Laying out a Prolate Ellipse
Often we are asked how to lay out the foundation for a prolate ellipse. Some people want to have their Monolithic Dome home shaped as a prolate ellipse. One reason people might want this design is because they have a narrow lot and need to squeeze the dome in the middle to make it fit. Sometimes they want the length of the dome to be longer so they get more of a look of what is on the outside of the building.
The layout for a prolate ellipse dome is a bit tricky. Obviously, when laying out a circle you simply drive a stake in the middle, measure out the radius and go around in a circle.
But when you are laying out a prolate ellipse, you have to have two points at what are called the foci (F1 and F2 on the diagram). The foci are along the center line of the prolate. Then you have to put a measuring device, like a tape attached to these foci, at the right distance. Finally, with a pencil, a pen or a screw driver you simply pull that tape around in a full circle and it will mark out the edges of the prolate.
Instructions for Laying out a Prolate Ellipse on the Ground
- Verify distance between the end points of the major axis
- Calculate x
- Locate the center of the long axis
- Measure from center along the axis using calculation of x to points F1 and F2
- Stake F1 and F2 on the major axis
- Attach a non stretchable tape between F1 and F2 that is exactly the length of the major axis
- At the center of the tape pulled to either side of A axis will be end points of B axis
- Measure length of B axis for check
- Use rod or pencil in loop of tape to trace the outline of the prolate ellipse
Remember the definition of an ellipse is that every point on the perimeter will be at the sum of the distance from F1 and F2 when added. The added numbers will be equal to the length of A axis.