Slant Range formulaThree-Dimensional Distance |
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| \( d \;=\; \sqrt{ \left( x_2 - x_1 \right)^2 + \left( y_2 - y_1 \right)^2 + \left( z_2 - z_1 \right)^2 } \) | ||
| Symbol | English | Metric |
| \( d \) = Slant Range | \(ft\) | \(m\) |
| \( x_1, y_1, z_1 \) = Point One Coordinates | \(ft\) | \(m\) |
| \( x_2, y_2, z_2 \) = Point Two Coordinates | \(ft\) | \(m\) |
Slant range, abbreviated as \(R\), also called line-of-sight, is the straight-line distance between two points in three-dimensional space, typically measured along a direct path that is not constrained to a horizontal or vertical plane. In fields like aviation, radar, satellite communication, and surveying, slant range is the direct line-of-sight distance from an observer or sensor, such as a radar antenna or aircraft, to a target or object, such as a vehicle, aircraft, or point on the ground. Unlike ground range, which measures the horizontal distance along the Earth's surface, slant range accounts for both horizontal and vertical separations, resulting in a diagonal path.
Slant Range formulaTwo-Dimensional Distance |
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| \( d \;=\; \sqrt{ R^2 + h^2 } \) | ||
| Symbol | English | Metric |
| \( d \) = Slant Range | \(ft\) | \(m\) |
| \( R \) = Horizontal Distance Between the Points Projected Onto the Ground | \(ft\) | \(m\) |
| \( h \) = Vertical Height | \(ft\) | \(m\) |
For example, in radar systems, the slant range is calculated as the distance from the radar to the target, factoring in the target's altitude and horizontal displacement. This measurement is needed for accurate targeting, navigation, and distance calculations in applications where elevation differences are significant. The slant range is typically determined using the Pythagorean theorem in three-dimensional geometry, incorporating the horizontal distance and the height difference between the two points.
