Thrust-to-Weight Ratio

Thrust-to-weight is the crudest question in rocketry and the first one that has to be answered: is the engine stronger than the vehicle is heavy? Below 1 the rocket sits on the pad and burns, which has happened, and the result is expensive. Above 1 the excess is what accelerates it, and the net upward acceleration is $(T/W - 1) \, g$ — a vehicle at 1.5 climbs away at half a g while its occupants feel one and a half.

This is the one formula in this whole shard where LOCAL gravity is the correct number. Everywhere else, $g_0$ is a defined constant of 9.80665 m/s² doing unit conversion. Here the question is genuinely whether the engine beats the gravitational field it is actually sitting in, so a lunar lander uses 1.62 m/s², a Mars ascent vehicle uses 3.72, and the same engine and the same vehicle produce completely different answers on different worlds. A lander with a thrust-to-weight of 0.6 on Earth has 3.6 on the Moon and flies perfectly well.

Higher is not better. Launch vehicles typically leave the pad between 1.2 and 1.5, and the reason for that narrow band is a trade between two losses that pull in opposite directions. Too low, and gravity losses mount: every second spent barely climbing is delta-v spent holding the vehicle up rather than accelerating it, and a vehicle at 1.05 wastes most of its propellant simply not falling. Too high, and the vehicle reaches high speed while still deep in the atmosphere, where drag losses and aerodynamic loads climb with the square of velocity. This is why first stages throttle DOWN through the region of maximum dynamic pressure rather than accelerating as hard as they can.

Read the ratio at the right moment. It is worst at ignition, when the vehicle is heaviest, and improves continuously through the burn as propellant leaves — a stage lifting off at 1.3 can be pulling 3 or 4 by burnout, which is what sets the structural design case and the crew acceleration limit. And a ratio below 1 is entirely normal for an upper stage or an orbital transfer engine, because in orbit there is no ground to leave and a long, gentle burn is perfectly efficient.