Equations for Estimating the Center of Gravity Height of a Motorcycle (Motorcycle Accident Reconstruction)

INTRODUCTION

Some accident reconstruction calculations will require an estimate of the center of gravity height for a motorcycle. For example, the center of gravity height may come into the calculation of the lean angle required for the motorcycle to follow a specific path through a curve. This analysis may play a role in determining the cause of a single vehicle motorcyclist crash on a curve [Rose, 2014]. Cossalter [2006] presented equations for calculating the lean angle of a motorcycle for a particular curve, taking into account the width of the motorcycle tires and the combined center of gravity height of the motorcycle and rider. Carter [2015] and Rose [2018] validated Cossalter’s equations. Foale [2006] has presented a method for calculating a combined motorcycle/rider center of gravity height once the center of gravity height of the motorcycle is known.

EQUATIONS FOR MOTORCYCLE CENTER OF GRAVITY HEIGHT

Cossalter [2002] tested two super-sport motorcycles and found that the center of gravity height was equal to approximately 37 percent of the wheelbase. Foale [2006] presented the center of gravity heights for 39 motorcycles. His data is included in Table 1, organized by motorcycle type. As this table shows, the center of gravity heights in Foale’s data ranged from 11.6 to 24.7 inches. Table 1 also includes the wheelbase for each motorcycle, along with the ratio of the center of gravity height to the wheelbase. In Foale’s entire dataset, the center of gravity height was, on average, 34.2 percent of the wheelbase, with a standard deviation of 6.7 percent of the wheelbase. For the sport motorcycles, the center of gravity height was on average 38.9 percent of the wheelbase, generally consistent with Cossalter’s data. The standard deviation on this was approximately 4.6 percent of the wheelbase. For cruisers, on the other hand, the center of gravity height was, on average, 27.2 percent of the wheelbase, with a standard deviation of 4.6 percent of the wheelbase. The average ratio for the touring motorcycles was 27.1 percent of the wheelbase, with a standard deviation of 5.8 percent. For standard motorcycles, the average was 37.2 percent of the wheelbase, with a standard deviation of 5.2 percent. Based on these numbers, it appears reasonable to lump cruisers with touring motorcycles and standard with sports motorcycle for the purpose of developing equations to predict the center of gravity height of a motorcycle.

TABLE 1 - Center of Gravity Data from Foale [2006]

TABLE 1 - Center of Gravity Data from Foale [2006]

DiTallo and his colleagues [2017] presented the center of gravity heights for 25 additional motorcycles and his data is included in Table 2. In DiTallo’s entire dataset, the center of gravity height was, on average, 34.0 percent of the wheelbase, with a standard deviation of 6.2 percent of the wheelbase. These numbers are consistent with Foale’s dataset. The center of gravity height for the sport motorcycles was on average 36.9 percent of the wheelbase. The standard deviation on this was approximately 5.2 percent of the wheelbase. For cruisers, on the other hand, the center of gravity height was, on average, 29.0 percent of the wheelbase, with a standard deviation of 3.5 percent of the wheelbase. Again, these numbers are consistent with Foale’s dataset (and Cossalter’s for sport motorcycles).

TABLE 2 - Center of Mass Heights for Motorcycles [DiTallo, 2017]

TABLE 2 - Center of Mass Heights for Motorcycles [DiTallo, 2017]

To develop equations to estimate the center of gravity height of a motorcycle, the Foale and DiTallo datasets were combined. Cruisers and touring motorcycles were then lumped together and standard and sports motorcycles were lumped together.  These combined datasets were used to calculate an average and standard deviation for each population. This resulted in the following equation for cruisers and touring motorcycles.

equation-1-motorcycle-cg-post.PNG

The following equation resulted for the standard and sports motorcycles:

equation-2-motorcycle-cg-post.PNG

The plus/minus on these equations is one standard deviation on each side of the mean.

DISCUSSION AND CONCLUSIONS

Equations (1) and (2) can be used to estimate the center of gravity height for a motorcycle when a measured center of gravity height is not available. The dataset used to generate these equations included 23 cruiser and touring motorcycles and 37 standard and sport motorcycles. This data is plotted on a graph in Figure 1. Wheelbase is plotted on the horizontal axis and the ratio of center of gravity height to wheelbase is plotted on the vertical axis. From this graph, it is apparent that standard and sport motorcycles generally have shorter wheelbases than cruiser and touring motorcycles and that the center of gravity height for the standard and sport motorcycles is generally a higher percentage of the wheelbase than for the cruiser and touring motorcycles. Figure 2 is a similar graph, but in this graph the actual center of gravity height is plotted on the vertical axis. From this graph, it is apparent that the standard and sport motorcycles generally have higher centers of gravity than the cruiser and touring motorcycles, though there is considerable overlap of the two datasets.

FIGURE 1 - Ratio of CG Height to Wheelbase as a Function of Wheelbase

FIGURE 1 - Ratio of CG Height to Wheelbase as a Function of Wheelbase

FIGURE 2 - Center of Gravity Height as Function of Wheelbase

FIGURE 2 - Center of Gravity Height as Function of Wheelbase

REFERENCES

1.     Carter, Neal, Rose, Nathan A., Pentecost, David, “Validation of Equations for Motorcycle and Rider Lean on a Curve,” SAE Int. J. Trans. Safety 3(2):2015, doi:10.4271/2015-01-1422.

2.     Cossalter, V., Doria, A., and Mitolo, L., "Inertial and Modal Properties of Racing Motorcycles," SAE Technical Paper 2002-01-3347, 2002, doi:10.4271/2002-01-3347.

3.     Cossalter, Vittore, Motorcycle Dynamics, Second Edition, 2006.

4.     DiTallo, Michael, et al., “Motorcycle Center of Gravity Data: Methodology and Reference,” Collision: The International Compendium for Crash Research, Volume 12, Issue 1, September, 2017.

5.     Foale, T., Motorcycle Handling and Chassis Design – The Art and Science, 2nd Edition, 2006.

6.     Rose, Nathan A., Neal Carter, David Pentecost, “Analysis of Motorcycle and Rider Limits on a Curve,” Collision: The International Compendium for Crash Research, Volume 9, Issue 1, 2014.

7.     Rose, Nathan A., Neal Carter, Connor Smith, “Further Validation of Equations for Motorcycle Lean on a Curve,” forthcoming from the Society of Automotive Engineers, 2018.

ABOUT NATHAN

Nathan is an accident reconstruction expert at Kineticorp. He is dedicated to mastering his craft, and for the past 20 years, he has dedicated himself to research and writing as a means of developing authentic expertise that provides real value to juries. Nathan developed this article as part of the research that will ultimately make it into his book on motorcycle accident reconstruction.