The centre of gravity is the point around which an object will balance. You will instinctively know where this is for simple uniform objects - right in the middle.

If you pick up an empty tray using just one hand underneath, like a real Italian waiter in a Venice café, you instinctively know to put your hand in the middle so that it balances - and it balances because you are putting your hand under the centre of gravity.

Now if you add a jug of water on one end of the tray, you instinctively know that you need to put your hand nearer the jug end of the tray, if the tray is to balance - again, because you are putting your hand under the centre of gravity.

In this case it is the centre of gravity of the tray-and-jug combined that you instinctively select - near the middle of the heavy jug, but offset a little toward the middle of the lighter tray.

So it turns out that you already know all about centres of gravity. Well done!

Basic Case

The diagram on the right is a weight distribution - the coloured boxes show the assumed weight per foot of trailer at each position along its length.

In this simplest case, we assume that all the trailer within its body length has a constant weight per foot (the green box) while the tongue has a lower weight per foot (the yellow box). The credit for this suggestion goes to Rik Keller on the T&TTT forum.

If we assume the weight per foot in each box is constant, we automatically know where the centre of gravity of each box is - right in the middle of its length.

Axle Weight

The assumption that the body's weight per foot is constant is fairly reasonable with one exception - the weight of the 'axle' (that is, the suspension, axle tube, wheels and tyres). This is quite a big percentage of the trailer weight and it's concentrated in one place, so it is sensible to estimate it separately.

The blue box shows the concentrated weight of the axle. Note that the weight per foot of the rest of the body length (the green box) has been reduced, since it no longer contains the weight of the 'axle'.

Galley Weight

Depending on the use to which we will put our trailer, we may be putting quite a bit of weight into the galley (kitchen) and this: things like loaded coolers, tinned goods and water tanks can all be quite significant weights on their own - add them together and they will alter the balance of the trailer quite a bit.

So it would be sensible to include a separate estimate for the weight of galley equipment and stores, the red box in the diagram.

If necessary, we could use another separate weight to account for any unusual feature of our trailer design. For example if we want to have a tongue box carrying one or two batteries, that will certainly affect the trailer balance and we could include it as another extra weight.

Detailed Analysis

If we take the aircraft designers approach and estimate the weight and position of every part of the trailer, we can will get the most accurate estimate of the centre of gravity.

This diagram shows the result of just such an estimate for my Superleggera design (without any extra galley weight).

If the same weight data is used in the 'Axle Weight' model above, it produces an estimate for the centre of gravity which is 16mm (5/8in) different from the detailed analysis result. That's an error of well under 1% of body length, so that seems a decent result.

If you would like to know how to do a detailed weight estimate, go here.

Here we have the trailer balanced on a see-saw (teeter-totter) so that it doesn't tip either way - the centre of the see-saw is right under the centre of gravity of the whole trailer. The trailer will balance when the effect of the main weight W1 trying to rotate the see-saw anti-clockwise is equal to the effect of the tongue weight W2 trying to rotate the see-saw clockwise, so they cancel each other out.

The rotating effect of these weights (their 'moment') is their weight times their distance from the point of rotation (the 'lever') - so a 5lb weight at the end of a 1ft lever has the same moment as a 1lb weight at the end of a 5ft lever - both produce a moment of 5 ft-lb.

So the moment of the body weight (Wb x Lb) must be equal to the moment of the tongue weight (Wt x Lt), so that gives us this formula:

Wb x Lb = Wt x Lt

or

Lb / Lt = Wt / Wb

Now, calculating moments relative to the centre of gravity isn't easy if we haven't yet worked out where the centre of gravity is. But, curiously, moments can be calculated about any point and they will still give the same result.

So if we take moments about the back end of the trailer, as in the diagram on the left, we know that the combined effect of the two weights Wb and Wt must be the same as all the weight concentrated at the trailer's centre of gravity. So that gives us another equation:

(Wb + Wt) x Lc = (Wb x Lb) + (Wt x Lt)

Now this is exactly what we need - because Lc is the answer we're looking for.

We can apply this same method to many more weights than just the two in this example, and that is what the spreadsheets do.

Determining how the total trailer weight is divided between the axle and the hitch is an upside-down version of the centre of gravity see-saw. Again the pivot of the see-saw is at the centre of gravity, but this time the ground and the tow vehicle are pushing up on the ends of the see-saw.

So the moment of the weight on the axle (Wa x La) must be equal to the moment of the weight on the hitch (Wh x Lh), so that gives us this formula:

Wa x La = Wh x Lh

or

La / Lh = Wh / Wa

You can check the logic of this by putting the trailer's centre of gravity directly over the axle - then La is zero, so Wh is zero - ie, there is no load on the hitch, which is what you expect.