Solved - Vertical parabolic curve - PVI, PVC and PVT and Elevations at different stations along Curve

Hi,  Here is the example which shows you how to solve for the vertical transition curve elevation.
Problem: A 3% grade intersects a -2% grade at station 4+350m with an elevation of 190.5m. Given that a 250m symmetrical parabolic curve highway is utilized, determine: elevation in meters at station 4+240
elevation in meters at station 4+260
elevation in meters at station 4+280
elevation in meters at station 4+300
Solution: Please refer the images below.


Curves - Degree (Chord and Arc Definition) - L,T,E,M,Lc,PT,, PC

If you are given with the degree, angle of intersection and Station of PI, how to find the L(length of curve), T(Tangent length), E(External ordinate), M, Lc(Length of chord), PT(Point of tangency) station, PC(Point of Curvature) station. The formulae and example is given in the following images.

Example has three parts, each part is a different question in itself.


How to Draw Contours using Judgement and Free Hand Method

There are other method of contouring like the arithmetic estimation, but for less accurate but quick draw, one can use their fine judgement and free hand technique to draw the contours for the given elevation points.  In the following example, the control points are already drawn. The square patterned control points' elevations are shown, one has to use the fine judgement to draw the contour lines. See how it is done, all you have to do is to judge the contour line's placement from the given elevations. 
Look at the nearest control point elevations. If the nearby elevation is higher, then the terrain is rising towards it, if it is lower, terrain must have a downward gradient.  Definitely the higher contour must lie towards the rising terrain and a contour with the lower elevation must lie towards the downward gradient. 
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Elevation of Intermediate Stations in Leveling - Height of Instrument Method


In a profile leveling process, in between two turning points(TPs), there are many intermediate stations that we take readings to find out the elevations of the those stations. These readings can be taken using a level, a theodolite or a total stations. Problem is that how to find out the elevation of those stations. Using a bench mark and its given elevation it can be learned from the following example. The method used is generally known as the Height of the Instrument method. If you have any doubt please let me know in the comment box.

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Closed Traverse - How to find out the Bearings of Traverse Lines

Let us learn to find out the bearings of the lines of a closed traverse with the help of the following example.  such problems occur in the Compass traverse or Theodolite Traversing.

you are given a closed traverse with four sides, three of its interior angles A, B and D are given. Find out the bearings of the four lines if the bearing of the line AB is given.

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Error and Correction in a Closed Traverse by Compass Surveying.


A closed traverse constructed after doing a compass survey can be checked for error by a simple formula.
As per the geometry, in a closed traverse with 'n' number of sides the total sum of the interior angles = (2n-4) * 90 degrees.

Example: Consider a pentagon with five sides and five number of interior angles A, B, C, D and E.

Sum of the interior angles = (2*n - 4) *90
= (2*5 - 4) *90
= 540 degrees.

If it was a hexagon, then n= 6
and sum of interior angles would be
= (2*6 - 4)* 90 =720 degrees

Apply this check to the closed traverse at hand and see the error.

Error =
Sum of the given interior angles - (2n- 4)*90

Correction = - Error.

Generally the error is equally divided among the interior angles of the traverse. So correction for each angle  = - (Error) / n

If the exterior angles are given, then the total sum of the exterior angles = (2n+4)*90
remember an exterior angle = 360- interior angle.
For example exterior angle at A = 360- Int. angle A.

Calculate the Error, E …

Happy New Year to Surveyors- Why no new posts?

Hi, Its been a long time since I came here to write a blog post. I feel that if I stay away a little longer I will get kind of disconnected. Its a new year, and like everyone else, I have new hopes and aspirations. 
To keep the connection with my lovely readers is one of my resolution, and it feels really awesome while I write this post. This blog has reached more than 1,50,000 views and is among the top viewed blogs that I write here. As you can see in the side links, there are around fifteen other blogs that I write, and only few of them are competitors of this blog.
One reason that I am not able to write here new posts, is that I am no more a Surveying teacher, and I am out of ideas and topics to write anything about. However I want to write here new posts, and as soon as I get the new ideas I will post here. If you can suggest me anything, please leave a comment, and I will see what I can do. 
Thanks! and once again a very happy new year to you.