4x4 Vehicle Recovery Capacity

I'm no mathematician, but these may help.

http://www.hitchinfo.com/index.cfm?event=new-to-towing

http://onlinetowguide.com/guidelines/towing_capacities.html

Thanks kramarat, but these are on road trailer capacities.

I am looking at emergency recovery of assorted vehicles.

As examples I know I can recover a 2 ton 4x4 from mud, which is likely a 4 ton pull, and a 26 ton HGV on tarmac, likely around a 2 ton pull. I am just trying to find some science to it :-)

In many situations it is quite easy. It is the weight of your vehicle multiplied by the friction coefficient of the surface µ, [which will vary according to static (non slipping) or dynamic (slipping)], for any surface that allows you to break traction on all wheels. For a 2 x 4, etc, it will be the weight over the driven axle, times µ, etc.

I agree with your weight over wheels for 4X2, but I am just not finding it calculated the way you are doing it, BUT CLEARLY I am doing something wrong as even in this link they then turn around and use the static value to compute the breakaway friction on a curve.

http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/ben_townsend/staticandkineticfriction.htm

Some common values of coefficients of kinetic and static friction:

Now, finally, how does all this relate to automobiles?

Lots of god answers here already...here is my 2 cents.

From what the OP clarified, he wants a horizontal force to calculate on flat ground if he were on dry pavement.

The simplified equation for friction is Force equals friction coefficient times normal force.

F=μF_n

The normal force is the force of your wheels against the pavement. In the case of a 4 wheel vehicle you have 4 forces. You could find the weight at each wheel on the ground, or average the axles or the entire vehicle. If you do each axle, you will have to divide by 2, all 4, divide by 4 then multiply the normal force (vehicle/4, axle/2 or weight at each wheel)

The friction coefficient factor for tire on concrete listed above should work fine. If we used 4000 kilograms (the friction coefficient is unit-less and will work with pounds or kilograms) we get the following equation.

Force=1*(4000k/4)

or by axle:

Force=1((2500k/2)+(1500k/2))

Drew K

I agree with kramarat. It doesn't matter. I've owned several macho 4 wheel drives and have never encountered the same conditions while pulling someone out of mud, sand, snow, water, ice, out of a ditch, out of a sink hole or across a river.

Much of a vehicle's pulling capability depends on the driver and the techniques they employ while pulling.

Even the type of strap/chain/rope or winch will have an impact on the results.

Just enjoy that feeling of accomplishment you get by helping the less skilled or less fortunate.

Thanks kramarat and lyn, but I have formula for the resistance of a stuck vehicle.

What I am after is the pulling capacity of my vehicles in a given scenario.

There must be a way to calculate how much rolling resistance I can pull?

You might try some of these, or maybe one of the guys with big brains will have a formula for you:

1. 4Wheel & Off-Road Forumsforums.4wheeloffroad.com/
   
2. 4x4 Trucks & SUVs, Four Wheel Drive Offroad Vehicle & Truck ...www.4wheeloffroad.com/
   
3. Pirate4x4.Com - The largest off roading website in the world.pirate4x4.com/
   
4. Answers to your 4 wheel drive questions and off-road training by ...www.4x4abc.com/
   
5. Tx4wd State Hub Sitewww.tx4wd.org/

Uphill or downhill?

There are too many variables.

Get a couple of these.

http://www.youtube.com/watch?v=tB2GYeQutW4

Isn't that sexist?

Anyway, two would be too much for anybody except a good Mormon, and they keep their "wives" in separate houses.

When he gets the answer, he needs to let this guy know.

http://www.youtube.com/watch?v=t2pGhOWAlaw

Definitions will help the conversation:

Static resistance: your traction limit if you are not moving but are pulling (winch)

Rolling resistance: the pull you need to move something or your friction limit (chained)

Recovery resistance: He is not on the road, now account for how stuck is he

Towing capacity: Total amount of weight your truck can pull before finding limit of your rolling resistance, straight and level vs curves vs wet or dry vs hills

The pulling capacity of your vehicle can be calculated, but is truly limited to your rolling resistance.

Once your tires roll you lose 30% of your traction, which is why wreckers use winches.

The second link I sent has an example of how to calculate the force, or you can take the towing capacity the manufacturer listed and increase it by 30 to 50 percent since we are not talking over hill and dale etc.

"Once your tires roll you lose 30% of your traction,"

Instead of roll I suggest slip, skid or slide - i.e. dynamic friction. A tyre rolling is usually not slipping, so static friction prevails.

Let me start by saying I am no expert, so any coaching is welcome.

My logic fell out of the two values for tire friction in the calculations I could find, static and rolling. After that of course the tables broke into surface conditions and the other variables.

Intuitively I'd argue that once you slip, slide, or skid your traction has gone down way more than 30%. But I can see how I might have swapped resistance and friction?

Better to think of static & sliding that static & rolling. Because tyres are meant to roll, but the tyre is not 'sliding' or 'slipping' on the road - not dynamic friction - unless you are drifting. Or dragging. ;-)

GA

Love the science but the feeling of accomplishment (and maybe $25 in your pocket) may be just enough.

Charts? Charts??? We don't need no stinking charts!

I never thought about the forces involved in pulling someone out. I just went for it.

Never took any money, either.

I'll admit, it's an interesting subject, and far more complex than one would assume by casual observation.

I'm down to one 4 wheel drive now and don't go out to play any more. Those days are over.

My scale for popping people out of holes was sliding, off-road in my area there wasn't much help to be had and I had people hike hours to get to me to ask for help.

Off-road everyone came out of the hole for free.

Now when I was back in the city there was plenty of commercial help available, if they wanted to give me $20 instead of call a wrecker for $50 I was game.

And if there were that many people in the ditch, Denver was getting a snow-pounding and the wreckers didn't mind if I helped out because they couldn't keep up anyway.

If your talking about raw pulling ability, this is all in the technique and weight handling capacity of the tools you're using...A vehicle that is much lighter than the vehicle it's trying to free, can still accomplish this task by several strategies...One would be to have winches on front and back, rear winch tied to tree or another vehicle, front winch to stuck vehicle....Then it becomes how much force you can apply until one of the components fail...

I have 4WD pickups as well and the formula I use is simple. Try until you get the other guy unstuck Thats it.

I have pulled a 20 ton pay loader out of a ditch with my 8500# F250 super duty before. Its no that my truck is that powerful but rather I simply had the traction advantage that was just enough to keep the pay loader from sliding back down while we both backed up.

Then there are other times where I could not get a 2400# car out of snow filled ditch either. There is no exact formula that covers every situation just experience and intuition.

GA. The pirate 4x4 link is a good one. I still maintain that there's no mathematical formula that he'll be able to plug in, while out in the field, that will be of any help.

I'd also consider the crane scale idea, combined with photos and notes for varying scenarios.

Yes, I, too was much younger when I roamed the AZ desert every weekend.

Those were some of the best times of my life. Even when we got caught in a flash flood while camped out one night.

Good find, for sure. Some great general knowledge.

I probably went through $5 grand in equipment figuring some of that stuff out

I finally ended up with a winch in my bed and deployable legs under the frame so the pull and the resistance were roughly the same place and to drive my resistance up. Also made heavy use of chocks.

Other techniques like chaining my truck to a tree before using my winch, ground anchors, multi-line pulls and snatch straps ensured I quit tearing my truck up.

Had I been as civic minded as the guy on Pirate, I should have written it all down too.

But I sympathize with our OP because all the best data was done for lifting operations, and the folks in the recovery field didn't share their knowledge for years. The mechanic who helped my do things like put my bumper back on also ran a tow service, so we'd sit down and draw out various recoveries he had done and what went wrong with some of them.

That Army link to self recovery is outstanding. Ought to be required for any 4X4 sales. But then they also oughta ask what you are going to tow when you buy a pickup, and they don't.

Where I live, there is a guy who has an old beat-up military 6x6 truck, 2-1/2 ton capacity. These were used during WWII and were the workhorse of the time. This guy pulled an 18 wheeler mired down in mud without as much as a wimper. If you could find one of these around, it would be your answer.

Low horsepower, lotsa gears!

Gearing wins about every time

But the guy already has trucks.

And are you sure about that weight for your trucks?

My medium duty Dodge weighs 8800 pounds?

Thanks all

Edignan, thanks the links. The Pirate 4x4 info on GVW/Rolling Resistance I have, but the calcs on the other confuse me

Winching is not an option, there are too many H & S regs in the UK now, you need to have certification to use them. My use falls between leisure and commercial, so I am only looking at towing stuck vehicles.

The scenario is how much pull I can exert with my vehicles, the opposite of the GVW/Rolling Resistance calcs. Simply using a strap on the level with my vehicle on tarmac. Other factors I can compensate for.

I am not after towing at any given speed, just my vehicles ability to pull in tons.

The Crane Scale idea would give me what I am after Kramarat. If I tied my strap to an immovable object and used my vehicle to pull it, the reading just before I lost traction (or something broke ) would be what I am after. Trouble is, I don't have access to one.

I gotcha

So I ~think Lyn, Stuart and I are converging on an answer

Take Lyn's comment about actual driving wheels, Stuart's on weight on wheels, and now we are down to the last link I posted.

I don't see a difference between calculating the curve value at the bottom of the page and a straight line value due to a load on a chain.

Stuart and Lyn?

Weight distribution won't change regardless if the wheel is driving or stationary, so it's a big variable.

Back to the OP.

You might be able to rent one for a day..........or less.

http://www.awmlimited.co.uk/acatalog/hire-stock.html

Something else to ponder is the ACTUAL NUMBER of wheels that are really driving the vehicle.

In low traction conditions, many "4" wheel drive vehicles are only being driven by a single wheel on each axle. The wheel with least traction, even.

Unless your vehicle is equipped with LOCKING differentials, front and rear, you may have only a 3WD or even a 2WD vehicle.

I know of no USA 4WD vehicles that come from the factory, or are even available, with a locking front differential.

Rear differentials must be ordered and are not standard equipment on many vehicles.

My diesel is 2.31 US Ton, my petrol 2.08 US Ton.

Everything is half your size this side of the pond

I need to sell you my truck

Kidding aside, I was struck by Lyn's comment as my 2 wheel drive has neither posi-traction nor a locking diff, so I can get stuck with one wheel on something loose.

And I know my pickup is 8800 pounds US as California charges even non-commercial pickups by gross weight for the annual registration

So going by the scale saved me some change (they list my truck at 9800lbs), but I still shelled our $690 for the privilege of sitting by the curb for a year.

Then I should whine about fuel prices, but look who I'm talking to. I'll shut up.

Gotta go walk a dog before she comes unhinged - brb

More than we ever needed to know.

TMI?

At least you didn't take pictures.

Now I have to go pick up a kid at the skating rink.

bbs.

Does this outfit make my buns look big?

I was trying to ignore all variables, otherwise what I am after is incalculable. Power, revolutions, gearing, wheel size, tyres, traction must all be assumed as known. After all, I am only after a ball park figure.

My diesel has one locking diff, my petrol two, but I am assuming all tyres are gripping, therefore all wheels are being driven.

Drew has the right formula; however, μ (coefficient of friction) varies widely with conditions.

Tethering the towing vehicle to a tree can improve matters....

Maybe not for the tree.

I've pulled out 3 tonne vehicles with a 500kg vehicle. In Australia we do a lot of beach driving and regularly recover those not so experienced. Snatch straps are the thing for it as the strap it self is elastic to a degree and this multiplies the recovery abilities of the vehicle exponentially as can be seen by the above example. Getting vehicles unstuck is only limited by your experience, the type of gear you have and your ability to think outside the box. Thats my 2 cents worth anyway.

So are we saying the towing force of my vehicles is limited to their weight? The friction calculation would seem to suggest this.

But what about the energy being exerted by the engine, surely the power input must equate to the power available at the tow bar, or will the excess energy just be lost in wheel spin?

What about these tractor towing contests, as in the earlier video, surely the rolling resistance of the ballast units must exceed the weight of the towing vehicle?

KERR is a whole different subject I am ignoring for the OP.

Thanks all your thoughts so far

The coefficient for friction is different for dynamic and static. As posted by others, static friction is significantly greater than dynamic. You will observe this when you try to slide a heavy box on the floor; it is easier once you get it moving than it is to start from standing still.

You can also observe this phenomenon with a simple inclined board and another block of wood, notice as you increase the incline it will hold steady until it is at a steep enough angle to overcome the static friction. You can then decrease the incline and watch it continue to slid. Many people will assume it keeps sliding because of momentum or the Newton law stating an object in motion will continue in motion until another force acts upon it. In reality, it keeps sliding because the friction is less when it is moving.

As was also stated already, a low power vehicle can pull a much larger vehicle out if it has sufficient gearing. The gearing provides mechanical advantage that is a force multiplier. Think of using a lever to lift a large weight, with a large enough lever and a fulcrum to rest it on you can move very large masses; a transmission is just a more complicated mechanical advantage machine.

The tractor pulls are a bit different, they are usually working in dirt and use the spinning wheels to dig into the dirt to get greater traction than if they were not slipping. The equations to determine the traction forces are much more complicated because they involve not only friction, but also moving the dirt and the force required to dig into the soil in the first place.

Rolling resistance is an entirely different matter. Technically rolling resistance is a complex property of matter. When you think of materials touching on a molecular level, you have electrons of one material interacting with electrons of the neighboring material. In a molecular bond, electrons are shared between atoms in a molecule; but in the case of neighboring materials there is no bond, but instead an association and the interaction of atomic forces. It is these associations that cause all forms of friction, that and surface irregularities and some other factors. When you consider rolling resistance, as the surface of the wheel rolls down onto the supporting material the electrons interact with the wheel, as that interaction is broken there is a slight resistance. Think of it as if the wheel were covered in velcro, and you must tear the velcro away as your roll the tire. Because the direction of rolling resistance is perpendicular to the surface, the magnitude is much smaller than the friction force parallel to the materials.

Ultimately, on flat dry pavement, the equation I gave is all you need to consider for towing or pulling a vehicle. If you are considering pulling on a non level surface, you need to account for the force of your vehicle against the ground. If you are on a 10° slope, picture a right (90°) triangle with the base parallel to the road and the weight of your vehicle being the long side. The third sided perpendicular to the road is the normal force caused by the vehicle's weight.

The normal force would then be calculated as:

F=weight*cosine(10°)

You will find that with this calculation the normal force is slightly less than the weight of the vehicle. If you are pulling the other vehicle uphill then this will result in a net loss in available friction because the direction you are pulling has a 10° angle in common with gravity, pulling the other vehicle downhill means gravity helps you (which just makes sense).

As long as you model your tow vehicle as sitting on dry flat pavement the only variable you can change would be the vehicle weight...unless you chock your vehicle or connect it to something else.

Drew K

"So are we saying the towing force of my vehicles is limited to their weight? The friction calculation would seem to suggest this."

Yes that's correct.

Thanks Drew, but more confused than ever

Surely static and dynamic friction would mostly only apply to the vehicle being towed, not the towing vehicle. I am only really concerned with the traction of the towing vehicle.

Assume I have attached my vehicle to a 100 ton fixed load, that I am never going to move. What I am after is the maximum pull in tons that I can exert on that fixed load. Assuming I am on concrete with maximum traction, level, with a fixed length strap.

As you say, sufficient gearing should allow me to pull a much larger load, but presumably traction will be lost at the point of maximum pull, which is the force I am trying to calculate.

Fixing or chocking my vehicle would only apply if I were winching, which I am not, I am simply using my vehicle to pull a load by driving it.

If you are pulling a truck in the mud, lets define it as a 1500kg truck, and it's friction coefficient is .7 (because it is in mud, friction is actually less). It also has to push it's way through the mud so that will add a resisting force. Mud is heavier than water, and also has a viscous fluid friction force that can be calculated (with some complex equations). The fact that the vehicle you are pulling may be trying to help will negate some of these forces. But lets guess that the mud adds a .2 coefficient to your tow.

Then, you would have the following equation:

F=.7(1500kg*9.8m/s²)+.2(1500kg*9.8m/s²)

F=13243.5N

Horsepower = (Force * Distance)/Time

Distance/time is velocity so Hp=F*V

so, if you have a 150hp motor you can manipulate that equation to find the velocity.

Velocity= (150Hp)/13243.5N

Velocity =8.4m/s But that is only if all 150 hp is converted to lateral motion and there is no loss in traction. Looking at that number, I think I may have missed something in my calculation because it is quite fast....I am attempting this well past the hour my brain usually stops doing math so well. I will review this and double check in the morning (but I won't be surprised if I wake to find it already done)

Drew

What Drew is trying to tell you is the static and dynamic calculations apply to both vehicles; because the question you ask - How Much? - is really when do my tires break loose.

Using your 100T example; lets use a snatch-em strap to think about it, your truck eases out all the slack, then begins to exert a stretch on the strap. The springs compress, the next thing that is going to happen as that pulling force goes up and up is your tires are going to break loose.(or hard parts are gonna break)

This is why the calculation of how hard you can pull comes down NOT to how much horse power you have, but to how much you weigh. (This is a simplification for our examples, obviously horsepower plays a part, BUT)

Going back to the Deuce and a half referred to earlier, great trucks. Only made about 120hp. But geared really low, weighed a LOT, able to convert lots of that 120 hp to pull because of great friction.

So in the winter when I was going to pull or winch people, I used to throw a half-ton of snow in my pickup. That fed both the momentum side of the equation and drove up the friction numbers - remember weight was in that equation?

If you will answer my question, I will answer yours.

Here's mine:

"How many shingles does it take to cover the roof of a dog house?"

Uhh,

Depends on the size of the camel!

So from that it looks like the simple answer is that the pulling power of my vehicles is effectively their weight, given as a simplification in ideal conditions. The limiting factor is the grip of the tyres.

That I can now relate to the pull required of any given vehicle in any given situation, and have a fairly good idea of what is recoverable with a straight pull.

When you get that broken down into a chart, please repost it

Take a small landrover, back stake it, put three turns on the capstan winch,

with a multi pull snatch block, and you'll move anything. (or break the tie.)

jt.

Here's one for Xmas, (I like) courtsey of www.mycall.mobi.

What's the difference between a kangaroo and a kangaroot?
a kangaroo is an Austrailian marcuipial and

a kangaroot is a Gordie fella stuck in a lift.!

Ahhh, capstans!

If only all 4x4s came with a capstan!

Back when Land Rovers were made by geniuses

Was so jealous I seriously considered installing one on my Dodge, safest way to approach many, many problems.

the off roaders around here mount the winch on square tubing that fits into the receiver, a 2nd receiver is mounted on the front bumper

I wouldn't mind having a pto driven capstan for my tractor

I always wanted to take the hardware from the oilfield and repurpose it to my pickup:

Just pull er up a few more feet the the nose should drop!

Now drive slow, be careful, but mostly DON'T be late!

But in general the amazing utility of a proper set of gin poles either bed or front mounted:

Or maybe I should quit half-stepping

That diagram with the car to the left and ground anchors to the right shows something I was thinking on trying to describe.

You can see 4 diagonal sticks placed in the ground with a cable going from the top of one to the bottom of the next. This is a powerful way to make a place to make a tie off point where there are no trees or posts.

The way it works is the sticks have a spade at the bottom, metal c or w channel with a flat bit on the bottom. You attach your anchor line to the bottom of the first and place 2 more behind the first and connect a line from the top of the first to the bottom of the second two so from above it looks like a triangle with the point being your anchor point.

You don't have to set the the spikes very deep, less than a foot is usually sufficient for a tremendous amount of pull.

Drew K

The mountains taught me to love a ground anchor - there isn't always a tree!

I am not totally happy with this, it is very rough and a bit confusing, but it suffices for the moment.

Wow, was totally kidding but terrific!

I'd run the math on some of the times vs plus vs minus, but all in all looking good!

How did you do your calculations?

That doesn't look unreasonable, but the angles are not accurate.

If your vehicle weighs 1500kg and the slope is 45° you get the following equation

1500kg*sin(45°)=787.98kg

I used sin(45°) this time because it gives the opposite side from the angle which is parallel to the incline. This gives the portion of the weight of the vehicle that is in the same direction that you are pulling.

787.98/1500 gives about 53%

Drew K

A good big winch and a really long, heavy rope, a few big hooks and straps. Hitch to a tree or something pretty heavy some distance away to break out of the initial mess caused by skidding etc.

The variables of road, tyres, mud, snow, rocks, holes, inclination, tyre treads, weight etc are too many, a good guess by an experienced guy is probably best.

A good big winch and a really long, heavy rope, a few big hooks and straps. Hitch to a tree

No disagreement, but apparently the UK has pretty strict rules once you break out a winch on public streets

Hi Edignan,

I guess so, I avoided saying fix it to a lamp post or down a gulley. In fact I pulled a tree over trying to pick up my caterpillar excavator on it's side.

Tracks and low gearing seem to be the answer, BHP just does it faster, a 1 hp engine can move a mountain given the gears.

a lamp post or down a gulley.

I like it, and apparently the Army has lots more manpower than most organizations!

I'll take the lamp post!

As an example of immense torque, with low HP, I once worked on a textile take-up roller.This motor was 1/16 hp, but was geared about like a clock motor.You had to mark the shaft to tell if it was running.There were over 1000 of them in one room, so there were always some of them with slack chains.When the chains back lashed, the gear head would pull the anchors out of a concrete floor or snap off grade 5 ---1/2 inch diameter bolts, and it only stopped when it double wrapped around itself and blew the fuse (a 600volt,1/16 amp).

Interesting. Needs a bit of thoughtful engineering. A slipping clutch seems the obvious answer, and Magne, USA make a magnetic clutch where you can adjust the torqe with the current.

Sort of the electronic version of a capstan and a rope?

Gotta go see

Yes, the plus and minus is the confusing bit Edignan, it works but needs to be clearer.

No calcs Drew, just collected the info from various sources. I think I have four versions now, all much the same. I will put them together next chance.

I think I have four versions now,

Ah you'll make a lovely member of our social circle! You're just right! Bent.

Think I have the final version now:

Do you think I need to revise the gradient factors Drew?

Yes the gradient needs to be revised, If you have trouble with the equation I posted earlier I will run the numbers and get back to you after work today.

Drew K

I am guessing I need a log book, and I havn't seen mine for around 40 years! However, hopefully the revised will be somewhere near - it needs to be round figures to be easy to calculate at a glance.

And I have summarised what is hopefully the answer to my OP, comments welcome:

What weight can a 4x4 vehicle pull?

In truth this question has so many variables it is virtually incalculable; but if we make certain assumptions and assume ideal conditions, it is the weight of the vehicle multiplied by the friction coefficient of the ground surface µ.

The coefficient of static friction for a tyre on concrete is 1, on wet tarmac is 0.6, and on snow is 0.3.

The simplified equation for friction is Force equals friction coefficient times normal force F=μFn

The normal force is the force of your wheels against the ground. In the case of a 4 wheel drive vehicle we have 4 forces, in total equal to the weight of the vehicle, providing all four wheels are being driven.

Therefore a 4x4 vehicle on dry flat concrete can exert a pull equal to its weight.

From this it will be possible to gauge a rough idea of the recovery possibilities using the Recovery Formula.

Note that this will reduce on different surfaces, be affected by inclines, and once static friction is lost (when the wheels lose traction and start to spin) will be reduced by around 30% or more.

Equally, the static friction exerted by a stuck vehicle is significantly greater than the dynamic friction exerted once it is moving.

And a great way to cross-check our tables!

Yes, I have that on my 'To Do' list RVZ.

I should explain the purpose of my quest.

I am Chairman of a local group of 4x4 owners who voluntarily provide their vehicles and themselves to assist the emergency services and community. I am updating our members handbook on recovery, and also want to get something out to our less experienced members before any snow comes.

Hopefully this information will dispel some myths and give members some idea of what is achievable and what needs the local farmers tractor

*facepalm*

Y'know, the tractor people do these calculations all the time. Conditions differ, but still...

Calculations just get in the way of getting on with it.

The folk at 1:20 into this video seemed to manage OK.

If only they knew it was impossible.....

Wal - your video link doesn't appear to be working.

Didn't you used to live in Paradise? Have you moved?

must be a typo buried in the url format

try this http://www.youtube.com/watch?v=DB-NhzZLLS4

paradise was a state of mind

Good towing job.

I am in Heaven (ok another state of mind) abt 460 km WNW of you.

Nice and cool?

HIIII

This is a very good idea, we need to use all resources for our betterment.A best Car recovery london service is one which helps us when we need them most...

Thanks