Another scale factor discussion

The distances won't change, but the coordinates will change by the adjustment to the origin. Let's look at it algebraically.

Originally, the Northing was calculated as (SPC - 0)*1.0003, assuming that the scale factor is the reciprocal of the Combined Factor. Now it's calculated as (SPC - 0.1)*1.0003. The difference between the two is

Diff = (SPC - 0)*1.0003 - (SPC - 0.1)*1.0003

Diff = ((SPC - 0) - (SPC - 0.1))*1.0003

Diff = (SPC - 0 - SPC + 0.1)*1.0003

Diff = 0.1*1.0003.

When you translate the origin, all of the points are translated along with it. Moving the origin Northing by 0.1 foot changes all of the Northings by 0.1 foot. But in this case, changing from 0 also means that the new coordinates also change by the scale factor.

An important question is whether the new translation was applied to SPC numbers or to the previously scaled numbers.

Posted by: @mathteacher

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The distances won't change, but the coordinates will change by the adjustment to the origin.

I may have misunderstood MightyMoe but I believe he was saying the point about which the scale factor was applied had changed. As opposed to the point of origin for the horizontal coords being changed. The horizontal origin is still 0,0 and no translation has taken effect. However the point about which the scale factor was being applied had indeed changed. At .1,.05 the difference is negligible. Should they have scaled around 100,000, 200,000 the results would be dramatically different even though no translation of the horizontal origin has occurred.

"However, through all the upgrades the scale point for the local scale modification has shifted slightly, it says N0.1', E0.05' for some reason."

It is the origin that changed.

@mathteacher No it is not. The point about which scaling occurs has changed.

Or maybe a better way to state it; The first .1' in northing is not scaled and the first .05' in easting is not scaled.

They're the same thing. If you scale about 1000, 1000 and then about 1001, 1001, all coordinates will shift by 1 foot in each direction. It's a simple translation, no computer required.

I suspect that at some point, probably very early in the genesis of the project, the scaling point was fixed at a coordinate that corresponded to a certain central measured point. Subsequent adjustments changed the coordinate value of that measured point, but the scaling point remained fixed. 

Posted by: @mathteacher

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If you scale about 1000, 1000 and then about 1001, 1001, all coordinates will shift by 1 foot in each direction.

Hmmmm. My experimental data says that is not true. This is a scaling, not a translation.

@mathteacher 

mathteacher, the origin point for the SP system isn't anywhere near 0,0, it's actually N=100,000m, E=400,000m, that would be at the origin latitude and longitude, 0,0 is far southwest of the origin point. The program wants to scale from a point, so you input 0,0 for the scale point and whatever the scale up from SP that you want using the scale factor. That's using Trimble and a local site scale function.

If you use AutoCad you need to apply the inverse number because AutoCad will divide the distance instead of multiplying it to get the surface coordinate. 

Each program probably treats it differently, AutoCad and Trimble are the two I use. 

My point being is that even if you change the scale up point from the original one, the coordinates will not change much. You can do the math from any point you wish. If you scale up from 100,000, 100,000 and change it to 100,100, 100,100, it will have the same effect to the final coordinate as changing 0, 0 to 100, 100. A scale factor of 1.0003, or the reverse of .9997 will change the final number by .03', .03'. and if N0, E0 changes to N.1, E0 the change in the final number for the northing is 0.00003'.

This works from any base scale point, many people will set on a point and to get ground coordinates let the DC calc a Scale factor from that point and apply it. This scales the distances from that point to ground and recalculates the coordinates. So you need to know the SF used and the scale point used to properly "get on" that system. Without those two numbers it's a more difficult math problem. Not insurmountable, but you have to understand what is going on. If coordinates were scaled from 0,0 then it's easy. Locate points with a given surface coordinate, find the SP number and divide. If all the points come up with an answer that matches to the 8th or more place, that's the scale factor. The more difference you have at each point gives you the error you're working with. At 6 places you're dealing with 1' in 1million feet, at 7 places it's .1' in 1mil. and so on. 

@norman-oklahoma 

The given information is that a scaling point of 0,0 has changed to 0.1, 0.05. The question is, did the other project coordinates change as well. 

The only way to know is to recalculate them and compare.

As an aside, the scale factor and the point scaled around are completely independent of each other. Choosing 0,0 makes the conversion arithmetic easier than choosing a point central to the project without affecting measurements.

However, the choice will affect the values of the coordinates.

@mightymoe 

The scale factor has nothing to do with the change in coordinate values created by changing the point you're scaling around.

If what you're saying is true, points scaled from somewhere other than the state plane origin would change only by the scale factor.

Access and TBC both will shift your scale origin under certain circumstances. The numbers you're dealing with are negligible but I hate being 'technically' wrong. It makes me feel a bit lazy. 

@mathteacher 

Forget about state plane, origin points and all that stuff. 

Think of a gird of northing and eastings or YX, a point has a N1,000,000, E1,000,000. You want new coordinates scaled up from 0,0 by a scale factor of 1.0003. 

To do so properly the point are inversed, the distances are multiplied by 1.0003 and new coordinates are calculated, which in my head will be N1,000,300.00, E1,000,300.00. Now change the scale up from point to N100, E100. Do the same process, inverse from the 1m, 1m point to the new scale up point, apply the scale factor to the distance, use the bearing and calculate a new coordinate for a surface coordinate, which in my head will now be N1,000,299.97, E1,000,299.97. I've done no calculations, no inversing, nothing, but I bet I'm correct. 

@mightymoe 

Calculate the distances from 0,0 to 1,000,003,1,000,003 and from 100,100 to 1,000,299.97, 1000,299.97.

Are they the same?

@mightymoe 

See, the problem with your second calculation is that the new Northing should be (1,000,000 - 100)*1.0003 = 1,000,199.97. That's a scaled 100 foot change in the Northing.

The distance thing above is a red herring. Of course those distances are going to be different. One is to 0,0 and the the other is to 100,100.

@mathteacher 

I'm gonna have to stand firm on my answers here MT. The 100' change of the scale point only introduces .03' of change in the surface coordinate, when you scale from the two different locations and use the same SF. Try it, work through the numbers inverse each one apply the scale factor to the resulting distance, use the inversed bearing and recalculate the new coordinate.  

Posted by: @thebionicman

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Access and TBC both will shift your scale origin under certain circumstances. The numbers you're dealing with are negligible but I hate being 'technically' wrong. It makes me feel a bit lazy. 

I'm with you, but I've learned when to leave well enough alone with Trimble. We got burned recently; Trimble was automatically exporting a US foot job to our new DC as international foot. The PC emailed some located evidence, and I calculated a couple of coordinates for him to set. Trouble is it was all 5' off. So an extra on our dime trip to fix it all. It took a while to figure out what the heck was happening. When you exported to the new TC5 for some reason it would send out IF instead of US feet. As long as you brought the data back into TBC all was well, but if you used field coordinates (which we often do) there was a 5' shift. Always be on your toes. 

@mightymoe 

Do what you think best. I've shown you that you're wrong and explained why.

Fundamentally, you're ignoring the change induced by changing the scaling point, and that change is what causes the change in all other coordinates.

When you scale around 0,0 only the scale factor enters the coordinate calculation. When you scale around a non-zero x,y point, those x,y coordinates enter the calculation.

Best of luck if a significant one comes up.

@norman-oklahoma 

I'd examine that experiment carefully. Intuitively, if you scale from a point that is one foot closer to the point you're scaling, that newly scaled point has to have a foot change in its coordinates to compute that shorter distance.

@mightymoe 

"To do so properly the point are inversed, the distances are multiplied by 1.0003 and new coordinates are calculated, which in my head will be N1,000,300.00, E1,000,300.00. Now change the scale up from point to N100, E100. Do the same process, inverse from the 1m, 1m point to the new scale up point, apply the scale factor to the distance, use the bearing and calculate a new coordinate for a surface coordinate, which in my head will now be N1,000,299.97, E1,000,299.97. I've done no calculations, no inversing, nothing, but I bet I'm correct."

Look carefully at your calculated coordinates. You're still on the 0,0 projection, but you've applied the scale factor twice to the first hundred feet.