Calculating moments is valid. Easier just to install the .061, mark the CG. Then install the .74 and add tail weight until CG falls at previous mark. See, no math! So easy , a caveman can do it.
Or take of the 061, and rubber-band the 074 to the nose. Move it back until everything balances, and that's where it goes. Note that you'll be off ever so slightly if you have to saw a bit off of the nose to make it fit.
As an alternative:
- Weigh the plane plus the 061. Don't forget to include the mounting screws and the prop.
- Weigh the 061 with mounting screws and prop, and muffler if you used it.
- Determine the fore-and-aft CG of the 061 in the condition that you weighed it. It should be somewhere around the front of the cylinder
- Determine the fore-and-aft CG of the plane with the 061 mounted.
- Determine the distance between the all-up plane CG and the motor CG
- Weigh the 074 in the same condition as the 061 (prop, screws, muffler)
- Calculate the new distance between the 074 CG and plane CG. It's equal to (old distance) * (061 weight) / (074 weight)
- Confidently rework your airplane with this new distance
OK, that was the theory part. Now, here's the
real part -- and remember, Floyd Carter and I are both engineers:
- Measure your wonderful new plane's CG
- Note that it is off
- Curse
- Rip the 074 off the nose, install it with rubber bands, and slide it fore and aft until the proper CG is found
- Mount it in that location
- Spend the rest of the life of the plane looking at the scars of the second rework and cursing yourself
Note that this method includes Floyd's method, and a whole bunch of work that is, ultimately, pointless. Weight and balance are never, ever right the first time -- this is why one of the valid civilian uses of uranium (well, depleted uranium) is as weights on aircraft, because it's dense and thus easy to find a spot to tuck it into an airframe. I've worked on teams that included mechanical engineers using new, fancy CAD programs with super-exact mechanical models of mechanisms and the materials that they were made of -- and when we shipped product, it always had weights attached to it. The engineering and pre-production prototypes had tire weights epoxied on; the inital production runs had brass or tungsten weights (our machine shop balked at depleted uranium) bolted on and a few tire weights scattered here and there, as the product matured the weights would get refined so that less hand-balancing was necessary.
But they always shipped with weights. And those weights were never found computationally.