Aircraft Weight and Center of Gravity Estimation

8.1 Overview

An aircraft must ascend to heights by defying gravity and sustain the tiring task of cruise – naturally, it is weight-sensitive. Anyone who has climbed a hill knows about this experience, especially if one has to carry baggage. An inanimate aircraft is no exception; its performance suffers by carrying unnecessary mass (i. e., weight). At the conceptual design stage, aircraft designers have a daunting task of creating a structure not only at a low weight but also at a low cost, without sacrificing safety. Engineers also must be accurate in weight estimation, well ahead of manufacture. This chapter presents a formal method to predict an aircraft and its component mass (i. e., weight), which results in locating the CG during the conceptual design phase. The aircraft inertia estimation is not within the scope of this book.

In the past, aircraft weight was expressed in FPS units in pound (lb) weight in the United Kingdom and the United States. With the use of kg as mass in SI, the unit for weight is a Newton, which is calculated as the mass multiplied by gravitational acceleration (9.81 m/s2). This book uses both the FPS and SI systems; this chapter addresses mass in SI and weight in FPS, sometimes interchangeably.

Material strength contributes to structural integrity. As stated previously, air­craft conceptual designers must have broad-based knowledge in all aspects of tech­nology; in this case, they must have a sound knowledge in material properties (e. g., strength-to-weight and strength-to-cost ratios). Higher strength-to-weight and strength-to-cost ratios are the desired qualities, but they act in opposition. Higher strength-to-weight-ratio material is more expensive, and designers must stay cur­rent about materials technology to choose the best compromises.

In the early days, designers had no choice but to use the best quality wood for aircraft construction material. Today, it is not a viable option for the type of load encountered and it also poses an environmental issue. Fortunately, the advent of duralumin (i. e., an aluminum alloy) in the 1930s resolved the problem, providing a considerably higher strength-to-weight ratio than wood. Having a mass-produced aluminum alloy also offers a lower material cost-to-strength ratio. Wood is eas­ier to work with, having a low manufacturing infrastructure suitable for homebuilt aircraft, but other civil and military aircraft use predominantly metal alloys and

composites. The last two decades have seen a growing use of composite material, and more exotic metal alloys offer still better strength-to-weight ratios.

Composites are basically fabric and resin bonded together, generally formed to shape in moulds. The manufacturing process associated with composites is yet to achieve the quality and consistency of metal; hence, at this point, the certifying authorities are compelled to apply reduced values of stress levels to allow for dam­age tolerance and environmental issues, as well as to keep the factor of safety at

1.5 (see Section 5.6). The manufacturing process also plays a role in deciding the allowable stress level. These considerations can erode the benefits of weight sav­ings. Research on new material, whether metal alloys (e. g., lithium-aluminum and beryllium alloy) or composites (e. g., fabric and resin) or their hybrid is an area where there is potential to reduce aircraft weight and cost. New materials are still relatively expensive, and they are steadily improving in both strength and lower costs.

8.1.1 What Is to Be Learned?

This chapter covers the following topics:

Aircraft mass, component mass, and CG position Parameters that act as drivers for aircraft mass Aircraft mass breakdown sequence Desirable CG location relative to aircraft Aircraft mass decomposed into component groups Aircraft component mass estimation methods Civil aircraft rapid mass estimation method Civil aircraft graphical mass estimation method Civil aircraft semi-empirical mass estimation method Bizjet example

Methodology to establish aircraft CG with Bizjet example Military aircraft rapid mass estimation method Military aircraft graphical method for mass estimation Military aircraft semi-empirical mass estimation method AJT and CAS examples (military aircraft)

Methodology to locate aircraft CG with AJT and CAS examples

8.1.2 Coursework Content

The coursework task continues linearly with the examples worked out thus far. Readers must now estimate aircraft-component mass, which gives the aircraft mass and its CG location. This is an important aspect of aircraft design because it deter­mines aircraft performance, stability, and control behavior.

Experience in the industry has shown that weight can only grow. Aircraft per­formance is extremely sensitive to weight because it must defy gravity. Aerodynam – icists want the least weight, whereas stress engineers want the component to be strong so that it will not fail and have the tendency to beef up a structure. The struc­ture must go through ground tests when revisions may be required. It is easy to omit an item (there are thousands) in weights estimation. Most aeronautical companies

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 Toren – beek [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.