Terramechanics: The Science Of Off-Roading

February 9th, 2023

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A lot of us have purchased, or have considered purchasing, a 4×4 vehicle. This could be because we like the benefits of extra safety or the visibility of the higher body. Or it could be that we want to go off-road in the vehicle and do a spot of exploring. However, when we get behind the wheel of one of these vehicles and head for the nearest dirt road or river, we don’t often stop to think about all the science behind what we’re about to do. The most we might think about are things like the power and torque needed – and possibly the basic physics involved in getting over or around a gnarly bit of terrain.

However, there’s a whole branch of science related to off-road driving, known as terramechanics. In fact, there’s a specialised scientific journal on the topic. Terramechanics has been a scientific topic since the 1950s, and the concept was introduced by a Polish-born engineer by the name of Dr Bekker, who was one of the key developers of the lunar rover vehicle used on the moon. However, much of Dr Bekker’s work was more down to earth – literally.

Terramechanics, in a nutshell, is the science of how a vehicle operates off-road on rough, uneven and soft terrain. It mostly considers the interaction between the wheels and the ground, although the science also acknowledges that things like the length of the wheelbase, the torque and the ground clearance are all very important factors. However, it’s what happens where the rubber meets the (off) road that gets certain people in white coats (probably dirty white coats) very excited.

Now, if you get right into terramechanics, the maths gets pretty complicated. If you’re like me, you probably left quadratic equations behind once you left high school. However, engineers and designers in the field of terramechanics use them all the time. I won’t get into the heavy-duty maths, but here, we’ll have a little look at some of the things that get thought of when the designers are coming up not just with new 4×4 models but also with the tyres that go on them.

Vehicle-related factors

Load: the weight of the vehicle plus what’s in it – probably you, a friend, the dog and something to eat.

Contact area: Exactly how much of the tyre is touching the ground. This is affected by the design of the tyre, the width of the tyre, how much air you put in the tyre and the condition of the tread.

Rolling resistance: Also known as friction.

Torque: You knew this one was going to be important, didn’t you? That’s why the torque – the measure of rotational acceleration (rather than linear acceleration) is always given in the specs of any vehicle.

Wheel width: Put simply, more contact area means more grip.

Wheel radius: There’s a reason why 4x4s have bigger tyres, and it’s not just for better ground clearance.

Terrain-related factors

Designers have to consider these factors when they design tyres and the vehicles. As anybody who’s done any off-roading will know, not all types of terrain are created equal, and the techniques and tyres that work well with, say, snow won’t work with sand.

In fact, a lot of what goes on in terramechanics considers the properties of the soil or the other terrain (snow and sand). You might think of soil as just mud or good plain dirt, but it’s pretty complicated stuff. It’s a combination of solids (the actual particles of soil), liquids (water) and gases (air), and it’s constantly changing even in a single place, to say nothing of how soil varies from place to place. I won’t bore you with all the different factors, what they mean and how they affect each other, but some of the most important ones that researchers have to specify when they run tests of new tyre designs or even whole cars are the following:

Moisture content: How much water is in the soil at any point. This affects the shear strength of the soil, which is very important in a lot of the formulae used in terramechanics to work out whether a wheel will lose traction or not. The shear strength of anything is its ability to stand up to a force that will make it slip sideways.

Porosity: How much air is inside the soil – these pores are where the water goes when you water the garden.

Particle size and shape: How big the minute particles of soil are and what shape they are has a big influence on how the dirt sticks together, holds moisture and compacts under pressure. Most of us have known since childhood that sand and clay are very different, and this difference is mostly down to particle size and shape.

Specific gravity: How dense a substance is. Yes, this is related to the specific gravity known to home brewing enthusiasts.

After considering these basic factors, things start involving complicated equations that make my head ache.

You know, I’m kind of glad that when I go off-road driving, I don’t have to keep all these factors and the science in my head – otherwise, I’d overthink everything all the time and wouldn’t enjoy the experience. An experienced off-road driver will be able to do by feel and “instinct” (i.e. right-brain thinking) what the terramechanics expert would have to calculate. All the same, I’m glad that there are people working hard to make sure that our vehicles and the tyres on them are the safest and best they can be.