Using Easy School Geometry

Create beautifully unique pergola rafter tails.

Copy this easy formula to draw your own hand crafted Pergola Rafter tails template. Using just four simple stage diagrams. When complete copy it onto thin plywood, cut it out and trace it on the ends of all your rafters.

Look at the following sequence thumb nail diagrams. And how the classical shape evolves. You will only need to draw the Stage1 diagram and make changes to it. Stages 2, 3, and 4 show the only changes you need to make.

Large diagrams and explanations come later.

Stage1

Stage2

Stage3

Stage4

Let's choose a 6" wide pergola rafter tails for now.

This formula I'm about to show you works for any size you are likely to meet.

Why use 6"?

Five, Six and seven inch are the more
popular rafter widths so I am choosing six inch width as a good example.

You will need:

Use three A4 sheets of paper. Overlap them half an inch. Tape/glue along their lengths. If you have used tape don't forget to turn the paper over for a better surface. You could also use lining paper if you have any spare.

The width "W" represents 6 inches. Each of the smaller spaces is W/4 or in this case 6"/4 = 1.5"

The length of the rectangle is 3xW=3x6"=18".

*[ For A 7" width rafter the small spaces would be W/4=7"/4=1.75" .*

* Similarly a 7" width rafter would be 3xW = 3x7" = 21" long. ]*

Copy the rectangle using faint pencil lines (4H). And make sure your rectangle will fit well on the paper that you prepared earlier.

The following diagram is a good way to get started.

Using a light pencil (4H) mark the mid point of left hand edge (X1). And do the same for the right hand edge (X2). Mark the mid point of top edge (Y1) and the mid point of bottom edge (Y2).

Draw a horizontal line from X1 to X2. And a vertical from Y1 to Y2. Mark the intersection wih W1.

Measure 9" from W1 going left and mark the point W2. Place your set square on the horizontal line at W2 and draw a vertical line 3" long up the page. Turn the set square upside down and draw another 3" line downwards.

Repeat
this again measuring 9" from W1 but going right. And very soon you can
complete the new rectangle. Now draw all the horizontal lines as shown.
There are five altogether.

All lines can be drawn with a light 4H pencil for now.

Next draw the pergola rafter tails shape. Which is made from straight lines only. I call this the Outline Template.

To do this draw over the lines AB and BC using a darker pencil (HB) this time. Draw FE and ED in darker pencil (HB). Leave AF in 4H pencil. Draw a line from C to D very faintly using 4H pencil. You may wish to erase all the faint lines now before the third stage except for CD.

Mark the point "O" half way between C and D. M1 and M2 are midway points between DO and CO.

Use the set square and a light 4H pencil. Draw a long perpendicular line - to the edge of the paper - from M1. Next adjust your compasses to 6" (W=6"). Place the point on D and make a small arc to cut the perpendicular line you have just constructed.

Keep the compasses setting 6" ( W=6") but now using the darker HB pencil place the point at the new intersection point. And draw an arc between D and O. Do the same for the point M2 using 4H pencil to begin with and HB pencil for the arc.

[If the compasses can't stretch to 6" release the pencil and slide it up so the compasses are holding it at the very top. ]

*[For a 7" width adjust the compasses to 7" (W=7") ]*

Erase all your construction lines (4H pencil) and there you have it. A beautiful pergola raftertails template.

For a simpler way to construct curves try the Circle Method using 6" as your radius.

Draw a Radius 6" circle on card. Cut the circle out. And move the card into Position 1. So it passes through D and O. Using an HB pencil draw the arc from D to O. Change to position 2 and do the same with the arc CO.

Now The Compasses Method - If you like a challenge!

First - construct the perpendicular bisector of the lines CO and DO.

You may remember some of this from high school.

Make your construction lines faint if you want to erase them later.

1) Open your compasses to about 3/4 of the length CO [ say 4"].

2) Place the point of your compasses at C and make an arc.

3) Without adjusting the compasses place the point at O and make another arc as shown.

4) Where the arcs cross draw a line.

5) Repeat for the line DO.

You're now going to draw the two curves. Which will give the **characteristic classical** effect we're looking for.

Instructions. 6) Open your compasses to 6" - the rafter width measurement. This is "w" in our top drawing. 7) Place the point of the compasses at C. And scribe a small arc to cut the perpendicular bisector. |

8) Keep the same compasses setting, place the point at this intersection. And carefully scribe an arc from C to O.

9) Using the same compasses setting place the point at D. scribe a small arc to cut the perpendicular as shown.

10) Once again place the point at this intersection. And carefully scribe an arc from O to D.

All sizes can be found at Pergola Rafter Tails Sizes.

Carefully cut out the design. And trace it onto thin plywood or hardboard. Use a jigsaw cut out your classical pergola rafter tails template. And transfer this shape onto each of your rafters. |

Your Pergola Story?

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