I've got this Extrawheel trailer (which is excellent BTW) which weighs 15 kgs fully laden when put on the scales.

However, what I would like to work out is how much weight am I actually pulling once it's moving.

Having flunked physics, all I know is that those chaps that pull 747s in the Strongman competions aren't really pulling the weight of a 747. So, how would I work it out?

I'm after an approximation and I know that surface, tyre, gradient, speed etc. all make a difference, but what would be a good approximtion?

Ta!

They are pulling the weight of a 747. They're not lifting it. What they're overcoming is the inertia of the object and the (at low speed) rolling resistance of the kit. The weight of it is almost irrelevant except during accelerations. I think your problem is you're trying to equate weight (the vertical effect of the mass due to gravity) to the force required to pull it (horizontally).

Correct. So What I want to determine is what is the equivalent weight if I were carrying it on my back instead of towing it with a trailer.

How much additional energy (kj or w) would be required to move it when carried v when towed?

There isn't really a short answer for this.

If you're on the flat, there's no extra effort from having a heavy pack on your back. There is some extra rolling resistance from towing a trailer.

If you're going uphill, you're having to carry the same amount of weight either way, so the drag of the trailer still makes it worse than carrying a pack.

In a real world, mountain biking situation over rough terrain, who knows? Never towed a trailer, but I'm prepared to bet it sucks.

There have been studies comparing weight carried on the bike verses weight towed, using heart rate as a comparison. Roughly speaking you can tow twice the weight for the same effort as carrying it on the bike (or more importantly take the same weight further). BUT, thats for a two wheel trailer (and one that joins the bike in the right place). The effort expended is as much about balancing the load as moving it forwards. With a two wheel trailer you put no effort into stabling the load, but with a one wheel trailer you do, so there is less and possibly no effort saved.

Towing two wheel trailers (on the road) is a hoot. Compared to panniers your bike handles exactly as it does unladed, just a bit more effort to get moving and quite a bit more up hills.

Off road though, two wheel trailers aren't much fun.