Good evening folks! Just been having trouble approaching a question like this in terms of finding the minimum ballast required. Just want to know the steps on how to go about it. I have attached the image above. Thanks

want to know the steps on how to go about it.

Pretty standard approach will fit the bill.

(a) stick the required load in and run the sums to see from where you are starting.

Put the occupants wherever you choose as you can move them after the first iteration. Put the cargo in the back as required and the fuel in the mains. Run the sums and see where that puts you. You should see that you have an aft CG consideration to address.

(b) then you need to make sure that you have the occupants 2-2-1 from the front which puts you as far forward as you can get prior to ballasting. You are after minimum ballast (which should always be a goal).

(c) play with the ballast - either trials if you are running longhand calculations or plot a suitable point on the graph if you want to work it that way.

The initial sums should make it pretty obvious what sort of ballast quantum you might need. Just be careful with the final answer as both the correct ballast answer and the pragmatic ballast answer are options.

Let us know how it turns out.

Hi John thank you for your explanation. Just also wondering when using the graphical method do we base our plotting points off our TOW or ZFW? ZFW is far aft of datum about 2505 kg at 2683 mm, when 120kg of fuel is added gives us 2625 kg at 2642mm which puts us in the CoG box. Just wanted to clarify when doing these. Thanks

when using the graphical method do we base our plotting points off our TOW or ZFW?

First, which of ZFW and TOW is causing you the greater problem, CG limit wise ? Let's get that one fixed first and then take stock of the situation ....

The ZFW CoG looks like is further aft then TOW, so from there we add as much ballast possible in the form of 5kg bags. Max we can add in the baggage compt is about 50 kg as we are trying to get as forward as possible also we can add weight in the 1st row ?

No need to rush. Sure, the aim is to get there reasonably quickly but, far more importantly, without making any mistakes. Make a significant mistake out in the aeroplane and you might kill yourself, in the exam, you might get the question wrong and fail the exam. Neither end result has much to recommend it.

Let's work it through, bit by bit, until we get to the final solution.

Let's have a think about your first observation.

The ZFW CoG looks like is further aft then TOW

Correct. But is that really important ? What we are really interested in is whether either of the ZFW and/or the TOW loading puts us outside the envelope. So, what is the story here ? Do we have either or both points outside the envelope ?

So we have the ZFW slightly outside the envelope and TOW inside the envelope. Sorry had to re plot ZFW just wanted to make sure.

Good man.

So, do we have a problem with the ZFW CG ?

Do we have a problem with the TOW CG ?

Looks like we have a problem with our ZFW CoG

That sounds to be a good call to me.

As an aside, we would be looking at the shape of the envelope and the slope of the individual load moments to make an assessment of where to go from here but let's just work it through and figure how it's going on the fly.

So, we have a ZFW problem. Pretty obviously, we don't have any options available to move things around once you have the occupants loaded 2 2 1 from the front so it's a case of needing some ballast. We wish to move the CG forward. The question says we want to use the minimum ballast feasible (that's always the case - unless the examiner makes some strange requirement for the questions - no point spending money (fuel) to carry weight which we have no commercial or other reason to carry). So, we plan to use the least amount of ballast by sticking it in the most forward location feasible. In practice, if that doesn't work by the time you have maxxed out in the most forward location, you might have to use some additional ballast in the next most forward location but that won't be necessary for this problem.

So, we can either play with some sums to zero in on the required ballast, or do it on the graph, plot a weight/CG delta and then interpolate from the graph to figure out the amount of ballast required.. Doesn't really matter which way you approach it in practice.

Have a go and perhaps you can walk us through your thought processes and working ?