Distances between two points calculated with geosphere::distm are different than distances plotted with leaflet

Question

I have two data frames of lat long points. DatasetA is a set of locations. Dataset B is a set of locations 50 miles away (longitudinally) from Dataset A.

I can plot the two data sets with no incident, as the code below shows. However, when I calculate the distance between the points of DatasetA and DatasetB (closest points), I get different distances:

> points$Distance2radius
[1] 44.13807 41.92467 39.39219 36.55992 33.44940

I am having trouble understanding why these would be different. I would assume that using the Haversine formula in distm would account for any spherical impacts on the distance calculation.

Any help would be appreciated.

library(leaflet)
library(geosphere)

### Make a dataframe of some test points ###

## Center of the US
dc.lat <- c(38.0000)
dc.long <- c(-97.0000)

## Make the data frame
lats <- c(dc.lat - 10, dc.lat - 5, dc.lat, 5 + dc.lat, 10 + dc.lat)
points <- data.frame(cbind(dc.long, lats))
names(points) <- c("long" , "lat")
coordinates(points) <- ~ long + lat

## The radius we are interested in, in miles
radius <- 50

## Add points that are the radius miles away from the center

points.at.radius <- data.frame(points)
#points$lat <- points$lat + radius/110.54
points.at.radius$long <- points$long + radius / 69.2
coordinates(points.at.radius) <- ~ long + lat

## Get distances with distm
distances <- distm (points, points.at.radius,
                    fun = distHaversine) / 1609

# Find the closest pint and add this distance to the data set
points$Distance2radius <-
  apply(distances , 1, min)

# Plot these points and the points that are 50 miles away
m <- leaflet() %>%
  addTiles() %>%  # Add default OpenStreetMap map tiles
  addCircleMarkers(data = points,
                   points$long,
                   points$lat,
                   color = "red") %>%
  addPolygons(
    data = gBuffer(
      points,
      width =  radius / 69.2,
      joinStyle = "ROUND",
      byid = FALSE
    ),
    color = "gray70",
    group = "IWER area"
  ) %>%
  addMarkers(data = points.at.radius,
             points.at.radius$long,
             points.at.radius$lat) %>%  addPopups(
               points$long,
               points$lat,
               47.597131,
               points$Distance2radius,
               options = popupOptions(closeButton = FALSE)
             ) 

  m  # Print the map

Answer 1

Quite straightforward with geobuffer .

Code

# Load libraries.
library(leaflet)
library(geosphere)
library(geobuffer)

# Set coordinates for center points.
coordinates <- data.frame(lon = -97,
                          lat = seq(28, 48, 5))

# Create SpatialPoints in the WGS84 spatial reference system,
# a.k.a. unprojected lon/lat.
points <- SpatialPoints(coords = coordinates,
                        proj4string = CRS("+init=epsg:4326"))

# Set radius as 50 miles.
radius <- 50 * 1609

# Created SpatialPolygons in the shape of an octagon. 
buffered_points <- geobuffer::geobuffer_pts(xy = points,
                                            dist_m = radius,
                                            step_dg = 360 / 8)

Test

> distm(points@coords[1,], 
      coordinates(buffered_points@polygons[[1]]@Polygons[[1]])) / 1609

     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
[1,]   50   50   50   50   50   50   50   50   50

You will find that this is the case for not only SpatialPolygon #1, but also for the other three objects.

Result

leaflet() %>%
    addTiles() %>%
    addCircleMarkers(data = points,
                     color = "red") %>%
    addPolygons(
        data = buffered_points,
        color = "gray70"
    )