I previously designed a 1-2 person lightweight tarp for camping trips.

Criteria

  • Sleep two people
  • Weigh

In this layout, the constraining factor on the size of the pyramid is the height of each triangle, or the slant height of the pyramid. By the pythagorean theorem, this is
$$
slantheight = \sqrt{inradius^2 + height^2}
$$
and the inradius in turn can be found by
$$
inradius = \frac{sidelength}{2*tan(\frac{180^{\circ}}{5})}
$$
Setting this expression equal to the width of the fabric, 62", gives the following ellipse, where x represents side length and y height:
$$
\sqrt{(sidelength/1.453)^2 + height^2} = 62"
$$
tarpcircle
Each point on the ellipse, then, represents a possible tarp that maximally uses a roll of fabric. Obviously only the first quadrant makes sense. From here it's a matter of preference, but I picked the point (~77", ~32") for my tarp.

Catenary curves

Gluing and sealing

The fabric I chose is impregnated with silicone. I swung by the hardware store to pick up a tube of curing silicone (I got GE Silicone II) and some mineral spirits with which to thin it. There are commercial seam sealers on the market, but I found them too thick and expensive.
20180817_194657-01

All the seams are flat-felled.

The hem and hardware
20180820_182555-01-01

Testing

I took the tarp up on an overnight to Tank Lakes with my sister. There was no rain, so it's anybody's guess how effective