No reason an asymmetrical flatbow/longbow would not work as good as an asymmetric recurve. The Yumi bow that symbolized the samurai is majorly asymmetric.
Remember too that "long" is relative. Many of the tribes of the Pacific Northwest used very short (as little as 36") Paddle Bows (so called from their general shape).
Can you afford
2 pieces 1.5" black glass @ $9 per piece = $18
Pint kit of Smooth On = $18 (makes several bows)
Straight length of 2x2 = $5
Masking tape + $4
Wood lams from me -- free
Oh... and you'll need a used bicycle innertube from your local bike shop.
Here's a picture of a fiberglass flatbow I made as a prototype. Two pieces of .04 fiberglass and a piece of scrap pine. 58" long, 56# @ 28". Shoots just fine. That 2x2 alongside the bow is what I used as a form. We can make you something similar about 40" long.
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