That will be a hard thing to do, short of removing the boat of the water, getting at least 2 scales at the same time, and what not.
Assuming the boat is dry in land.
Assume that the CofG is somewhere near the end of your keel, or slightly aft of the mid part of the keel. or thereabouts. And anywhere from one foot to 2 feet from the bottom of it, and in the bottom if you have a led keel
The centre of gravity should have been calculated by the boats manufacturer and you should be able to get that info from them, i shouldn't think it was too important to work out your exact CofG and that using what GIU (alex) said should work fine.
Most modern travel lifts will give you load reading from the front and rear belts. By carefully setting the belts vertical and by taking careful measurements of the distances from the belts and from the bow and stern you should be able to reasonably accurately approximate the fore and aft center of gravity.
The above posters are assuming that you are trying to determine the horizontal center of gravity and not the vertical center of gravity, or so it appears to me. If that is so, the travel left method may work quite well or you may use a slightly more tedious method.
Hang a weighted string over the side from the deck edge. Have someone walk forward to the bow. Measure the angle that the string has moved off vertical. Reposition the string to various fore and aft locations while having the same person return to the same spot forward each time. The position where the angle is the smallest will be the longitudinal center of flotation or the center of gravity at the waterplane. This should be close enough for your purposes.
If you desire the vertical center of gravity with any degree of accuracy and you do not have the hydrostatic curves of the vessel it gets a bit more involved. I'd refer you to John LaDage's Stability and Trim for the Ship's Officer where you'll get a concise explanation of terms used as well as some practical advise. You'll need to calculate the vessel's metacentric height through a somewhat convoluted series of steps and then do an inclining experiment across the deck of the vessel with a weight. That will yield KG or the height of the CG above the keel.
I would imagine that all he is interested in is the longitudinal CG since he's probably trying to decide where to place the wheels on the trailer. The vertical CG wouldn't matter much since there is little room for adjustment there.
If the lift has scales in each of the lifting webs, what you need to do is record the weights and carefully measure the positions of the lifting webs from a fixed reference point on the boat (say the tip of the bow). Then it's easy:
*multiply the distance from the reference point of each web by its recorded weight.
*add the results of the two products together.
*divide the result from above by the total weight. This result is the distance of the CG from your reference point you chose earlier.
I sort of built my own trailer for my Cal25. I didn't use a very scientific method though. I searched the internet for pictures of Cal25 boats on trailers and came up with a rough idea of the minimum trailer length that I could get by with, and then went out and purchased a used powerboat trailer that was long enough, and modified it. I didn't have my Cal to get measurements from. It was in San Francisco Bay and we live in West Florida. I made adjustable stanchions out of pipe and adjusted them to fit after the boat yard lifted it out and set it on the trailer. Since then we have launched and recovered it with no problems, although I do intend to add guide boards to make it easier to insure that the keel is in the right position before pulling out of the water. I don't know how to upload pictures to a thread so I'll upload a few pictures of our trailer project to my gallery incase you want to check them out. Good Luck with your project.
If you feel like doing a lot of pencil-and-paper, tape-measure, and computer work, you can divide your boat's volume up into a large number of approximately uniformly dense subvolumes, each with easily computed centers (and therefore centers of volume). Then you just take the weighted sum of the cartesian coordinates of the centers (weighted according to mass).
To some extent you can simplify the problem by taking advantage of the symmetries of the boat. If you assume the boat is laterally symmetric, then the CoG is on the central vertical plane, and the problem becomes two-dimensional. You just need to draw up an accurate cross-section of your boat and then do a process similar to the above. Manufacturers' cross sections seem fairly easy to come by, and will be good approximations to a boat with empty tanks and well-trimmed solid ballast.
Would probably be an interesting exercise for any boater... would also be interesting to write a computer program that analyzes an image of the cross section, asks the user for some information about materials, and computes the CoG! Okay I'll get right on that.
I liked the travel lift idea, but the lifting webs will have to be vertical, or at least the angles of them to the vertical must be known. The only trouble is what it costs to have them lift it.
If you had another trailer for an afternoon, particularly if it had one axle, it could be done.
If you know the vessel's weight, you could measure what the toppilng moment is. Typically, the trailer would want to tip forward, so if you could measure the force at the towbar ball to correct it, then classic moment balance would betray the C of G.
Allow the distance from the towbar ball to the axle to be : a
With the trailer laden, allow the force at the towbar ball to be : F
Allow vessel weight to be : W
Allow the C of G to be an (unknown) distance b forward of the axle.
Moment balance dictates.... F*a = W*b
such that... b = F*a/b
When you have worked out what b is, chalk the hull with a vertical line.
This approach neglects the toppling momernt of the trailer arnm itself. If you don't want to ignore it, the equation needs modifying a wee bit.
I haven't figured out how to measure the forces yet as a bathroom scale is not likely to work.
If you have a crane, one easy way is to keep lifting the boat onto the trailer until it balances. make sure that the towbar is connected though, as it may topple backwards if it is not.
When they set my boat on the trailer I had them move it forward and backward a little at the time until I could see the amount of tongue weight that I wanted by the way the front and rear suspension on the towing vehicle reacted. Then we jacked up the adjustable stanchions to put a little pressure on the hull. Tied her down and hauled her 2500 miles with no issues. Of course I did check every one of my welds every time we stopped. I had finished the last weld on the trailer conversion about four hours before we headed out to the west coast to get the boat.
Does your boat by any chance sit in a cradle instead of on stands? We figure out the CG of skids we build so we can cut the forklift pockets in the right place. We put a pair of railroad toe jacks on either side and lift the skid 1/2" or so. We keep moving the jacks towards the heavy end until it balances.
You might be able to do this for a keel boat if your keel is sitting on cross beams so the jacks would fit under the keel. You'd lift a little and watch whether the boat tends to tilt fore or aft.
I've built trailers for a Catalina 22 and a Hunter 27. They trail best when you have at least 200 lbs of weight on the tongue, depending on the size of your tow vehicle. Any less and braking hard will be really exciting! This is also true if your boat has a deep keel, which puts the center of gravity real high. Then I'd load the tongue weight even more.