Additional Math Pages & Resources

Wednesday, January 18, 2012

How Much Dirt, How Fast, How Far: Part I

Today's math blog is for men and women who have always dreamed of driving a tractor. A big Caterpillar - a loud, grumbling, earth-moving, wheeled, push-pull tractor scraper. Like one of this pair of Cat 627F monsters:

That's right, they are a pair that work together as a team. Notice in the shot above that the rear tractor is connected so they can push and pull each other. Here's a better angle:

 In the photo below, the back tractor has disconnected and the tow bar is raised.

Now you may be wondering why a tractor driver needs math. Let me show you. Today we will just collect some data. We will list some things to consider when choosing an earth-moving strategy (guided by the Cat manuals). Our 627F models are:

  • Length (each) 50 feet
  • Weight 84,000 pounds (empty)
  • Horsepower 330 front and 225 rear
  • Fuel capacity 262 gallons (consumption ~ 40 gph)
  • Top Speed 32 mph
Now, what can they do?

  • Maximum load  48,000 pounds
  • Maximum volume  44 cubic yards
  • Width of cut ~ 10 feet
  • Depth of cut into soil ~ 12 inches per pass
  • Depth of spread soil ~ 21 inches per pass
Here's what our team of scrapers can handle when it comes to the type of soil:

  • Dry  (0-10% moisture)
  • Moist (10-20% moisture)
  • Wet (20-30% moisture)
  • Sand
  • Sand and Gravel (rocks up to 3")
  • Rock (up 50% may be up to 12" diameter)
Larger rocks, harder surfaces, wetter soil, steep banks, very soft sand, etc. all fall outside the preferred conditions for our scrapers. Once we've defined the material we are moving and the grade, we have to worry about getting stuck in the sand or mud. So we consider the condition of the soil:

  • 3% (no tire sinkage into the surface)
  • 5% (up to 2" sinkage into soil)
  • 10% (up to 5" sinkage into soil)
  • 15% (up to 8" sinkage into soil)
  • 20% (up to 12" sinkage into soil)
Finally we need to plan based on the optimal soil delivery distance - how far must it be moved? Very close, and we can just push it with a scraper. Too far, and we need a dump truck. In the middle, we can use our soil movers. Their maximum optimal moving distance is under 2 miles.

Tomorrow we will do some calculations!