Groundschool — Theory of Flight
Weight and balance
Revision 21c — page content was last changed December 5, 2008; consequent to editing by RA-Aus member Dave Gardiner www.redlettuce.com.au
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Groundschool — Theory of Flight |
Weight and balanceRevision 21c — page content was last changed December 5, 2008; consequent to editing by RA-Aus member Dave Gardiner www.redlettuce.com.au |
There are fixed limits to the payload an individual aircraft may safely carry. The payload is the total weight of pilot and passenger, fuel, baggage and portable equipment; i.e. it is the difference between the empty weight of the aircraft and its gross weight at take-off. That load must always be distributed so that the aircraft's balance — the position of the aircraft's centre of gravity — is maintained within defined longitudinal limits otherwise very dangerous instability conditions will exist.
9.1 Maximum take-off weightIn the RA-Aus context, maximum take-off weight [MTOW] has a number of connotations:
The European Union certification standard for very light aircraft is CS-VLA (formerly JAR-VLA) which has an MTOW of 750 kg. Since 1996 the published RA-Aus policy has been that the regulatory MTOW for aeroplanes registered by RA-Aus, that have been CS-VLA certificated to 750 kg (or any other suitable design standard that allows 750 kg), could be extended to 750 kg. CASA have a low priority certification project (CS 06/01) underway which may result in the inclusion of that change in CASR Part 103 sometime. If implemented, it would allow owners of RA-Aus aircraft — with a design MTOW up to, or greater than, 750 kg — to apply to RA-Aus for a variation in the allowed MTOW; providing all other conditions were met. From a purely safety viewpoint, the most important MTOW is the designer's calculated maximum safe operating weight, which may be less than, or greater than, the MTOW allowed under the relevant CAO. The design MTOW is related to the category of operation and the flight envelope. In the 'normal' category, applicable to all ultralights, the structure, particularly the wing, is required to cope with minimum structural load factors of +3.8g to –1.5g. Thus, the wings of an ultralight aircraft with a certificated MTOW of 544 kg would be required to cater for a minimum design load of 544 × 3.8 = 2067 kg. No matter which CAO regulatory limit ultralights are generically permitted to operate at, no aircraft may fly above the RA-Aus accepted MTOW for that particular aircraft type, which may not be as much as the regulatory limit or the design maximum safe operating weight. The RA-Aus accepted MTOW is the MTOW we refer to from this point. PayloadBear in mind that these limits relate to the structural strength of a new aircraft — and structures lose strength as they age; maybe more so if they are a very lightweight structure with little fail-safe provision. However, as aircraft age they also suffer from service weight pickup. They tend to put on weight through modifications, additional instruments or avionics, larger fuel tanks, heavier tyres and accumulation of paint and dirt; all of which reduce payload capability and make it rather easy to unwittingly exceed MTOW.In the general aviation field, most of the privately-owned recreational tourers are single-engine, fixed-undercarriage, four-seat aircraft, like the Piper Warrior or the Cessna 172. Generally these aircraft have a MTOW around 1150 kg — comprising an empty mass which is about 55% of MTOW and a fuel capacity about 15% of MTOW; consequently, 30% of MTOW (around 345 kg) is available for carriage of the pilot, passengers and baggage. International regulations state that when calculating payload capability — the difference between empty mass and MTOW — each person on board [pob] is assumed to weigh 77 kg. Most two-seat light and ultralight aircraft do not have a high payload capability; consequently a full fuel load — which weighs about 0.71 kg/litre — and just an average 77 kg pilot and passenger might constitute, or exceed, the maximum payload. A most important part of pre-flight planning is to estimate the weight of the payload. It is also advisable to re-weigh the empty aircraft occasionally to re-establish the empty weight and the cg position when empty. |
Exceeding MTOW has consequences that increase exponentially with the excess weight:
If MTOW is exceeded and the cg location is outside its limits, then very dangerous longitudinal stability conditions are introduced. [ The next section in the airmanship and safety sequence is the following section 9.2 'Balance — containing cg position within limits' ] |
9.2 Balance: containing cg position within limitsBalance refers to the location of the cg along the longitudinal axis. Location of the cg across the lateral axis is important, but the design of practically all aircraft is such that the empty weight is generally symmetrical about the longitudinal centreline. However, the location of the cg along the longitudinal axis is both variable and critical for stability. Consequently, the cg position must be assessed by the pilot before every take-off — even if the total weight is well below design maximum safe operating weight.The lateral and longitudinal position of the cg on any flight will vary according to the weight in the pilot and passenger seats, the amount of fuel in the tank(s), the placement of any baggage and other gear, and also the weight and location of modifications and additional installed equipment. (The load must be properly secured. The last thing you need is a heavy object banging around the cockpit in turbulent conditions and damaging the canopy or something equally vital. Anything loose in the cockpit/fuselage has potential to jam the control circuits or to move rearward in the fuselage during take-off acceleration or while climbing, thus adversely affecting the cg position.) Cg rangeFor safe aircraft operation, there must be calculated limits to the forward (nose-heavy) and the aft (tail-heavy) cg position. Those limits — measured from a datum point — are specified by the manufacturer or by the amateur designer. (The datum point is an imaginary vertical plane through the fuselage, possibly located at the engine firewall, the wing leading edge or perhaps the back of the spinner.) If the cg is situated between the fore and aft limits, the aircraft should have positive static longitudinal stability.Care should be taken when flying amateur-designed aircraft, as the cg range for that aircraft may not be within practical safe limits, making the aircraft dangerously unstable in some conditions. In the 'Aerofoils and wings' module it was stated that the wing aerodynamic centre [ac] is situated near 25% mean aerodynamic chord [MAC]. For longitudinal stability in light aircraft the most forward position of the cg allowable might be about 15% MAC and the most aft position about 35% MAC, basically 10% either side of the wing ac; or perhaps the aircraft neutral point. Forward cg limit — nose-heavyThe forward cg limit is determined by the elevator's ability to flare the aircraft at low speed when landing in ground effect; i.e. the least forward cg position where full up-elevator will obtain sufficient moment arm to rotate to the stall aoa, without requiring the pilot to exert an excessive pull on the control column. The forward position is constrained because the further forward it is, the more download the horizontal stabiliser/elevator is required to produce to balance it. Consequently, the tailplane must fly at a greater negative aoa — thus decreasing total aircraft lift — and the wing must then fly at a greater aoa to counter the loss. This results in more drag from the wing and the tailplane and, consequently, reduced performance. The pitching moment characteristics of the wing must also be considered.If a nosewheel undercarriage aircraft is landed in a nose-heavy condition, the possibility of touching down nosewheel first — wheelbarrowing — is greatly exacerbated; a slowing aircraft, pivoting on the nosewheel, is in a grossly unstable condition. The possibility of an extreme ground loop, with consequent aircraft damage, is high. Also touching down nosewheel first can result in a bounce that is difficult to control and may end up wiping off the nosewheel gear. Aft cg limit — tail-heavyThe aft limit is determined by the amount of reduction in the length of the horizontal stabiliser moment arm — which decreases the effectiveness of the moment — and the increase in the nose-up pitching moment of the cg/ac couple, because of the cg distance behind the ac. It is the elevator authority available at low speed that determines the aft cg limit. A cg outside the aft limit will decrease or remove longitudinal stability, and the ability to recover from stalls and spins and may itself lead to a departure stall (i.e. a stall shortly after starting to climb out from the airfield with the engine at maximum power) because there is insufficient elevator authority to lower the nose; even with the pilot applying maximum forward pressure. A go-around with the cg near the aft limit — with flaps extended, full power, and nose-up landing trim still applied — can be particularly dangerous for the unwary pilot.An aircraft does not have to be near MTOW for the fore or aft cg limits to be breached, as can be seen in weight/cg position limitations. Cg position will change as fuel is consumed. Actually, the pilot of a light aircraft can vary the cg position just by leaning forward or backward in the seat! The following is an extract from an RA-Aus incident report: "The aircraft, with instructor and student on board, was returning to the airfield when a pitch-down occurred. (Unknown to them, the elevator control horn assembly had failed.) Control stick and trim inputs failed to correct the situation, but a reduction in power did have a correcting influence, though not enough to regain level flight. A satisfactory flight condition was achieved by the pilots pushing their bodies back as far as possible and hanging their arms rearward. A successful landing at the airfield was accomplished." Mean aerodynamic chordThe cg location can be expressed as a percentage of the mean aerodynamic chord [MAC], which is particularly useful for designer/builders. For a rectangular wing of constant aerofoil section dimensions, MAC is just the chord. For a symmetrically tapered wing, it is the average of the root chord and the tip chord. Further information is in 'ascertaining MAC graphically'. The position of the fore and aft cg limits is measured as a percentage of MAC, from the MAC leading edge. Usually for a single- or two-seat aircraft, the most forward position would be aft of 15% MAC and the most aft position would be forward of 30–35% MAC. Thus, the allowable cg range in a light aircraft shouldn't exceed 20% MAC. The linear distance between the fore and aft limits is perhaps 15 to 20 cm.Weight/cg position limitationsTo demonstrate how the weight and balance limits for a particular aircraft may vary according to the planned flight operation, I have selected a four-seat aircraft that is certificated for operation in three certification categories — normal, utility and acrobatic. The following data is extracted from the aircraft flight manual.The maximum take-off weight (in pounds) for operations in each category are: normal 2335 lb, utility 2137 lb and acrobatic 1940 lb. The fore and aft cg limits are measured in inches from the datum point and also shown as a percentage of MAC. The maximum number of persons on board [POB] allowed for each condition is shown.
The table data is summarised below in graphical form, depicting the weight/cg envelope. The vertical axis depicts weight in pounds and the horizontal axis the stations in inches from the datum. The section outlined in blue is for normal operations with a +3.8g limit load factor, the green outline is for utility operations (training, spinning) with +4.4g limit and the red area is for acrobatic category operations with a +6.0g limit. To determine the fore and aft cg limits, first ascertain the weight position on the vertical scale and read across within the appropriate category. For example, with weight 2180 lb in the normal category, the forward cg limit is at 96 inches from the datum and the aft is at 103.58 inches.
Note the very restricted cg and MTOW range for aerobatics — 4.51 inches (11.5 cm) or 7.5% MAC — and the requirement for the forward limit to start at 18.5% MAC, the most forward position. On the other hand, when the aircraft is at maximum normal category weight the cg range is only 5.39 inches (13.5 cm) — but now the cg range is required to be at the other end of the scale, between 27% and 36% MAC. The only occasion when the aircraft balance can be anywhere in the specified range of 18.5–36% MAC (10.51 inches or 27 cm) is when the aircraft is operating in the normal category at a weight less than 2000 lb. The area sliced off the top left corner is fairly representative of most weight/cg limitation envelopes for medium to higher-performance light aircraft. [The next section in the airmanship and safety sequence is contained within section 11.6 Causes of take-off accidents] |
Ascertaining mean aerodynamic chord graphicallyFor a rectangular wing of constant aerofoil dimensions and constant chord, the MAC is just the chord. For a symmetrically tapered wing it is the average of the root chord and the tip chord. The diagram below is a representation of the graphical method for calculating the MAC position on such a wing. The method works just as well for more complex wing plan forms.Note that for aerodynamic calculations the aircraft wing includes the area within or above the fuselage and the root chord is always on the fuselage centreline. The position of the wing aerodynamic centre is marked with the red asterisk.
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9.3 BallastingSometimes an aircraft, with a tandem pilot/passenger seating configuration like the Breezy, will require a specified/calculated ballast weight to be strapped in an unoccupied passenger seat, unless the passenger seat is located at the cg position. There are also pusher engine designs that are entirely dependent upon sufficient minimum pilot weight to put them in balance range, so a lightweight pilot may have to sit on a ballast bag. With tandem two-seaters there will be both a minimum and maximum pilot weight for cg range, but that in turn could be influenced by rear seat weight to keep within MTOW. In some cases, the rear seat also has a moment arm and can affect the front seat arm, depending upon rear seat weight.Regulations require that any ballast, baggage or other cargo that is stowed on a passenger seat must not weigh more than 77 kg; the weight should be evenly distributed and positioned so that neither the cargo nor its restraints can interfere with the operation of the aircraft controls. In addition, if fitted with removable dual controls, the control column at the passenger seat should be removed. It is advisable that the cockpits of two-seaters — particularly tandems — but any aircraft that is dependent upon the presence of a minimum and maximum pilot weight, should be clearly placarded with the minimum/maximum seat weights shown in the flight manual. The need for ballasting is not confined to ultralights. The cg position of the four-seat Beech Sundowner is outside the forward limit when the only occupants are two above-average weight people in the front seats, and in such conditions the aircraft has a tendency to wheelbarrow on landing. Flying an unbalanced ultralight — i.e. in a tail-heavy or a nose-heavy condition — even though the cg is not outside the limits, increases pilot fatigue because of the need to maintain a constant heavy pressure on the control column if no trim device, or a limited device, is fitted. 9.4 Calculating cg position and momentUnloaded aircraftThe longitudinal position of the cg and its moment about a datum point are readily calculated. A measuring tape, heavy-duty bathroom scales, plumb bob and a chalk line are needed. The following is the procedure for an empty light nosewheel aircraft.Chalk a straight line on a level surface that is at least the length of the fuselage, then chalk another line perpendicular to that. Roll the aircraft along the longitudinal line until the axles of both main wheels are directly over the cross line. Chalk another short cross line to mark the nosewheel axle position. Mark a position on the longitudinal line that is directly below the front or back end of the spinner thus providing a datum point. Measure the longitudinal distance (the nosewheel moment arm) from the datum to the nosewheel axle line and the distance (the mainwheel moment arm) from the datum to the main wheels axle line. Place the scales under the nosewheel, block up the mainwheels so that the aircraft remains level and note the weight. Then place the scales under one of the mainwheels and block up the other main plus the nosewheel. Note that weight. Repeat for the other mainwheel. Add the weight on the nosewheel to arrive at the aircraft empty weight (or perhaps its weight with full fuel). Multiply the nosewheel weight by its arm to get the nosewheel moment and the added mainwheel weights by the axle arm to get the mainwheel moment. Add the two together to arrive at the total empty aircraft moment. The cg location from the datum equals the empty aircraft moment divided by the total aircraft weight. For example: Nosewheel weight = 80 kg and arm = 0.5 m Thus nosewheel moment = 40 Mainwheel weight = 2×160 kg and arm = 2.5 m Thus mainwheels moment = 800 Empty aircraft weight = 80+160+160 = 400 kg Empty aircraft moment about the datum = 40 + 800 = 840 Cg location when empty = 840/400 = 2.1 m from the datum Loaded aircraftThe cg location with pilot/passenger aboard can be calculated if a point about 20 cm forward of the seat back (being the approximate centre of mass position of a seated occupant) is marked on the longitudinal chalk line; the distance from the datum point to that point is the front seat(s) moment arm. The front seat(s) moment is the occupant(s) weight multiplied by the arm, and the new cg location is the empty aircraft moment plus the front seat moment divided by the empty aircraft weight plus occupant weight.For example: Side-by-side front seats arm = 2.3 m Occupants weight = 150 kg Thus front seats moment = 345 Empty aircraft weight = 400 kg Empty aircraft moment = 840 Total aircraft weight = 550 kg Total aircraft moment = 1145 cg location = 1345/550 = 2.08 m from the datum Similar calculations can be made to include fuel weight and baggage distribution and weight. Aircraft or kit manufacturers should provide data defining a datum point together with the associated arms for the pilot/passenger seats, fuel tanks and baggage compartments, plus the fore and aft cg limits expressed as a distance from the datum point. With such information the pilot can calculate the loaded cg position using the measured weights of occupants, fuel and baggage. The aircraft manufacturer should provide a loading chart to facilitate calculations. Of course the manufacturer's chart is useless (and you may make the aircraft dangerously unstable) if you stuff baggage and equipment into any available space outside the designated and designed baggage compartment. The next module in this Flight Theory Guide discusses weight-shift control. |
Groundschool — Flight Theory Guide modules
| Flight theory contents | 1. Basic forces | 1a. Manoeuvring forces | 2. Airspeed & air properties |
| 3. Altitude & altimeters | 4. Aerofoils & wings | 5. Engine & propeller performance | 6. Tailplane surfaces |
| 7. Stability | 8. Control | [9. Weight & balance] | 10. Weight shift control | 11. Take-off considerations |
| 12. Circuit & landing | 13. Flight at excessive speed | 14. Safety: control loss in turns |
Supplementary documents
| Operations at non-controlled airfields | Safety during take-off & landing |
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