I was trying to figure out if the navigation size was the best ratio for users. The best way I had to test that was by using a tester! I kept the navigation size the same in both instances, I simply worked with how large the screen was projected on the wall. Based on these tests, I believe that the smallest the speculative should be projected for the knob to be adequately used is 66 inches by 105 inches ( 5.5 feet by 8.75 feet).
tested screen for size.
projected at a height of 48 inches and 76 inches wide.
close up of 48 inches height, hand closed is about 1/2 of the knob's width.
projected at a height of 66 inches by 105 inches wide.
close up of 66 inch height. closed hand is 1/3 to 1/2 the knob's width.
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