To find the cloud ceiling (the height of the lowest cloud base above the ground) using a spotlight on the ground and the angle of the light beam hitting the clouds, you use basic trigonometry, specifically the tangent function. Given:
- The horizontal distance from the spotlight to a reference point (e.g., hangar door) is known (for example, 0.75 km).
- The angle between the ground and the beam of light shining up to the clouds is measured.
Method:
- The cloud ceiling height hhh can be calculated using the formula:
h=d×tan(θ)h=d\times \tan(\theta)h=d×tan(θ)
where:
* ddd is the horizontal distance from the spotlight to the reference point on the ground,
* θ\theta θ is the angle of elevation from the ground to the point where the beam hits the clouds.
For example, if the spotlight is 0.75 km from the hangar door and the measured angle is 20 degrees, then:
h=0.75×tan(20∘)≈0.75×0.364=0.273 km=273 metersh=0.75\times \tan(20^\circ)\approx 0.75\times 0.364=0.273\text{ km}=273\text{ meters}h=0.75×tan(20∘)≈0.75×0.364=0.273 km=273 meters
This means the cloud ceiling is approximately 273 meters above the ground
. This approach is a simplified version of what optical drum ceilometers do, using triangulation to determine cloud height by measuring angles and distances on the ground
. Modern ceilometers often use lasers or LIDAR to measure cloud base height more precisely, but the spotlight and angle method is a practical and straightforward way to estimate cloud ceiling in aviation contexts
. Summary:
- Measure the horizontal distance ddd from the spotlight to a fixed point.
- Measure the angle θ\theta θ between the ground and the light beam hitting the cloud.
- Calculate cloud ceiling height as h=d×tan(θ)h=d\times \tan(\theta)h=d×tan(θ).
This method helps pilots know the cloud ceiling, which is crucial for flight safety and planning
