# Accuracy Analysis of the Measurement of Centre of Gravity and Moment of Inertia with a Swing
## 1 Introduction  
The exact knowledge of the ten inertia parameters, which include the location of the centre of mass and the inertia tensor, is critical for many applications including the motion of rigid bodies. [PERSON] & [PERSON] [1] provide an overview of the different available quantification of those parameters and divides them into static and dynamic methods. A measurement and calculation of the static equilibrium of forces and torques allows only the mass and centre of gravity (CG) of the investigated object to be determined. The dynamic methods are further grouped into methods with no limitation on rigid-body motion, large angular motions with small rotational velocities and small angular motions [1]. The method based on the principle of the gravitational pendulum belongs to the latter mentioned category and simplifies the problem to a physical pendulum. The necessary equations are presented in Section 2.4. The quality of the results is dependent on an accurate measurement of the distance between the centre of gravity and the pivot point. This approach is reduced to a one degree-of-freedom problem similar to a torsion pendulum method, which can be used to measure rotational inertia [2, 3, 4]. This approach is practical to conduct, measure and analyse the properties of rigid bodies. The other dynamic methods require force and displacement measurements and have to be calibrated carefully [5].  
Large engineering objects, for example, vehicles, are typically investigated based on an approach where they are hung from four points [6, 7] or placed on a frame with fourload cells [8]. Similar experimental set-ups can be found in the literature, which are limited to three rods [9; 10] or three load cells [11; 12]. [PERSON] et al. [13] report solutions to measure extremely large cylindrical objects with two rail-based measurement devices each including four load cells. [PERSON] et al. [14] present an example application of the investigation of a heavy duty vehicle deploying a mobile crane to lift and hold the armoured vehicle. For vehicle applications the inertia parameters are critical for drive dynamic, stability [15; 16] as well as crash studies.  
The position of the centre of gravity as well as the moment of inertia are essential input for the simulation of motions and forces of floating devices. CG is especially important for ships [17; 18] and floating structures [19] including falling lifeboats [20] or floating wind turbines [21]. New and refitted ships are typically investigated with an inclination test [22; 23] to ensure the precise location of the CG and that the desired stability is achieved. In the case of scaled experimental devices, the distances have to be scaled based on the specific scaling similarity [24]. The outer shape as well as the correct mass (distribution) can typically be reached to a high degree of accuracy in the scaled model. Ballasting constraints and instrumentation requirements typically lead to larger relative tolerances for the exact location of the CG as well as the MI. However, even if the CG target can not be met, accurately assessing the location at model scale allows the error to be incorporated in the subsequent analysis. Typically, this involves some form of numerical modelling in which the model CG and inertia properties can be recreated and compared to the full-scale prototype.  
The paper presents the experimental set-up with the new swing, which is part of the FloWave Ocean Energy Research Facility [25; 26; 27; 28; 29] at The University of Edinburgh. The measurement procedure and the relevant equations are described in Section 2. Section 3 provides the detailed results and analysis for the CG and MI for the empty swing as well as an example measurement for a simple model. The practical implementation of the system is discussed in Section 4, including lessons learned for future measurements as well as potential improvements. Section 5 summarises the findings and provides an outlook on future research questions.