Crazy geospatial radius calculation

geocalc_test.php

<?php

$db = new PDO('mysql:host=localhost;port=3306;dbname=homestead', 'homestead', 'secret');
$db->setAttribute(PDO::ATTR_DEFAULT_FETCH_MODE, PDO::FETCH_OBJ);

#4980,Long Prairie,MN,verified,45.971955,-94.866789

$lat = 45.971955;
$lon = -94.866789;

$rad = 30; #KM

$R = 6371;  // earth's mean radius, km


$maxLat = $lat + rad2deg($rad/$R);
$minLat = $lat - rad2deg($rad/$R);
// compensate for degrees longitude getting smaller with increasing latitude
$maxLon = $lon + rad2deg($rad/$R/cos(deg2rad($lat)));
$minLon = $lon - rad2deg($rad/$R/cos(deg2rad($lat)));

  $sql = "
    Select id, name, state, latitude, longitude,
           acos(sin(:lat)*sin(radians(latitude)) + cos(:lat)*cos(radians(latitude))*cos(radians(longitude)-:lon)) * :R As D
    From (
      Select id, name, state, latitude, longitude
      From cities
      Where latitude Between :minLat And :maxLat
        And longitude Between :minLon And :maxLon
      ) As FirstCut
    Where acos(sin(:lat)*sin(radians(latitude)) + cos(:lat)*cos(radians(latitude))*cos(radians(longitude)-:lon)) * :R < :rad
    Order by D";

  $params = array(
    'lat'    => deg2rad($lat),
    'lon'    => deg2rad($lon),
    'minLat' => $minLat,
    'minLon' => $minLon,
    'maxLat' => $maxLat,
    'maxLon' => $maxLon,
    'rad'    => $rad,
    'R'      => $R,
  );
  $points = $db->prepare($sql);
  $points->execute($params);


foreach ($points as $point) {
        echo "$point->id|$point->name|$point->state\n\n";

}

/*
Response with a radius of 30km:

vagrant@homestead:~$ php test.php
4980|Long Prairie|MN

4901|Eagle Bend|MN

5054|Sauk Centre|MN

*/