Regardless of target orbit, how can I calculate the maximum weight one engine can lift?
If the raptor's TWR is 140 and its Thrust is 1.81 MN then:
W = F / TWR = 12,900 N ==> m = W / g = 1.3 tons
Not logical. If the super heavy has 39 engines... it could pick up only 50 tons...
What's incorrect here ?
As Uwe notes, Raptor 2's thrust is higher than the figure you gave, about 2.3 MN.
Thrust and weight are both measured in force units -- Newtons in metric, pounds-force in US customary units. 2.3 MN of thrust can lift 2.3 MN of weight. The gravity you're trying to lift against is the conversion factor between mass in grams and force in Newtons. Dividing 2.3 MN by Earth's gravity, 9.81 m/s2, yields 235000 kg.
Thus, each Raptor can lift 235 metric tons from Earth's surface, and a 33-engine booster at full throttle can lift as much as 7,755 tons.
That thrust is more than 150% of the Earth-surface weight of the 5,000 ton Starship/Super-Heavy stack, so it will lift off easily.
The other way you could calculate this is by multiplying the TWR of the engine by the engine's mass: 140 x 1600kg = 224000 kg. Presumably the difference is due to rounding-off of the TWR and engine mass figures.
The thrust-to-weight ratio is defined as a dimensionless number. Therefore the same unit should be used for both thrust and weight.
Raptor 2 has a thrust of 2.3 MN and the ratio is 140. A super heavy with 33 engines has a thrust of 75.9 MN. That is 7.737 metric tons. The total weight of the rocket is the dry weight of the rocket structure plus all fuels plus the payload.
