NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: LOP by Sextant Box Shadow
From: Lu Abel
Date: 2008 Jul 19, 15:38 -0700
From: Lu Abel
Date: 2008 Jul 19, 15:38 -0700
In a similar vein, once on a very clear, calm night I looked aft of my boat and saw a crystal-clear image of the moon on the water. I wondered if I could use the image as one would in an artificial horizon. I grabbed my sextant and tried it. The result was pretty reasonable -- my sight was off by about 10 miles, which I attributed more to night vision challenges and/or my own shaky hand than difficulties with the concept. Lu Abel frankreed@HistoricalAtlas.net wrote: > Greg, you wrote: > "My sextant box was sitting before me on the dock casting a shadow. Could > this shadow provide me with a LOP? The answer is yes. The inverse tangent of > the sextant box height divided by the length of the cast shadow generates an > hs. " > > The limiting factor in these sights is determining whether the surface is > level. It would be interesting to test some built surfaces (houses, docks, > parking lots, etc.) and find out what sort of typical scatter there is in > leveling. When I was growing up, the scatter for dock surfaces was five > degrees at least with some outliers at 20 degrees tilt, but they build 'em > better now. :-) > > And you wrote: > "I wasn't sure whether to treat this hs as an upper or lower limb so I just > did the reduction as an upper limb to see what would happen." > > You can figure out which limb is associated with the different parts of the > shadow by imagining what an ant would see. Imagine an ant behind the box > where the Sun is completely concealed. As it crawls out (in a direction away > from the Sun), it encounters a little "penumbral band" where the shadow > tansitions from fully dark to fully light. If the ant looks over his > shoulder just as he enters the penumbral band, he will see the Sun's upper > limb just appearing. When he is dead center in the penumbral band, he will > see the center of the Sun just clearing the top of the box. And as he > finally exists the penumbra, he sees the lower limb of the Sun just clearing > the top of the box. You can try this yourself with the shadow of a building. > The order is reversed, of course, when the shadow is being cast by an > overhanging eave. > > Shadow fringes and spots of light on the ground under trees contain some > interesting information. Since the Sun's angular diameter is nearly > constant, the width of the shadow fringe, or penumbral band, is related in a > simple way to the distance between the object casting the shadow and the > shadow itself. An angle of 32 minutes of arc is a ratio of 107:1. So if I > see a tall building casting a shadow with a penumbral band that is five feet > wide, then the portion of the building creating that portion of the shadow > would be about 535 feet away. Note that you have to measure the shadow width > in a direction that is perpendicular to the light rays from the Sun. If the > shadows are faint or confused, you can do this also by walking back and > forth. Find the spot where the Sun's limb first appears. Then walk until the > whole disk of the Sun is clearly visible. The distance between those two > places, multiplied by 107, gives the distance to the object in question. > > Similarly, if you're walking down a shaded sidewalk and you see circles of > light on the ground along your way, each of those circles is a simple image > of the Sun created by small gaps in the foliage above you. The gaps are not > circular. It's the Sun's circular disk that makes the circular patches of > light (and during a partial solar eclipse, you would find that the images > match the partially obscured Sun). As with the penumbral shadow fringes, the > distance to the gaps in the foliage creating the patches of light can be > determined by multiplying by 107. This is an easy way to get the height of a > tree. You find the end of the tree's shadow and then you look for the first > few circular sun images inside the main shadow --they're created by gaps in > the foliage near the very top of the tree. A little geometry then converts > that slant distance to height. I figure it's accurate to about +/-10% > without detailed measurements. > > -FER > PS: works with the Moon, too. > > > > > > --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---