Hi.
If you missed the last video, where we performed the field procedure for a survey resection,
go ahead and click in this corner.
It's going to direct you to the last video I shot to see exactly what goes into the field
procedure of a survey resection.
Then come back to this video to figure out how to calculate the coordinates of the unknown
points.
All right.
Let's go ahead and get started.
What we see here is the data that we captured in the field.
In this column right here, we have the horizontal distance from our total station to the sighted
points.
Blue -- green -- the unknown pink point -- orange -- and then going back to blue.
In this column here I have the average angle measure between both trials.
You can go ahead and measure as many times as you want.
The more times you do it the higher your accuracy is going to be.
Just be sure to average all your results and have one data set to work with.
Now in theory we went around in a circle.
Therefore, all of our angles are supposed to equal 360 degrees.
What we're going to do is add up all of our averaged angles and see what our result is
going to be.
Now in order to add up all these angles, you could do it by hand by adding up all the seconds,
the minutes, and the degrees. and then transferring over and simplifying your answer.
However, I'm going to recommend you guys use a calculator.
This is the Casio FX 115 ES Plus.
Figure out the name.
This is a 12 to 15 dollar calculator that can be picked up at pretty much any store
and is allowed by NTEES on all fundamental exams including the fundamentals of surveying
and fundamentals of engineering exam.
I highly recommend you purchase this calculator and get familiar with its interface.
All right.
Let's go ahead and add up our angles.
We have 56 degrees, 36 minutes, 37 seconds plus 72 degrees, 10 minutes, 38 seconds plus
74 degrees, 30 minutes, 25 seconds plus 147 degrees, 42 minutes, and 36 seconds.
All right.
Our answer is 360 degrees, 00 minutes and 16 seconds.
When we subtract that from 360 degrees, our error is 16 seconds.
Now in reality, this is a circle.
So it should only be 360 degrees.
To correct our error, we're going to have to adjust all of the angle measurements.
To do so, we're going to take the error and divide it by the number of measures.
The formula for this adjustment is error divided by number of angles.
Our error is 16 seconds.
We have four angles.
So that means four seconds of adjustment.
Because we are over 16 seconds, we are then going to subtract four seconds, from every
angle.
So minus four seconds on all of these which gives us 65 degrees, 36 minutes and 33 seconds
-- 72 degrees, 10 minutes and 34 seconds.
74 degrees, 30 minutes and 21 seconds and 147 degrees, 42 minutes and 32 seconds.
These are now our adjusted angles.
I'm gonna go ahead and just move all of this out of the way.
Move it down here.
Now, I want you to categorize your angles in the following manner.
This angle is going to become angle 1.
These two are going to be angle 2.
I'll explain why we're doing this in a second and then this one is going to be angle 3.
Now the unknown point pink, we don't have coordinates on this point.
Therefore, we need to be able to combine the angle between green and orange in order to
calculate our resection.
Because remember, angle one is truly from blue to green.
Now this angle 2 is green to orange.
And angle 3 is orange to blue.
So that means that when we add these two angles together, we get 72 degrees, 10 minutes, 34
seconds, plus 74 degrees, 30 minutes, and 21 seconds.
And our answer here is 146 degrees, 40 minutes and 55 seconds.
And then this is just 147.
All right.
Now let's reveal what the coordinates are of orange, blue and green.
These are the northings and eastings.
Remember, northing is technically the Y coordinate and easting is the X coordinate.
In surveying, they're flipped from traditional plotting.
Now I want to introduce you to a new software.
This software is called Adjust.
It's a free computational software that anybody can download.
Go ahead and click on the link in the description and download your version of Adjust.
You can use different tools to do different surveying tasks and together we're gonna be
using it to perform the three point resection.
All right within Adjust, I want you to go to programs, coordinate computations, coordinate
geometry, and select option 6 -- three-point resection.
In this menu you're going to be asked to give the coordinates of three known points.
Go ahead and input the coordinates of blue, green and orange in that order and then place
the degrees, minutes and seconds of the angles that we calculated.
All right.
Now that we have the coordinates of our total station set up, we need to calculate the coordinates
of our unknown pink point.
In order to do that, we're going to find the azimuth of the point just adjacent of it,
the green point.
I have drawn up this sketch right here.
As you can see the orientation is -- north is up -- our total station is in the middle
as it sights blue, green, pink and orange.
We're going to find the azimuth of this line right here.
In order to do that, we're going to use the following formula.
The azimuth is equal to the arc tan of the easting of green minus the easting of the
total station divided by the northing of green minus the northing of the total station.
All right, so here are the coordinates of those two points.
Remember we calculated the total station coordinates.
And the green coordinates were given to us.
All right, so let's take our calculator and punch in these numbers.
So the arc tan of the easting of green, so that is 13517052.81 minus the easting of the
total station which is 13517029.31.
And we're going to divide that by the northing of green, which is 420384.92 minus 420339.60.
And then that gives us the answer of 27.408.
I want you to remember, we're working in a quadrant system so when we draw in our quadrant
lines, we can see that the point is going in a northeast direction.
Meaning that both the northing and the easting are positive.
So when we calculate our azimuth, it's also going to be positive.
This number here is the degree measure and to convert to decimal degrees, it would be
0.408 times 60 is equal to 24.498 and we multiply 0.498 times 60 and we get 29.928 estimate.
So we can simplify this as 27 degrees, 24 minutes and 30 seconds.
So that is the azimuth between the total station and point green.
Now we're going to use this azimuth to figure out where point pink is located.
We have this angle right here.
Because we measured it, right?
This angle is 72 degrees 10 minutes 34 seconds.
So we're going to add this internal angle to our azimuth.
We will have 64 seconds.
We will have 34 minutes.
We will have 99 -- can't have more than 60 seconds.
So this will become four seconds and this will become 35 minutes.
So now we have the azimuth to this line, 99 degrees, 35 minutes 04 seconds.
We also have a distance between the total station and the pink unknown point.
It's 36.01 feet.
Now in order to calculate the coordinates of pink, we're going to take the northings
and eastings of our total station coordinates.
We will then add the distance and then multiply it by either the cosine or the sine of the
azimuth.
That's going to finish up these calculations.
I go down here just a little bit.
So the northing of pink is equal to the northing of the total station plus the distance times
the cosine of the azimuth and the easting of pink is equal to the easting of the total
station plus the distance times the sine of the azimuth, so this ends up looking like
420339.60 plus 36.01 times the cosine of 99 degrees 35 minutes and 04 seconds.
Over here, we'll do 13517029.31 plus 36.01 times the sine of 99 degrees 35 minutes and
04 seconds.
Plug it in to our calculator.
420339.60 plus 36.1 times the cosine of 99 degrees 35 minutes and 04 seconds, gives us
420333.59 and then easting 13517029.31 plus 36.01 times the sine of 99 degrees 35 minutes
and 04 seconds gives us 13517064.82.
All right.
Now let's compare our calculated answers to what we captured with the GPS completely independently.
Completely different method and these are the coordinates that I recorded with a GPS.
So our difference in our northing is about -- 15 hundredths of a foot and our easting
is right on.
And there you have it.
That is how you calculate the coordinates to your surveying resection.