diff --git a/src/test/java/org/elasticsearch/test/unit/index/search/geo/GeoDistanceTests.java b/src/test/java/org/elasticsearch/test/unit/index/search/geo/GeoDistanceTests.java
index 3783357c3fe..649769e26d5 100644
--- a/src/test/java/org/elasticsearch/test/unit/index/search/geo/GeoDistanceTests.java
+++ b/src/test/java/org/elasticsearch/test/unit/index/search/geo/GeoDistanceTests.java
@@ -21,10 +21,13 @@ package org.elasticsearch.test.unit.index.search.geo;
 
 import org.elasticsearch.common.unit.DistanceUnit;
 import org.elasticsearch.index.search.geo.GeoDistance;
+import org.elasticsearch.index.search.geo.Point;
 import org.testng.annotations.Test;
 
 import static org.hamcrest.MatcherAssert.assertThat;
 import static org.hamcrest.Matchers.equalTo;
+import static org.hamcrest.Matchers.greaterThan;
+import static org.hamcrest.Matchers.lessThan;
 
 /**
  */
@@ -35,18 +38,33 @@ public class GeoDistanceTests {
     public void testDistanceCheck() {
         // Note, is within is an approximation, so, even though 0.52 is outside 50mi, we still get "true"
         GeoDistance.DistanceBoundingCheck check = GeoDistance.distanceBoundingCheck(0, 0, 50, DistanceUnit.MILES);
-        //System.out.println("Dist: " + GeoDistance.ARC.calculate(0, 0, 0.5, 0.5, DistanceUnit.MILES));
         assertThat(check.isWithin(0.5, 0.5), equalTo(true));
-        //System.out.println("Dist: " + GeoDistance.ARC.calculate(0, 0, 0.52, 0.52, DistanceUnit.MILES));
         assertThat(check.isWithin(0.52, 0.52), equalTo(true));
-        //System.out.println("Dist: " + GeoDistance.ARC.calculate(0, 0, 1, 1, DistanceUnit.MILES));
         assertThat(check.isWithin(1, 1), equalTo(false));
 
-
         check = GeoDistance.distanceBoundingCheck(0, 179, 200, DistanceUnit.MILES);
-        //System.out.println("Dist: " + GeoDistance.ARC.calculate(0, 179, 0, -179, DistanceUnit.MILES));
         assertThat(check.isWithin(0, -179), equalTo(true));
-        //System.out.println("Dist: " + GeoDistance.ARC.calculate(0, 179, 0, -178, DistanceUnit.MILES));
         assertThat(check.isWithin(0, -178), equalTo(false));
     }
+
+    @Test
+    public void testArcDistanceVsPlaneInEllipsis() {
+        Point centre = new Point(48.8534100, 2.3488000);
+        Point northernPoint = new Point(48.8801108681, 2.35152032666);
+        Point westernPoint = new Point(48.85265, 2.308896);
+
+        // With GeoDistance.ARC both the northern and western points are within the 4km range
+        assertThat(GeoDistance.ARC.calculate(centre.lat, centre.lon, northernPoint.lat,
+                northernPoint.lon, DistanceUnit.KILOMETERS), lessThan(4D));
+        assertThat(GeoDistance.ARC.calculate(centre.lat, centre.lon, westernPoint.lat,
+                westernPoint.lon, DistanceUnit.KILOMETERS), lessThan(4D));
+
+        // With GeoDistance.PLANE, only the northern point is within the 4km range,
+        // the western point is outside of the range due to the simple math it employs,
+        // meaning results will appear elliptical
+        assertThat(GeoDistance.PLANE.calculate(centre.lat, centre.lon, northernPoint.lat,
+                northernPoint.lon, DistanceUnit.KILOMETERS), lessThan(4D));
+        assertThat(GeoDistance.PLANE.calculate(centre.lat, centre.lon, westernPoint.lat,
+                westernPoint.lon, DistanceUnit.KILOMETERS), greaterThan(4D));
+    }
 }