Effects of the centre of gravity on aircraft's stability

[JB312]

TL;DR Summary

How to determine the effects of a heavy storage tank located at the rear of an aircraft might have on aircraft stability.

I'm working on a feasibility study for the integration of a liquid hydrogen storage tank for a Boeing 737-800. The tank weighs approximately 5000 kg and must be located towards the rear of the aircraft. I understand that this will shift the centre of gravity slightly further back and consequently affect stability. I want to test how various positions of the tank might affect this stability. If I could define the force balance equations and then generate some plots to show how each of the stability factors varies as the position of the tank changes and then find a happy medium that would be great. I'm just not sure how I should go about doing this, or what force balance equations/stability factors to use etc. Or if anyone has any other ideas to go about it, it would be most appreciated. Thanks in advance.

 

[Filip Larsen]

I am no load and balance expert, but I will assume that the "easiest" approach given an existing 737-800 configuration is to consider the equivalent to load for the tank, i.e. if you are able to place the tank in the rear storage area while remaining within existing limits for load and balance, including placing ballast in the frontal storage of the plane if needed. This approach will obviously not be applicable if you plan to put the tank load outside the certified load areas for the specific aircraft.

 

[Baluncore]

Tanks are mounted at, or symmetrically about, the centre of lift. The fuel is selectively taken from tanks to maintain the balance of the aircraft. That is why there is no fuel tank at the rear of an aircraft. If there was a rear tank, there would need to be another tank mounted forward, that contained fuel that could be used at the same time, or water as ballast, that could be dumped.

 

[russ_watters]

I'm sure weight and balance data from the pilot's operating handbook for a 737 can be found via Google. It'll include equations for calculating location and a map of acceptable results. It's not that you calculate performance, you just need a result in the acceptable envelope.

 

[Janus]

As Russ has already mentioned, you need to stay within the CG envelope. In essence, you don't want things to get to the point where control surfaces are not capable of achieving the correct pitch for the aircraft( especially during times like take-off and landing).
It is also important to work things out for both fuel load at take off and fuel load when reaching one's destination. For example, let's say you are in a small aircraft with passengers and luggage in the rear. You work out your CG while fully fueled and it works out okay.
When you get to your destination, you've used a considerable amount of your fuel load. Now it isn't any shift in fuel weight position that is the issue, it is that the plane is lighter as a whole and your rear passengers and luggage now make up a greater percentage of the craft's weight, causing the CG to shift to the rear. To much of a shift, and you may not be able to hold the right angle of attack and stall during landing.
You'd use a chart something like this: