What is Counter-Rake?
The thingy you’ve gotta build lies diagonally across a raked deck. How do you figure out the length, angle and bevel; so it sits vertical? Counter-Rake !
How to determine the counter-rake by compass and straightedge construction
Erect these five references
1- Horizontal reference
2- Vertical reference
3- Rake (2″ in 1 foot- in this example)
4- Parallel to rake line (at the width of flat)
5- Parallel to the vertical Reference (at the width of flat)
On those references erect these four lines
6- From the rake line at A, draw a line at the known angle athwart the rake (from the layout – 22.5º in this example); of sufficient length to cross 5 (or 4) – The distance AB is the length of the counter-rake.
7- Strike an arc of length AB from C (an arbitrary point convenient usually at 1-1/4 times the width of the flat away from A – to avoid entanglement) to intersect the rake line parallel.
8- Draw the line CD from the center of this arc to where it intersects the parallel (#4)
9- Erect a perpendicular from the center of arc to the parallel (#4)
The angle between this perpendicular and CD is the angle of the counter-rake. The smaller angle between #2 or #5 and a perpendicular to line AB (at A or B) gives the edge bevel for the flat.
Round numbers are given for this example, however, no calculation is required. In actual practice the numbers actually needed are often not remotely round.
The entire procedure may be performed, and the resulting length and angles, may be obtained and transferred to the work using only a beam compass, a straightedge and a bevel gauge. The procedure may be performed full size or at any convenient scale. Remember, however, that at 1/4″ – 1′-0″ scale a 1/16” pencil line is nearly 1″ wide; which can affect the results.
Note: If the rake you are dealing is a compound rake use the preceding construction to obtain the “true dip” (actual slope) for your counter-rake calculation.