I’ve worked sprang without a loom, trying different methods.
Well, to begin, here are two frames that I like for the ease of construction and minimal cost.
The first is very like an Archie Brennan frame.
It’s plumbing pipe, elbows, threaded rod and nuts.
At the hardware store, if you ask for half-inch pipe, also ask for half-inch threaded rod.

Plumbing pipe sprang frame

Now, you might want to duct-tape the elbow joints to the plumbing pipe, to avoid the disaster of those joints coming loose while you work. The beauty of this frame is the ease with which you measure out the warp directly onto the frame. The tension adjustment is with the nuts on the threaded rod.

A student brought another frame to a sprang class. I’ve found a local woodworker who will make more of these frames.

Another sprang frame

detail of frame construction

Either of these frames can be adjusted as the tension in the cloth increases. You can also purchase different lengths of dowel or plumbing pipe to accomodate longer warps.

Now for the No-Frame ideas.

Weaving a hat, backstrap method

The upper bar was laid across a table top.Chairs were placed on either side of me, pushed up tight to the table. They held the bar in place. The lower bar (chopsticks) were tensioned backstrap method.

For longer warps, I’ve been known to attach to my kitchen door. Here I’m working on a pair of socks, two socks created at the same time. I work at a comfortable height, and shove each row upwards and then downwards.

Working sprang without a frame, using a door

When the work progressed and working height became uncomfortable, I transferred the attachment site to a hook in the wall. Tension in both cases was provided by my feet.

The work continues, sitting on a chair