8.2 Introduction

have a special division to manage weights – weights-control engineers – a difficult task to perform.

8.2 Introduction

Because aircraft performance and stability depends on aircraft weight and the CG location, the aircraft weight and its CG position are paramount in configuring an aircraft. The success of a new aircraft design depends considerably on how accurately its weight (mass) is estimated. A pessimistic prediction masks product superiority and an optimistic estimation compromises structural integrity.

Once an aircraft is manufactured, the component weights can be easily determined by actual weighing. The aircraft CG then can be accurately determined. However, the problem in predicting weight and the CG is at the conceptual design stage, before the aircraft is built. When the first prototype is built, the weights engineers have the opportunity to verify the predictions – typically, a 4-year wait! Many of the discrepancies result from design changes; therefore, weights engineers must be kept informed in order to revise their estimations. It is a continuous process as long as the product is well supported after the design is completed.

Mass is the product of the solid volume and average density. For an aircraft component (e.g., wing assembled from a multitude of parts and fasteners), it is a laborious process to compute volumes of all those odd-shaped parts. In fact, the difficulty is that the mass prediction of complex components is not easily amenable to theoretical derivations. The typical approach to estimate weights at the conceptual design stage is to use semi-empirical relationships based on theory and statistical data of previously manufactured component masses. (A 3-D CAD model of parts provide the volume but may not be available in the early stages of conceptual design.)

The mass of each component depends on its load-bearing characteristics, which in turn depend on the operational envelope (i.e., the V-n diagram). Each manufacturer has a methodology developed over time from the statistics of past products combined with the physical laws regarding mass required for the geometry to sustain the load in question. These semi-empirical relations are proprietary information and are not available in the public domain. All manufacturers have developed mass-prediction relationships yielding satisfactory results (e.g., an accuracy of less than ±3% for the type of technology used). The semi-empirical relations of various origins indicate similarity in the physical laws but differ in associated coefficients and indices to suit their application domain (e.g., military or civil, metal or nonmetal, and level of desired accuracy). Nowadays, computers are used to predict weight through solid modeling – this is already in conjunction with semi-empirical relations. The industry uses more complex forms with involved and intricate manipulations that are not easy to work with in a classroom.

The fact is that no matter how complex academia may propose semi-empirical relations to improve accuracy in predicting component mass, it may fall short in supplanting the relationship available in the industry based on actual data. Of necessity, the industry must keep its findings “commercial in confidence.” At best, the industry may interact with academia for mutual benefit. An early publication by Torenbeek [3] with his semi-empirical relations is still widely used in academic circles. Roskam [4] presented three methods (i.e., Torenbeek, Cessna, and U.S. Datcom)

that clearly demonstrate the difficulty in predicting mass. Roskam’s book presents updated semi-empirical relations, corroborated with civil aircraft data showing satisfactory agreement (this may be useful to homebuilt aircraft designers). The equations are not complex – complexity does not serve the purpose of coursework. Readers will have to use industrial formulae when they join a company. This chapter explains the reasons associated with formulating the relationships to ensure that readers understand the semi-empirical relations used in the industry.

The author recommends the Society of Allied Weights Engineers (SAWE) (U.S.) as a good source for obtaining semi-empirical relations in the public domain. Some of the relations presented herein are taken from SAWE, Torenbeek, Sechler, Roskam, Niu, and Jenkinson ([2] through [7]). Some of the equations are modified by the author. It is recommended that readers collect as much component weights data as possible from various manufacturers (both civil and military) to check and modify the correlation and to improvise if necessary.

Revision of mass (i.e., weight) data is a continuous process. In each project phase, the weight-estimation method is refined for better accuracy. During the conceptual design phase, semi-empirical relations based on statistical data are used; in subsequent phases, more detailed analytical and statistical methods are used. CAD solid models offer accurate geometric representations to improve volume prediction. Actual mass is known when components are manufactured, providing an opportunity to assess the mass-prediction methodology. The unavoidable tendency is that aircraft weight grows over time primarily due to modifications (e.g., reinforcements and additions of new components per user requirements). Although strengthtesting of major aircraft components is a mandatory regulatory requirement before the first flight, structural-fatigue testing continues after many aircraft are already in operation. By the time results are known, it may not prove cost-effective to lighten an overdesigned structural member until a major retrofit upgrading is implemented at a later date.

The importance of the Six Sigma approach to make a design right the first time is significant to weights engineers. Many projects have suffered because of prototypes that were heavier than prediction or even experienced component failure in operation resulting in weight growth. The importance of weight prediction should not be underestimated due to not having an analytical approach involving high-level mathematical complexity, as in the case of aerodynamics. Correct weight estimation and its control are vital to aircraft design. One cannot fault stress engineers for their conservatism in ensuring structural integrity – lives depend on it. Weight-control engineers check for discrepancies throughout project development.

Mass prediction methodology starts with component weight estimation categorized into established groups, as described in Section 8.6. The methodology culminates in overall aircraft weight and locating the CG and its range of variation that can occur in operation. Estimations of aircraft inertia are required to assess dynamic behavior in response to control input but then are not needed until completion of the conceptual design study – hence, inertia is not addressed in this book. Iteration of the aircraft configuration is required after the CG is located because it is unlikely to coincide with the position guesstimated from statistics in Chapters 6 and 7. A spreadsheet is recommended for calculations.

comprise about 10 to 15% of the MEM for civil aircraft and about 15 to 25% of the MEM for military aircraft. The use of composites is increasing, as evidenced in current designs. Although composites are used in higher percentages, this book remains conservative in approach. All-composite aircraft have been manufactured, although only few in number (except small aircraft). The metal-composite sandwich is used in the Airbus 380 and Russia has used aluminum–lithium alloys. In this book, the consequences of using newer material is addressed by applying factors.

8.4 Aircraft Mass (Weight) Breakdown

Definitions of various types of aircraft mass (i.e., weight) (see Section 4.5) are repeated here for the convenience of readers.

is the mass of an aircraft as it rolls out of the factory before it is taken to a flight hangar for the first flight.

OEM (operator’s empty mass) = MEM + Crew + Consumable (8.2)

The aircraft is now ready for operation (residual fuel from the previous flight remains).

The MTOM is the reference mass loaded to the rated maximum. This is also known as the brake release mass (BRM) ready for takeoff.

Aircraft are allowed to carry a measured amount of additional fuel for taxiing to the end of the runway, ready for takeoff at the BRM (MTOM). This additional fuel mass would result in the aircraft exceeding the MTOM to the maximum ramp mass (MRM). Taxiing fuel for midsized aircraft would be approximately 100 kg, and it must be consumed before the takeoff roll is initiated – the extra fuel for taxiing is not available for the range calculation. On busy runways, the waiting period in line for takeoff could extend to more than an hour in extreme situations.

MRM (maximum ramp mass) ≈ 1.0005 × MTOM (very large aircraft) to

1.001 × MTOM = MTOM + fuel to taxi to end of runway for takeoff (8.4)

This is also known as the maximum taxi mass (MTM) and it is heavier than the MTOM.

ZFM (zero fuel mass) = MTOM minus all fuel (nonusable residual fuel remains) (8.5)

8.5 Desirable CG Position

Proper distribution of mass (i.e., weight) over the aircraft geometry is key to establishing the CG. It is important for locating the wing, undercarriage, engine, and empennage for aircraft stability and control. The convenient method is to first estimate each component weight separately and then position them to satisfy the CG

Figure 8.1. Aircraft CG position showing stability margin

location relative to overall geometry. A typical aircraft CG margin that affects aircraft operation is shown in Figure 8.1.

The aircraft aerodynamic center moves backward on the ground due to the flow field being affected by ground constraints. There is also movement of the CG location depending on the loading (i.e., fuel and/or passengers). It must be ensured that the preflight aftmost CG location is still forward of the in-flight aerodynamic center by a convenient margin, which should be as low as possible to minimize trim. Where the main-wheel contact point (and strut line) is aft of the aftmost CG, the subtending angle, β, should be greater than the fuselage-rotation angle, α, as described in Section 7.6. The main wheel is positioned to ease rotation as well as to assist in good ground handling.

Advanced military combat aircraft can have relaxed static stability to provide quicker responses. That is, the margin between the aftmost CG and the in-flight aerodynamic center is reduced (it may be even slightly negative), but the other design considerations relative to the undercarriage position are the same.

Initially, locations of some of the components (e.g., the wing) were arbitrarily chosen based on designers’ past experience, which works well (see Chapter 6). Iterations are required that, in turn, may force any or all of the components to be repositioned. There is flexibility to fine-tune the CG position by moving heavy units (e.g., batteries and fuel-storage positions). It is desirable to position the payload around the CG so that any variation will have the least effect on CG movement. Fuel storage should be distributed to ensure the least CG movement; if this is not possible, then an in-flight fuel transfer is necessary to shift weight to maintain the desired CG position (as in the Supersonic Concorde).

Fuel loads and payloads are variable quantities; hence, the CG position varies. Each combination of fuel and payload results in a CG position. Figure 8.2 shows variations in CG positions for the full range of combinations. Because it resembles the shape of a potato, the CG variation for all loading conditions is sometimes called the “potato curve.” Designers must ensure that at no time during loading up to the MTOM does the CG position exceed the loading limits endangering the aircraft to tip over on any side. Loading must be accomplished under supervision. Whereas