I have been one of the primary operators of a ladder truck in my fire department since the truck was delivered in 2000. Recently, we (some of the drivers and officers) have had an internal dispute over the possibility of the truck to slide down a hill when it is in use. I contend the truck isn’t sliding anywhere, others (after participating in an outside training on a different, and much older, style of truck where sliding has happened) are wailing that the truck is going to wander off on its own with the slightest provocation. I realize anecdotes are not evidence, but I have operated the truck literally hundreds of times, many times in some substantially marginal locations, and have never, ever had it slide. But I digress…
I am looking for someone who rememebers the high school AP physics that I should have remembered on my own to put some math behind (or against) my claim.
The givens:
The truck weighs 66,000 lbs. The aerial ladder weighs 9,000 lbs and will rotate 360 degrees extended 100’ up or 92’ horizontal.
The frame of the truck is extraordinarily rigid. For our purposes, assume no flex in the frame when the truck is set up.
There are four jacks that are connected to the frame that lift the truck off of the ground when in operation. The jacks total width is 12’ tip-to-tip, call it 22’ front-to-back.
The tires are not touching the ground when the truck is set up (removes the entire truck’s weight from the suspension).
When the truck is set up, the jacks are extended downward to level the body/frame. The maximum slope that can be corrected is 5 degrees.
Each jack has a steel ground-contact surface measuring 10" x 14". The steel is a mill finish, I am not sure of what alloy or Rockwell. Each ground contact plate is on a sperical bearing that allows the plate to sit on unlevel ground.
When set up, the steel jack plate is set on top of an aluminum auxiliary jack plate. The aluminum plate is 24" x 24", distributing the truck’s weight over a larger surface area. The plate is 6061 with a plain finish.
The best photo I can find to describe the jack arrangement is here. The bottom photo is the most representative (although missing the auxiliary plates). This truck is not the exact model, but is close enough to get the arrangement across.
The problem:
If the truck is set up on a 5 degree down slope (front-to-back) (which is the maximum it can be set up on), on asphalt, will the mass of the truck overcome the breakaway force required to let this thing slide? I do not know the coefficients of friction for the steel jacks, aluminum auxiliary plates, or asphalt.
I would like to know what mass of a truck would slide when up on the jacks.
For the calculations, I am assuming that the frame does not flex when the aerial is moved about, which would allow the jacks to “walk” themselves across the plates. If someone would like to model that, good luck. I can attest that the frame flex is nearly non-existant, but I am sure there is some give there.
Any help is greatly greatly appreciated, of course.
For a first-order approximation, whether something will slide or not under the influence of gravity depends only on the slope and the coefficient of friction. It doesn’t really matter that this is a fire truck, how much it weighs, or what the ladder is doing. The relevant factors:
-aluminum-on-asphalt static coefficient of friction. Can’t find any values that are exactly what we’re looking for. The closest I can find is 0.7 for sliding friction between steel and pavement. Static friction coefficient is almost always greater than sliding friction, but just to be conservative, we’ll stick (!) with 0.7.
-aluminum-on-steel static coefficient of friction. These guys claim 0.6. this is less than the aluminum-on-asphalt number, which means the first thing that’s going to slip is the aluminum/steel interface. So we’ll use 0.6 as our limiting value.
The slope where sliding would begin is where TAN(angle) = 0.6. So our critical slope angle is 31 degrees. That’s a pretty hairy-steep slope.
Note that the mass of the truck doesn’t particularly matter. If it weighs more, then gravity is trying harder to make it slide, but it’s also providing a higher limit for friction forces; the two effects cancel each other out.
Bottom line, 5 degrees is a very conservative number; you shouldn’t be anywhere close to sliding off of the jacks on a slope like that.
I was going to say that 30 degrees is where you have to worry about sliding, but **Machine Elf **has a more robust argument than my seat of the pants value.
The 5 degree limit has much more to do with balance and extended equipment than it does with sliding. The bucket truck I worked had outriggers that could compensate for that much angle.
Machine Elf, thanks for verifying what my gut had said. Much appreciated. Its amazing how a simple formula can be displaced by other information. Yet I can still relive the 1986 World Series. Hmph.
For those who came in looking for drifting fire engines, I have had the back wheels of this truck going in a radically different direction than the front, though not intentionally, and in snow/ice. It is a frightening proposition, and one I hope never to repeat again. The ladder on top of the truck weighs 9000 lbs, is over nine feet off the ground, and has a mind of its own when the truck is moving sideways. Five pairs of very big eyes and several seat cushions that needed to be cleaned later, everything came back in line and we continued on our way. Never again.
If the ladder weighs 9000 lbs., might it being in a lowered or raised position affect the truck’s center of gravity enough to make any difference in possible slippage?
Given how far from sliding your truck is at 5 degrees, I’m wondering why the other truck is sliding. Machine Elf’s derivation should work for either truck. What’s different about how the other truck is set up?
The design of the other truck does not provide as stiff of a base for the aerial to operate from as the truck I use. The one that was supposedly “walked” down a hill was this type (not this truck specifically, but a cousin). Much older, a different jack system, and a more traditional chassis. When the platform is rotated around and constantly moved, the chassis flexes, torquing the two stabilizer arms, and forcing the truck to studder-walk itself. There is a sideways force that pushes a stabilizer horizontally a small bit, followed by the other stabilizer being pushed horizontally a bit. The truck was also supposedly on a steeper hill than we can set up on (which is very likely) Enough of those small motions forces the truck to walk, which is “allowed” by the steel jacks on the aluminum auxiliary plates. Personally, I think it was an improperly set up truck, but I wasn’t there, I’m only addressing the claims of an “expert.”
My stance is that there’s an apples-and-bicycles comparison being made. The naysayers are claiming a sliding problem, I contend there is a chassis flex problem that we do not have, yet we are not treating the (non-existant) problem as a sliding problem. The math says its not a sliding problem. Ergo, we’re about to take some silly actions to correct a problem that we don’t have.
One variable that can enter your equation is water changing the coefficient of friction. If the steel plate is wet, you probably have a lower coefficient. If it’s greasy, you have a much lower coefficient. You’re still probably nowhere near having issues at 5 degrees.
To slide on a 5-degree slope requires a coefficient of friction of 0.09. For that, you need something very soft and slippery on a hard, polished surface. Chart here suggests that polyethylene plastic on polished steel would give 0.2, which would provide an uncomfortably small safety factor of about 2, but theoretically still wouldn’t slide.
Clearly a truck whose outriggers are moving off of their original touchdown points aren’t sliding; the only other possibility is walking.
Oh man and I too had a story about being in a pumper fishtailing in the snow. Those of us in the jump seats got real quiet real fast. Math is useful but a lot less exciting to remember.
why are the wheels not chocked? I don’t care how much your truck weighs it can’t be more than a 747 and I’ve never seen one slide over a wheel chock from it’s own weight. Granted they aren’t parked on steep hills but they do move back onto the chocks all the time.
not the front end. And even if the whole thing was on jacks the concept of chocks does not change. It’s still a wedge against something whether it’s a wheel or the frame.
