Balancing a traverse using azimuths and computing lat/dep

> I'm sure this is something very simple that I'm just missing here, but it has completely stumped me so far.
Since this traverse does not close on itself it follows the the lats/deps will not sum to zero. They should sum to the difference between the given northings and eastings of the beginning and ending points.

Difference in Northings (FOX -DOG) 1181.64 - 22093.20 = -20911.56

Difference in Eastings (FOX -DOG) 2474.77 -2522.88 = -48.11

Also, either they have the sketch rotated or the eastings of the two points reversed, or something.

Note that when you run a traverse that closes on itself (ie/ begins and ends at the same point) the difference between the given northings and eastings of the beginning and ending points is zero.

I get:

A,16693.09,1270.76
B,10863.99,2917.02
C,4743.27,1352.38

Departures all get larger (more negative), latitudes larger smaller larger smaller in absolute values.

Closing line (after angle balance) is S 14-02-10 W 0.247'.

Precision 1:87,523

Fox
S 13-03-16 W 5543.37'
A
S 15-46-15 E 6057.11'
B
S 14-20-22 W 6317.54'
C
S 17-29-29 E 3734.30'
Dog

Thanks Norman, that helps a lot.

I wouldn't be surprised if something was wrong with the numbers or drawing, this book is riddled with mistakes both minor and major.

LOOK at the coordinates of FOX and DOG:

FOX  22,093.20 North
      2,522.88 East

DOG   1,181.64 North
      2,474.77 East

 1181.64 - 22093.20 = -20,911.56
 2474.77 -  2522.88 =     -48.11

Work from there...

Loyal

I get:

Awesome Dave, thanks. I think I like your formatting better, seems to be faster and save space as well.

I get:

Not sure if you'll see this, but what was your reason for converting the azimuth to bearings on the right page, personal preference?

I get:

Also, I noticed that all the rounding up of these numbers that the book suggests I do is throwing my calcs off a little. I see you did some rounding up yourself, what do you do to make sure it evens out at the end?

For example for side AB I have sin(164°13'44") x 6057.12 = 1,646.30, however the book calls for 1,646.26.

I get:

Well, I agree with you...

I recall when my brother and were studying for the LSIT, way back in the last millenium, we bought a book of test questions. At least 20% of the questions had wrong answers or the question was so poorly worded that the "correct answer" was moot.

Having helped write tests myself, all I can say is that writing tests is not at all a simple task and many people spend little or no time thinking about or checking their own questions and answers.

I know this doesn't help, but I do feel your pain...drink heavily and just skip questions that appear idiotic.

I get:

I have 1646.26 aftter adjustment.

I used bearings because it's easier for me...they would have to be converted back to azimuths to satisfy the problem requirements.

Cos bearing = latitude, sin bearing = departure. Inverse tan dep/lat = bearing (you have to figure out the quadrant).

I get:

I'm getting 6057.05 / 21,652.09 x 0.247 = 0.06909 for the adjustment of line AB, rounded up to .07. The length of line AB is 6057.05 + .07 = 6057.12. When I take the sin of 164°13'44" and multiply it by the adjusted length of 6057.12 my result come to 1,646.29527 rounded up to 1,646.30.

What am I doing wrong as my answer is not coming up to 1646.26'?

Thanks!

I get:

Multiply by the lat misclose and the dep misclose seperately to get the respective corrections.

Departure=
6057.05 / 21,652.09 x -0.06 = -0.02 for the adjust.

I get:

Ah, now it all makes sense. I thought I was supposed to use the error of closure for both latitude and departure adjustments. Thanks again.

EDIT: One last question, if you see this edit, you've got -1252.12 for the adjusted departure of FOX-A, however I get -0.01536 for the adjustment, which I would round up to -0.02 and therefore get -1252.13 for my adjustment. How did you make the determination not to round up for that number?

I get:

> Not sure if you'll see this, but what was your reason for converting the azimuth to bearings on the right page, personal preference?

He did that after the fact. Always use azimuths when adjusting, longhand, so that the sign of the lat or dep is preserved when taking the SINE or COSINE. When you do this, you only need to add up negative and positive numbers and not remember the sign.

Rounding

You should always carry extra digits through all computations and only round at the end.

Any rounding is introducing error. At the end, the proper rounding error is commensurate with the overall accuracy of the input data and thus insignificant, and the rounding is done to avoid expressing false precision.

Intermediate roundings are unnecessary additional sources of error that can accumulate to degrade your final answer.

Rounding

I was taught to carry 6 then round to 4 on coordinates. Otherwise, you get weird bearings not working by a second or two at times.