Mechanics Tutorial 4 - Vehicle Stability


Moments can be used to explain stability (or otherwise) in motor vehicles.


Stability in vehicles

Some people like to buy sports utility vehicles (SUVs).  They are very fashionable as luxury cars. 



They remind me of a computer I used at work more years ago than I care to remember.  It was called a Televideo but that was a con.  It was neither a telly nor a video.  In the same way, an SUV is neither a sports car, nor a utility vehicle.  A sports car is designed to have nimble and agile handling characteristics, but many of these lumpish and brutish vehicles have dreadful handling characteristics that make them rather unpleasant to drive. 


Utility vehicles are designed to lug large and possibly dirty objects about the country.  However a good number of SUV owners would have a fit at having dusty bags of cement in the back of their exceedingly expensive vehicles with their even more expensive personalised number plates.  Some may tolerate muddy dogs in the rear luggage compartment, especially if they have spent a satisfying afternoon blasting wood-pigeons from the sky...


Some of these hideous hulks luxury cars have serious stability problems when going round sharp corners.  When you have spent Ä75000 on such a vehicle, you donít want it rolling overÖ


Let us look at how we can explain stability in vehicles.  This bus has a low centre of mass and a wide track (distance between the wheels)


You can see that there is a line of action of the weight that acts vertically downwards from the centre of mass.


If we tip the bus over:


The line of action of the weight is still acting vertically downwards, but one of the tyres is acting as a pivot.  There is an overall turning moment; in this case it's anticlockwise, so the bus will go back to the vertical.


Letís analyse this further:

The bus has its centre of mass half-way between the wheels.  The distance from the centre of mass to the tyre is d metres, and its height above the road is h metres.  If the mass of the bus is m kilograms, its weight is mg newtons.


Suppose we tip the bus over by an angle of q to the road:

The angle Q is q.  By simple geometry we can say that angle P is q as well.


There will be a turning moment anticlockwise.  This is given by:

Moment = mg ◊ d sin q


The bus will go back onto its wheels (with a bang).


There is a critical point at which the bus might fall back or tip over.  This is where the centre of mass is directly above the point of contact of the tyre with the road. Point P is vertically above point Q.

If we know what distance d is and the height h are, we can easily work out the angle at which the bus will tip over.  The distances are shown in the diagram.


tan q = h/d


If the bus tips over q degrees to the horizontal, it is also tilting at q degrees to the vertical.


Question 1

If the height h was the same as d, what is the maximum angle of tilt that the bus could make?


Question 2

A lorry has a mass of 10 000 kg.  Its track (width between the wheels) is 2.0 m, and its centre of mass is 0.75 m above the road surface.


It is travelling due North.  A cross-wind from due West is acting on the side of the lorry.  This is acting on the lorry with a force of 5000 N, and the line of action of the force is 3.0 m above the road surface.


 (a) Show that the maximum angle to the vertical that the lorry could tilt before it tips over is about 37o.

 (b) Calculate the moment made by the wind, hence the angle to which the lorry would tilt.

 (c) Will the lorry tip over?



Now suppose the bus tips further:


This time the line of action of the weight is to the outside of the tyre, so the turning moment is clockwise.  The bus tips over on its side.  (This has happened; a driver was late going off shift and was hurrying to get back to the garage.  Going too fast round a sharp bend, the bus tilted too much and tipped onto its side.)


The line of action of the force is now outside the wheel, so there will be a clockwise moment to pull the bus right over.


The turning moment will be given by:


Moment = mg ◊ d sin q


Although they are tall, double-decker buses are very stable.  They test buses by putting lots of sandbags on the seats upstairs (with nothing downstairs) and tilt them over on a tilting platform.  The centre of mass is low enough to ensure that they are tilted to more than 60o off the vertical before they tip over.


Lorries have a higher centre of mass on their trailers, due to the load.  If you live in the country and get stuck behind a hay-lorry, you may see it swaying alarmingly. This kind of accident tends to happen with lorries when they drive through strong cross-winds on exposed roads.



Stability in Aeroplanes

When an aeroplane flies, there is a centre of lift, which is an imaginary point through which all the lift from the wings appears to act.  Ideally the centre of mass of the aeroplane should be directly underneath this.  Since the line of actions of both forces coincide, there is no turning moment, and the aeroplane is stable.





When the pilot uses the elevators (flaps at the tail to make the aeroplane move up and down), a force is applied to the tail, causing a turning moment to act.



When the pilot wants to turn, he uses the ailerons (flaps at the end of each wing).  One aileron is raised, and the other is lowered, to make a couple.  The aeroplane rolls.




Now suppose the aeroplane takes off with both wing tanks full of petrol.  The pilot can take petrol from both tanks, and he selects which tank to use.  He needs to keep both tanks balanced, by using 10 litres from one tank, then 10 litres from the other tank.  Every few minutes he needs to change over the tanks.


Suppose he forgets to change over, and takes almost all the fuel from the right tank.


Question 3

 How do you think this will affect the handling of the plane? Explain your answer.



The management of the fuel is an important part of the air-work of the pilot of a light aeroplane.  However many light aeroplanes can take petrol from both tanks at the same time.  Unless there is a problem with one of the tanks, that is what is done normally.


If the aeroplane is not balanced, it is possible for the turning moment to be cancelled out by using the control surfaces.  All aeroplanes have trim tabs which are little flaps that can push the nose up or down to balance the plane.


Recently there was a tragic accident involving an aeroplane in Africa.  One of the passengers had smuggled on board a young crocodile that was a pet.  It got out from its box and all the passengers rushed to the front of the plane.  There was a big nose-down turning moment which the pilot could not balance with his controls.  The plane nose-dived into the ground.