The influence of rider and passenger mass on the static centre of gravity.
Adding the rider to the vehicle changes the centre of gravity of the outfit.
This change is towards the added mass, the rider, and can be calculated relatively easily, but as the rider is "dynamic", that is the rider centre of gravity can be moved intentionally through the application of "body English" to assist the handling of the outfit.
This means that the calculated new CG is of limited use practically, but the rider’s knowledge of the change in CG is helpful, and the cornering dynamics of the outfit can be calculated to at least give some performance parameters for the outfit.
Having used the beam reactions system to calculate the position in three dimensions of the static CG of the outfit, there are a number of way of integrating the two CG's together, the easiest being the use of vectors, so that is what I propose to use.
Some notes on vectors first, there are two ways of representing a force, a scalar (a magnitude but NO direction) and a vector (both a magnitude AND direction).
All groups of forces acting on something can be resolved to one vector, and any single vector can be broken down into any number of separate forces, so long as all directions are known.
These vectors can be added and subtracted using simple rules.
Marine navigators use vectors constantly to find the resultant direction and speed of a vessel when acted on by a current.
If the addition of all the vectors acting on a point makes a closed loop, then there is no resultant vector and the point is stationary.
Tony Foale has looked into the solo motorcycle version of this in his book "Motorcycle Chassis design", and I will borrow some of his research and apply them to sidecars.
The first assumption I will make is where the CG of the rider is located, and this is slightly ahead of the riders lap, and just above the thighs.
To use vectors to calculate the new CG, the riders CG needs to be broken down into vertical and horizontal components, this sounds scary but is easy.
The vertical component is the difference in height between the static CG and the riders CG, so measure the riders CG from ground level and subtract from that the static CG height, if the result is positive then the riders CG is above the static CG, if negative then below the static CG.
The mass of the outfit is the sum of the three reactions from the calculations for static CG, remembering to apply the multiplier appropriate to the second-class lever proportions used.
The horizontal change in CG is on the line between the static CG and the riders CG and the distance it moves is again proportional to the difference in masses and the horizontal distance between the masses (the vertical difference has already been calculated).
The calculations so far have been for one additional mass, to add more than one mass is relatively simple.
The horizontal components for the masses can be added together to make one resultant vector that the above calculations are used with.
The horizontal components are measured from the static CG as follows.
The vertical change in static CG is calculated in a similar way, with the differences in vertical CG now being a single mass (the sum of the two masses) acting at a point along the difference in vertical height between the masses proportional to the two masses.
Here it is assumed that the sidecar passenger’s CG is lower than the rider’s CG.
The result of all this is a CG for the outfit with added masses, but as stated earlier this doesn’t take into account any “body English” involving these masses.