Fishing Line Experiment Calculator

To view this page properly please use a browser that supports MathML such as Firefox. The source code is freely available on GitHub so you can check the calculation code (it's written in LiveScript which compiles to JavaScript). Bug reports and suggestions can be added to the issues log.

Line properties at zero tension `T_0`
mThe length of line used to calculate the line density.
g
`mu m`explainhide
Regular positions along the line should be measured with a very high resolution micrometer and the average taken.
Apparatus setup
mThe distance between the two poles (the depth meters at each end).
mexplainhide
The line length from the anchor to pole A plus the unstretched line length from pole B to an indicator on the line.
kg/`m^3`explainhide
This table shows how the water density varies by temperature. Enter 999 for pure water at 15.6°C.
mmexplainhide
An experimenter using a ruler with very fine 1mm gradations may be able to estimate to within ± 0.1mm at best. However, this figure is somewhat subjective and may vary with difficulties such as parallax, lack of magnification, the clarity/focus of the water/line, whether the ruler is part obscured, etc.
Measurements at maximum tension `T_max`
N
mHow far the indicator moves when `T_max` is applied.
`mu m`explainhide
Regular positions along the line should be measured with a very high resolution micrometer and the average taken.
mm/minexplainhide
A slow vertical drift of the control line indicates a prevailing current and/or mis-calibration of the water density. Enter a -ve number for upward drift or +ve for downward.
Calculated conditions at line's midpoint
mm mm)
mm
mm mm mm.
Calculated line properties
kg/`m^3` kg/`m^3`
`mu m`
(should be between 0.3 and 0.5)equation
GPaequation
(must be less than 1)explainhide
Calculated as `(v d_T) / nu` where `v` is the drift velocity, `d_T` is the line diameter at `T_max` and `nu` is the kinematic viscosity of water at 17°C. A value < 1 indicates laminar flow.
explainhide
Calculated using the Oseen approximation by Lamb, and valid only for `Re < 1`. See Figure 8.
Uncertainty analysis
mmexplainhide
A threshold beyond which a set of measurements might contain outliers. For example, given a set of measurements of `DeltaY` normally distributed with average `DeltaY_(conc)`, if `sigma < sigma_o` then every measurement will be lying closer to `DeltaY_(conc)` than `DeltaY_(flat)`. If `sigma > sigma_o` then some measurements might be outlying closer to `DeltaY_(flat)`.
mm = % of `sigma_o`.explainhide
The expected SD caused by water/line level reading errors in a set of measurements of `DeltaY`. The % is a guide as to whether the reading precision is good enough for the given pole span. A value < 50% sufficiently allows for other random errors, whereas a value > 100% means other random errors will start producing outliers.

Theory

The purpose of this experiment is to determine the curvature of the earth solely by mechanical measurement. A neutrally buoyant fishing line should form a perfectly straight line when held under high tension in a long stretch of still water. If each end is at depth `Y` beneath the water surface `S` and we measure the depth `Y + DeltaY` at the line's mid-point, then: