Friday, June 20, 2014

Rake Crown Moulding Geometry

The proper way of installing exterior rake crown moulding is with three different crown moulding profiles.(Source: Gary Katz) One for the level-horizontal crown moulding at the bottom of the rake, one for the rake and one for the crown return at the top. The main difference between Rake Crown Moulding with Three Different Profiles and Rake Crown Mouldings with No Transitions is the crown projection from the vertical wall. Both styles have crown mouldings that have different spring angles as each face is turned in a vertical or horizontal plane. The second difference is the crown moulding profile. With Rake Crown Mouldings with No Transitions, mainly meant for interior MDF crown moulding, there's only one crown moulding profile. The exterior gable rake crown moulding with different profiles can use 2 or 3 different crown moulding profiles.

The difference between Rake Crown Moulding with Three Different Profiles and Rake Crown Mouldings with Transition Pieces is the transition piece used to turn the crown moulding in different horizontal and vertical planes. The crown projection from the vertical wall, run dimension, stays the same for some of the crown moulding, but not all of the crown moulding. Crown moulding from an horizontal to rake crown moulding will have the same  crown projection from the vertical wall, however rake crown moulding to a horizontal crown moulding will not have the same crown projection from the vertical wall.

Todd Murdock pointed me in the correct direction for developing the geometry for different rake crown moulding profiles and Gary Katz at  is preparing an article by Jed Dixon, Keith Mathewson, and Todd Murdock for developing the three different crown moulding profiles for rake crown using moulding planes-knifes for cutting the profiles.
Link to the article

Here's a couple of pictures and text from an article  published in Building Age in 1929. This was common knowledge before World World II and is in most of the carpentry books published before the  production housing boom after the war. 

Mitering Rake and Level Mouldings
School of Science and Technology, Pratt Institute, Brooklyn, N. Y.

A RAKING moulding is a term used for mouldings which are inclined ; as, in a gable, a moulding following the pitch or slope of the roof. To make a miter between a rake moulding and a level moulding, the profile or outline of one of them must be modified in order that the joint may be made. The cut for the level moulding is an ordinary miter cut or angle of 45 degrees. The cut for the rake moulding is the same as a jack rafter top and side cut. These cuts can best be made in a miter box using either the graphic method or the steel square method.

Richard M. Van Gaasbeek makes the statement "The cut for the rake moulding is the same as a jack rafter top and side cut.". This is true when the rake crown moulding is cut in the nested position in a miter box or compound miter saw with the top edge of the crown moulding against the fence of the miter box or miter saw. The nested crown moulding creates the compound cut that is same as cutting  jack rafters. Cutting horizontal crown moulding nested is the same as cutting purlins or square tail fascia. The top cuts are the same, but  the side cuts are not the same.

All nested crown moulding cuts in the horizontal plane, with the bottom edge of the crown moulding nested against the fence are the same as purlin or square tail fascia cuts.

All nested crown moulding cuts in the vertical plane, with the top edge of the crown moulding nested against the fence are the same as jack rafter cuts.

Developing the actual crown moulding profiles is not that easy in Google - Trimble SketchUp. Here I've used the three different crown moulding profiles shared by Todd Murdock at JLC Finish Carpentry. I've rotated the crown moulding profiles in to the position that would have been used to draw - develop the profiles using geometry. The one constant used in developing the three different rake crown moulding profiles is the vertical projection from the wall. The vertical projection from the wall is the "run" dimension used to calculate the spring angle of the crown moulding.  The "rise" dimension will be different for each of the crown moulding profiles. 

Here you can see the run dimension for all three crown moulding profiles is 1 11/16" and the rise dimension for all three of the profiles are different. Resulting in different spring angles for each of the crown moulding profiles.

To develop the geometry for the rake crown moulding start by drawing Face A, horizontal crown, using the dimensions of the horizontal crown moulding. Then draw a line using the roof slope angle. Next develop Face B, rake crown, by drawing a line perpendicular to the roof slope line and using the same "run" dimension for the top of the crown moulding. For the third crown moulding, Face C, that is horizontal crown draw a line that is plumb or parallel to the back side of Face A. Again use the same "run" dimension for the top of the crown moulding Face C.

Next, develop the geometry for the folded out roof surfaces for the crown mouldings to determine the miter angles of each piece. The yellow area in the drawing uses the "run" dimension for the plan view of the crown moulding profiles.The crown slope angle of each of the profiles is used for the roof slope angle for developing the profile rafter length for each of the roof surfaces. The red triangle  in the drawing is the hip rafter and the miter angle for Face A is the same as the jack rafter side cut angle. For Face B in blue the jack rafter side cut angle is not used. You have to develop a line in the blue triangle that is equal to the same length as the hip rafter length in the red triangle. Swing an arc from the CP point in the drawing, using the radius equal to the length of the hip rafter in the red triangle. This will locate a point that is tangent to the base line of the blue triangle.  Draw a line from the tangent point  back to CP point. This line will determine the miter angle for the bottom of the rake moulding. Use the same arc-circle technique for the miter at the top of the crown moulding return. 

To develop the miter angle for the rake crown moulding at the peak of the roof, use the roof slope angle to draw a triangle using the "rise" dimension of Face B for the one leg of the triangle. Where the roof slope angle line intersects the base of the roof surface draw a line as shown to determine the miter angle on Face B at the peak of the roof.

Another example of the geometry used to determine the miter angles for a roof slope angle of 42.00° and a spring angle of 42.00°. The one miter angle at the bottom of the rake moulding is equal to 0.00°. I tested the CrownMoldingTools app on my current task model that's not finished. Since the crown spring angle is equal to the roof slope angle the horizontal crown moulding is the same as square tail fascia.

Crown Molding Tools

These compound cuts were anything but obvious, and changed with every roof pitch. Using mockups and trial and error, we eyeballed our way to some surprising ....
AUGUST 2008 l JLC l 4
21st-Century Greek Revival by Trevor Kurz

Finding Profile of Raking Molding.
From J. Q. F.—I would like to know whether you have heretofore published any Illustrations on the subject of raked moldings at half pitch similar In profile to that shown In the Inclosed sketch, and If so when. I should like to know the rules governing this problem, as I am frequently puzzled with it.

Answer.—We have In the past given more or less attention to the subject indicated, but as these volumes are now out of print we give a complete answer at this time. The sketch sent with the inquiry of our correspondent is that of a crown molding of ordinary profile, no plan or other view being given to show the adjacent arms of the miters which determine the desired result The problem in connecting with raking moldings which presents the greatest difficulty, however, is that in which an inclined molding is required to miter with a level return which is usually at right angles, it is sometimes at an oblique angle in the plan. We shall conclude, therefore, that this arrangement of parts is the cause of our error.

It is possible that the practical workman will prefer a method by which these results can be obtained without the use of drafting instruments. Such a method is not only possible, but quite practicable. To obtain the profile of the inclined or pediment mold shown in Fig. 2, let it be supposed that the fascia boards and the fillet of the level cornice below the pediment have already been cut and secured in position. First cut a piece of molding of normal profile to form the return P, cutting on its forward or right end an outside miter in the miter box in the usual manner, and fasten the same in position on the building as shown pictorlally at A of Fig. 4. Next cut a short piece of wood, say a foot in length, of rectangular profile, whose thickness shall exactly equal the projection of the mold as shown by 1 B of profile P1 Fig. 2, and whose width shall be equal to or even greater than the vertical width of the desired molding. Such a piece would have the general appearance of a short piece of studding dressed on all sides and may to called a blank. Cut a pitch board whose angle shall be that of the gable, and, having placed the same in the miter box with its vertex to the left, place the blank upon its upper edge and saw an outside miter; in other words, miter it to fit against the return piece A just as though it were the finished mold.
  • A Miter is a joint in a molding, or between two pieces not moldings, at any angle.
  • A Butt Miter is the term applied to the cut made upon the end of a molding to fit it against another molding or against a surface.
  • A Gable Miter is the name applied to the miter either at the peak or at the foot of the moldings of a gable or pediment.
  • A Rake Miter is a miter between two moldings, one of which has undergone a modification of profile to admit of the joint being made.
  • Square Miter is the common term for a joint at right angles, or at 90°.
  • An Octagon Miter is a miter joint between two sides of a regular octagon, or between any two pieces at an angle of 135°. 
  • An Inside Miter indicates a joint at an interior or re-entrant angle.
  • An Outside Miter is a joint at an exterior angle.

Here's an example of large rake crown moulding on Gary Katz's website that should be cut laying flat in the compound miter saw.

If the roof slope angle were 38° and the crown spring angle were 38°, then yes, the rafter tails are cut square (90°) to the surface of the roof or top of common rafter. The miter angle would be 0.00° and the saw blade bevel angle would be 56.14°.

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