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As we can see the max thrust thrust each F119-PW-100 (engine used by F-22) can produce 155.7kN or 35,000 lbst of thrust with full after burner hence the total combined thrust 70,000 with after burner. Without after burner each engine can produce 97.9kN or 22,000lbst of thrust hence total output of 44,000 lbst
Now MTOW for F-22 is 83,500 lbs. Now we can calculate its thrust to weight ratio at this weight
With after burner
70,000/83,500 = 0.8383 ≈ 0.84
Without after burner
44,000/83,500 = 0.5269 ≈ 0.53
Now lets calculate the theoretical maximum thrust to weight ratio ( Only empty weight and nothing else). Its empty weight is 43,340 lbs
70,000/43,340 = 1.615
This is just the theoretical maximum T/W ratio of the F-22 which is of no use but i still wanted it include it anyways
Now lets calculate its thrust to weight ratio at 50% fuel with full air to air loadout with a pilot
In full air to air loadout it can carry 6 AMRAAMS and 2 AIM-9X so the weight would be around 2,318 and lets approximate it to 2,350 for the pilot as well
The F-22 can carry 18,000 lbs of fuel and 50% for it would be 9,000 so the total misc. weight would be 11,350. So the total weight of the F-22 would be 54,690. Now lets calculate thrust to weight ratio
With after burner
70,000/54,690 = 1.27
Without after burner
44,000/54,690 = 0.804
This gives us a range for thrust to weight ratio at minimum of 50% fuel to be 1.27 to 0.8. As the payload increase the weight would also increase and hence decreasing the Thrust to weight ratio
If something is wrong with my calculation or anything else i would appreciate it if you guys can point it out