Kreissegment Verhalten von Sehnenlänge und Segmenthöhe

sehnenlänge.R

radius <- function(h, s){
  # Abbruchbedingung
  h <- ifelse(h > s/2, NaN, h)
  
  n <- ((4 * h^2) + s^2) / (8 * h)
  
  return( n )
}

library(ggplot2)

p <-ggplot(data.frame(x = c(0.0, 20)), aes(x))

plot(
p + stat_function(fun=radius, aes(color="10"), args=list(s=10), n = 100000)
  + stat_function(fun=radius, aes(color="20"), args=list(s=20), n = 100000)
  + stat_function(fun=radius, aes(color="30"), args=list(s=30), n = 10000)
  + stat_function(fun=radius, aes(color="40"), args=list(s=40), n = 10000)
  + scale_y_continuous(limits = c(0, 200))
  + ylab("Radius [mm]")
  + xlab("Height of Segment [mm]")
  + guides(color=guide_legend(title="Kreissehne [mm]"))
)

For what is it?
I want to build a device to measure the radius of a surface by using the circular segment formular. Two pins in the distance of s and a moveable center pin will be put on the surface. while the to pins in distance s are fixed, the center will move the distance h. With this formular you can calculate the radius.

It is nice to see, that for large radii, a very small measuring error produce a much different radius. but for a radius in the range of 2*s, it is quite easy to measure it (even if the accuracy is small)