This flapping paper plane folding method I am learning from a college student over ten years ago.
It happen at a Physics class, a paper plane competition. Tens of paper plane throw out altogether, one of them not fly too far but draw all students and my attention, because the paper plane flapping like a bird in the air!
I catch that student and teach me how to fold it. He say the folding method learn from the internet, but the page not mention it will flap. I have lost that web page but I guess this folding method designed before internet born.
Step 1: Prepare a A4 Paper
Any A4 paper should work, recycling paper preferred. In my experience, 80gsm is a bit too light, 100gsm or above is better.
Step 2: Fold in Half
Step 3: Fold in Half Again
Step 4: Same Fold in Other Side
Step 5: Turn a Right Angle
Step 6: Fold in Diagonal
This is the most difficult step, it can help by drawing a diagonal line with ruler before folding.
Step 7: Flip Horizontal
Step 8: Same Fold in Other Side
Step 9: Fold a Triangle at the Corner
Step 10: Same Fold at the Other Side
Step 11: Flip and Turn a Right Angle
Step 12: Fold in Half
Step 13: Fold 2 Upper Corner
The folding angle for the corner is a little bit arbitrary, but you can see a straight line from the upper and lower triangle after the fold.
Step 14: Fold Lower Triangle Up
Step 15: Flip Horizontal
Step 16: Fold the Triangle Down
Step 17: Fold in Half
Step 18: Fold Out the Wing
The fold out portion is arbitrary, just the size that your fingers that can hold the paper plane body.
Step 19: Flip Horizontal
Step 20: Same Fold in Other Side
Step 21: Done
keep the wings in v-shape
Step 22: Hold the Paper Plane Method
Use 2 fingers hold the paper plane body thickest part, check the wings in v-shape and at the same angle.