis cell for notes

Numbers in Red are varibles

Right angleleg

arc

chord

height

A1

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


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


45. 00°

22. 50°

45. 00°

22. 50°

flip fo r each cut

saw blade

Tablesaw j ig


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"


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"


102.90"


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"

33. 39 °

33 .39 °

7. 25 "

11. 00 "

2 26. 19 "

1 49 .09 "

36 .00 "

72. 00 "

Arc length formula

radius height Angle rads Angle degrees

28.8434 2.8493 0.89646 51.3636

156.24848875

Arc Length formulachord height

50.5000 10.5000 0.788175769870474 25.1103035203742

Arc length formula

Chord Radius Angle rads angle degrees

50.5000 30.0000 2.00072 114.6331

Rise # of Plys

12 4 Springback

0.750

0.00 0.00

Tree type Elastic factor

Alder, red -0.07

Ash white 0.13

Aspen, quaking 0.11

Basswood 0

Beech 0.1

Birch, yellow 0.25

Butternut -0.19

Cherry, black 0 -0.36

Cottonwood -0.09

Hickory, pecan 0.12

Hickory, shagbark 0.33

locust, black 0.25

Maple, silver -0.28

Maple, sugar 0.17

Oak, northern red 0.17

Oak, souther red 0

Hold cursor over this for notes

Elasticfactor

Correctionpercentage(decimal)

Tested correctionfactor (decimal)

A15

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

1.06 1.375 0.656749181602387 37.629


Regular polygon angle finder

number of sides rads degree of angle

8 2.356 135.000 45.000

crown molding

compound miter formula

slope degrees (smaller angle of

right triangle)

wall angle degrees(from 180 degrees,

example-enter 45 for135 degree wall

Wall angle toenter into cell c3

14.04°

108.00°

0.548137919826493 31.4059893971383 0.59440382978 34.0568307725207


miter cutdegrees

bevel cutdegrees

5 .63 1°

s ide s ide

lines of vert ical

wal l an gle

1 22 .22 0°

P a u l H u nt in g to n

E15

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

102.129 4.000 327.948 102.546 10430.332641

0.15634535623775 323.95563155585

Chord Rise Radius Arc length

102.129 4.000 327.948 102.546 2607.5840.15634533116534

Alternate method of routing large arcs

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

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.

1.618 ratio

height width height width

11 17.798 5.2533993 8.5

Golden Mean Rectangle

Architectural proportion

10.500"

6.489"

2.63"

4.25"

2.63"

4.25"

formulas spreadsheet

Documents

table edge

ellipse table

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