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Math Help - acreage formula... Please Help an Old Guy !

  1. #1
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    acreage formula... Please Help an Old Guy !

    Hello my friends.... I've always been fascinated my mathematics/numbers, but have never been particularly good at it. Be thankful for your gift !!!! I'm a State Trooper/Pilot with the Oklahoma Highway Patrol. Yesterday I provided air support to ground units with a very large grass fire here in Oklahoma. After the fire was out, I flew the entire outer parameter of the fire which was obviously quite arbitrary. The length of the parameter was 64.8 nautical miles. Could some one help me with figuring the acreage of this fire?

    One U.S. survey acre is equal to 62,726,400,00015,499,969 m2 = 4046.8726098 m2.

    Thank you so much for your help.
    Trp. Roy Anderson #404
    Oklahoma Highway Patrol
    Air Support Unit
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  2. #2
    Member Mentia's Avatar
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    Trooper Anderson,

    Thank you very much for the work you do. Unfortunately, it is very difficult to know the area of an arbitrary shape knowing only its perimeter length. Consider a box with width 9 meters, height 1 meter. Then the perimeter is 20 meters with an area of 9 square meters. If the box is 5x5 meters, the perimeter is again 20 meters, but this time the area is 25 meters.

    All I can do is provide you with a maximum upper limit to the area. This would be a perfect circle shape. If the perimeter of your burn swath is 64.8 nautical miles then the maximum area it could possibly have is 283,200 acres.

    My guess is that it is probably around 3/4 of that, which is 212,400 acres. But this is pure guesswork.

    If you have a map of your flightpath, say from GPS data, then there are ways to get that area much more accurately.
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  3. #3
    Member Mentia's Avatar
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    If you would like to know how I got the 283,200 acres:

    Perimeter = 2*Pi*Radius = 64.8 nmi

    Then,

    Radius = (64.8 nmi)/(2*Pi) = 10.3132 nmi

    Area of a circle = Pi*(Radius)^2 = Pi*(10.3132 nmi)^2 = 334.149 sq. nmi

    1 square nautical mile = 847.55 acres

    Then,

    334.149 sq nmi = 283,200 acres
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  4. #4
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    Thank you Mentia for your replay and explanation. I'm quite blessed to have my job & you're welcome.

    Also, when I refered to the parameter what I was infering was the circumference, but I do not believe this would make any difference.

    Thank you again.
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  5. #5
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    If you mean that the region was circular (or close to circular) and c is the circumference, then A= \frac{c^2}{4\pi}.
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  6. #6
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    Not really.... perhaps Parameter is more correct. In any case the Dept of Forestry folks somehow came up with 54,770 acres? Hey, I just drive airplanes and helicopters....What do I know. LOL

    Thanks for your inputs, I was just curious how one could solve this.

    Roy Anderson
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