and you want to know where its center of gravity might fall (for weight ... exact center of gravity. Where it spins freely and ... we call functions. The functions are.
I here are some handy ways to do shop calculations quickly. If you have an irregular piece of metal, for instance,
and you want to know where its center of gravity might fall (for weight and balance calculations), you can cut out a piece of cardboard the same size as the piece but in reduced scale, stick pins in it and spin it until you find its exact center of gravity. Where it spins
ing shows. The distances from the leading edge to the trailing edge of the elevator are drawn at each station and also entered on the chart. These dimensions are then multiplied times a multiplier. Station 0 and the last station always have a multiplier of 1. The second station away from station 0 and the second
method of determining an area is known as "Simpson's Rule". You can either make a scale drawing with some convenient scale like 3 inches to 1 foot or you can take the dimensions directly off the part. Pitts builders will recognize the top view of their elevator. It has an area of approximately 3 square feet (each
station away from the last station always use a multiplier of 4. In between
side).
need it for the one item it is really not a sound investment. The diagram shows an elevator area calculation. The diagram looks down on the elevator. The first thing you need to do is divide the area into an equal number of sections. Eight is a convenient number and seems to work quite well. If you have an irregular length (as we do in this illustration - 39-3/4"), eight doesn't conveniently divide into that. Just get a ruler that seems to fit the space between one end and the other and turn it diagonally until you have eight equal dimensions as the diagram shows. This very conveniently divides the drawing into eight parts. The stations are numbered across the bottom from inboard centerline to the outboard tip. Always use zero as the starting number. You should realize that although you have eight parts, you have nine lines from zero to eight. These are called stations as the draw-
multipliers, go 4, 2, 4, 2, etc. The station measurements in inches are multiplied times this mystical multiplier to get what we call functions. The functions are then totaled and as the chart shows, the function is multiplied times the distance between stations; in this case, 4.96875" and divided by 3. This gives you the square inches of the elevator surface which you can divide by 144 to get square feet. Multiply times 2 to get the total elevator area as you have only calculated one side. Once you have done this process one or two times and kept your notes, you will find it a simple process to do. I checked these calculations with the planimeter and found this method was very close to the planimeter's measurements. Basically what this method does is boil down some very complex mathematics to simple shop terms. This
freely and does not stop at the same spot each time is its CG. If you need to know the area of an irregular surface you can always put a square grid over the top of it and count
the squares but this is pretty laborious. You can also buy a fairly expensive tool known as a "planimeter" but if you only
64 JANUARY 1990
Area of Elevator By Simpson's Rule Station
Inches
X
0 1
1
2.125
4
20.000
2
27.250
3
2.125 5.000 13.625 16.625
4
66.500
4
15.250
2
30.500
5
13.750
4
55.000
6
12.000
2
24.000
7
9.125
4
36.500
8
0
1
2
Total
Function
0 261.875
Total Functions x Common Interval = Area
3
(One Side)
261.875 x 4.96875 = 433.73 sq. in. 3 433.73 sq. in. H- 144 = 3.012 sq. ft.
Area 1 side x 2 = Area (Both Sides) 3.012 x 2 = 6.024 sq. ft. (Both Sides)
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