Question on Crane Physics (CG/CM)

[gambleda]

Hello,

In the picture provided, can anyone tell me if the Center of Gravity or the Center Mass of the Crane changes dependent upon where the load is lifted from and why. Assume the weight of the load is constant. The only thing that changes is the location of the weight being lifted.

Thanks.

[rmarz]

gambleda - It almost sounds like a trick quiz question. Logic suggests that as long as the load is in the same vertical plane at all 3 positions it exerts the same force vectors on the crane, and the cranes center of gravity or mass doesn't change. The tricky part is the mass of the cable that spools off the reel in the three different positions. With the load at the lowest position, more cable mass is added to the load plane and less is on the reel. The lower reel mass actually changes the c of g of the crane.

Rick Marz

[gambleda]

Thanks for the reply Rick,

Is there a way to mathematically show that this does happen? Basically I've been told, the weight of the wire rope has no effect on the load or CG. Logically, to me, the CG would have to change however minute it may be, but showing that it does is where I lack the expertise. Any help would be greatly appreciated.

Thanks

Gamble

[deleted-71588]

Basically I've been told, the weight of the wire rope has no effect on the load or CG.

Given that there are no dimensions on the diagram, there is no way to calculate the distance the amount of cable mass moves. From a practical point of view, the entire mass of the cable independent of where it is physically located is from an engineering math point of view probably insignificant wrt the mass of the crane plus the mass of the load. From a crane operator point of view, the tipping force from a load acceleration times the mass of the load is probably several orders of magnitude more significant than the entire mass of the cable.

Essentially, some interesting mathmatical subtlties of engineering calculations end up being ignored because they don't change the calculations enough to warrent the added complexities.

[deleted-71360]

For stability, the center of mass must be between the front and rear axles.

Using the empty mass of the truck and the distance from the front axle to the center of that mass, you get a torque around the front axle. The force on the rear axle must counteract that torque and provide a steady-state condition.

Lifting the load causes a torque around the front axle in the opposite direction as that from the truck's mass. As long as this torque is less than the truck's mass-generated torque, the truck is still stable. The center of this combined mass must still be between the front and rear axle.

If the load's torque exceeds the truck's torque because the ccenter of mass is beyond the truck's front axle, the truck will rotate around its front axle and fall into the hole.

Now that you know how to describe the problem in words, add the numbers to determine how much load you can lift and still be stable.

Also, the weight of the cable becomes part of the load's weight for these calculations, and in general, the cable is a small fraction of a load that would need this type of analysis. Think of the cable in terms of 100 pounds and the load in terms of 10,000 pounds, and the truck in terms of 50,000 pounds.

Then let the experienced craine operator do the heavy lifting, that is what they have training, experience, and licensing for.