Aperture sights are capable of producing 1 moa groups, but the target needs to be larger. I have a rule of thumb-- magnification X target size in moa= 10-12 is comfortable. So if you use apertures, use a target about 4" at 40 yards.
The ten ring ring in ten meter target shooting is 0.5mm. Top competitors have then at most a 5mm c-t-c 60 shot groups at 10m, i.e less than 2 moa standing!