Lambert Conformal Conic Projection
Lambert Conformal Conic Projection & Convergences
1️⃣ Earth Convergence (Meridian Convergence on Earth)
Definition: The angle between two meridians at different longitudes on the Earth’s surface.
Formula:
$$ \gamma_e = \Delta \lambda \times \sin(\text{mean latitude}) $$
Meaning:
- Represents how much the meridians converge as you move east–west.
- The closer you are to the poles, the larger the convergence.
Example: At 60°N between 10°E and 20°E:
$$ \gamma_e = 10° \times \sin(60°) = 8.66° $$
2️⃣ Map Convergence (Lambert Map Convergence)
Definition: The angle between Grid North (map north) and True North on a Lambert Conformal Conic projection.
Formula:
$$ \gamma_m = \Delta \lambda \times \sin(\text{standard parallel}) $$
Notes:
- The standard parallel is the latitude where the cone touches or cuts the Earth.
- It is constant for the whole map, so the map’s convergence is uniform (simplified).
3️⃣ Relationship Between Earth and Map Convergence
| Type | Formula | Depends on | Description |
|---|---|---|---|
| Earth convergence | Δλ × sin(mean latitude) | Actual position | Real geographic convergence |
| Map convergence | Δλ × sin(standard parallel) | Map construction | Approximation used in Lambert map |
➡️ On a Lambert map, the Earth’s variable convergence is replaced by a fixed value based on the standard parallel.
4️⃣ Grid / Map / True North
| Term | Definition |
|---|---|
| True North | Direction toward the Earth’s geographic North Pole |
| Grid North (Map North) | Direction of the meridians on the map grid (toward the cone’s apex) |
| Convergence (γ) | Angle between True North and Grid/Map North |
5️⃣ Projection Method in Lambert Map
How points are projected:
- Points are projected orthogonally (normally) onto the conical surface, not from the Earth’s centre.
- Therefore, it’s a normal conic conformal projection, not a central one.
✅ Exam answer:
“In the Lambert Conformal Conic projection, points are projected normally to the conical surface, not from the Earth’s centre.”
6️⃣ True North vs. Apex of the Cone
- The apex of the projection cone lies on the axis of the cone.
- The True North direction follows the Earth’s rotational axis.
- In general, these two axes differ slightly, so True North and the direction to the apex are not identical. → The difference = meridian convergence (γ).
7️⃣ Key Takeaways for ATPL Exams
✅ Earth convergence: ( \gamma_e = \Delta \lambda \times \sin(\text{mean latitude}) ) ✅ Map (Lambert) convergence: ( \gamma_m = \Delta \lambda \times \sin(\text{standard parallel}) ) ✅ Projection: normal to the cone, not central ✅ Apex and True North differ in general → map convergence ✅ Identical only if cone axis = Earth’s axis