Introduction One of the problems that arises when building a model aircraft is the correct placement of the Center of Gravity. When building from a plan or an ARTF the problem does not arise, as the designer should give full details on the plan or in the kit. However, when you are building 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. Heavy fast radio models generally glide like bricks so we need to get the C of G correct for that first flight.
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. 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 to suit 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.
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 eg. 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. Find the aerodynamic center for each 1/2 wing and then join these points up. The combined position for the aerodynamic center for the wings falls somewhere on this line. The lower wing of a Biplane is less efficient than the upper wing so the point will be nearer the upper wing. On a Triplane it will fall more or less on the middle wings MAC.
Flying Wings & Deltas Use the calculators given below but put in zeros or very low values (0.01 for example) for the Tailplane. Some of the calculators do not accept zero as a value. The results are confirmed by the positions on models that fly well. Zagi & Ripmax Rapier etc.
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 lisrted 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
www.smithymfc.co.uk/html/c_of_g.html
http://adamone.rchomepage.com/cg-calc.htm
http://www.geistware.com/rcmodeling/index.htm
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 always 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 the C of G (exactly).
Neutral Point This is a point on the aircraft's center line where all the lift forces (Wings,Tailplane, Fuselage etc.) are assumed to act. The center of gravity must always be in front of this point by a factor known as the Static Margin. See below.
(Aircrafts) Center of Lift Same as the neutral point.
Static Margin The distance or amount, usually expressed as a %, expressing the location of the Center of Gravity in front of the Neutral Point. Usually between 5 and 15%. 5% would be suitable for a highly responsive aerobatic model and 15% for a docile trainer. 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 actuall flies the aircraft interpreting the inputs from the pilot. The simple Dive Test will show if the C of G is about correct. From a good height put the model into a power off vertical dive, with controls at neutral. If the model pulls out by itself the C of G is not far out. If it continues down, pull out quickly and add weight to the nose. Works every time.
Wing Chord The distance across a wing parallel to the fuselage center line 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.
Tip Chord The chord at the outer end of the wing.
Mean Aerodynamic Chord (MEC) A point out from the wings root where all lift (for that surface only) is assumed to be located. Once the MEC is located then the 1/2 wings Aerodynamic Center is located on this line 25% back from the leading edge.
Wing Aerodynamic Center (WAC) 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. The calculations in the links above determine this point for each lifting surface. This can be determined by the use of nomograms, mathematical calculation or by simple geometric methods. Common examples of the geometric method are shown in the drawings below.
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.
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 2008 Illustrations © Colin Usher 2008
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