Hi all,

Looking for a more efficient way in calculating the maximum weight to add for weight & balance problems.

Is there a way to determine the exact weight you can Add without any trial & error method?

Any help would be appreciated.

Probably not much in the way of efficiency gains to be made, I'm afraid. On the other hand, once you have done the hard yards in (b), below, you certainly can run the problem very quickly.

Keep in mind that you

(a) are endeavouring to end up at a weight/CG co-ordinate by one means or another. The usual mandraulic techniques are pretty straightforward and easy to run. Certainly, they are quick and will give you more than adequate accuracy.

(b) if you wish to model it on a PC, the model numbers will be different for each aircraft so, either you have to model each aircraft separately, or set up an all singing, all dancing, generic model into which you can pour some data points for the Type/Model and have the program run the sums in the background to set up the particular model required. Then you can enter the starting co-ordinate, the desired end point and press the "go" button.

But, why would you go to the bother of doing all this ?

Just to finish off the comments,

(a) you can run a simple graphical analogy to (b) just by plotting the load line on the envelope. In fact, this was a very common technique we used to set up load rule style loading systems. We didn't actually plot lines, rather we used transparent overlay sheets which could be used over and over. You can do the same sort of thing in a graphics package and, once you are on top of things, that approach can sing very nicely.

(b) you can avoid the trial and error by setting up the problem as a simultaneous solution of multiple equations. Not overly difficult but way beyond what the pilot needs to be able to do. Again, there is an overhead in the time to set it all up at the start and it changes for each aircraft Type/Model. This is the basic idea in the models one would set up in (b), above, but you can also do it on paper with a calculator.

Thanks for you’re reply John.

As I cant use a PC for the equations, paper & calculator is my only option.

At this stage I am using a formula which doesnt take long to work out once the ZFW has been calculated but it doesnt get me an exact weight and probably should of stated I am trying to obtain some accuracy over efficiency.

Thanks again for the detailed response

On page 165 of the CPL Performance Book I have demonstrated a mathematical solution for weight to shift and weight to add or subtract. It can't be used for adding or subtracting weight if you are working on the forward limit, because the forward limit itself changes with weight. You will then need more advanced mathematical solutions such as John describes.

Most students find it easier and faster that drawing lines on charts and interpolating values - especially for a CASA exam where the question may not be multi-choice but require and answer typed into a computer.

The method is specific for the exam aeroplane 'Echo'. However it can easily be adapted for any real aircraft.

At this stage I am using a formula which doesnt take long to work out once the ZFW has been calculated but it doesnt get me an exact weight and probably should of stated I am trying to obtain some accuracy over efficiency.

Perhaps you can detail what you are doing at present and we might be able to offer some comments to help you tidy things up a bit.

There shouldn't be much difficulty in getting an "exact" weight. However, please do keep in mind that "exact" can only refer to the arithmetic. As the starting data (empty weight and empty weight CG) is never exact in the real world, the answers can only ever be approximate - never exact. The exams are a bit different in that they are a little artificial but that's the way of life, I guess.

John hits the nail on the head. We get carried away with being arithmetically perfect and ignore the fact that much of the starting data is approximate. How do you know exactly how much fuel is in the tanks? How accurate is your dipstick? Is it calibrated to a fraction of a kilogram?

Is the weight in each compartment acting at the exact arm given in the manual. If the arm of the rear compartment is given as 5000mm, is the weight distributed on the floor of that compartment acting at exactly 5000mm?

The graphs allow for this so that you can be sure you are safe - not perfectly accurate.

If I may add some amplification to Bob's comments -

(a) as part of the certification flight test process, the TPs make assessments based on the Standards (eg FAR 23) and associated support documents (eg AC 23-8C). If the design folk get things reasonably right, the TP confirms that all is well, otherwise there are changes made to improve the aircraft. In concert, these provide for acceptable handling and performance.

The envelope limits generally are not cliff edge situations, rather there is a progressive degradation from good to bad to disastrous and the TP is the link in the chain which puts the final line in the sand for certification acceptability.

(b) in operational practice, the operator (pilot) has to make allowance for reasonable misloading. So, for instance, if there is a problem with a freight compartment's not being loaded at the declared centroid (ie the nominal loading arm), then there needs to be an allowance made in how the loading system is applied to ensure that the final weight/CG is unlikely to get itself outside the approved envelope.

Unfortunately, CASA doesn't require either the WCO or the aspiring pilot to know anything much about the techniques used to achieve this (although this is likely to change in due course - refer www.casa.gov.au/rules-and-regulations/st...l-officer-and-weight).. In US practice, it is referred to as a "curtailment process".

For the practising pilot, the aim is

(a) loading should be run as accurately as is feasible

(b) if there has to be an error, then do your best to make it conservative (eg, if you are ballasting to get back into the envelope, go a bit further than the sums require to gain a little fat at the limit).

(c) make sure you don't get yourself outside the envelope at any stage of flight for there be dragons there.

Thanks John & Bob, appreciate it

Our interest is in trying to help you get around your problem. If you post a scan of a couple of sample calculations, perhaps we can do just that ?