# when given bearing, angle, and distance, how to find change in location in 3d

I am helping a drilling team find the surface location representing a point in the ground. I am given the following values:

surface location latitude and longitude Drilling depth (length of drill pipe in the ground) direction (azimuth) of the drill Inclination vertical deviation from straight down.

so, for example... if the entry point of a drill is at `Lat: 29.45753895`, and `Long: -096.63472555`

and I'm given `depth: 1000 ft`, at `azimuth: 1.45 deg`, in `direction 45.23 deg`

How do I figure out where on the surface does those numbers represent where the drill head is?

• what do you mean by direction here?. and the depth refers that the pipe will be 1000 ft underground? – Moh Feb 17 '18 at 17:32
• I believe direction is the cardinal direction horizontally. meaning 45.23 should be something close to a NW heading. – arcee123 Feb 17 '18 at 23:58
• I believe depth is length of drill. I assume the drill is heading in a consisting direction, but I think the azimuth and direction implies it is not necessarily straight down. hence I can feel a geometry solution here somewhere, but I am uneducated in doing the proper formula development. – arcee123 Feb 18 '18 at 0:00

To give an appropriate answer your question, we should know some important other information.

However, A simple answer for (Change in location) can be given by defining your starting point from the coordinates you have (lat, long), and from the direction and distance (pipe length) to define the path by calculating the middle and final points coordinates, vertical direction to define the drilling profile on the start point, depth (not known yet) will be needed just to define how much will be the depth of the drilling (distance from ground surface to the pipe underground).

A more complicated answer to such a project can be explained by two stages (design criteria and the field criteria).

Design Criteria:

• The start point will be the point of coordinate (lat, long) that you already have which is given. Here, is very important to know in which coordinate system this point is projected.
• From the direction (Azimuth is given) and the pipeline length (is not given), you can define your path.
• You need also the excavation depth (how deep the pipeline underground? is it fixed for all the path or it changes according to other parameters) and you will need other factors for the excavation layout.
• AutoCAD Civil 3D is a good software to design your pipeline path in 3D also it's easy to use (you can find some resources) when you have all of this information.
• Also, you will define the stations on the path (points) by calculating the coordinates of them (easily) using your starting point coordinate and direction (e.g each 100ft, 50ft) to be easier as dividing the drilling work.

PS: the work area is very important to be studied to define how the path will change accordingly and what are the obstacles that maybe you will face during work.

In Field:

to help your drilling team: you will need a sketch with all information for the path, also the methodology of the drilling.

So, in this case, the most important part is the drilling depth (back to design stage).

• If the depth of the pipeline is deep, here you must use surveying techniques (Plumbing and Gyroscope) to transfer your network to the bottom of the path (surface underground) so you can guide your team by defining points to be followed during the drilling stage. Otherwise, you will have errors and your drilling will follow the defined path (such a big problem)
• after transferring your network to the bottom, some adjustment calculations are needed to define the final points, directions of the path.
• Before drilling, you will project all of points, directions, and path. So your team can start work under supervision.

Of course, this is just a summary to give an idea how this work should be done.