I have a math question. If something is off by 5 mm, how far off would it be at a distance of 1 mile?

Question

Let me clarify, if I am taking a measurement and I am off by 5 mm, and that discrepency is compounded as it travels over distance, how large of a discrepency is there when it reaches 1 mile?

What I am trying to figure out is when using a total station during land survey, if the station is set and measurements taken, but then the machine is bumped and the original point of reference is off by 5 mm, how large of an impact does it have at a distance of 1 mile? Does that help?

Answer 1

Here's an example that might help...

let's say that you are trying to dig a ditch in a straight line to connect 2 pipes that 1 mile apart. If you dig a perfectly straight ditch that is going exactly in the right direction then you will have no discrepancy and everything will line up perfectly.

Now let's say that your equipment is only accurate to 5mm per 100 feet. Meaning that for each 100 feet of ditch that you dig you run the risk of veering off course by 5mm.

So if you take one mile which is 5,280 feet and divide it my 100 feet you get 52.8. Then you multiply 5mm by 52.8 and you get 264mm which is about 10 inches.

So you dig your 1 mile trench and you get to the other side and you realize that you are 10 inches off from where you want to be :(

Hope this helps.

Kevin.

Answer 2

I can't tell you unless you also say the value of the measurement you took. If you were measuring a football field and were only off by 5 mm, the error would still be small. But if you were measuring your pinky nail and were off by 5 mm, that would be a huge error discrepancy after being compounded over a mile.

Answer 3

We need to know the length you are measuring also. Say you measure out 1 meter ± 5mm. There are 1609.344 meters in one mile, so you would multiply your 1 meter by that. Then take your error value for each step and compound it.

error = (final value) * sqrt( (individual error)/(individual measurement)^2)

So in this case it would be:

1609.344*sqrt((0.005/1)^2) = 8.047 meters

That's with a 1 meter measurement at the begining, you need to change it to whatever you measured as a distance. With a 5 meter measurement it would be:

(1609.344/5)*sqrt(0.005/5)^2) = 0.322 meters

Notice the error is smaller the larger your original measurment, that's because it's not being compounded as much. Hope it helps.

Answer 4

off by 5 mm at what distance? it's a proportion, and you need 3 terms.

Answer 5

doing homework on the internet gives false results

Answer 6

Off by 5mm what?

Answer 7

sorry i didn't get it something is missing