I am tasked with weighing a fixed wing aircraft. the aircraft can not be leveled because the leveling points are damaged. therefor it is going to be weighed not leveled, an inclinometer will read a pitch angle and three scales will read the reaction from the LH and RH mains and nose. after the reactions are known and the pitch angle is know, how can I correct the cg for a leveled aircraft.
You have a problem because you would have to know where the vertical center of gravity is to be able to mathematically calculate a correction factor to apply to the weighing points. The higher the vertical C of G is, the more rear weight bias you will get if the plane is nose-high from level, or front weight bias if nose-low. How much to allow for? You don't know.
When the plane is level, it doesn't matter where the vertical CG is. You would be better off finding some other part of the structure that is aligned with the longitudinal axis from drawings or the maintenance manual, typically something like an upper fuselage longeron, to level the airplane.
Aassuming that the CoG is in the center line of the aeroplane, you can derive the leveled CoG if you use an inclonometer, but you would have to measure this at two different angles. Then simple high school triangulation would result in the CoG reading.
That is for a very accurate determination. If using only one measurement at an angle, there will be a measurement arror introduced by the vertical location of the CoG, proportional to the cosine of the inclonometer angle:
- cos 0 (level) = 1.0, no error from vertical variation of the CoG.
- cos 1° = 0.999985, an error of 0.015% times variation of vertical CoG distance.
- cos 5° = 0.9962, an error of 0.38% times variation of vertical CoG distance.
Not huge. I don't know what the required precision is for determination of the CoG, and what the upper/lower possible vertical CoG limits are; these would be used in calculating the tolerance of the single CoG measurement at a known angle.