You seem to assume a zero length runway; and the distance from the takeoff point after 1nm, 90 deg turn, 1nm is 1.414nm not 2nm...
With a runway of nearly 1nm long, a takeoff run in the low 100s of metres or less, and a bit of headwind, the crosswind turn could well be barely beyond the end of the runway; the downwind turn moments before the downwind call abeam the upwind threshold. That's how it is where I fly, tight circuits at a military base.