It seems the CG is played with when the plane doesn't fly right. When this happens I've tended to add nose weight to presumably make thing more stable, often without success. With the help of experienced people, I've found that my poorly flying planes are too nose heavy. It seems that there is such a thing as too stable, or is it that there is simply a range for the CG and too far forward or back are both bad, except that too far back is much worse than too far forward.

There are several methods for determining proper CG,
some more controversial than others.
One is the dive-test.
The (sail) plane is placed into a shallow dive (45 ^{o})
and watched to see if it noses up, down or continues straight.
A nose heavy plane requires an elevator setting
producing excessive down force.
In a dive test, as the plane increases speed,
the elevator produces greater down force
pulling the plane out of the dive.
Conversely,
a tail heavy plane would have an elevator setting
producing less down force.
Such a plane test would presumably increase its dive angle.

I've also people fly inverted and observe the amount of elevator needed to maintain level flight. A nose heavy planes requires excessive elevator. Another is if a sailplane is thrown out of a thermal, the plane is presumably nose heavy. But wouldn't it be great if we could eliminate all this testing, and and simple calculate the proper location.

In his book __Model Aircraft Aerodynamics__,
Martin Simons describes how to calculate
the *neutral-point* of an aircraft.
The neutral-point (NP) is the point around which all the
aerodynamic forces are balanced.
It is therefore a very good reference point for the CG.
A conservative CG would be ahead of the NP.
I've found that the final CG location of my planes
is usually very close to the calculated NP location.
The equation is

hwhere_{n}= h_{0}+ h_{s}V_{s}( a_{s}/ a_{w}) (1 - (de / da ))

h _{n}neutral-point h _{0}aerodynamic center of the wing, typically 0.25 h _{s}stabilizer efficiency typcially 0.6 (0.9 for a T-tail) V _{s}stabiliser volume coefficient a _{s}lift curve slope of stabiliser a _{w}lift curve slope of wing de / da change in stabiliser downwash angle versus change in wing angle-of-attack, typically 0.5 to 0.33

The typical values for
h _{0} , h _{s} and
de / da
are more than adequate in most cases.
All that is needed are the stabiliser-volume
and lift-curve values.

The tail-volume is calculated by multiplying the area of the stabiliser, including the elevator, by the distance between the tail and wing. This is called a volume because the results are in cubic inches or meters. The value is then divided by the area of the wing, and the average wing chord. Dividing by the wing area makes it relative to the wing area, a ratio to the wing area, and dividing by the wing chord makes the NP value relative to the chord, a percentage/fraction of the chord value.

Vwhere S_{s}= (S_{s}L_{s}) / (S_{w}c)

Consider the *Airbear* as an example.
It is a handlaunch glider described in *Model Aviation*.
It is a simple design with both rectangular wing and stabiliser.
The wing is 60" by 8.5" and the stabiliser is 18" by 5".
The stabiliser if 24.6" behind the trailing-edge of the wing.
For the Airbear,
the tail-volume coefficient is

V_{s}= (18 * 5) * 24.6 / ((60 * 8.5) * 8.5) = 0.51

The lift-curve, a_{s} / a_{w},
also need to be calcuated.
This relates how much the lift-coefficients
of the stabiliser and wing change
with an equal change in angle-of-attack.
In other words,
how much does the lift-coefficien of the tail change
compared to the wing.
But before this ratio can be calculated,
estimates for the lift curve slopes are needed for both
the wing and stabiliser.
The lift curve slope is how much the lift coefficient changes
per degree change in angle of attack.

The theoretical lift-curve slope
for wings of infinite length is typically 0.11 per degree
(a wing at an angle-of-attack of 9 ^{o}
has a lift coefficient of 0.99).
A wing of infinite length would have zero induced (or vortex) drag
since there are no wing tips.
A wind-tunnel measurement effectively measures
a wing of infinite length because the test wing section
fits between and abutts against the walls of the wind tunnel.
The lift-curve can be estimated for a real wing
knowing its aspect ratio.
The aspect ratio is the wingspan divided by the average chord.
The average chord of a rectangular wing is simply the chord value.
The adjusted lift slope is calculated

a = A awhere_{0}/ (A + 18.25 a_{0})

aFor smaller wings, such as a stabiliser, the theoretical value is 0.095 per degree_{w}= (7.0 * 0.11) / (7.0 + 18.25 * 0.11) = 0.085

a_{s}= (3.6 * 0.095) / (3.6 + 18.25 * 0.095) = 0.064

Finally, putting all these values together in the original equation,
and using a value in the middle of the range
for *de / da*,
(0.4),
the NP value for the Airbear comes out to

hIn other words, the NP on the Airbear is located 37% behind the leading-edge of the wing, about a inch further behind the 1/4 chord point. The following table shows calculated values for a few other planes (gliders). The NP of all of them is greater than 33%. It also shows the affect of increasing the Airbear wing from 60" to a more common 2 meter wing, the NP moves forward. A longer tail or bigger stabiliser would similarly cause the NP to increase, move rearward._{n}= 0.25 + ( 0.6 * 0.51 (0.064 / 0.085) * (1 - 0.4) = 0.37

I hope this note shows you how to calculate the neutral-point of your plane to compare it to what your current CG location is.

Wing | Stabiliser | Tail Arm | Tail Volume | Lift Slope | Neutral Point (%) | Plane | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

span | chord | area | span | chord | area | stab | wing | a_{s}/a_{w}
| ||||

72.0 | 8.0 | 576 | 19.5 | 3.9 | 76.1 | 21.5 | 0.35 | 0.071 | 0.090 | 0.786 | 33.7 | Drifter-2 |

99.0 | 9.4 | 931 | 24.0 | 5.3 | 127.2 | 26.4 | 0.38 | 0.069 | 0.092 | 0.744 | 33.9 | Olympic-II |

68.0 | 7.8 | 530 | 19.5 | 4.3 | 83.8 | 21.1 | 0.43 | 0.065 | 0.089 | 0.730 | 34.8 | 1-26 |

72.0 | 8.0 | 576 | 18.0 | 5.0 | 90.0 | 24.6 | 0.48 | 0.064 | 0.090 | 0.714 | 35.7 | Airbear -2m |

60.0 | 8.5 | 510 | 18.0 | 5.0 | 90.0 | 24.6 | 0.51 | 0.064 | 0.085 | 0.750 | 37.0 | Airbear |

49.2 | 9.1 | 450 | 19.7 | 5.5 | 108.7 | 22.0 | 0.58 | 0.064 | 0.080 | 0.798 | 39.5 | Bantam |