on the ellipsoid is the same when projected onto a plane. 3-2  Proscribed Projections a.  STANAG 2211 states that the Transverse Mercator Projection is the preferred projection for all military mapping.  It goes on to state; however, that the preferred projection is not necessarily the one used on all military maps. b.  The following is a list of projections that are proscribed for US military topographic maps and charts that display a military grid on a standard scale (see paragraph 3-4c).        1.  Topographic maps at scales of 1: 500,000 or larger which lie between 80° South latitude and 84° North latitude are based on the Transverse Mercator Projection.     2.  Topographic maps at scales of 1: 1,000,000 which lie between 80° South latitude and 84° North latitude are based on the Lambert Conformal Conic Projection.     3.  Maps at scales of 1: 1,000,000 or larger covering the Polar Regions (south of 80° S latitude and north of 84° N latitude) are based on the Polar Stereographic Projection.     4.  Maps at scales smaller than 1: 1,000,000 are based on the projection best suited for the intended use of the map. c.  Military maps of non-US areas produced by other nations may not always conform to the above standards.  Also, US made maps of foreign areas may be based on other projections due to treaty agreements. 3-3  Scale Factor a.  For most military applications, map distance and ground distance are considered the same; however, for some geodetic and artillery operations, especially when long distances or high accuracies are involved, it is necessary to correct between map and ground distances. b.  A scale factor is necessary to compensate for distortions created when projecting an ellipsoidal surface onto a cylinder, cone, or plane (depending on the projection type).  The scale factor of a projection is the ratio of arc length along a differentially small line in the plane of the projection to the arc length on the ellipsoid.  This number depends on both the location of the point and on the direction of the line along which arc length is being measured.  However, for conformal projections, the scale factor is independent of the direction of the line and depends only on the location of the point.  The scale factor is labeled "k". c.  The scale factor is considered exact (unity) when it has a value of one.  This is at the points of tangency or secancy between the ellipsoid and the projected surface.  In a projection where the projected surface is tangent to an ellipsoid, the scale factor increases away from the point of tangency.  In a  projection where the projected surface is secant to an ellipsoid, the scale factor decreases toward the central meridian or origin and increases away from the points of secancy. d.  True ground distance can be converted to a map distance by multiplying the ground distance by the scale factor. 3-4  Map Scale a.  A map scale is a representative ratio of map distances to ground distances.  These ratios vary from map to map.  The scale of a map is customarily chosen to correspond to the ratio at a given point or along a given line (if constant along that line) multiplied by a suitable scale factor (usually close to unity).  It is usually expressed as a common fraction having one as a numerator and the integer closest to the actual ratio as a denominator. b.  Maps used by the military vary from small-scale planimetric maps showing all of the continents to large-scale topographic maps suitable for tactical operations of small units and fire control.  Military maps are classified according to their scale:     1.  Small-scale:    1: 600,000 and smaller     2.  Medium Scale:    larger than 1: 600,000;                            smaller than  1: 75,000     3.  Large Scale:    1: 75,000 and larger     Map scales can sometimes be confusing in the sense that the scale is smaller as the number increases.  This confusion can be cleared by viewing the map scale as a DRAFT 3-2