PPRuNe Forums - View Single Post - Exam Question about Weight, Balance and MAC
Old 25th August 2009 | 00:18
  #11 (permalink)  
john_tullamarine
Fleet Manager
25 Anniversary
 
Joined: Apr 2001
: ATPL
Posts: 7,448
Likes: 310
From: various places .....
I'm not familiar with this "FS" acronym. What does it stand for?

For W&B work, the easiest way to think about arms is to consider a datum being some place where you can hang your tape measure on a nail tapped into the side of the aircraft. The scale reading on the tape measure gives you the arm of the location (fore and aft of the datum in all cases - and sideways from a separate lateral datum for rotorcraft).

Fuselage Station is the usual longitudinal scale used by the OEM to define locations along the aircraft and, usually, is just a linear scale along the aircraft starting at the OEM's declared datum.

Note that the datum is just some declared position and has no intrinsic significance ie you can use a datum different to the OEM's if you chose and this is quite the typical circumstance with trimsheet design. Likewise, in ft's solution earlier, he chose to nominate a datum position at the LEMAC.

I can't quite grasp the understanding of finding the CG by dividing the total moment with the total mass.

ft's explanation might be a tad involved for your question unless you are comfortable with algebra. The following says much the same but puts a slightly different emphasis on it.

Basics for working out a centre of gravity (centre of mass, for the purists) are -

(I'm presuming that you are reasonably comfortable with (a) through (d) but it is convenient to review the material for completeness)

(a) we are looking for some position which can be thought of as a balance point for the whole aircraft

(b) if we could (and most times that is impracticable) put a pivot at this point, the aircraft would balance, ie not tip one way or the other. In physical terms this means that there is no leftover tipping tendency. The buzzword we use for "tipping tendency" is "moment" but it doesn't matter which term you use.

(c) it follows that (b) requires the total tipping tendency one way to be the same (size-wise) as the total tipping tendency the other way.

Working this out is the purpose of the normal moment sum we do when calculating W&B longhand. It would be just as valid to replace the pluses and minuses with two columns labelled something like "nosedown tipping" and "noseup tipping" - indeed, on some standard calculation forms one sees two separate columns for + and - which harks back to the olden days when we used to do it all longhand.

For the purpose of thinking about tipping tendency, we might consider the datum to be the point at which we put a pivot point for the calculation ...

(d) now, unless you happen to be very lucky, and guess a position for the datum which coincides with the CG (when you would cancel all the moments out), you are most likely to end up with some residual, or left over, moment.

(e) we now need to figure an arm from the datum to a position where a load equal to the total aircraft weight would give a moment sufficient to balance the residual moment. Why is this important ? .. because, if we then moved the datum to this position and redid the sums, then we would end up with no residual moment .. ie we would be at the CG.

(f) we could figure this position out by trial and error along the lines of -

total aircraft weight x trial and error arm = residual moment

and eventually end up with the answer ... or,

using a basic algebraic technique (transposition) we can figure the arm directly by reworking the equation to a similar form

arm = residual moment/total aircraft weight

and this arm is the CG.
john_tullamarine is online now  
Reply