**Introduction **One of the problems that arises when building a
model aircraft is the correct placement of the Center of Gravity. When assembling
an ARTF or scratch building from a Plan the problem does not arise, as the designer
should give full details on the plan or in the kit. However, when you are building
to your own design you may need to work out where the C of G is located. This
is not a problem with a "normal" model, but what about Biplanes, a Beech
Staggerwing, Delta's, Canards & other odd layouts. Full size designers have
powerful computers and wind tunnels but we must get it right for that first flight.
Once in the air you are fully committed and an error will almost certainly cause
a crash or at best a very twitchy flight. There is little point going into computational
details here as there are one or two good programs on the Internet that will do
most of the work for you. You will find links below to the ones I have located
as they are quite hard to find and suggest you try these out, they all give more
or less the correct answer. In the good old free flight days, test glides were
the norm, trimming out a model into long grass until the model flew straight and
level just off the stall. Test glides of heavy fast radio models are not possible
so we need to get the C of G correct for that first flight. If in doubt use the
old rule of thumb "1/4 of the wing chord back" This is generally not
far out. See also the "model of a model" method.

**Calculation
Problems** There are however a couple of problems. Most of the calculations
involve an element of guesswork so the final result can only be at best described
as a very accurate guess. For example tailplane efficiency varies between 30 and
100% and you need to make an educated guess as to the value you use in your calculations.
A tailplane close to the wings trailing edge and in the wake vortex will come
out as low as 30%, a "normal" location 60% whilst a canard (foreplane)
is in the 95-100% range as it operates in "clean" air. A high set "Tee"
tail will be closer to 90%. Do not bother with lifting tailplanes. A flat plate
or thin symmetrical type is just as efficient. Secondly the C of G needs to be
in front of the Neutral Point, but how far? Again a degree of intelligent guess
work is required. The accepted figure is between 5 & 20%, 15% is a good compromised
for first flights. See note below. Once you have a model that flies, at least
well enough to land in one piece, you can then adjust the C of G based on the
results of the first flight. Some links are given below where you can find Nomograms
etc. to do most of the calculations for you and I will add others as I find them.

**Fly by Wire Fighters **Variously known as CCV (Control Configured
Vehicles) or ACT (Active Control Technology) these aircraft are designed to be
unstable and only fly under the full control of high speed computers, with minimum
input from the pilot, where the roll and pitch sensors input to the control surfaces
at 100 x per second. Not quite as fast as our 2.4GHz ! Some very successful large
turbine models of full size CCV aircraft have been built and fly very well. The
only difference being in the location of the C of G. CCV aircraft have this AFT
of the NP whereas models should have this in front of the NP or Neutral Point.
(or Center of Pressure CP) It should be noted that CCV aircraft have a tailplane
significantly SMALLER than would be considered normal. This should be taken into
account when designing a MODEL otherwise it may not be large enough for normal
control. The WWII Spitfire has a very small tailplane to reduce drag and increase
manoevreability.

**Terminology** There is a lot of confusing terminology
regarding this subject and an attempt has been had to clarify these in the notes
at the end. Please read these first. In most engineering calculations weights
& pressures are *assumed* to act a one point ie. at the C of G. We know
this is not exactly the case as the weight of any object is spread over its entire
volume/area, not always evenly, but spread nevertheless. Concentrating this mass
or weight at one (imaginary) point makes meaningful calculations possible.

**Biplanes
and other multi-wing aircraft.** I came across these diagrams in an old copy
of the ** Aviation Handbook - Johnson - 1931** and it does seem to be
a very authoritative method of determining the location of the MAC

This article is reproduced with the kind permission of Alasdair Sutherland and should enable any modeller to determine the MAC on any Biplane

Solving Incidence and Balance Issues on Biplanes. Page 1 Page 2 Page 3

Figure A...Figure B ...Figure C ...Figure D-1 ...Figure D-2 ... Worked Example

**Determining the
C of G by the use of a Model ** By building an accurate small scale model of
your new model it is possible to determine very accurately where the C of G lies.
Make a model (say 1/4) the size of your model as accurately as possible c/w with
profile fuselage, tailplane and fin. Make the wings and tail in sheet balsa and
round the LE/TE. Test glide the scale model until a nice flat glide results. Remove
nose weight until a *very* slight stall results. This is the AFT position.
Now add weight until the glide is unacceptable. This is the most FORWARD position.
Check the location on the test model and set the C of G on your full size model
somewhere in between these two extremes. At least it should fly with reasonable
safety and is better than nothing for very unorthodox or hard to compute models,
such as Rear Swept Biplanes or Canards.

**Flying Wings & Deltas**
Use the calculators given below but put in very low values (0.01 for example)
for the (non existant) Tailplane. Some of the calculators will not accept zero
as a value. The results are confirmed by the positions on models that fly well.
Zagi's, Rapier, Delta 363 etc.

**Gordon Whitehead - Winning Formula **This
article appeared in the May issue of Radio Modeller 1994 and is a very comprehensive
look at Center of Gravity calculations. Interestingly it covers a wide variety
of Multi Wing Aircraft as mentioned above. It probably gives the best method of
calculating Centres of Gravity you are likely to find with an accuracy way above
anything modellers are likely to require.

Scanned copy of the original article Page 1... Page 2... Page 3...Page 4

**Rene Jassien **Looking through
some old Model Aircraft Magazines (circa 1983) I came across an article by Rene
Jassien a well known and very successful competition flyer in the 1980's This
article gives a multi-factor method of calculating the Center of Gravity to very
precise limits. Specifically designed for competition use where the C of G may
be set back as much as 75% from the leading edge of the wings mean chord, or may
be even BEHIND the trailing edge. This is due mainly by the use of *lifting
tailplanes* set a long way back from the wings trailing edge. As you can see
the theoretical values matched very precisely the actual settings on real well
designed and successful models.

Surprisingly when the dimensions of a * Frontier
Basic Trainer* were fed in the solution was 24%, much in line with what
one would use for such a model. To make the calculation very simple I have produced
an Excel spreadsheet, just feed in the numbers and out pops the solution. Please
note that this formula and the models it was designed for are 25 years old and
model design and technology may have moved on. Presumably the way aircraft fly
has not, so the solutions may still have real value.

Excel
spreadsheet with a worked example for * La Fleche* all weather Wakefield
.

Excel spreadsheet with a worked example
for a * Frontier* Basic R/C Trainer.

Scanned copy of the original article Page 1... Page 2 **

** As I was unable to contact Rene Jassien this article is reproduced without his permission.

**Barnaby Wainfan** is not an author/designer
who springs to mind but he has produced an excellent book on "Airfoil Selection"
and he has also produced some foils of his own, these are hard to find and may
be listed as BW types or as Wainfan. The book can be obtained from http://www.aircraftspruce.com
navigate to *Books/Videos then Books then Design.* The **Aircraft Spruce
Company** site is a mine of information for modellers & full size builders/flyers
alike. Well worth a visit.

**Model Aircraft Aerodynamics** by Martin
Simons is one of the best books on the subject. Motorbooks International Wisconsin
USA ISBN 0-85242-915-0

See also **Dr. Martin Hepperles'** web site on
Aerodynamics for Model Aircraft
Go to the **Flying Wings** Section on the left.

Links to sites with C of G calculators and further information.

www.palosrc.com/instructors/cg.htm

http://adamone.rchomepage.com/cg-calc.htm

http://www.geistware.com/rcmodeling/index.htm Go to Tips & Techniques/Construction Tips/Calculators/Aircraft Balance Calcs.

Designing the C of G using Moment Arms

**Notes on Nomenclature.**

** Center
of Gravity or C of G** This is a point on an aircraft that when suspended
it would balance in a normal flying attitude. It is should always be on the longitudinal
center line (nose/tail) It is the only parameter that can be easily adjusted once
the model is designed and built, by adding weight to the nose or tail. To determine
a models C of G suspend it from any point by a piece of string, say an undercarriage
leg. Project the axis of the string onto the fuselage side and repeat for some
other point, say a Wing Tip. Where the projections cross is exactly the C of G

* Neutral
Point (NP) or Center of Pressure (CP) *This is a point on the aircraft's
center line where all the lift forces (Wings,Tailplane, Fuselage etc.) are

Model Aircraft (usually highly refined competition models) with very long moment arms can easily have the Neutral Point well AFT of the wings trailing edge, giving rise to a surprising location for the C of G which may well lie on or even AFT of the wings trailing edge.

The neutral point is quite difficult to calculate but the method in this article gives an excellent practical method. It works by making a card model where the C of G of the wing and tail has been (artificially) re-located to the 25% position, which is now the center of lift or Neutral Point

** (Aircrafts)
Center of Lift **Same as the Neutral Point or Center of Pressure

** Static
Margin** The distance or amount, usually expressed as a %, expressing the
location of the Center of Gravity in front (or behind) of the Neutral Point. Usually
between 5% and 20%. 5% would be suitable for a highly responsive aerobatic model
and 20% for a docile trainer. 15% is a good starting guess. Modern "Fly by
Wire" combat aircraft are designed to be unstable as this gives fast control
response. The speed of control input required to fly is beyond the capacity of
the human brain so a computer actually flies the aircraft interpreting the inputs
from the pilot. The simple

* Wing Chord *
The distance across a wing parallel to the fuselage center line. Usually identical
to the length of a normal wing rib.

** Mean Chord** The average
of all chords.

* Chord Line *A line joining the leading edge
and the trailing edge of an airfoil section. Note as a rule of thumb, most aerofoils
only start to produce lift when the Chord line is at 2 degs positive.

** Tip
Chord **The chord at the outer end of the wing.

** Root Chord **The
chord at the inner end of the wing.

** Mean Aerodynamic Chord (MAC) **A
point out from the wings root where all lift (for that 1/2 surface only) is assumed
to be located. Once the MAC is located the Aerodynamic Center is located on this
line 25% back from the leading edge.

* Wing Aerodynamic Center (WAC)
*For any conventional aerofoil, each wing, tailplane or fin has its center
of lift at approx. the 1/4 chord position. i.e. 25% in from the leading edge and
at some point out from the wing root. (MAC) With a correctly designed aerofoil
this 25% point does not move significantly in

** Tailplane Efficiency **See para 2
above. Varies between 30 & 100% dependent on location.

** Half Span
**In all these calculations it is usual to consider one half of the model
only. If the total span is 600mm but the fuselage width is 60mm wide at the wing
root then the 1/2 span is 600 - 60 / 2 = 270mm. Ignore any Dihedral loss unless
significant.

** Wing Taper Ratio **Tip Chord divided by Root Chord.
eg. Root Chord 200mm, Tip Chord 50mm Wing Taper Ratio is 200/50 = 4:1

** Aspect
Ratio **Basically the Span / Chord. eg. A plain rectangular wing of 1000mm
Span with a Chord of 50mm has an Aspect Ratio of 1000/50 = 20:1 For tapered, swept
wings or delta's you must use the Mean or average Chord value.

Text © Colin Usher 2011 Illustrations © Colin Usher 2011

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