Earth Curve Metabunk Calculator

Calculator

Surface distance

Distance unit

Observer eye height

Observer unit

Target height

Target unit

Planet radius

Radius unit

Output unit

Refraction factor k

Horizontal FOV in degrees

Image width in pixels

Midpoint obstruction height

Obstruction unit

Observation note

Use refraction-adjusted effective radius

Example Data Table

Distance	Observer Height	Target Height	Refraction k	Expected Use
6 mi	6 ft	100 ft	0.13	Refracted hidden height near 3.32 ft
10 mi	6 ft	150 ft	0.13	More hidden height from longer distance
20 km	2 m	80 m	0.13	Metric horizon and visibility check
3 mi	30 ft	60 ft	0	Geometric-only comparison

Formula Used

Effective radius: R' = R / (1 - k). Use k = 0 for pure geometry.

Horizon distance: horizon = arccos(R' / (R' + h)) × R'.

Curve drop: drop = R' / cos(d / R') - R'.

Hidden height: hidden = R' / cos((d / R') - arccos(R' / (R' + h))) - R'.

Visible height: visible = target height - hidden height. The value is clamped at zero.

Midpoint bulge: bulge = R' × (1 - cos((d / R') / 2)).

How to Use This Calculator

Enter the surface distance between the observer and target.
Add observer eye height above the local surface or sea level.
Enter the target height from its visible base reference.
Keep the default Earth radius, or enter another planet radius.
Use k = 0.13 for a common refraction estimate, or turn it off.
Select the output unit and press the calculate button.
Download the result as CSV or PDF for reports.

About the Earth Curve Metabunk Calculator

This tool estimates how Earth curvature affects long distance views. It follows the same practical idea used by curve calculators that compare drop, horizon distance, bulge, and hidden height. The goal is not to prove a photograph alone. The goal is to give a clear geometric estimate before other effects are judged.

Why observer height matters

A viewer above sea level can see farther than a viewer standing at the surface. Even a small eye height changes the horizon. That is why the calculator asks for observer height first. The hidden height is calculated only after the horizon from that eye level is known.

How refraction changes results

Air can bend light slightly downward. This often makes distant objects look a little higher than a simple geometric model predicts. The refraction factor increases the effective radius used in the math. A common value is near 0.13, but real weather can change it. Water, temperature layers, pressure, and local terrain may create strong differences. Record the source of each measurement. Note camera altitude, target base elevation, and weather. These notes make repeated checks easier and reduce common mistakes during later review sessions.

Using the output wisely

The calculator returns several values. Drop is the fall below a tangent line. Hidden height estimates the lower part of a target blocked by curvature. Bulge describes the midpoint rise above a straight chord. Horizon dip gives the small angle from eye level to the visible horizon. These values help compare field notes, videos, and photographs.

Limits of the model

The Earth is treated as a sphere with a selected radius. Real terrain, tides, waves, camera height, lens distortion, and mirage effects are not fully modeled. For best results, measure distance and heights carefully. Use local pressure and temperature data when possible. Do not rely on one image if the conditions are unknown.

Best workflow

Start with the default Earth radius. Enter distance along the surface. Add viewer height, target height, and the expected refraction factor. Compare geometric and refracted values. Export the table for notes. Then test several refraction values to see how sensitive the result is. This gives a balanced range instead of one rigid number.

FAQs

What does hidden height mean?

Hidden height estimates how much of the target is below the horizon line for the observer height and distance entered. It is a model value, not a final proof of what a camera must show.

What is curve drop?

Curve drop is the amount the surface falls below a tangent line over the selected distance. It does not include observer height unless hidden height is calculated.

Why is refraction included?

Atmospheric refraction bends light in many real observations. The calculator uses an effective radius method so you can compare pure geometry against a refracted estimate.

What k value should I use?

A common rough value is 0.13. Use 0 for no refraction. Change the value when you have better weather, pressure, or temperature gradient information.

Can this calculator model mirages?

No. Strong mirages and temperature inversions need more complex ray tracing. This calculator gives a practical first estimate for normal viewing conditions.

Why do results differ from simple eight-inches rules?

Simple rules ignore observer height and often use short-distance approximations. This calculator uses spherical formulas, selected radius, and optional refraction.

Does target height include elevation?

Enter the target height above the same reference surface used for the observer. Add base elevation when the target sits above sea level or local terrain.

Can I use another planet radius?

Yes. Enter any positive radius and choose its unit. The same formulas then estimate horizon, drop, bulge, and hidden height for that sphere.