Weight/Balance

[Maxflyer]

I am nearly at the end of my PPL training. Flying has been all OK. Have taken all exams apart from flight perfromance and planning. I am currently reading the Trevor Thom study book on this and cannot get my head around the Mrces, Mments and Datums issue. Can anyone suggest any other study text or web site that may help this idiot?

Any help appreciated. Tim Johnson

[Genghis the Engineer]

The Operators Manual (the proper official one, not somebody else's unapproved version) will have a weight and balance section which should guide you through the process reasonably simply, I'd try that.

G

[Saab Dastard]

tmybr,

You aren't an idiot, you can't be if you can afford to fly! Then again, maybe we are all barmy shelling out so much for the £100 cup of coffee!

Anyway, I'm a civil engineer (or was) and statics used to be meet and drink to me, so I've written a few notes that you may find useful. Be warned - it's quite long.

A moment is a force multiplied by a distance.

Weight (mass x acceleration due to gravity) is one of the most familiar forces we deal with – it is easy to forget that it is a force.

So for weight and balance calcs, the moments we are concerned with are weights x distances.

Imagine two children on a 4m long see-saw. One is 15 kilos, the other is 30 kilos. How do we get the see-saw to balance? If they are both the same distance from the pivot (say 2m), the see-saw will sink to the heavier side. Now think of the moments – 2m x 15k and 2m x 30k or 30 and 60 – so it is obvious that the see-saw will sink to the heavier side, as the moment is twice as great as the other.

So to balance, the distance of the heavier child from the pivot must be half that of the lighter one – i.e. 1m and 2m respectively. Now the moments will be the same and the see-saw will balance – 1x30 = 2x15.

Lets take this a step further. Assume that the weight of the see-saw is zero to simplify the explanation, so we have two weights (30 and 15k) acting down and the upward reaction of 45k (30 + 15) at the pivot. Now start at one end of the 4m see-saw and calculate the moments. 1m along is the downward 30k weight, then 2m along (midpoint) is the 45k (30 + 15) upward reaction at the pivot and finally at the far end, 4m away is the other downward force of 15k. Put algebraically, 1x30 – 2x45 + 4x15. (Note that I have chosen to show upward forces as negative and downward forces as positive). 30 – 90 + 60 is zero.

What this is demonstrating is, that for a body in equilibrium, the sum of the moments about any point will always be zero. Check from the other end – you have 3x30 - 2x45 + 0x15, again zero.

(The assumption that the see-saw has zero weight is obviously not true in reality, but in fact has no relevance in this example, as the weight of the see-saw itself and the upward reaction to it at the pivot are always equal and opposite and act in the same straight line and therefore cancel each other out – after all, the see-saw is balanced with no-one on it.)

So how does this apply to aeroplanes?

Well, the aeroplane’s pivot point is its centre of gravity. This is the “balance” point, the point that the entire weight of the aeroplane is deemed to act through. If you could drive a steel pin horizontally through the fuselage at precisely the CoG, you could hang the aeroplane up by picking up the pin and it would balance perfectly, neither the tail nor the nose would drop.

Remember that the sum of the moments must be zero, measured from any convenient point. For many single-engined aircraft, this point, or datum, is taken as the tip of the spinner. So we could take the weight of each item in the aeroplane – engine, wings, seats, fuselage, wheels etc. etc. and multiply it by its distance from the spinner (or datum) to find the moment for each component (the weight of each component acts through its own individual centre of mass).

Now the entire weight of the aeroplane acts through the CoG, and for equilibrium, that is the point through which the upward reaction – the steel pin through the fuselage – must pass. The total weight x the distance to the CoG from the spinner is also a moment.

So the sum of the moments of all the components minus total weight x distance of CoG from spinner (datum) is zero. Put another way, the sum of the moments of all the components = total weight x distance of CoG from spinner (datum).

The manufacturer has provided figures for the particular aircraft in the POH. These give the empty weight and position of CoG for this configuration of static loads.

But now we want to add fuel, passengers and baggage. So what happens to the CoG? It will change position, of course. Fortunately, the manufacturer also tells us lines of action (distance from datum) of these variable loads. We now know the weight of the fuel (flight planning), passengers (ask!) and baggage (weigh) and the distances of each from the datum. So now we can calculate the moments for them.

At this point we know the total weight (empty) and the total moment (empty) from the POH, and the additional weights and their moments.

So the total weight (full) is the empty weight plus the additional loads, and the total moment (full) is the total moment (empty) plus the additional moments.

Since the sum of the moments is equal to the total weight x distance to CoG, we can find the new position of the CoG (full) by dividing the total moment (full) by total weight (full). This gives the position of the CoG (for this particular loading configuration) from the spinner, or aft of datum. Plot the weight against CoG position on the graph for the aircraft type and check that it falls within the allowable area for normal or utility operation.

You can see that if the CoG moves aft it gets closer to the elevator and if it moves forward it gets further from the elevator. Remember that the force that the elevator generates is the same for a given deflection irrespective of the position of the CoG. Therefore, the greater the distance between the CoG and the elevator the larger the moment that the elevator will generate and so also the lesser the distance, the lesser the moment. In extremes, this can cause stability and control problems.

I hope your brain hasn't exploded or turned to jelly!

Good luck

SD