MO, how are you making out? I threw some numbers around just for fun. No "right" or "wrong" here; I made assumptions about some of the dimensions by putting my electric eye on your drawing. Dimensions are in decimal inches.
Assuming: The curve of the ellipse is 8 below the bottom of the collar tie and 8 in from the post (measured along the tie beam). The line of the joint below the rafter is perpendicular to the rafter and 102 down from the rafter peak as per the drawing. Again assuming the ellipse is 8 from the rafter as measured along this joint, the the ellipse passes through a working point 101.65803 horizontally from center and 71.85423 above the tie beam.
Shooting an ellipse through these points:
Semi-Major Axis on the x-axis = 153.25949
Semi-Minor Axis on the y-axis = 115.81764
Note that the major axis actually lies 14.81764 below the upper face of the tie beam.
A scale drawing produces a curve which is reasonably close to that shown on your drawing. The trouble is that cutting the four curved sections from 14 wide stock will whittle them down to toothpicks. (I'm trying to maintain a minimum depth of about 8 inches). Moving the working points around doesn't accomplish much. So ... make the arch out of more pieces????
I'll try to post a scan of my sketch tomorrow.