Actually the bat wing is easy to calculate without a computer. The rear is an ellipse, an easily known equation. Remember high school geometry class? The leading edge also is a straight line. Integrate between the two lines for area. Take 25% and viola, CG of said wing panel. Do this on all the wing panels in question, weight the wing panels to lift generated and viola, you get your MAC.
Integration between two lines is generally the 3rd quarter of calculus. Don't need calculus on a delta wing though. Delta wing is very straight forward. Find MAC of each wing panel, same way you do for a straight wing. That finds overall MAC of wing shape. How much wash-out you decide to add to compensate for the delta wing induced angle of attack is a bit of rule of thumb. I suggest looking at all modern commercial airlines, actually not a good example as they calculate wing flex and rotation in their wings for cruise, so ground orientation is generally shows far more wash-out than what is seen in the air. A better example would be the frontal aspect of an F-4 and other fighter planes when viewed from the front. This will most closely represent how much wash-out you need depending on the swept back angle.
Likewise this also explains why many delta wing RC planes have very poor handling qualities as their wing tips stall. Why? Because many RC builders don't know delta wings create an induced angle of attack and therefore they build like a standard trainer with no wash-out and the tips stall sending the airplane right INTO the ground. I have seen this many times on guys with turbofans and turbines. The designer didn't know what the heck they were doing, but they got the kit sold anyways! Uh, Hem, BUYER BEWARE!
ORIGINAL: rctech2k7
Sorry it's quite confusing to write that in simple word but thanks for asking. Here's my explanation. First your guess is correct because he used TLAR and it did work. Second pertains not on your comment but for those who used TLAR in CG location on their build aircraft prior to maiden. For me this method require a lot of skills to become successful. Actually not just skills even how expert the pilot is anything could happen. However cg calculation in the example is not easily accessible due to the nature of the wings and TLAR is the most common used in estimate and it's the closest one available. In some aspect it is critical depending on the skills of the test pilot and the cost that may bring considering all safety procedure has been implemented on the test site. The problem is the non linear structure of the wings which require method to determine cg location prior to maiden in order to become successful as possible on the first flight. This pertains to the subject matter of having complex shape wing. A method that will generate function to represent wing chord for determining MAC. In other words without this, other method needs to be consider like graphical analysis, taking small increment of chord, etc. to be used in approximation rather than using integration since curve tracing is complicated although the wings can divided in portions. On our example look like the leading edge has linear portion while a semi ellipse is on the trailing edge. In addition to become more accurate such as calculating wing area for wing loading of such design may solve easily by integration IMO (because computer is available now a days). Aerodynamics is the law that governs our aircraft, airspeed is the reason why airplane stays safe in the sky. However there are hidden parts in aerodynamics which cannot be expressed in math. Those things require wind tunnel to determine. I've been in electrical and it's invisible form of energy but from small scale power plant to large scale, ohm's law is always there. From small energy cell to utilization there's always simple calculation available if we could only know it's accurate and easy.