I am kind of confused as to how I can route my air correctly to each space with a ducted mini split. I want most of the air going to my main room which 260 sq ft. and then the rest going to my bathroom which is only 70 sq ft. Is there a correct way to come off the unit to make sure I am heating and cooling each room accordingly.
Start by running a room by room heating/cooling load calculation. The loads are not likely to be directly proportional to load area.
Then look at the maximum (highest blower speed) numbers for the cassette in question, and divide the cfm proportional to the loads. (If the difference in room load is bigger for cooling than heating or conversely, use the lesser proportion.) eg: Say the heat load of the 70' room is 650 BTU/hr and it's cooling load is 1100 BTU/hr, and the heating load of the 260' room is 2400 BTU/hr, with a cooling load of 4100 BTUhr.
The ratio of cooling loads between the rooms is 4100/650= 6.3:1, the ratio of heating loads is 2400/650= 3.7:1. The ratio of heating less, so we'll divide the max cfm into a ~3.7/1 ratio.
Say you're looking at a 3/4 ton Mitsubishi
-KA/KD09 as the solution. The max cfm is 317 cfm @ 0.2" w.c. static pressure across the system. Dividing that proportionately, the 70' bathroom gets 317/(3.7 +1)= 67 cfm, the big room gets 317 - 67= 250 cfm. The ideal duct system would be designed to deliver those proportions almost exactly when the registers are wide open, tweaking the flows with the registers when changing from heating to cooling mode.
How can I calculate what size ducts I'll need to use to split off from the unit to each room?
Duct induced static pressures are largely about two things- velocity, and turbulence around turns.
You may find these discussions useful. But at the bottom line, if the ducts are large enough, with a low enough velocity and radiused rather than sharp-throated turns, most of the static pressure will be induced at the filter and the heat exchanger in the cassette.
How low a velocity is low enough? Assuming it's all within conditioned space,
shoot for something less than 400 feet per minute and the absolute lengths will matter a lot less. Using
this handy nomograph (developed for this purpose by
a home energy retrofit company in CA) you'll see that the KD/KA09 example above, the room getting the 250cfm would be best served with a 12" round duct, the room getting the 67 cfm would take a 6".
On another note how well do mini split cassettes with branch ducts work? This is another option I have been exploring. I could put the cassette in the ceiling and run a duct off that for about 15 to 20 ft to the bathroom.
As in the above, try to keep the velocities in each trunk and branch in the 250-400 cfm range. This will mean narrowing down the trunk after branches to keep the same velocity range.
As a general rule, hard-piped ducts are more consistent, but flex can be used if it's fully stretched taut (except where it must turn). Floppy flex induces far too much turbulence, increasing the friction/static pressure.
Also, installing conical reducers ahead of the register boots helps in two ways- it increases the velocity for better "throw" into the room, and allows use of smaller registers/diffusers. The only place you want the velocity to be higher than 400 cfm is where it enters the room, to improve the mixing within the room. While that short narrowing induces some amount of static pressure, it's far less than if it were a high velocity along the full length & every twist & turn of the duct path.