How to adjust the center of gravity of an aircraft if not level when being weighed?

how do you adjust the center of gravity when weighing an aircraft in not-leveled position using platform scales under the nose and the main gears, and dropping a plumb bob to mark the gears locations.

I drew in the approximate location of the screws used to hold a level while leveling the Cessna Cardinal for weighing.

When my plane was weighed, they had to lower the nose by deflating the nose strut some, and raise the main gear, to get the aircraft to the level position indicated by the manual, with a level across the leveling screws on the side of the fuselage. I don't know that there is a procedure to weigh it in a not-level position.

• Is the question how do you level it, or how do you adjust the center of gravity? Those are two different things. Commented Jan 10, 2020 at 15:49
• Doesn't lowering the nose and raising the mains adjust the center of gravity? I would expect that to move it forward. Along with having full tanks, which are in front of the main gear. Commented Jan 10, 2020 at 15:57
• No it doesn't matter how you drop the nose or prop up the main gear as long as the airplane's longitudinal axis is level. Commented Jan 10, 2020 at 16:46
• sorry, I think I didn't ask the question correctly. I am tasked with weighing a fixed wing ATR 42 cargo aircraft. The leveling points on the cargo door of the aircraft are damaged. So I need to weight the aircraft without leveling. I am going to find a place on the aircraft to use an inclinometer to read a pitch angle and then generate some math to adjust the cg. I just was wondering if anybody has done that kind of weighing.
– Mike
Commented Jan 13, 2020 at 2:17

As Crossroads shows, the data provided for W&B calcs is based on a level fuselage. If the fuselage is not level, you would need to do some math to calculate adjustment factors for the wheel weight values, and to do that you would also need to know where the vertical C of G is. Good luck with that. So there's no work around that I've ever heard of, and you're kind of stuck with leveling the aircraft properly.

Just to put it into perspective:

$$Sine$$ 4 degrees × 100 = 7 % grade

$$Cosine$$ 4 degrees x 100 = 99.75 % of perfectly levelled scale.

So unless your scale is on a fairly steep mountain grade, your main concern, if any, is to level the plane. It would seem to be much easier to use a block and a bubble, with an appreciation of the fact that the "ball" inclinometer instrument in your aircraft works exactly in reverse, seeking the "lowest" point instead of the highest.

The alternative would be plum-bobs and a lot of math. However, with spreadsheets such as Excel, it would make an interesting project.

Keep in mind pitch (within reason) does not affect center of gravity. The torque arms will shorten proportionally. The plum-bob tells you where to set the scale. Formulas in your spreadsheet can be validated by checking results at various pitch angles for each aircraft.

Validation is highly recommended for an application as crucial as CG.