Corrugations: Fast or Slow?
last updated 19/05/2020
Corrugations on dirt roads are a major pain in the ass. Corrugations cause accelerated vehicle wear, mechanical failures, discomfort for passengers and additional wear on the cargo being carried in the vehicle. Corrugations can even contribute to accidents, injuries and death, since a tyre running over corrugations will have reduced traction as it spends a lot of its time without solid contact with the ground. This can increase stopping distance or increase the risk of losing control around a corner.
Unfortunately, if you’re going to drive on dirt roads, you’re going to have to suffer from corrugations. They’re everywhere, particularly in Australia where the dry conditions accelerate corrugation formation. So if avoiding corrugations is not an option, how can you minimize their impact?
There’s two schools of thought when it comes to choosing a vehicle speed to minimise the effect of corrugations:
- Drive fast to skip over the top.
- Drive slow to reduce the impact forces.
Which is better? Let’s examine the two different approaches to see if we can find out.
Why Drive Faster?
Driving faster may help reduce the magnitude of the wheel articulation. The speed that the suspension can recoil down is limited. Going faster provides less time for the tyre to recoil down into the trough between corrugations. Less time means less vertical distance is travelled. This reduces the overall up and down travel of the wheels and suspension. Less travel means less force transmitted to the car, less wear and fewer failures. The wheel is skipping over the top of the corrugations.
Why Drive Slower?
Driving slower reduces the speed at which the tyres strike into each corrugation. Reducing the speed reduces the acceleration that the wheel has to endure. The force of each corrugation is reduced, which means less wear and fewer failures.
Two Opposing Mechanisms. Who Wins?
We can see that driving faster simultaneously increases the speed at which the tyre slams into the corrugations but reduces the magnitude of the wheel movements. And driving slower simultaneously reduces the speed of each impact whilst increasing the amount that the wheel moves. Which way yields the lowest overall wear and risk of failure? Can maths help?
WARNING: The following section contains maths. Skip to avoid boredom.
Acceleration = force × mass. This means the force applied to a system is proportional to the acceleration that the system is experiencing. We can use acceleration as an indicator of how much wear is occurring. Lets define a few variables and use them to calculate acceleration:
S = speed of the vehicle in km/h
f = frequency of corrugations in Hz (number of corrugations encountered per second)
A = amplitude of corrugations in meters
d = distance between corrugations in meters (wavelength)
Driving at speed S over corrugations d meters apart yields a frequency of:
f = S × 1000 /3600 / d
We see frequency is directly proportional to vehicle speed. They move together in the same proportion. This means a 10% increase in speed yields a 10% increase in frequency. Doubling the speed also doubles the frequency.
We will use a sine wave to model the up and down movement of the wheel. At frequency f and amplitude A, the vertical displacement of the wheel is:
vertical displacement = A sin (2π × ft) where t = time in seconds and displacement is in meters.
Taking the first derivative, we get velocity:
velocity = A × 2π × f cos (2π × ft) m/s
Taking the derivative again, we get acceleration:
acceleration = A × 4π² × f² sin (2π × ft) m/s²
From this equation we see acceleration is proportional to amplitude (A) and frequency squared (f²). Moving the wheel more distance causes more stress and moving the wheel faster causes more stress, but moving it faster has a greater impact since the relationship is quadratic.
What happens if we double the speed? Since speed and frequency are directly proportional, doubling the speed S is the same as doubling the frequency f. Substituting double the frequency (2f) into the equation for acceleration:
acceleration at double speed = A × 4π² × 2f × 2f sin (2π × 2ft) = A × 4π² × 4f² sin (2π × 2ft)
Doubling the speed increases the acceleration by a factor of 4. This means four times the force. What about the amplitude, A? Since the wheel has less time to articulate down between peaks, the amplitude A must be reduced.
To reduce the overall acceleration, amplitude A must reduce by more than a factor of 4 when speed is doubled.
Or more generally, to reduce overall acceleration when speed increases, amplitude A must reduce at a rate faster than the square of the increase in speed.
How Does Speed Effect Amplitude?
Empirically it does feel better in the car when you drive faster. Is that because the wheel is moving significantly less?
Your soft and flabby ass, combined with the soft and cushy seat that it rests on, forms a high frequency filter. The sensation of the corrugations is dampened as the frequency increases. This leads to the following conclusion:
The smoothness that we perceive when increasing speed is over-estimated
When observing the wheels of a vehicle driving quickly over large corrugations, they appear to be moving furiously. This means high acceleration, high forces and high wear. It’s hard to imagine that amplitude reduces at a rate faster than speed squared. The fact that acceleration and force are proportional to speed squared is a big setback for the go fast argument. Amplitude must be inversely proportional to speed squared just to break even. Amplitude must reduce at a rate even faster than that for there to be any benefit at all.
This analysis is inconclusive. We’ve shown that a blanket “go fast is better” may not necessarily be true, it’s more complicated than that. But we can’t tell from the above analysis whether slower or faster is better. Lets look at some other criteria to help decide.
Going slow means less heat loading on the tyres and no high speed impacts that can smash the rim into the tyre or rip the tyre off the rim. This means you can reduce the tyre pressures more if you go slow. So, even though the wheel has more time to fully articulate down into the trough of each corrugation, this is offset by more deflection in the softer tyre. That means the relative advantage of going fast is even weaker.
A significant contribution to corrugation formation is suspension articulation. See this article for more details. Reducing tyre pressure and going slowly reduces the force that the vehicle’s articulating suspension applies to the ground. This means corrugations take longer to form and won’t become as large. What an awesome reason to go slow. Less corrugations for everyone!
Another factor that doubly compounds the corrugation forming power of driving fast is the constant speeding up and slowing down required to negotiate obstacles, causeways, creek crossings, cattle grids, etc. Accelerating and braking can add energy to the articulating suspension and so increase the formation of corrugations.
Imagine a world with significantly less corrugations. Less vehicle wear, less time spent maintaining vehicles, less time wasted recovering from vehicle failures, reduced maintenance costs, fewer frustrated outback travellers, fewer accidents, less taxpayers’ money spent attending to accidents, less taxpayers’ money spent on grading outback roads, more money available to improve education and health systems, more research into curing cancer, with some cash left over for free icecreams for everyone. All these advantages from simply letting a bit of air out and driving a bit slower.
I think this world of fewer corrugations is impossible to achieve. If there’s a dirt track with little to no corrugations, someone will come along with rock hard tyres at high speed and ruin it for everyone. It takes discipline and an ability to think more than 5 minutes into the future to air down and go slow even when the track is pretty good.
The Effect of Speed on Distance d
Increasing the speed of a vehicle increases the distance between corrugations. This means that by driving fast you are forming corrugations for future road users that give the tyre more time to articulate down into the valley between corrugations. That is the exact opposite of what you are trying to achieve by driving fast. The advantage of driving fast is lost by the effects of driving fast. What a conundrum!
Assuming your tyres aren’t under-inflated and overheating, the most common way to damage a tyre on a dirt road is by impact fractures. This happens when your tyre is too hard and you hit an obstacle too fast. Higher speed is doubly bad for impact fractures, since you need to run higher pressure and the impact force will be greater. Some people regularly have tyre failures. It’s a normal part of their outback touring. Some people never have tyre failures. I’ve never had a tyre failure. Different speeds must be a contributing factor.
The basis of the go fast argument is skipping across the top of the corrugations. If this is happening then, for a large portion of the time, each tyre has poor contact with the ground. Traction is reduced. If you’ve done a lot of driving on dirt roads you may have experienced the car drifting sideways when encountering a patch of severe corrugations. The wheels are spending too much time unweighted or in the air. Braking and cornering ability are diminished. Risk of losing control is increased. Accident risk is increased. Going slow increases traction.
Throwing Stones at Others
Going fast means cracking a few windows of your fellow road users and maybe taking off a few chips of paint too. Good dirt driving manners means going slow to avoid damaging other people’s property.
Going fast generates more dust. Apart from reduced visibility and increased accident risk, more dust in the air means more dust is ingested into engines, more dust is ingested into lungs and more dust getting into all your gear.
Going slow is an easy and effective way of saving fuel. Going slow reduces wind resistance and reduces mechanical friction which translates to substantial fuel savings.
Going slow also reduces speed variability. You aren’t constantly slowing down and speeding up as you overtake slower vehicles, negotiate corners, creek crossings, concrete causeways, potholes, cattle grids, dips and bumps. This is a further source of fuel saving and reduced engine wear when going slow.
Impact Loads with Large Obstacles
Going fast means greater impact loads and more risk of damage if you smash into an exposed edge of a concrete causeway, cattle grid, rock or pothole. This means more wear on the vehicle and increased risk of failure. Even if you save some wear on the corrugations, you lose it on the big bumps.
No matter how good you are at driving fast whilst anticipating conditions further down the track, sometimes bull dust might catch you out. Large holes or obstacles can be completely concealed by bull dust. There’s no chance of slowing down since there is no chance of noticing the hazard in time. Going slow mitigates this risk, since even if you don’t notice a hazard, you’ll be going slow enough such that major damage to tyres and suspension is avoided.
If a kangaroo jumps out in front of you or if a wheel falls off your car or if some gear falls off the roof rack of a leading vehicle or if a truck veers onto the wrong side of the road, you’re more likely to be ok if you are going slow. You have more time to react, correct, adjust and slow down to either completely avoid an accident or substantially reduce the severity of it.
Overall Fatality Risk
Increasing speed simultaneously increases the risk of an accident and increases the severity of an accident if it does occur. You crash more often, and when you do crash you die more often. Search the internet for “speed vs fatality rate” for further reading of the many studies that have been done on this relationship.
Note that the information provided by these studies comes almost completely from bitumen roads, where there is no reduction in traction when speed increases. What happens if you simultaneously reduce traction as you increase speed, as is the case for corrugations? Then you crash and die even more frequently than what the studies suggest. What about reduced visibility from dust, ruts and dips from water damage, exposed rocks, poorly maintained creek crossings, more interactions with wildlife and livestock, long response time of emergency services and generally more hazardous nature of remote area travel?
Personal Experience with Failures
On my travels I’ve seen many vehicle failures, repeated tyre problems and caravan / camper trailer failures. Out of interest, whilst trying to assist in diagnosing the failure or making a plan for recovery, I often discuss the driver’s thoughts about speed and corrugations. In my experience nearly all the time these people are part of the go fast party. Not always, but usually.
It’s not uncommon to have someone overtake you aggressively on a dirt road, only to see them on the side of the road some time later with the bonnet up or checking something on a tyre or inspecting something that’s nearly falling off their camper trailer.
Overtaking on a dusty corrugated road is stressful and dangerous. You’re in the plume of dust of the vehicle in front, visibility of oncoming traffic is obscured, there’s obstacles to contend with, there’s reduced traction, there’s poor road conditions, there’s wildlife.
Going slow means overtaking is very rare. It’s great to not have to overtake. And not just great because you avoid the actual overtaking manoeuvres, but doubly great because you feel good that you’ve freed yourself of time constraints. You’re not worried about saving a few minutes. You’re no longer in competition with the other people on the road. You’re not trying to prove to the other drivers that they can’t hold you back.
Not having to consistently apply heavy brakes to negotiate obstacles is also excellent. Low speed variability, no big bangs from high speed impacts, no nervous approaches to obstacles when you’ve noticed it too late and you’re going too fast, no feeling of time pressure. It becomes a pleasurable leisure cruise.
I think a lot of people are confused about how much time they might save by driving aggressively. Once you take into account slowing down for obstacles / road conditions, stopping for toilet breaks, stopping for food, getting stuck behind slower moving traffic and stopping for fuel, the amount you can improve your average speed by driving aggressively is actually not much. If you use 30% more fuel it also means you need to stop for fuel 30% more often, further offsetting any improvement in average speed that driving aggressively may provide.
How long does it take to work to pay for unnecessarily consumed fuel and additional maintenance costs? How long does it take to work to pay for vehicle repairs? How long does it take to change a tyre that was unnecessarily destroyed? How long does it take to work to pay for that tyre? How long will you be delayed if you smash into a kangaroo at high speed? How long will you be delayed if you have a major mechanical failure? How much time do you lose if you die?
I think when you consider all these things, on average driving aggressively doesn’t save much time at all. It’s possible, depending on your luck, that driving fast slows you down. That’s how we have stories like The Tortoise and the Hare and expressions like:
The more haste, the worse speed
We’re in a hurry so we need to go slow
You need to have a long term vision to understand that going fast might slow you down. With instant gratification being the cultural norm, more people want to immediately feel like they’re winning the race rather than achieve a long term goal like maximise the time they have to go camping and travelling with their friends and family.
I think aggressive driving behaviour comes from the desire to feel like you’re winning, feel like you’re optimising your time compared to other drivers, feel like you’re in front of the race, feel like you’re in control of your mission rather than slower drivers controlling you. It is also related to insecurity and status anxiety, with overtaking others helping to cope with insecurity whilst protecting the ego from damage that being overtaken by others may cause. Driving aggressively doesn’t have much to do with saving any time. It’s the same thing you see in normal city roads – people jostling for position, cutting people off, being assholes to eachother. It’s the rat race on the road. The same concept applies for outback dirt roads.
I don’t know for sure if going fast or going slow minimises the impact of corrugations on your vehicle and the gear it carries. Based on the quadratic relationship between acceleration and frequency and the linear relationship between acceleration and amplitude, my money is on going slow being better. Based on my observations with real failures, again my money is on going slow being better. Add on top of that all the other advantages that we know we get from going slow makes the decision easy.
How slow is slow? Pick a speed that feels like you’re not shaking the crap out of the vehicle. For a maintained, properly formed dirt track with low to medium level corrugations, maybe 80km/h is a good figure, with tyre pressures maybe 2/3 to 3/4 highway pressure. For big whopper ass kicking corrugations I reduce tyre pressure to about half highway pressure and sometimes even a bit further, and slow down to maybe 30km/h. Sometimes even slower for patches of extreme corrugations, speeding up to a maximum of maybe 50km/h on the good bits, capped at 50 regardless of track conditions due to the low tyre pressure.
For more details on what causes corrugations, see this link.