Where would be the best places to add weight to a ship? one Big lump in the middle, two smaller lumps close to mid ship but slightly fore and aft, two lumps of weight further apart closer to the aft and fore ends of the ship?
my methods are generally built around wood hulls. so take that caveat I use the center of gravity to set the hull flush on her scale waterline. that's usually at the center of the boat's length. (Unless you have a sweep-deck like texas or arkansas and want to make her flush. then you have to do math. a free-body diagram will help) So. draw a line proportional to your ship with CG at center. weigh all of your components. measure where they are in relation to the center of gravity. I do my best to keep over half of the hull weight within the 25% of the hull length to either side of the CG. the further the weight is from the CG, the more it will proportionately impact the list of the hull. for example, on Texas, I have fifty 150 gr bullets that act as the forward ballast, and forty that act as my aft ballast. the boat floats level without them. they bring the hull down to the waterline I want. But the two ballast modules have the same impact because the fifty bullet module is closer to the CG than the forty. Sorry if this is confusing. I did all of the physics portion of my degree like five years ago, so I can *do* it better than I can describe it. but the placement and size of your ballast is directly proportional to where it is with respect to the center of gravity. If you have the room, I'd place it in the core of the hull, as low and flat as possible, to either side of the water channel. If at all possible, use lead plates. the more of the boat's mass that you have concentrated around the center of gravity, the better. the bow and tern of my boats are for all intents and purposes, empty.
Consider the figure skater. When they spin and hold their arms apart, they spin slowly, but when they bring them in close, they spin much faster. You want your weight as close to the center as possible, but ... that is also subject to the caveat of where you can fit stuff. And obviously as low as possible too.
It all comes down to basic physics, your desired moment of inertia and leverage. A tiny weight at the extreme bow or stern is very effective at adjusting trim, but has adverse effects on your turning. As Commodore and Anvil_x have explained, that is due to the rotational inertia. In general it is preferable to shift your batteries/bottle/lead ballast 1/8" forward or aft rather than putting a trim weight in the extreme bow or stern, if you are able to do so. If your design is already locked down so you cannot shift major components, then a trim weight is your only option. Other things to keep an eye out for: you want the ballast as low in the boat as possible. For example, I recently cut out several big chunks of my water channel so I could move my lead ballast further down. It was only 1/4" lower than before but it was a very noticeable improvement, and the lead became my new water channel so survivability was not harmed at all. I have also seen people place lead sheets along the bottom of the boat, or add bilge keels made from lead. Also, while you want the mass concentrated on the center lengthwise, you want it spread out as much as possible width-wise. Just like having weights at the extreme bow and stern slow down your turning, having weights at the extreme port and starboard beam slows down your rolling side-to-side. All that said, objective one is to get a boat that floats upright and at the desired waterline. All that other performance-enhancing stuff can come later. Like I said, I only recently cut chunks from my water channel to improve stability. As built, stability was good enough that it wouldn't capsize while just sailing around, so I focused on making the rest of ship work good first.
