NavList:

For a low altitude observation ~ 0° the radius of the circle is 5,400 nm. The circumfrence is 33,929 nm so one degree along that circumfrence 94 nm. From where would you plot that azimuth? You can't do it from your AP but must do it from the GP. The scale errors would not allow much accuracy. However, you can establish an "Estimated Position" or MPP, Most Probable Position, by dropping a perpendicular from the DR to the LOP. However this is NOT a fix since any error or uncertainty in the DR is carried forward onto the MPP. If you use your DR as your AP (Bygrave slide rule, HO 211, HO 208, etc. but not HO 249 or HO 229) then the intersection of the azimuth line with the LOP is automatically your MPP. In flight navigation it is standard to allow for a DR error of 10% of the distance flown but I have never seen a similar estimate for DR uncertainty in marine navigation.  But using this estimate, then after a day of sailing without a fix the uncertainty circle would be about 12 NM radius so you can mark out along the LOP that estimate both to the right and left of the MPP and you are unlikly to be further out along the LOP. And you should remember that the LOP is thick, about 1.5 nm on each side of the plotted line to allow for commonly accepted accuracy in celestial observations. 

gl