Dome - Outer Skin Profile
Dome Profile as Defined on the 20th Century Fox Blueprints
According to Dwg. No. 60, the dome outer skin profile is defined on Dwg. No. 33 which has not yet been published.
The dome profiles on the ANH elevation views and the dome profile on the ESB drink tray blueprints are very likely trace overs of Dwg. No. 33. All of these drawings define an ellipse that sitting directly on the head race that has a major diameter of 10-5/8" and a minor diameter of 9-1/4". The major diameter is composed of the dome itself with a height of 10-1/2" and the 1/8" gap between the dome and the race.
The actual construction of the dome profile from the major and minor axis would likely have been done using one of two tradition drafting methods.
The four circle method creates an approximation of an ellipse exclusively using only compasses. The complete ellipse is built up from four circles. This method is an approximation and varies from a true ellipse by a about 1/64" at a couple of locations along the length of the curve.
The French curve method creates an approximation of an ellipse using a compass and a French curve, This method is an approximation and varies from the true ellipse an amount depending on how many point samples are created as passing points for the French curve tool.
Dome Profile as Defined by Peteric Engineering
Dr. David Watling of Peteric Engineering in an interview with Brandon Alinger recounts "We were provided with drawings for the body of R2 and plaster moulds for the head, leg and foot. The mould for the head was cast in a studio lamp reflector. The reflector used was slightly damaged which accounts for the dent in the mould, we were told not to copy the dent." The photos of the mold shows the extent of the damage that was at the top of the reflector.
Dome Profile as Defined by a fiberglass ESB production dome
possible shape changes due to rubber mold
Regardless of the actual construction of the curve on the print, even in 1976, an aerospace spinning shop would have had the capability of creating an exact mathematical conic ellipse given the major diameter and minor diameter. The OpenR2 ANH spec will define the outer skin as a revolve of a true mathematical ellipse with a major diameter of 10-5/8" and minor diameter of 9-1/4".
This comparison shows the geometry that was likely produced by the spinning shop superimposed on what would have been a second generation fiberglass cast from the aluminum spun dome. The slight "bulging" around the center of the fiberglass cast could be a result of the casting process if a rubber mold had been used.