Balancing

Calculating the optimum balance point

René JOSSIEN's formula :

There is, in the FF world, a well known and proof formula for calculating the optimum position of the centre of gravity for a model. This formula has been established many years ago (in the sixties) by the René Jossien, a French free flight's specialist who has also issued many articles on peanuts in the MRA magazine under the nickname "Le Saint" in the seventies.

This empirical formula is the result of statistical analysis carried out on hundreds of successful free flight models of all classes (Peanut to FAI power - See hereafter). It was published for the first time in the French newsletter "Vol Libre" (Association des Amateurs d'Aéromodèles Anciens). It can also be found in some MRA articles (for instance, MRA N°466 - September 1978 issue) as well as in 1998 Symposium documents of the National Free Flight Society (NFFS - 1998 Symposium Report - pages 52 to 54). René Jossien has slightly adjusted his formula year after year to take into account the evolution of model techniques and FF rules. The version presented hereafter is dated April 2002. It was published by René Jossien in issue #147 (02-4) of Vol Libre.

This formula is based on the model's specifications : Wing surface (SA), Tail surface (SS), Projected wingspan (EP) and Great lever (GL) which is the distance between the wing leading edge and the stabiliser leading edge. It takes into account flight conditions and model types and can be used not only for all FF categories (and there are many of them - See hereafter) but also for R/C models (slow-fliers, park-fliers, etc...). You can use it also with old vintage models for instance to find the COG position when it is not indicated on a plan.

April 2002 Version :

COG = KA + [(KSSSGLEP)/(SASA)]

in which we have :

COG : Distance from wing L.E. to plumb line of C.G. in % of the wing mean chord (from the mean chord L.E.),
KA : Wing coefficient (without unit) - See below,
KS : Stabiliser coefficient (without unit) - See below,
SS : Stabiliser area,
GL : Distance between the L.E. of the wing mean chord and the L.E. of the stabiliser mean chord,
EP : Projected wing span (Excluding the fuselage width for very broad fuselages),
SA : Wing area (excluding the surface covered by wide fuselages).

Units: The formula remains valid for any kind of units, provided they are consistent, i.e. :

Length in cm and area in cm2,
Length in dm and area in dm2,
Length in inches and area in square inches.

Wing coefficient KA :

KA = 20 + A + B + C

A (Coefficient related to wing's height above fuselage's axis).

= 0 for a low wing,
= 2 for a mean fixed wing,
= 3 for a wing set at a height of 3% of the span,
= 5 for a wing set at a height of 6% of the span,
= 6 for a wing set at a height of 9% of the span,
= 7 for a wing set at a height of 12% of the span.

B (Coefficient related to wing's airfoil).

= 1 for half-symetrical airfoil (like Clark Y),
= 2 for flat-bottom airfoil,
= 3 for cambered airfoil,
= 4 for more cambered airfoil,
= 5 for most cambered airfoil (like indoor F1D).

C (Coefficient related to model class and usage) :

Weather or flight pattern		Scale Ste Formule Peanuts	F1B day RC glider R/C gas	F1A - A1 Electric CO2 - C d'H.	F1B sun set 0/T Wakefield P30	Open gas 1/2 A Indoor duration	F1C with VIT
Turbulent w.	Very good climb	-6	-4	-2	+1	+4	+1
All weather	Good climb	-4	-2	0	+3	+6	+3
Calm weather	Good glide	-2	0	+2	+5	+8	+5

Stabiliser coefficient KS :

KS = k + D + E

k (Coefficient according to pilot's skills)	k = 20 for initial training and beginners, k = 24 for final trimming.
D (Coefficient according to fin design)	= 0 for single fin, = 1 for small fins at stab. tips or stab. with minor interference, = 2 for big fins at stab. tips.
E (Coefficient according to stabiliser airfoil)	= 0 for symmetrical airfoil, = 1 for flat-bottomed airfoil, = 2 for moderately cambered airfoil, = 3 for more cambered airfoil, = 4 for heavily cambered airfoil (like indoor F1D).

An Excel spreadsheet you can download in a French or an English version will do the calculations for you !

You can also download an .exe software (by Chris Stoddart) also based on this formula, with its documentation in Microsoft Word format.

You will find on this site an historical account on the formula and examples of differences recorded between calculated and actual values for CoG positions on various models. Very often, these differences are less than 1%. Impressive !

Nota : - When the wing is rectangular, the mean chord has the same length as the root chord.
- When the wing is not rectangular, the mean chord is the chord running through the centre of gravity of the surface of the half-wing (can be found by balancing an half-wing template on a sharp edge parallel to the root chord).

Free Flight classes (according to 2002 FAI rules) :

As you can see below, there is a wide range of FF models, from few grams (even less !) to several kilograms (F1E). Therefore, it is not a surprise you can also use René Jossien's formula with all R/C model types.

Classes	Type	Brief description
F1A	A2 "Nordic" gliders	Surface : 32 to 34 dm2 (Span : around 2 m) Mass : 410 g minimum., Launching cable : 50 m max., World championship class.
F1B	Rubber powered models Wakefield Cup	Surface : 17 to 19 dm2, (Span : around 1,8 m) Mass : 200 g mini. (without motor), Flight duration : 3 to 4 minutes, World championship class.
F1C	Power models (2,5 cm3)	Swept volume : 2,5 cm2 maximum, Mass : 300 g/cm3 minimum, Wing loading : 20 g/dm2 minimum, Motor run: 5 s maximum, World championship class.
F1D	Indoor Models Rubber powered models	Span : 550 mm maximum, Mass : 1,2 g minimum Ceiling heights : - Category I : less than 8 m, - Category II : from 8 to 15 m, - Category III : from 15 to 30 metres, - Category IV : higher than 30 metres, World championship class.
F1E	Slope soaring gliders automatic steering	Surface : 150 dm2 maximum, Mass : 5 kg maximum, Wing loading : 100 g/dm2 maximum.
F1F	Helicopters
F1G	Rubber powered models Coupe d'hiver type	Mass : 70 g (less motor) minimum, Motor mass : 10 g maximum, Flight duration : 2 minutes.
F1H	A1 gliders	Surface : 18 dm2 maximum, Mass : 220 g minimum., Launching cable : 50 m max., Flight duration : 2 minutes.
F1J	Power models 1/2A class	Swept volume : 1 cm3 maximum, Mass : 160 g minimum, Motor run : 7 s maximum.
F1K	CO2 powered models	Surface : 12 dm2 maximum, Mass : 75 g minimum.
F1L	Rubber powered models Indoor - EZB type	Span : 458 mm (18') maximum, Wing chord : 76 mm (3') maximum. Mass : 1,2 g minimum (less motor), Structure : Balsa.
F1M	Rubber powered models Indoor - "F1D beginner"	Span : 460 mm maximum, Mass : 3 g minimum without motor.
F1N	Indoor HLG
F1P	Power models	Swept volume : 1 cm3 maximum, Span : 1,5 m max., Surface : 26 dm2 minimum, Mass : 250 g minimum, Motor run : 10 s maximum, World championship class.

Some other classes :

Micro 35	Rubber powered models Indoor	Span : 350 mm maximum, Mass : 1,8 g mini. (less motor) for cadets and juniors.
Sainte Formule	Rubber powered models Indoor - semi-scale	Span : 330 mm maximum, Mass : 3 g mini. without motor.
F4F	Peanuts Indoor - scale	Span : 330 mm maximum, Rubber powered.
Maquette 66	Outdoor Scale

Vol Libre : International newsletter dedicated to free flight.

Published by André SCHANDEL
Subscription 6 issues (2003) : Europe 32 Euros (André SCHANDEL)
USA and CANADA : 35 $ (Peter BROCKS)

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