Hi. I'm Rami Tamimi.
And welcome to my new office. This will be the space that I kind of work
in from now on. I hope you guys like it. Today we'll be calculating the coordinates
of our survey traverse, using the latitudes and departures between points taken from
our angles and distances that we measured in the field.
[♫Music♫] All right.
If you haven't seen the last video, I recommend you click on
the I in the corner, watch and see what the field procedure is like. What goes into the data
collection, all the different setups that we had, then come back to this video and we will calculate
all those coordinates using one reference point. I'm gonna direct our attention to the computer so
that we can see all of the data that we collected. Right here we have a sketch of our work and
here are all the numbers that we measured in the field. If you recall, we initially set
up on pink. We then backsighted the reference point and foresighted green. Then we set up
on green. Backsighted pink. Foresighted red. Then set up on red. Backsighted green. Foresighted
blue. Set up on blue. Backsighted red and foresighted orange. Set up on orange. Backsighted
blue. Foresighted pink. And finally set up on pink. Backsighted orange and foresighted green.
Between all of these points, we have angles and distances. Referring to the internal angles of our
traverse. You're also gonna notice that there's a forward distance and a backward distance. The
forward distance are all of the distances that we took when we were taking a foresight. And
the backward distance is all the distances that we took when we were reading a backsight.
We then take the average of these two so we can increase the level of accuracy with our
distances -- which is what we see right here. Now the first step is going to be
to add up all of our internal angles so that we can calculate what our misclosure is.
Not all these measurements are internal angles. Everything except for the first one is. Because
remember, that angle is this angle right here and that's not necessarily, you know, going from
one line to the other. That's why we measured this last one right here, which is actually from here
to here. So just disregard this angle right here when we're adding up our angles. The best way to
add up your angles is -- by using this calculator. Have you bought this calculator yet? If you
haven't, click the link in the description to buy this Casio calculator. This is not a
sponsored video. I am not being paid by Casio. I just don't you to be using a graphing
calculator that you are not allowed to use on your NCEES licensing exam. This is approved by
NCEES for all licensing exams. So practice on it. Learn it. Become best friends with it.
So that you can use it on your exam. All right. I'm done ranting.
So we're gonna go ahead and add up all of our angles.
67 degrees, 17 minutes 47 seconds plus 217 degrees, 40 minutes, and 20 seconds
plus 70 degrees, 4 minutes, 46 seconds, plus 48 degrees, 9 minutes, 53 seconds plus
136 degrees, 47 minutes and 39 seconds. And we get a total of 540 degrees,
00 minutes and 25 seconds. Now, remember, to calculate misclosure,
it is error divided by number of angles. So that is going to be 25 seconds, over five
angles. But because we have 1-2-3-4-5, gives us an error of five seconds per angle. So because
we're 25 seconds over, we're going to then have to subtract five seconds from every angle. So now
this one will become 67 degrees, 17 minutes and 42 seconds. This one is 217 degrees, 40 minutes, and
15 seconds, 70 degrees, 4 minutes, 41 seconds. 48 degrees, 9 minutes, 48 seconds.
And 136 degrees, 47 minutes, 34 seconds. So now we have 540 degrees.
If you're ever unsure about what your angles are supposed to add up to, the
formula for figuring out internal angles is 180 times N minus 2 where N is number of angles.
So in our case, 180, 5 minus 2, is equal to 540. Now that we have our adjusted angles,
we're going to be using them to calculate our azimuths. This is gonna be a little tricky and
it's a little bit tedious, but bear with me. We will get through this. Let's refer to our sketch
to give us a better idea of what we're doing. The most important thing with the sketch is
the north arrow. This north arrow will indicate exactly where you have in terms of orientation.
Knowing where you are will help determine the location of your next point. So we know that
the north arrow is pointing up. By knowing our orientation, this will help us determine
where we're going to get to the next point. I want you to think about it like this. I'm
gonna draw something like this at every one of these points. So when we look at our quadrant
system, you see we're heading in the northwest direction, meaning that our azimuth needs to
be above 270 degrees because risk management, this is north and this is west. Now in the last
resection calculations video, we had determined the azimuth between the reference point and pink.
In that video, I called it like the total station setup point and the unknown pink point,
something like that. It's the exact same point. I just changed the name of those points.
Go ahead and refer to that video if you want to see how we calculated the azimuth between these
two points but we're going to use that azimuth as a reference to determine the azimuths for
the rest of our points. If you guys recall that azimuth was 99 degrees, 35 minutes and 4 seconds.
Now we want to determine the azimuth here. If we're gonna take a look at the reference point
--and where this 99 degrees is, it lies in this area. This is a big exaggerated but you get what
I'm saying. To figure out where that line is on point pink, we need to then take the back azimuth
of that point. To determine the back azimuth, we need to add 180 degrees. So we're gonna start
with our reference azimuth, add 180 degrees to it and then we measure the angle from here to
here. 67 degrees, 18 minutes and 26 seconds. So we will add that as well and that will give us
our azimuth from pink to green. So the azimuth to green is the reference azimuth of 99 degrees, 35
minutes and 4 seconds plus 180 degrees, so that we get the back azimuth of it. Plus the angle measure
of 67 degrees, 18 minutes, and 26 seconds and that gives us 346 degrees, 53 minutes and 30 seconds.
Okay, same process now. We're going to then again draw up this shape. And you can see that the
line is in the southwest quadrant, which means our azimuth needs to be greater than 180 degrees
but less than 270 degrees. We have this azimuth and we have this angle measure which is adjusted
at 67 degrees, 17 minutes, and 42 seconds. Now what we have from pink is this azimuth right
here. If we were to take the reverse azimuth that comes down here, we would need to subtract 180
degrees. So if we take our reference azimuth, subtract 180 degrees and then add our measured
angle, that'll place us right here. So to get to red, we need to take our azimuth of
346 degrees 53 minutes and 30 seconds. We will then subtract 180 degrees to get the back
azimuth and then we will add our angle measure of 67 degrees 17 minutes and 42 seconds and that
gives us 234 degrees, 11 minutes and 12 seconds. Let me bring this down one line so that
it's a little bit cleaner for you guys. Now this right here is the azimuth to red.
Let's head back up here and look at the next point. We look back here and we see we want
this azimuth, so we need to subtract 180 cause what we have right now is this right here at
234 degrees so if we subtract 180 from that we'll end up on this line right here and then
we have an angle measure from here until here. When we zero'd out our backside at green and
then measured blue. So taking the reference point, subtracting 180 to get the reverse
azimuth and then adding our angle measure. So that is 234 degrees, 11 minutes and 12
seconds minus the back azimuth so 180 degrees and we're going to then add the angle of
217 degrees, 40 minutes and 15 seconds. And that will give us 271 degrees,
51 minutes and 27 seconds. Now let's look at the setup in blue and we draw
in our -- we see it's the same situation. I mean, we are coming out here with an azimuth.
We need to go back azimuth, so we're gonna subtract 180 degrees to get us on this line
and then we have this angle measure here. So all we have to do then is just add that angle
measure to get to orange. We do. 271 degrees, 51 minutes and 27 seconds minus 180 degrees
because we have to measure that back azimuth, and then we're gonna add 70 degrees, 4 minutes
and 41 seconds and that gives us 161 degrees, 56 minutes and 8 seconds.
Now we are set up on orange and we want to get to pink.
This is a little bit strange because now we have the azimuth coming down. We need to then add
180 degrees to get back. It will be the azimuth of this line coming back. We're gonna add
180 degrees because what we have right now from blue is coming down like this. So we want
to get to the other side of it. Then we're gonna add the angle measure which is from here to here.
But the problem is, we're crossing the 360 degree mark and there are no angles above 360 degrees.
Any time you go over 360 degrees, subtract 360 from it. Always do that because you can't go
above 300 -- you can't be like, I'm at 400 degrees azimuth. No. Like you subtract 360 from
the 400 and then you're at 40 degrees azimuth. So make sure we do that. We're gonna subtract 360
degrees from our end total because we're gonna go over 360 since we crossed the 360 line or the
north line if you want to be more technical. Setting this one up, it's gonna be to
pink, 161 degrees. 56 minutes. 08 seconds. We're going on the back azimuth but we're on
the opposite end so we're gonna add 180 degrees, we're gonna add the angle measure
of 48 degrees, 09 minutes, 48 seconds and subtract 360 degrees from that and
we will have 30 degrees, 5 minutes and 56 seconds. Last one. Almost done. We're
setting back up on pink. Once again, we have the back azimuth.
Now since this is coming up here, we are then going to add 180 degrees plus our
angle measure from here to this line right here. So now we're going back up to green and this
is just so that we can get the internal angle. Nothing more. Maybe it'll help us check
our coordinates but 30 degrees, 5 minutes, and 56 seconds plus 180 degrees, plus 136 degrees,
47 minutes and 34 seconds is equal to 346 degrees 53 minutes and 30 seconds. Hey look! That number
matches this one. We did something right. Okay, now that we have all of our azimuths, the
next step is going to be to calculate the latitudes and departures between the
points. Latitude and departure is defined as the distance that is traveled in
each direction being northing and easting. Latitude is associated with northing.
Departure is associated with easting. Northing, is equal to
latitude. Easting is departure. And we use this to find the difference
between coordinates to then verify where the location of coordinates are.
The formula to calculate latitude is always going to be the distance
times the cosine of the azimuth. And to calculate departure, it's always
going to be distance times the sine of the azimuth. So we're gonna use these formulas
to calculate all of the latitudes and departures for all of our points.
I have set these equations all up based off of this formula.
For pink, 35.51. For green we get negative 11.98. For red, we get negative 25.89.
For blue we get negative 18.99. For orange we get 27.46.
For pink, we get 29.57. And for green we get negative
11.98. Now you might be asking, why is it that green is the same but pink isn't?
So this right here is the change in how far we're going in the X direction between points. When
referring to pink the first time, the change is coming from the reference point because that
was the first point we backsighted to. But looking at pink the second time we're coming
from orange. So the change is coming from orange. With green both times we were backsighting
pink. That's why the change is the same because it's from the same point. I'm gonna go and
erase these answers. I'm gonna erase the word sine here and replace it with cosine.
Write cosine on all of these. And this no longer is easting. This
is now going to be the northing. So now we're gonna calculate the latitudes,
which is the change in the Y direction between each of these points.
However, instead of using sine, we're gonna use cosine.
And when I do this, we get for pink a negative 5.99 -- for green, we get 51.42.
For red we get 18.68. For blue we get 0.62. For orange we get a negative 84.22. For pink
we have 51.02. And for green we have 51.42. Same situation here with pink and green. Pink
is gonna be different because it's referencing a different backsight. Green will be the same
because it's referencing the same backsight. Now we're gonna go ahead and add up the latitudes and
departures so that we can figure out our error. You're only going to be adding up the ones inside
of the traverse. Anything that's referring outside of the traverse or is repeated, we're not going
to include. So since the first point is referring to the reference point, that's not a part of the
traverse. That's just to set up our orientation. And this last green right here is not a part of
the traverse either because we already included it up here. So you're going to be adding up these
departures and you're gonna be adding up these latitudes. In the departures, I ended up with
0.17. And in the latitudes I ended up with 0.16. Usually your error between latitudes and
departures should be very similar, like within like a couple hundreds of a foot. If you have got
a lot of error in one and not a lot in the other, then you might have done something wrong but
usually, they come out pretty close to each other. To make this correction, the same formula as
before. Error divided by number of angles. So the first one, we have 0.17 over 5 and that is
equal to 0.034. In the second we have 0.16 over 5 is equal to 0.032. So because we're over, we're
gonna subtract this number from all the latitudes and departures. Now let's take a look at the
green. Because we're at a negative 11.98, we're then going to subtract 0.034. And that will give
us a negative 12.014. All right. Let's do it for the rest of these. For red we will have a negative
25.924. For blue, we'll have a negative 19.024. For orange, it'll be 27.426 and for pink it will
be 29.536. Now over at the latitudes, green is 51.388. Red is negative 18.712. Blue is 0.588.
Orange is a negative 84.252. And pink is 50.988. And now when we add all these up we should have
no error in our differences between departures and latitudes. All right. Now you've got your
adjusted latitudes and departures. We're gonna use this information to now calculate the coordinates
of all of our points. To calculate coordinates, all it is going to be the reference northing plus
the latitude gives you the pink northing and the reference easting plus the departure gives you
the pink easting. Then what you're gonna end up doing is using the pink northing plus the new
latitude will give you the green northing and the pink easting plus the departure will give you
the green easting. And so on and so forth. You're just gonna keep using the last coordinate and
adding the change in latitude and departure to the northing and easting respectively to get
the new coordinate. So the easting plus the departure is 13517064.82. Taking the northing of
the reference point and adding the latitude which is a negative 5.99, I get 420333.61. Now I'm going
to take the easting of pink and add the departure. Which is a negative 12.014. And I get
the easting of green is at 13517052.81 and the northing, we add this latitude, so we
have 420385.00. Now we're going to use this easting plus this departure to get the easting of
red, we get 13517026.88. The northing 420366.29. Now the easting of blue, 13517006.86. The
northing of blue is now 420366.88. Now the easting of orange is going to be 13517035.29.
The northing is going to be 420282.63. The easting of pink is going to be 13517064.82.
Notice how this easting is the same as this easting. The northing is now going to be 420333.61
and the same thing here. The northing is the same up here and we're gonna calculate green and that's
going to be 13517052.84. We have a difference here of 3/100ths of a foot and we're gonna have
420385.03. Same thing here. 3/100ths of a foot. And that is how you calculate the coordinates of
your traverse. It's long, it's tedious, I know but you can do it. I just want to compare these
coordinates to my record coordinates that I took with a GPS observation just to kind of see how
close we are. Let me just bring these coordinates in and we will compare what we got with what is
recorded with GPS and you can see here these are the differences. I mean they're all relatively
close like within a couple tenths, I would say. Like this one is 1/10th. This right here is right
on, actually and then on the easting -- or on the northing side, we're about 15/100ths. Over
here we're at 2688. Here we're at 2692 so okay, also, barely a couple hundreds there. This is
one -- this is 66.29 and 66.26. So 3/100ths of a foot. I mean we are coming in really close.
We are meeting the standard and that's what is important. We are meeting the standard. I hope
you guys enjoyed today's video. I know it was longer than usual but I hope you stuck around and
were able to finish up your traverse calculations. If you liked today's content and you want to
see more of it, be sure to give me a "like" on this video. Subscribe to my YouTube channel so
I can continue to provide surveying videos for you and with that, I'll see you next time.
[♫Music♫]
