Chicago skyline across Lake Michigan

A visible skyline is not the same as a visible shoreline. Test the height of a specific building feature against the observer’s height and the actual light path.

Keep the original observation attached

Joshua Nowicki · Grand Mere State Park · 30 April 2015

Dated original
Nowicki’s own gallery identifies Grand Mere State Park and 30 April 2015.
Observation terrain
The Michigan DNR describes dunes and Lake Michigan shoreline; the named park alone does not specify the camera’s elevation.
Starting calculation
90 km separation, 2 m eye height and 400 m target are editable scenarios, not recovered photograph metadata.
Needed for an exact image match
Camera coordinates and height above that day’s lake level; identified building features; uncropped frame, time and vertical atmospheric profile.

Compare eye height, distance and light path

RUN THE NUMBERS

Change the sight-line scenario

These starting values define a comparison scenario. Replace the eye height, surface distance, target height and atmospheric assumption with your own paired observation.

Unit changes preserve the same physical inputs. The working tape stays in SI units.

Calculation inputs
km

Longer distances increase curvature drop and, beyond the eye horizon, hidden height.

m

A higher observer reduces hidden height but does not change tangent-plane drop at that distance.

Zero means straight rays. Positive k bends rays toward the surface; this constant-gradient scenario does not model a mirage.

m

Height of the target above the same smooth surface. Compare it with hidden height to find its visible part.

km

Mean Earth radius is 6,371.0084 km. A different radius changes physical drop, horizon and bulge together.

Hidden target height566.42m

Minimum radial height at the target needed to meet the limiting ray; zero before the observer’s horizon.

Visible target height0 m

The entered target above the limiting ray; zero means the whole target is below that smooth-surface sightline.

Solid: effective-radius surface and heights · dashed: limiting sightline · vertical scale expanded

Match one feature, not the word skyline

Select the roof, antenna tip or visible lower edge of one identified building. Those heights are different. A statement that “Chicago is visible” does not specify whether the water-level base, the upper storeys or a displaced refracted image is being seen.

The photographer’s named park contains shoreline and dunes. A location name cannot replace a measured eye height. Move the eye-height control through beach-level and elevated scenarios while retaining the same target and distance; compare hidden height with the chosen building feature.

Compare atmospheric scenarios with the same observation

Start with zero refraction, then compare an entered effective-radius coefficient. Keep the surface separation, eye and target fixed. The output shows how much of the target lies above a limiting ray, rather than treating tangent-plane drop as hidden building height.

A vertically changing refractivity profile may lift, stretch, invert or duplicate distant features. A single coefficient cannot reconstruct all of those effects. Use the layered-ray tool to compare gradients and collect temperature, pressure and humidity with height when repeating a lake observation.

What the dated image establishes

The original gallery anchors one photograph to an author, named park and date. It does not establish every geometric input in the starting scenario. Preserve the original frame and distinguish its capture date from the date on a repost or caption.

Compare repeated photographs from the same camera location and focal setting. An image that changes shape with weather is a different observation from a fixed straight-ray silhouette. Record which features move, whether the lake horizon is sharp and how the camera height was measured.