Weight and Balance
The weight and balance calculation ( German weight and balance ) as part of the flight preparation of aircraft is used to calculate the loading plan and to determine the center of gravity. It is the pilot's responsibility to ensure that the maximum take-off weight is maintained and that the center of gravity is within the permissible range. The corresponding limitations are recorded in the aircraft documentation, which is part of the flight and operations manual.
The weight and center of gravity determination is an essential part of flight planning because
- the weight of the aircraft has a decisive influence on the amount of fuel required ,
- the weight must also be taken into account when calculating the take-off speeds ,
- various structural load limits must be complied with (e.g. MTOW , maximum weights for holds),
- the center of gravity of the aircraft influences the setting of the trim tab during take-off and
- the center of gravity of the aircraft in large long-haul aircraft during flight has an impact on fuel consumption.
Accordingly, weight and balance is also a teaching subject for pilots, a section in the aircraft operating manual and an important criterion in the design and construction of aircraft. Most airlines also have a Weight and Balance department in the Operations division .
Meaning and units
The English term Weight and Balance literally means weight and balance in German . It has not become entirely correct to speak of weight measured in Newtons , although, strictly speaking, the mass is given in kilograms , tons or pounds . The formally correct designation is not weight and balance, but mass and balance (literally in German: "mass and balance"). The term mass and balance is becoming more and more popular.
Determination of empty weight and center of gravity
As part of the type and type approval, the weight and center of gravity of the empty aircraft are determined by means of the aircraft weighing . The frequency at which this weighing must be repeated differs depending on the type of aircraft. So-called “fleet sampling” can be used for commercial aircraft operators. Groups of identical aircraft are formed, all of which are within a weight corridor. When weighing an aircraft in the group, the weighing frequency of all other aircraft in the group can be extended accordingly, provided the weighed aircraft does not deviate too far from the group average. This reduces aircraft downtime and the labor of weighing itself, thereby saving costs.
Center of mass and point of lift
Reference point
The center of gravity is measured from a specified reference point. From a mathematical point of view, it is irrelevant where exactly this defined reference point is located, since it only defines the coordinate system. The position of the individual forces is indicated in relation to this reference point. The empty aircraft (without fuel, passengers and cargo) has a precisely measured center of gravity. The individual fuel tanks have a defined focus, as do the individual cargo holds and the individual seating positions for pilots and passengers. In the upper part of Figure 1, the common reference point is the aircraft nose, while in the lower part of Figure 1, a mark on the aircraft is used as the reference point (e.g. the partition between the cockpit and the passenger cabin).
Balance of forces and moments
For reasons of flight mechanics, the aircraft has a foremost (blue arrow) and a rearmost (green arrow) center of gravity, which must not be exceeded (Fig. 2). The aircraft weight is based on the center of gravity. It can be changed before the flight by loading and refueling and decreases during the flight by the fuel consumption. In most large transport aircraft, the aircraft weight by the pilot can also fuel draining (Engl. Fuel dump ) are reduced or influenced by pumping able. This guarantees that not only the weight and buoyancy forces, but also the torques around the center of gravity remain in balance.
Downforce on the elevator
Airplanes are designed so that the center of gravity (center of gravity - CG) before the center of lift (center of lift - CL) is (see also: neutral point and pressure point ). In addition, a weak downward force on the elevator stabilizes the horizontal position of the aircraft's longitudinal axis (Fig. 3). The lift starts at the lift point of the wings . It can be increased by increasing the airspeed . The pilot controls the downward force on the elevator with his control horn or stick . The elevator acts like an upside-down wing, generating downward lift instead of upward lift.
Without this downward force of the elevator (e.g. if the elevator breaks), the aircraft would inevitably nod with the bow down (Fig. 4).
Shifts in the center of gravity
If the center of gravity is shifted further forward, the balancing downward force on the elevator must be increased accordingly in order to maintain a level flight (Fig. 5). Such a mass shift can occur due to the loading of the aircraft, the fuel consumption in flight or by pumping the fuel between different tanks. In emergencies, passengers can also be moved.
In the opposite case, when the center of mass shifts further back, only a very small downward force is required on the elevator to balance the aircraft horizontally (Fig. 6). Shifts in the center of gravity in flight also occur when cargo is dropped from transport machines , when parachutists or airborne troops are dropped , when refueling from the air or when bombs are dropped.
Theoretically, the extreme case is conceivable that the center of mass is shifted so far back that it reaches the lift point (Fig. 7). In this case the horizontal control (around the transverse axis) of the aircraft becomes very unstable. [Document?] It then wants to break out constantly up or down because of minor disturbances ( turbulence ). However, only very weak forces on the elevator are required for correction. However, in addition to downward forces, the elevator must also be able to generate upward forces.
If the center of mass is shifted so far back that it lies behind the lift point, then the elevator only has to generate lift force in order to steer the aircraft in a horizontal position (Fig. 8). This type of configuration is not used in practice in modern commercial aircraft.
Reduced trim
In modern aircraft, the center of gravity is closer to the lift point (Figure 9) so that less altitude trim is required and thus fuel can be saved, because every altitude trim (downward force on the elevator) leads to downforce (or lift) on the elevator. Since the elevator is an aerodynamic wing, every lift (whether positive or negative) also generates additional air resistance, the induced air resistance . Any additional air resistance increases fuel consumption and thus reduces the aircraft's profitability.
Duckwing
There is a completely different spatial relationship between the lift point and the center of mass and the elevator in duck wings (Fig. 10). While in conventional aircraft the horizontal stabilizer has to generate downforce for reasons of longitudinal stability, in canard aircraft it generates lift.
Small aircraft
Using the loading plan and the trim plan, the pilot must ensure that the maximum flight mass is not exceeded and that the aircraft is loaded correctly. The center of gravity of the loaded aircraft must lie within the specified maximum rear and front center of gravity.
For the calculation, the pilot uses tables that he takes from the flight and operations manual. The use of graphic aids (diagrams) is also common. This work is also often done with the help of a computer program.
The center of gravity of the aircraft ready for take-off (CG) must be within a prescribed area.
Reference point
Measurements are made from a specified reference point ( reference datum or zero reference datum ) that is clearly marked or clearly described. The length measurement is only carried out as part of the approval and annual weight control of the aircraft. When preparing for the flight, the pilot does not measure with a tape measure, but calculates with these lengths.
For example, on the Cessna 172, the reference point is the front of the firewall - the firewall between the engine and the cabin. The position of the reference point is irrelevant for the calculations, since all distance information relates to this reference point. It is just a little unfavorable if the reference point is too close to the center of gravity, as positive and negative values then occur at the same time.
Calculated determination of weight and trim
All relevant individual weights are added (in the example: 1047 kg). Your total must not exceed the permitted take-off weight (in the example: 1090 kg - according to the flight manual). The individual weights are: weight of the empty aircraft, the pilots, passengers, luggage, cargo, fuel, etc.
For each of these positions, the flight manual specifies the length of the lever arm (usually in cm), i.e. the distance from the reference point (in the example: 217 cm for pilot and passenger). Different lever arms and moments are specified for the different rows of seats, as well as for the different luggage compartments.
The moment is calculated by multiplying the weight and lever arm (in the example: pilot and passenger weigh together 150 kg ⋅ 217 cm = 32580 kg⋅cm). The moments calculated in this way for the individual charging stations are added. This gives the sum of the moments (in the example: 240749).
The overall center of gravity is now obtained after dividing the total moment by the total weight.
![{\ displaystyle center of gravity [cm] = {\ frac {total moment [cmkp]} {total weight [kp]}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4295fd8ceb06b1cb293b88a02cc1a1e1c9257acf)
(In the example: 240 749 kg cm / 1047 kg = 229.9 cm)
| Example of a mass calculation for a light aircraft | |||
|---|---|---|---|
| station | Weight | Lever arm | moment |
| [kg] | [cm] | [kg ⋅ cm] | |
| Empty plane (empty weight) | 651 | 215 | 139965 |
| Pilot and passenger | 150 | 217 | 32580 |
| Passenger 2 and 3 | 75 | 300 | 22500 |
| Luggage room | 35 | 362 | 12670 |
| tank | 190 liters 136.8 kg | 241 | 32969 |
| total | 1047 | 240749 | |
In our example, according to the flight manual, the permissible limit position for the center of gravity is: front 227.3 cm, rear 241.9 cm (CG range; range for shifting the center of gravity). So the calculated current value for the center of gravity is 229.9 cm in the permissible range.
The maximum take-off weight of 1090 kg (according to the flight manual) is not exceeded with a current take-off weight of 1047 kg.
Here is another example of a calculation table. The table in the aircraft manual is in this not yet completed form.
| station | Weight × lever arm = moment | ||
|---|---|---|---|
| [kp] | [cm] | [cm ⋅ kp] | |
| Empty weight | 278.1 | 39.7 | 11040.6 |
| 1st seat | 217 | ||
| 2. Fuel | 300 | ||
| 3. Baggage | 362 | ||
| Total weight:. . . . . kp | Total moment :. . . . . cm⋅kp | ||
In the Anglo-American area, lbs are also often used as units for weight, inches for the lever arm and in-lb for the moment.
Graphical determination of the torques
For the graphical determination of weight and balance, the total weight is added up, as in the above-described calculation. The length of the lever arm and the moment are then determined graphically. Figure 1 shows an example of such a graph. The graph is not identical to the table above as it relates to a different aircraft.
In this example the pilot is flying alone. He has a weight of 85 kg. A horizontal line weighing 85 kg is drawn from the left side of the graphic (Fig. 2) to the straight line that corresponds to the pilot's lever arm (in our example: solid red line). Another line is then drawn vertically downwards from the straight line and the moment (referred to here as the weight moment) is read off. In our example it is 75 m⋅kg. In order not to let the numbers get too big, the aircraft manufacturer decided to use m instead of cm for this table. 75 m⋅kg correspond to 7500 cm⋅kg.
The gradient of the different straight lines for the different charging stations expresses the length of the lever arm. The graph replaces the multiplication of weight and lever arm for the purpose of determining the moment.
The individual moments determined then have to be added up again. Another graph is used to check whether the total weight and the sum of the moments are within the permissible range (Fig. 3). Weight and moment (trim) must be in the red box. Since the given empty weight of the aircraft cannot naturally be undercut, the box for the permissible weight and torque range is moved to the lower edge of the diagram in practice (Fig. 4). Most of the time it is not a perfect rectangle, but variously modified figures. In Figure 4, for example, the center of gravity must not be too far forward for high take-off weights.
Figure 5 shows the loading diagram (envelope curve for the center of mass moment) for another aircraft. With increasing load, the overall center of gravity must be further back. Furthermore, a distinction is made between the use of the aircraft for the private sector ( normal category ) and for the commercial sector ( utility category ). For commercial use as a traffic machine, there are much tighter and stricter requirements in terms of weight and center of gravity and a center of gravity that is shifted further back is no longer permissible.
Figure 6 shows an example of how the diagram can be used. In this example, a total weight of 1020 kg and a total moment of 1140 m⋅kg were calculated; the individual moments for this were determined using graphs as in Figure 1. A straight line is drawn from both numbers in the graphic. Since the intersection is within the allowable range on the graph, Weight and Balance is fine.
helicopter
Even if the center of gravity at take-off (blue star) is still within the permissible range, it can leave the permissible range (red star), especially in the case of helicopters, because the fuel consumption reduces the weight and the center of gravity then exceeds the narrow permissible limits - or can fall below. It may therefore be necessary to shift the center of gravity during the flight to correct the weight loss.
Large aircraft
Airlines can within the framework of aircraft handling the work of preparing the loading plan (engl. Loadsheet ; L / S) and the trim plan (engl. Trim sheet ; T / S, and often a common Load & Trim Sheet ) to the consuming load planning often by a handling partner ( handling agent , ramp agent , load controller , weight and balance agent ) to relieve the pilot during flight preparation and to shorten block times. In any case, the pilot must then countersign the completed load sheet. Low-cost airlines often have the crews create the load sheets manually in order to save costs. In the case of smaller commercial aircraft (up to B737 / A320), the passengers are often not trimmed to calculate the center of gravity as they actually sit, but rather with the so-called "standard seating" (= even seat distribution according to the rule of three). As a result, the center of gravity of the aircraft is not determined with absolute precision - but this has no influence on flight safety, since such minor inaccuracies are not relevant.
In many airlines the pilots receive a “computerized” load sheet (with the weights for T / O fuel, trip fuel, passengers, baggage, cargo, etc.) with which they can then create their own trim sheet.
The Lufthansa allows for departures from Germany and much of Europe, Africa and Asia create their load sheets in the "Load Sheet centers" Cape Town, Istanbul and Brno. If the central load control system fails, the pilots have the option of creating the load sheet themselves on their business notebook. Lufthansa Cargo operates its own “Weight & Balance” office in Frankfurt for the departures in Frankfurt and some European stations without their own load sheet creation (currently Milan and Amsterdam). From there, the load sheet data is printed out manually in paper form by a driver and brought to the aircraft and handed over to the ramp agent there . After checking, the operator then hands over the load sheet to the pilot. As is the case with the Lufthansa Passenger Airlines load sheet control center, data is rarely transmitted to the pilot in the cockpit via ACARS .
SAS has already outsourced this work to Bangkok . With easyJet , the load sheets are created by the pilot using a computer on board.
The Weight and Balance Manual (WBM) contains all the information necessary to calculate the mass and center of gravity of the aircraft. The ATA iSpec 2200 prescribes the appropriate terms and abbreviations to be used for the Weight and Balance Manual in civil aviation.
literature
- Federal Aviation Administration Flight Standards Service (Ed.): Aircraft Weight and Balance Handbook . FAA-H-8083-1B. 2016 (English, faa.gov [PDF; 12.5 MB ; accessed on February 19, 2020]).
- Werner Horvath: Determination of the mass and center of gravity of small aircraft . Ed .: Dieter Thomas (= Neue Flugtechnische Schriften . Issue 10). 2nd Edition. TFT-Verlag, 2007, ISBN 978-3-931776-29-9 .
Web links
- Weight & Balance optimal load planning and control through the use of the electronic load sheet (Load Control).
Individual evidence
- ↑ EASA Part C AMC (PDF) p.237ff, European Aviation Safety Agency. 2014. Retrieved June 30, 2014.
- ↑ Optimum CG position. What is the best CG position for an aircraft? (PDF) Airbus. 2009. Retrieved June 30, 2014.