Lion’s share of offshore surveys is carried out in Universal Transverse Mercator projection (UTM). However often clients require hydrographers to carry out their work in Transverse Mercator (TM). And that would be no problem at all if only they didn’t ask for TM with scale factor of 0.9996 and with 500.000m False Easting which is in fact an ordinary UTM! And that’s what really grinds my gears.
In this blog post I will not dig into details of what Mercator projection is, this information can be found on Wikipedia. What I will explain is the main difference between these two projections. Look at two pictures below: obviously, in TM, the projection plane (always a cylinder in Mercators) is tangent to Earth’s surface and its circumference touches the globe along the central meridian of projection. As opposed to TM, in UTM the cylinder is secant to the surface; it intersects the globe creating two standard meridians 180km away of the central meridian.
Transverse Mercator
Universal Transverse Mercator
Why couldn’t we use just a Transverse Mercator for all offshore projects? The answer is simple: Mercator projection is a conformal one; it means it preserves angles (shapes) but distorts lengths (size). Transverse Mercator has no distortion along the central meridian (scale factor is 1), but distortion rises up to 1.0008 as we proceed further from the center line towards the end of a 6-degree zone. To more or less evenly distribute distortion across the zone, scale factor 0.9996 for the central meridian is used. In this case, scale factor throughout the zone doesn’t exceed 1.0003.
Distortion of Transverse Mercator (upper) and Universal Transverse Mercator
But why is it 0.9996? Why not 0.9997 or 0.9995? Imagination is not enough to understand this; we need to dig deeper into calculus for that. It’s not my intention to transform this blog into a University course, therefore I’ll just tell you why:) As from calculations, to reduce distortion twice near the end of the zone, we need to use scale factor at the central meridian computed as:
SFo = 2/(1+SF_max),
where SFo is a sought-for value, and SF_max is maximal distortion (1.0008). Check out yourself!
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Two other distinguishing features of TM and UTM are grid axis(x,y and E,N) and grid origins (false Easting (and false Northing in Southern Hemisphere). False Easting and Northing are used to ensure the coordinates always stay positive. So, when your client asks you to set up projection as TM but with UTM settings (scale factor and grid origin), just kick him for a trivial ignorance of survey basics! Because he asks for UTM!!!
Excuse might be given only in case the survey area is located between UTM zones and distortions are likely to be high. In that case, setting up a TM with a central meridian passing through the center of the area (you cannot change UTM’ central meridians as zones are fixed) and UTM’ scale factor and grid origin would be good solution. But not great…and you know why? Because scale factor must anyway be set as 1.0000 instead of 0.9996 to have no distortion in the area. And original TM is better than UTM in this example…And what do you think? Have you experienced this in your survey life?
I hope you find this information useful! Waiting for your comments and suggestions!
Mr.Surveyor
Pictures are taken from www.e-education.psu.edu