4 Ogee Offset-No Seams

Study the shop drawing. Remember that the first number for the duct size is always what we “see in the view”. The second number is the depth, or hidden view.

1. Cheek- If we look vertically at the opening size of 4” and the offset of 3”, the dimensions total 7”. The length is given at 7”. So our blank size is 7” x 7”.
   
2. For the wrapper, we use a very specialized formula: (4x(√O²+L²)-L)/3. In our case, we get 7 13/16”. The second dimension comes from the depth, which is given at 6”. That gives us a blank size of 7 13/16” x 6”.
   

1. Geometric Construction Method
   • Draw a center line from end to end
     
   • Divide that line into 4 equal parts (using ruler on a diagonal) and number the 3 points
     
   • Create perpendiculars from points 1 and 3 aimed towards the offset
     
   • The point where the perpendicular lines cross the outside of the blank size becomes the radius point for the arcs
     
   • From these 2 points, set your compass to the inside and outside of the opening and swing arcs. A note: if you draw a diagonal line from radius point to radius point, this line will indicate where the lines transition along the ogee curve
     

2. Math Method
   • Using the formula (O² x L²)÷(4 x O) we will calculate a radius point at 6 1/16”
     
   • Measure this distance vertically towards the offset, from the center of the opening.
     
   • This point becomes our radius point. Set your compass to the inside and outside of the opening and swing arcs. A note: if you draw a diagonal line from radius point to radius point, this line will indicate where the arcs transition along the ogee curve