A circle, not the driver, is in charge here. Fix the steering wheel at a steady angle, hold the throttle so the speed stays roughly constant, and the boat settles into what physics calls uniform circular motion, a regime where every point of the hull keeps turning through equal angles in equal intervals of time.
The counterintuitive part is that precision seems to appear from nowhere. In reality it comes from centripetal force, the inward force that constantly redirects the boat’s velocity so it bends into an arc rather than shooting straight, and from the hydrodynamic side force generated by the hull and rudder as water pushes back against their deflection.
Once those forces balance, geometry stops being negotiable. For a given speed v and a fixed steering angle that sets an effective lateral force, the turning radius R locks to the textbook relation a = v^2 / R, where a is centripetal acceleration, so keeping v nearly fixed keeps R nearly fixed as well.
Human perception then finishes the trick. Small ripples, minor throttle variations and slight steering play only create gentle wobble around that stable radius, yet from above the wake reads as an almost perfect circle, plotted not by intention but by the quiet rigidity of Newtonian mechanics.
