# Stability in Passenger Trolleys

David Grant-Taylor

Many will be aware of the diagrams that often accompany the discussion of capsize in boats, and the concepts are similar for trolleys on rail tracks, but for the land based systems we have less complexity because the righting moment is produced only by the solid structure of the trolley and does not vary or move in the same manner as a floating object. Nonetheless, the concepts are the same, and we will talk about overturning moments and righting moments in a similar way. Some of the use of terms is a bit careless, but the intent is always clear, and we should be aware of the risk involved in carrying active loads.

## General description

The basic requirement for stability in a system is that when subject to an overturning moment, the centre of mass of the system rises as the system responds to the moment applied to it. If the centre of mass falls then the system topples. This condition is an energy statement; the stable condition is one where the energy is at a minimum (weight is as low as it can be). We can interpret this to mean that when the centre of gravity (C of G) passes outwards of the track, then the system is likely to topple, detailed consideration of the rising or falling of the centre of mass only becomes important in the event of very compliant suspension systems.

 Fig 01 Partial capsize in our sit-astride carriage Fig 02 Partial capsize in our sit-in well carriage Fig 03 Beginning of capsize, sit-astride trolley, slow passenger response

We will first look at a simple case of one adult on a carriage with an invisible hand causing the capsize. In some of our older style carriages we have a considerable degree of security produced when the foot boards hit the ground, the righting moment is now supplied at the extreme outer part of the carriage. If the passenger is fast to respond and holds himself vertical, then the centres of mass are all inside the vertical lines passing through the points of contact with the ground and the system will be stable in the partially capsized state. The passenger's C of G in this situation is still inside the outer support and there is a fair chance he will not topple.

This security feature does not help with our well type carriages because the passengers C of G moves outboard of the outer edge of the carriage before this edge touches the ground. Further, the passenger would have to be very limber as their hip touches the rim of the carriage and will inhibit active prevention of a capsize.

Even though the carriage might not topple further if it is empty, the passenger would still topple onto his side. Interestingly for the sit-astride carriage, the passenger can respond slowly or only partially as the carriage begins to fall, and his C of G will only pass outside the lateral support when the tilt of the trolley gets to 20° or so. This gives more time to respond, but in the only capsize that I have seen I was very surprised at the speed of events, and I think passenger response will not be immediate.

## The Effect of Heavily Laden Carriages

We can now complicate the system by considering what happens if the trolleys are carrying a full load. The trolleys weigh round 50kg, and we could expect adults to weigh 75 or more, and younger passengers to run from 30 to 50 kg. If we suppose that there is only one fidget on the trolley, then the live load is small compared with the fixed load, and the overturning moment is small compared with the ordinary righting moment. This means that the leaner can hang out lot further before overturning ensues. Further, younger passengers have a C of G that is nearer to their seat than does an adult and this decreases the tipping moment they can exert.

 Fig 04 Loading conditions: 2 adults + 3 children 270kg 1 fidget 40 kg Trolley 50kg Total: 360 kg So now I load on 2 adults 75kg each, 3 nice kids 40 kg each, and fidget of 40kg. Suddenly the fidget leans out sideways with their arm on the edge of the wagon, and everyone else stays still, no doubt shocked by this behaviour. Thus roughly we have 40kg centred about 300mm off the centre line, 270kg of people with centre of mass very close to the centre line and 50kg trolley centred on the centre line. Fig 05 Moments diagram This is the first of the diagrams of moments. For each of these give a description of the situation, the values of the moments and the reactions at the wheels. In this convention, the up arrows are the reaction of the rails holding up the trolley, and the down arrows are the masses of the trolley and passengers. In the table, the numbers are given as mass in kg, distance from centre line in mm (e.g. 120:53 is 120 kg, 53mm from centre line). Obviously if the reaction at the wheel falls to 0 then the wheel will lift, and the trolley will capsize.

Description Vertical down movements Reactions at wheels Result
One fidget leaning horizontally, all others still Stable
One fidget leaning horizontally, all others lean out about 10° to see too Incipient capsize
Two adults lean out 20° to smile at little Johnny the lean-out behind Capsize begins

There are some pretty strong lessons to be learned here. The first is that silly kids are not, of themselves, the really scary thing. Their parents, because of their height and weight, are able to cause capsizes with quite small leaning movements. If their bums stay on the seats, it is unlikely that a moderate sized child will cause a capsize. An ounce of prevention (quick safety talk at the station) is worth a pound of cure (bandaids etc for the broken).

Sit-astride cars have inherent safety because of the foot boards and those making the sit-in style of car should give thought to mounting skids or some such at the outer extremities. Finally I should hasten to add that these are my personal views and are not intended to reflect the views or the consensus of views of any organised body associated with model engineering clubs.