G'day and welcome back to Buildsum and in this video we're gonna keep going with our
calculating
the area of a trench
So in the last video we used the average depth method
And as I said, it's not the most accurate method to get you in the ballpark
In this video, we're going to look at something called Simpsons rule and it's going to help us get a more accurate
calculation of the area under our surface and in our trench
So you can see we've got exactly the same trench is the average depth video and all the measurements there
But to apply Simpsons rule we need to identify some points
okay, so
first thing with Simpsons rule
Simpsons rule refers to a length then when it refers to our length its talking about the length of each of our sections
Not the entire length of the trench like average depth just the length of each one of our sections
So L is the length of one of our sections
Simpsons rule also needs to know the first reading that we need to consider which is this one here
And it also needs to know the last reading
So they have to be picked out separately. And then for the rest of the readings, it really just goes with odds and evens
so obviously
First reading would be an odd, but we're gonna keep that as first second ones are even odd, etc. Ok, so that's the
Points, we have to identify the Simpsons rule
Okay, so that is the formula for Simpsons rule. So what it is, it's the length divided by three times
The first and the last height added together
Then we add the
We add two times the sum of all our odds
So we take all our odd readings and we add them together and then the time some by two and then we have to add
the sum of all our evens, so
Times by four so four times sum of all our evens the way even points so times that by 4
Okay, so let's have a go at doing that
Okay so 5
Which is the length of one of our sections
Divided by 3. That's what Simpsons rule says. Okay times our first reading which is in this case
0.750
Plus our last reading which in this case is 1.169
All right. We'll do that in a minute then 2 times
All our odd readings. So 1.117,
0.963
0.544
0.744
we add them together then we get a times them by two and
All our even readings so we add up all our evens
All right, and we're going to times that by 4 at the end, okay, so let's keep working through that
so if we add our
First and last together we get 1.919
Sorry, I'll start with start. So 5 divided by 3 gives us 1.667
First and last RL or first and last reading and added together gives us 1.919
All right, if you add all these readings together
We get3.368 and if you add all these readings together, we get
4.551
Okay, you still have times up by 4 and we still have to time this by 2 so we'll do that for the next step
okay, so that's the same that's the same 2 times 3.368 gives us 6.736 and
4 times 4.551 gives us 18.204
All right, so these now I'll get added together
Okay gives us 26.859
times that by our original number here 1.667and
We get a total area for this trench of 44.774 square meters
Using Simpsons rule so just as a comparison when we did the depth method on the same trench we ended up with
44.718 so we were slightly under and as I said, that's the course of the fact that when we do average depth
We're not allowing for the curve of the ground
So we're close in the ballpark, but not spot-on
okay, so that's why we're better off using Simpsons rule if we have an EVEN number of
sections to our trench
Okay, so now we know the area of our trench
Obviously we can work out the volume. So
area times by the width of the trench so 44.774
times by let's say the trench is 0.5m wide gives us a total volume of
22.387
cubic meters of material to be removed as that trench
So, there you go, that's how we use Simpsons rule to calculate
The area and then the volume of soil that we would remove from a trench
G'day I'm back
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