I tried a computation that I think may be correct. It gives 319 metres of northing separation between rhumb and creat-circle paths. In case it's of any intere

I tried a computation that I think may be correct. It gives 319 metres of northing separation between rhumb and creat-circle paths. In case it's of any interest, the R code is below. # Northing distance between rhumb and great-circle paths. library(oce) lat <- c(57+18.280/60, 56+54.152/60) lon <- -c(3+55.948/60, 4+56.664/60) # Great-circle path, first in longitude-latitude space, and then # (for Mercator projection) in easting-northing space. gc <- oce::geodGc(lon, lat, 0.01) # same results for 3rd arg any value < 0.01 gcXY <- lonlat2map(gc$longitude, gc$latitude, projection="+proj=merc") # Create function, f(easting), that computes northing value on # a rhumb line. We need this to make the two lines share easting # values. p <- oce::lonlat2map(lon, lat, "+proj=merc") m <- lm(y ~ x, data=p) X <- seq(p$x[1], p$x[2], length.out=length(gc$longitude)) Y <- predict(m, data.frame(x=X)) f <- approxfun(X, Y) # interpolating function # Compute the northing error. northingError <- f(gcXY$x) - gcXY$y maxNorthingError <- round(max(abs(northingError)), 1) message("maxNorthingError=", maxNorthingError, " [m]") plot(gcXY$x, northingError, type="l", xlab="Easting [m]", ylab="Northing error [m]") mtext(paste("max northing error ", maxNorthingError, " [m]"))