The three speed regimes
A bullet's flight passes through speed regimes defined relative to the speed of sound (Mach 1, about 1125 fps at sea level, varying with temperature). Supersonic (above ~Mach 1.2) is the bullet's happy place — stable, predictable, the regime your DOPE is built in. The transonic zone (roughly Mach 1.2 down to Mach 0.8, about 1340–900 fps) is the danger zone, where the airflow around the bullet shifts from fully supersonic to subsonic unevenly and the bullet can be buffeted and destabilized. Subsonic (below Mach 1) is stable again but by then the bullet is slow, dropping steeply, and has usually lost the energy and precision you care about.
Why the transonic zone wrecks accuracy
As the bullet decelerates through transonic speeds, the shock wave around it becomes unstable and asymmetric. Small yaw motions that were damped at supersonic speed can be amplified; the center of pressure shifts; the bullet may begin to wobble or "go to sleep" poorly. The visible result is groups that suddenly open up — a load that holds tight sub-MOA at 800 yards might scatter to several MOA at 1100 as it enters transonic, with increased vertical and horizontal dispersion that no wind call explains. Crucially, this is also why you don't true your solver in the transonic zone (ab-01): the drop data there is erratic and fitting a solution to it produces garbage. Some modern, very-high-BC bullets transit transonic more gracefully than older designs, but the general rule stands: precision degrades in the transonic region.
Finding your transonic distance
Your transonic distance is where the bullet decelerates to roughly Mach 1.2 — the practical edge of reliable precision. It depends on muzzle velocity, BC, and air density (DA), so it's specific to your rifle, load, and conditions, and it moves: thinner air (high DA) keeps the bullet supersonic longer, pushing the transonic distance farther out; dense, cold air brings it closer. A solver reports the velocity at each distance — find where it crosses ~1340 fps (Mach 1.2) and that's your practical precision limit for the day. Example: a 175gr .308 at 2600 fps might go transonic around 1000–1100 yards in standard conditions and noticeably farther on a hot, high day. Higher-BC cartridges (6.5mm, 6mm, the magnums) push transonic much farther, which is a large part of why they're chosen for ELR.
Defining your maximum effective range
"Max effective range" is not where the bullet can reach — it's the farthest distance at which you can reliably deliver the hit the target demands, accounting for the rifle, the load staying supersonic, the energy required, and your own skill. Bound it by the most limiting factor: usually whichever comes first of (a) the transonic distance, where precision falls apart; (b) the range where retained energy drops below what the target requires; and (c) your personal ability to read wind and hold under field conditions. For most precision rifles, staying supersonic is the binding constraint, so your honest max effective range is at or just inside your transonic distance. Know that number for your rifle and conditions, log how it shifts with DA, and don't take a first-round-hit shot past it expecting precision — beyond your max effective range you're rolling dice, and the marksman's whole discipline is to not roll dice.