Why the center of gravity is critical
The center of gravity (CG) is the point at which the model behaves as if all its mass were concentrated in a single spot. A correct CG setting determines longitudinal stability, the ability of the model to return to straight and level flight on its own after a disturbance.
If the CG is too far forward, the model will pitch down steeply, lose altitude quickly and require significant elevator deflection to hold level flight. If the CG is too far aft, the model becomes longitudinally unstable. Even a small disturbance causes growing oscillations or an uncontrolled pitch-up ending in a stall.
Mean Aerodynamic Chord (MAC)
The CG position is defined relative to the Mean Aerodynamic Chord (MAC). The MAC is a reference chord that represents the aerodynamic properties of the wing regardless of its planform shape (rectangular, tapered, elliptical).
For a rectangular wing the MAC equals the airfoil chord. For a tapered wing the MAC is found graphically or calculated from a formula that uses the root chord, tip chord and taper ratio.
A typical CG position for glider and trainer models is 25% to 33% MAC measured from the leading edge. 25% MAC is a more forward (safer, more stable) setting, while 33% MAC is a more aft (better performance, less stability) setting. Beginners should start at 25% to 28% MAC.
Longitudinal balance
Longitudinal balance concerns the mass distribution along the model's longitudinal axis (nose to tail). This is the primary parameter to set first. Moving the CG forward increases longitudinal stability but also increases induced drag (the model flies with deflected elevator) and shortens flight time. Moving the CG aft reduces drag and improves performance but reduces the stability margin.
In practice, longitudinal balance is adjusted by adding ballast (lead, shot) in the nose or tail. A better solution is to reposition heavy components (the battery in RC, the motor) instead of adding dead weight.
Lateral balance
Lateral balance concerns the mass distribution along the lateral axis (left wing to right wing). The model should hang level when supported under the fuselage at the CG point. If one wing is heavier, the model will tend to turn toward that side.
Wing mass differences are compensated by applying pieces of lead tape to the tip of the lighter wing. It is important to place the ballast as close to the tip as possible, because a smaller mass at a greater lever arm has the same effect as a larger mass closer to the axis.
Methods of checking the CG
The simplest method is the two-finger test. Support the model from below with two index fingers at the CG point marked on the plan. The model should hang level or with a slight nose-down tilt. If the tail drops, the CG is too far aft.
A more precise method is to use a balance stand. Commercial stands have adjustable supports that let you find the balance point accurately. For large-span models it is worth building a simple fixture from two vertical strips and a wire axle.
On RC models you can perform the dive test. At a safe altitude, put the model into a nose-down attitude at roughly 30 to 45 degrees and release the sticks. A correctly balanced model should pull out of the dive gently. If it pulls up sharply, the CG is too far forward. If it continues to dive or begins to oscillate, the CG is too far aft.
Why a tail-heavy model pitches up
A model with the CG shifted too far aft has too little longitudinal stability margin. In flight physics this means that the neutral point (the point at which a change in angle of attack produces no pitching moment) is close to the CG or even ahead of it.
When such a model encounters a gust or a small disturbance that increases the angle of attack, the extra lift generated ahead of the CG is not sufficiently counterbalanced by the stabilizer. The nose rises further, the angle of attack keeps growing until the wing stalls. This process is self-reinforcing and without pilot intervention (in RC) or proper trimming (in free flight) it leads to loss of the model.
Practical tips
Always start with the CG recommended on the plan. If the plan does not specify a CG, use 28% to 30% MAC as a starting point for trainer models. After every modification (motor swap, battery change, equipment change), recheck the balance.
Record your CG settings and their effect on the flight. A trimming log lets you quickly return to a proven configuration. In competition, a CG shift of 2 to 3 mm can noticeably change the model's behavior in thermals.