Additional Math Pages & Resources

Tuesday, February 23, 2010

Ship Shape Limbo

Limbo is a game where people bend over backwards to shimmy under a moveable stick. See the photo to get an idea about the game.

You win if you make it underneath without touching the stick. You lose if your chin or hands touch the stick, if you knock it off the holder, or if you fall down or touch the ground - it's much harder than it looks!

Where does the math come in? Well, a similar activity is played out every time a ship passes under a bridge. In most cases, there's plenty of room above the ship. But not always. And the pilot MUST be good at math.

The distance a ship sticks up out of the water is called the air draft. The clear air below a bridge is called the air gap.

The air gap minus the air draft has to be a positive number, or the ship will hit the bridge. Here's a drawing from the NOAA website showing the Air Gap under the Bayonne Bridge in New York.

This bridge has an air gap of 154.1 feet. If the ship's air draft is say 153 feet, it should clear, right? NOT RIGHT!  Here is the measurement a few hours later...
Things can change quickly in the ship-limbo game!
  • Ships float higher in salt water, and lower when in fresh water
  • Increasing a ship's load makes it float lower in the water, until it sinks or scrapes the bottom
  • Tides cause the water levels to change constantly
  • Winds cause the water to be higher or lower on one side of the canal
  • Waves and wakes cause ships to move vertically 
  • It can be difficult to know the exact air draft of a ship
  • If ships aren't loaded correctly, the front or back might be slightly higher than the middle
  • Traffic on the bridge causes the bridge to sag slightly
  • Winds cause bridges to move from side to side (up to 27 feet for the Golden Gate bridge!)
Our government is very concerned that ships don't hit bridges. Here's the Air Gap graph for today. Notice that it changes by more than 4 feet in less than 4 hours and might now be under 150 feet.

This is such important information that the numbers are calculated every 6 minutes and posted on the web. Here's a text summary for right now:
Observations for New York/New Jersey PORTS 2010-02-23 15:01:02 EST
High water conditions exist for Kings Point, The Battery, and Sandy Hook.
Water levels are rising above predictions by up to 2.1 feet at Kings Point, Sandy Hook, and Battery.
Currents at The Narrows are flooding at 1.1 knots.
Reported winds are generally from the northeast, between 5 and 16 knots with gusts to 19 knots.
Reported air temperatures are in the mid to high 30s °F, and reported water temperatures range from the high 30s to the low 40s °F.
Barometric pressure is falling, with readings between 1007.4 and 1008.8 mb.
Air gap is 150.5 feet and decreasing at Bayonne Bridge Air Gap, and 227 feet and decreasing at Verrazano-Narrows Air Gap
    Miscalculating the clearance can ruin a bridge, sink a ship, and/or result in deaths. Here's a picture of a freighter that failed to clear a bridge. Four lives were lost and a ship and bridge ruined.

    A bridge over the Chesapeake was knocked down by the freighter you see here.

    I found a story about the Narrows Bridge in Vancouver that was struck by a run-away barge. The barge didn't ruin the bridge at first, it was simply stuck in place. But as the tide lifted the barge, it also lifted the bridge span off its supports, and the span fell into the water - thus ruining the bridge and the waterway access at the same time!

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