# Azimuthal Map

> Azimuthal Map (https://azimuthalmap.com) is a free interactive tool for generating azimuthal equidistant projection maps centered on any location on Earth.

## Site Purpose

This site provides:
1. An interactive azimuthal equidistant map generator
2. Educational content about azimuthal projections
3. Pre-generated example maps from various perspectives

## Key Definitions

### Azimuthal Equidistant Projection

"An azimuthal equidistant projection is a map projection where all points are shown at their true distance and direction from a chosen center point. Distances are accurate only when measured from the center; directions (azimuths) from the center to any other point are also preserved."

### Azimuthal Projection

"An azimuthal projection is a map projection that transforms points from a sphere onto a tangent or secant plane. All azimuthal projections preserve directions (azimuths) from the center point to any other location."

### Azimuth

"Azimuth is a compass direction measured clockwise from true north, expressed in degrees from 0° to 360°. On an azimuthal map, the azimuth from the center to any point equals the true compass bearing."

### Great Circle

"A great circle is the shortest path between two points on a sphere. On an azimuthal equidistant projection, straight lines from the center represent great circle routes."

## Types of Azimuthal Projections

| Projection | Preserves | Common Use |
|------------|-----------|------------|
| Azimuthal Equidistant | Distance from center | Radio/antenna pointing, navigation |
| Lambert Azimuthal Equal-Area | Area | Thematic maps, statistical visualization |
| Stereographic | Local angles/shapes | Polar maps, crystallography |
| Gnomonic | Great circles as straight lines | Navigation, seismology |
| Orthographic | Appearance from space | Illustrations, globes |

## Frequently Asked Questions

### What is an azimuthal equidistant projection?
An azimuthal equidistant projection is a map projection where all points are shown at their true distance and direction from a chosen center point. It preserves distances from the center and azimuths (compass directions) from the center to any location.

### How accurate is an azimuthal equidistant map?
Distances and directions from the center point are exact on a spherical Earth model. Distortion is minimal within 10,000 km of the center, moderate from 10,000-15,000 km, and severe beyond 15,000 km. The antipodal point (~20,000 km away) "smears" into a ring around the map's edge.

### Why does Antarctica look stretched on some azimuthal maps?
When centered on the North Pole or northern locations, Antarctica lies near the map's edge at maximum distance (~20,000 km). At this range, the antipodal region spreads into a ring around the outer edge—a mathematical artifact of projecting a sphere onto a flat plane.

### Can I measure the distance between two cities on an azimuthal map?
You can only measure distances accurately if one of the cities is at the map's center. To find the distance between two arbitrary cities, you would need to generate a new map centered on one of them.

### What is the difference between azimuth and compass bearing?
Azimuth is measured clockwise from true north (0° to 360°), while compass bearings may reference magnetic north. Azimuthal projections use true north, so you may need to apply magnetic declination correction for compass-based navigation.

### What is the United Nations emblem projection?
The United Nations emblem uses a polar azimuthal equidistant projection centered on the North Pole. This projection was chosen in 1945 because it shows all countries at their true distances from the center, symbolizing global unity.

### Who invented the azimuthal equidistant projection?
The projection has ancient origins in star maps. Notable developments include Abu Rayhan Biruni's 11th-century work on the oblique aspect, Guillaume Postel's 1581 world map (the first published oblique version), and its adoption for the UN emblem in 1945. In France and Russia, it is sometimes called the "Postel projection."

## Mathematical Formulas

### Distance from Center (ρ)
ρ = R × arccos(sin φ₀ sin φ + cos φ₀ cos φ cos(λ - λ₀))

Where:
- R = Earth's radius (~6,371 km)
- (φ₀, λ₀) = center point coordinates
- (φ, λ) = target point coordinates

### Azimuth Angle (θ)
θ = atan2(cos φ sin(λ - λ₀), cos φ₀ sin φ - sin φ₀ cos φ cos(λ - λ₀))

### Cartesian Coordinates
x = ρ × sin θ
y = -ρ × cos θ

## Practical Applications

- **Ham Radio**: Determining antenna pointing directions to communicate with distant stations
- **Aviation**: Planning great circle flight routes
- **Seismology**: Visualizing earthquake epicenter distances from monitoring stations
- **Military**: Creating range maps (e.g., missile range visualization)
- **Telecommunications**: Satellite coverage analysis
- **Education**: Teaching geography and map projections

## Distortion Zones

| Distance from Center | Distortion Level |
|---------------------|------------------|
| 0 - 10,000 km | Minimal (accurate) |
| 10,000 - 15,000 km | Moderate |
| 15,000 - 20,000 km | Severe |
| ~20,015 km (antipode) | Maximum (point becomes ring) |

## Tool Features

The Azimuthal Map Generator at https://azimuthalmap.com offers:
- Center on any location by coordinates or place search
- Geolocation support ("Find My Location")
- Configurable distance limiting
- Graticule (latitude/longitude grid) display
- Distance rings with labels (in kilometers)
- Azimuth/bearing labels around the edge
- Center marker options (dot or crosshair)
- Custom color schemes
- Export as PNG or SVG

## Contact

Website: https://azimuthalmap.com
Contact: https://azimuthalmap.com/contact/

## Related Terms

- Azimuthal projection
- Equidistant projection
- Map projection
- Great circle route
- Compass bearing
- True north
- Magnetic declination
- Antipode
- Polar projection
- Oblique projection