EARTHWORK END AREA METHOD 1

[LAWR]

WHAT IS THE FORMULAS FOR VOLUME USING THE END AREA METHOD?

 

[jartgo]

I assume you are referring to the average end area method. In this method you essentially take the average of two areas and multiply that average by the distance between the areas.

The equation is actually in the name: "Average end areas"
V=[(A1+A2)/2]*L
where A1 and A2 are the actual end areas, and L is the distance between the areas.

As a simple example, if you have one cross section that is 50 s.f. and one cross section that is 150 s.f., while the sections are 50 feet apart, you have 5000 c.f. of volume between the sections.

 

[BigH]

We used to use (A1+A2+(A1*A2)^2)/3.

 

[Apakrat]

If I am intruding, or my assumption be wrong, please just ignore this old coot!

Don't know if this will help or not, but am assuming "LAWR" possibly may be un-familiar with the actual DMD area method employing the double meridian method to calculate the area of a tract of land with numerous corners which have been surveyed and coordinates calculated for each property corner.

El = Elevation in "X" units
D = Distance in "X" units from a mean point

End Area One = {[Elb-Eld)*Da]+[Elc-Ele)*Db]+[Eld-Ela)*Dc]+[Ela-Elb)*Dd]}/2

End Area Two = {[Elb-Elc)*Da]+[Elc-Ela)*Db]+[Ea-Elc)*Dd]}/2

(End Area One + End Area Two)/2 = Volume in "X"^3 units


At 74th year working on IR-One PhD from UHK - - -

 

[thegraduate]

jthompson is right. It is basically Reimann sums. The shorter your length between your average areas, then the more accurate will be your results.

 

[DRC1]

One thing to remember is that the distance between the sections is the straight line distance betwwen the ceters of gravity of each section and that sections are perndicular to the striaght line distance. This is important on wide sections and computing volumes on a curve.

 

[jdonville]

BigH has the correct formula. It is the formula for a prismatic frustum, and should work well as long as the adjacent area shapes are not wildly dissimilar.

Jeff