[Lewis Thomson (OP)]

Richard is looking for answers to this question.

"I own a rear wheel drive Transit minibus which I’m converting into a camper. I live in the North East of Scotland and the winters can be quiet snowy. I’ve heard people say that it’s helpful to put extra weight over the rear wheels to give extra traction in the snow.

My question is exactly how much extra weight would I add to give maximum traction? If adding extra weight does give more grip then does there come a point when the extra traction required to move the increased load outweighs the extra grip provided by the added weight? My rear tyres are 225mm wide with one per side. The standard weight over the rear axle is approx 1300kg as the vehicle has an unladen weight of about 2900kgs. My driving includes some hills but nothing too steep, maybe a 10% incline. If there’s a mathematical formula for working this out I’d love to know it, and the answer to how much weight I need to add."

Can you help them find answers? Leave your answers in the comments below...

[alancalverd]

Sadly, it depends a lot on the quality of the snow. There's a good reason why Arctic languages have many words for the different  types, compactions and temperature histories of white stuff.

[vhfpmr]

If you had a 4WD, for any given amount of friction the steepest gradient you would be able to climb is equal to the coefficient of friction: CoF 30%, max gradient 30%. (One way to measure CoF is to put an object on a sloping surface, then raise the tilt until it just slips.)

With a 2WD like a Transit you will only get the same limit if you put all the weight over the driven wheels, but if you were to do that not only will you be left with no steering, you'll also pull a wheelie every time you try to accelerate. Your problem is that the 'optimum' trade off here is not only subjective, it's also dependent on the gradient.

[Bored chemist]

Adding dead weight will also wreck the fuel efficiency.
Putting winter tyres on the vehicle is a better option.

[Petrochemicals]

That would be friction

Depending on the situation, the calculation of the normal force {\displaystyle N}N might include forces other than gravity. If an object is on a level surface and subjected to an external force {\displaystyle P}P tending to cause it to slide, then the normal force between the object and the surface is just {\displaystyle N=mg+P_{y}}{\displaystyle N=mg+P_{y}}, where {\displaystyle mg}mg is the block's weight and {\displaystyle P_{y}}P_{y} is the downward component of the external force. Prior to sliding, this friction force is {\displaystyle F_{f}=-P_{x}}{\displaystyle F_{f}=-P_{x}}, where {\displaystyle P_{x}}P_x is the horizontal component of the external force. Thus, {\displaystyle F_{f}\leq \mu N}{\displaystyle F_{f}\leq \mu N} in general. Sliding commences only after this frictional force reaches the value {\displaystyle F_{f}=\mu N}{\displaystyle F_{f}=\mu N}. Until then, friction is whatever it needs to be to provide equilibrium, so it can be treated as simply a reaction.

As long as the engine has power so the wheels turn you are OK, but the problem could be that wheels loose traction because the surface is not capable of bearing the force exerted  on them, adding more weight may just make the force exerted greater and the wheel traction even less if friction has been defeated. The balance of the vehicle may affect the traction by flattening the tyre or compressing the surface under the wheel more increacing its capacity of either force bearing or giving a greater surface area thus spreading the load over a larger area, but this comes with problems of bogging down and sinking in or rilling resistance, one reason why a citroen 2cv is a match for a big 4x4  is it is incredibly lightweight thus doesn't sink in as much, doesn't need to plough through a great depth on its tyre, doesn't need a humongous surface area.


 A pair of snow chain is probably better.