A few weeks ago there was a mention about being 1" off an angle and what does that mean over 1000'.
I drew a little picture and calculated that to tan(1/60)*1000 giving me 0.2909
Today I was looking at the that same picture thinking that didn't seem right.
I think my math was wrong.
It should have been tan(1/3600)*1000 giving me 0.004848
That sounds more like it.
Am I correct in the second re-thinking?
(this is all in feet)
Thanks for checking my work.
E.
Your 2nd answer is correct.
I use the rule of thumb that 1 minute=0.03' per 100 feet.
multiplying by 10 and dividing by 60 gives me 0.005,
so I am sure that your solution is correct.
> A few weeks ago there was a mention about being 1" off an angle and what does that mean over 1000'.
> I drew a little picture and calculated that to tan(1/60)*1000 giving me 0.2909
>
> Today I was looking at the that same picture thinking that didn't seem right.
> I think my math was wrong.
>
> It should have been tan(1/3600)*1000 giving me 0.004848
>
> That sounds more like it.
> Am I correct in the second re-thinking?
>
> (this is all in feet)
>
> Thanks for checking my work.
> E.
I typically use the sin function as an approximation, my calculation would be (nearly identical)...
(sin (1/3600))(1000ft) = 0.004848 ft
(tan (1/3600))(1000ft) = 0.004848 ft
Thanks fellers.
I was pretty much sure my original math was wrong for 1".
It would be correct for a full minute of error if I'm correct.
E.
20" = 0.01/100
well, 20" = 0.0096'... per 100' but close enough.
1" = 0.0005' per 100'
multiply by 10 and
1" = 0.005' per 1000'.
Now use the calculator to get closer (that 0.0048... number)
To give non surveyors a sense of precision I will say:
One second of angle equals one foot in 40 MILES.
But even good for some surveyors.
Why use plane trigonometry? Are you solving a right triangle?
Use some basic geometry. Given a distance (R) and angle (theta) solve for the arc length (S) using
S = R times theta (in radians).
One second in arc is 1/3600 of a degree. Convert decimal degrees to radians by multiplying by ( pi / 180 ).
It is just an expedient shortcut that gives the approximate value.
> I use the rule of thumb that 1 minute=0.03' per 100 feet.
> multiplying by 10 and dividing by 60 gives me 0.005,
> so I am sure that your solution is correct.
I have been using 0.029 per minute per 100 feet for so long I almost forgot when I learned it.
I can't tell how many times in the last 20 years I have used it in the field when checking rod locations in subdivisions and had younger crew members look at me like I was using magic to get the answers.B-)
I guess I was misled by the implied precision of the answers. BTW, if you remember the factor representing one second of arc in radians you can just multiply the factor by the magnitude of error. The formula in the previous post can also be rearranged to solve for the angle or length of line.