Elevation / pipeline Elevation calculation

We do inspections using a robotic camera in the pipeline. It’s tractor type camera. (Ref. photo)

While driving the camera through the pipeline it gives us the camera tilt degree output.

The camera System gives us output as below,

As below.

Awaiting for your answers. If you need any further info. Let me know.

• You can convert "tilt" to gradient, and then use y=mx+c to calculate the X/Y coordinates of your next point based on that slope Apr 18, 2018 at 16:09
• Thanks for the reply @JonathanRSwift . Can you show me one example, how it’s calculated? Apr 19, 2018 at 5:48
• Just a visual ? No EMI or UT ? Seems inefficient. Apr 19, 2018 at 17:22
• @user268699 is m the total distance travelled, or the distance travelled since the last measurement? Apr 19, 2018 at 18:08
• @Andrew distance traveled from the beginning of the pipeline. Apr 19, 2018 at 18:34

Assuming you know the original starting position, you can use trigonometry to work out the profile of the pipeline.

If you take coordinates $(x_n,y_n)$, and with a measured 'inside pipe travel distance' of $d_n$ meters inside the pipe, down a slope of $\theta_n°$, then that coordinate can be caluclated:

$$x_n=x_{n-1}+\left(d_n-d_{n-1}\right)\sin\left(\theta_n\right)$$ $$y_n=y_{n-1}-\left(d_n-d_{n-1}\right)\cos\left(\theta_n\right)$$

It is important to note, that while the negative incline of the pipe is increasing, this approach will slightly over-estimate the altitude of each point, and slightly under-estimate as it is levelling out. Over a long run of pipe, this should even out, and the total change in altitude from end to end will be fairly accurate.

Here is an image of the graph that I was able to generate using the data that you supplied above:

• Thank you for your answer. Really appreciate it. I’ll discuss this one with our team. Apr 19, 2018 at 18:36
• Jonathan, could you please help me to solve one example equations for one degree value? I’m not familiar with this math. Highly appreciate your help. Apr 21, 2018 at 20:42
• Jonathan could you please help me on this? I try to solve how you find the solution using that formula. Or can you send a soft copy of that graph to my email. ([email protected]) May 1, 2018 at 5:09
• You have a table of values for $d$ and $\theta$, which can be referred to sequentially as $d_1$, $d_2$ etc. $d_n$ is the term for any chosen value, and $d_{n-1}$ refers to the value of $d$ at the previous point. To calculate the X/Y coordinates of any point, simply use the formulas I have supplied above. N.B you need to know the X/Y coordinates of the first point. May 1, 2018 at 12:17