diff --git a/src/modules/sbstudio/plugin/model/safety_check.py b/src/modules/sbstudio/plugin/model/safety_check.py
index 59e93da..7675fc1 100644
--- a/src/modules/sbstudio/plugin/model/safety_check.py
+++ b/src/modules/sbstudio/plugin/model/safety_check.py
@@ -314,10 +314,13 @@ def should_show_proximity_warning(self) -> bool:
         """Returns whether the proximity warning should be drawn in the 3D view
         _right now_, given the current values of the properties.
         """
+        # self.min_distance has to be extended a bit (by about 1cm) because of
+        # numerical inaccuracies that yield false warnings during takeoff when
+        # the grid spacing is equal to the safety distance
         return (
             self.proximity_warning_enabled
             and self.min_distance_is_valid
-            and self.min_distance < self.proximity_warning_threshold
+            and self.min_distance + 1e-2 < self.proximity_warning_threshold
         )
 
     @property
diff --git a/src/modules/sbstudio/plugin/tasks/safety_check.py b/src/modules/sbstudio/plugin/tasks/safety_check.py
index a68a635..c0e695e 100644
--- a/src/modules/sbstudio/plugin/tasks/safety_check.py
+++ b/src/modules/sbstudio/plugin/tasks/safety_check.py
@@ -208,7 +208,7 @@ def run_safety_check(scene: Scene, depsgraph) -> None:
         [
             pos
             for name, vel in velocity_snapshot.items()
-            if (vel[0] != 0 or vel[1] != 0)
+            if hypot(vel[0], vel[1]) > 1e-2
             and (pos := snapshot.get(name, _ZERO))[2] < min_altitude
         ]
         if min_altitude is not None and min_altitude_found < min_altitude