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    Need dip? Throw a rock...
    From: Frank Reed
    Date: 2011 Jun 19, 21:26 -0700

    I don't think this method has come up before on NavList...

    Many times over the years we've discussed methods for estimating height of eye to get the correct value for the dip of the horizon. Dip is proportional to the square root of the height of eye. The time that it takes a dense enough object, where freefall can be assumed, to fall to the ground or the surface of the sea is also proportional to the square root of the height. So throw a rock and time the flight time to the nearest tenth of a second (with some device) and you get the dip. If I've done this right, you just multiply the number of seconds by 4 to get the dip in minutes of arc. So 1.5 seconds to drop implies 6.0' of dip.

    One of the toughest circumstances, which comes up often when practicing sights, is an observer standing atop some platform or cliff with a broad beach below sloping away to the water's edge. It's really tough to guess the total height of eye in cases like this one. So bring a slingshot. Since the horizontal motion is not connected with the vertical motion, as long as the object is dense enough for freefall with minimal air resistance, if you launch your rock aiming straight at the horizon, the time to reach the water will give a pretty good value for the dip even if the water's edge is dozens of feet away in front of you.

    There are many ways to time this electronically. Plenty of smartphone apps can do this: tap when you release, tap on impact. You could also make a video of it. If your video replay software can count individual frames and you know the frame-rate, you can time the fall time to better than a tenth of a second.

    The big catch in the physics of this problem is air resistance. You need to throw an object that is dense and relatively large. A one or two inch rock will work reasonably well. A lead weight, like a fishing sinker, would do nicely (but note: since it's illegal to fish with lead sinkers in many places, it's probably also illegal to toss them at the water intentionally). Obviously if you use something like a styrofoam ball, it would be seriously affected by air resistance, and the fall time would be much longer. You need something that "drops like a rock".

    PS: Sorry I haven't posted in the past four weeks. I've had a really rotten few weeks and I'm just getting back to normal now.

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