I am trying to make a 4 axle mobile crane, similar to a Liebherr LTM 1070-4.2. I am using the largest wheels I can get, the 30mm diameter wheels. What would the point be of using a central differential, and should I use it in the crane.

I don't think, that for this central differential is crucial, but of course, it could just add to technical complexity, it would be more interesting for You and other forum members.

Do you want to move the crane using electric motors, or is the drivetrain there to move a fake engine? 

For the fake engine: please use a center diff.

For moving the crane, don't.

the purpose of a central diff is for axles moving at different speeds... so if they're not, like 42082, then you don't need one. Doesn't matter about motors or fake engines, they're not the decision points... its relative axle speeds.

As far as I can see, if the central diff is presented, it's the single one between 1+2 and 3+4 axles. The LTM 1070-4.2 has 3+4 axles driven and 1+3+4 in some modifications, so I wouldn't use it for 3+4...

The need for a central differential depends on the steering configuration of the axles. Each axle will have it's own turningradius. If these radii are very different from each other the wheels will turn at different speeds when going through a corner. And then you need an extra differential between the axles to compensate for that.

If you make a symmetric configuration (that is the front wheels steer exactly opposite of the rear wheels) there is no practical need for a central diff. The 1st and 2nd (and also the 3rd and 4th) axle will have a slightly different turningradius, but in practice that difference is neglible in LEGO.

If however all wheels turn the same direction (but with different angles so that they all have the same center point for their turningradius) then you will get progressively larger turner radii and extra diffs between some of the axles might be needed.

 

My point was: If you want to move the entire crane, don't add an additional weakpoint, like a center diff. Put a seperate motor for each driven axle, thats it.