Longer Variant. Increase Payload = 400 kg, Fuselage = 300 kg, Furnish = 200 kg, Fuel = 300 kg, and Others = 200 kg. Total increase = +1,400 kg; MTOMLong = 10,900 kg (no structural changes).

Smaller Variant. Decrease Payload = 500 kg, Fuselage = 350 kg, Furnish = 250 kg, Fuel = 350 kg, and Others = 250 kg (lightening of the structures). Total decrease = −1,700 kg; MTOMSmall = 7,800 kg.

8.12 Center of Gravity Determination

After obtaining the component masses (i.e., weights), it is now time to locate the aircraft CG. A reference-coordinate system is essential for locating the CG position relative to an aircraft. A suggested coordinate system is to use the X-axis along the ground level (or at another suitable level) and the Z-axis passing through the farthest point of the nose cone (i.e., tip), as shown in Figure 8.1. Typically, the fuselage axis is parallel or nearly parallel to the X-axis. In the example, it is parallel, with x measured from the aircraft nose and then converted to the MACw. Table 8.6 can be used to determine the CG location.

The first task is to estimate the CG position for each component group from the statistical data. Figure 8.4 provides generic information for locating the positions. During Phase 2, when more details of the components emerge, the CG positions are fine-tuned and the estimation is iterated. Typical ranges of the CG position relative to the component are given in Table 8.6. At this stage, the extreme forwardmost and rearmost CG positions (i.e., x coordinates) have not been determined and will be done later. In this book, it is demonstrated that the CG falls within the forward and aft CG limits, as shown in the worked-out example in Section 7.14. The CG

height from the ground is represented by the z coordinates. The CG should lie in the plane of symmetry (there are unsymmetrical aircraft).

It must be emphasized that the conceptual design phase relies on designers’ experience that is available in statistical data. Typical aircraft-component CGs result in the CG locations; therefore, the components must be positioned accordingly. At the conceptual design phase (i.e., not yet manufactured), it is not possible to obtain accurate component weights and their CG locations are yet to evolve. Designers’ experience is the way to minimize error. However, errors at this stage do not hinder the progress of the conceptual design, which is revised through iterations for better accuracy. The industry can then confidently predict the final accuracy level within ±3 to ±5%, which is sufficient to study the competition before the goahead is given.

The expressions for x, y, and z coordinates are as follows:

Section 8.14 presents the worked-out example to compute x¯ and z¯.

Immediately after the go-ahead is obtained, significant budget funds are released for the project-definition phase (see Chapter 2). During this phase, major structural details are drawn in CAD to obtain more accurate component weights and the CG location. Bought-out items for the systems, undercarriage, and power plant also are identified, and the suppliers provide accurate weight and CG data. During the project-definition phase, very accurate predictions (i.e., < ±2 to ±3%) can be obtained.

If the computations do not indicate the CG within the specified ranges, the wing and/or the engine(s) are moved to bring the CG near the desired percentages of the MAC until a satisfactory solution is reached. Moving the wing also moves the CG and the neutral point, which may require iteration (also known as wing-chasing problems). The fuel tankage can be slightly modified. Batteries are heavy and can be moved to fine-tune the CG location to the desired position (as well as any other heavy items that can be moved).

8.12.1 Bizjet Aircraft CG Location Example

Table 8.7 and Equations 8.54 and 8.55 are used to locate the CG. SI units are used. Both the mass and the CG location are slightly different than the preliminary data. This results in the CG angle, β = tan−1 (8.4 – 7.44)/1.357 = tan−1 0.7 = 35 deg. This is a satisfactory angle to cover the maximum fuselage-rotation angle at takeoff. The CG is located almost at the middle of the baseline aircraft length, and the wing is positioned just behind it, which indicates that the CG is in the forward position. Proper CG positioning can be established after the aircraft neutral point is determined; the forward and aft CG limits can be ascertained by fine-tuning the