Firing across the Strait

If the gun is laid without compensating for the Earth’s rotation, the round does not fall where it was aimed. This is laying and firing. Wind is part of that same uncorrected fall. That miss is a few hundred metres. When the published elevation cannot reach the aim, the round falls short by kilometres. The map marks that gap “Falls short”, separate from “No compensation”. The line of sight runs from the gun you select to the chosen aim point. The guns on the other shore are suggested, and so are cited sinkings. Beside that line: the published range, the flat line of sight, and the spherical depression. The figure shows the shell’s path. A straight aim does not carry the shell to a ship at this distance.

The selected gun is the observer. The solid line starts there and ends at the aim. A dashed line is another gun in the same battery, to that same point. There is no separate observer point. A cited sinking has its own pin, separate from the observer, from “Falls short”, and from “No compensation”. When the published elevation cannot reach the aim, a mark on the line reads “Falls short”. That gap is the published range. The brown mark, labelled “No compensation”, is only the extra miss from leaving Earth’s rotation and the wind uncorrected. It is drawn from where the same elevation falls with rotation and wind ignored, and a short brown dash joins the two. The dash is a few hundred metres, so at this zoom the label and the metre readout carry it. Hold Ctrl and scroll to zoom the map. The scroll wheel alone moves the page.

Ballistic path

Ballistic path
Straight aim

A straight aim does not carry the shell to a ship at this distance. The brown line is that straight aim. The blue curve is a simplified ballistic path, not a firing table and not a corrected lay. Gravity is 9.80665 m/s². The speed is the published muzzle velocity already used to fit the drag, and the drag is that one quadratic coefficient. The curve is the simplified path that reaches the same horizontal distance as this flight, under that drag and gravity. The elevation on the figure is a label so the curve can be read. It is not a lay. Wind and the Earth’s rotation are not in this curve. The height scale is larger than the distance scale, so the arc can be read.

Published range

Rotation and wind

Lines from this battery

Each gun has its own line to the same aim. The heights are the ground at each pin.

Note

The sphere has a radius of 6,371 km. It is not an ellipsoid.
Bearings are clockwise from true north. Compass letters are N, E, S, and W.
Gun heights are the EU-DEM 25 m ground at the pin, to the nearest metre: Winnie 95 m, Pooh 70 m, Jane 102 m, Clem 102 m, Todt turret 1 57 m, Lindemann 76 m. That is the ground, not a measured gun axis. Lindemann’s present surface includes later Channel Tunnel spoil, so 76 m is today’s ground at the pin, not a 1942 floor. A point chosen on the map is sea level. The page does not look up a height for it.
No refraction, tide, or waves. The horizon on this page is geometric.
The observer is the selected gun. There is no separate observer point to move. This is not a measured director tower. Winnie and Pooh had no local observation post and no radar; the page does not draw a director for them.
Click the map to choose an aim point. The list, and a click on a gun pin, suggest the guns on the other shore. Cited sinkings are suggested too, whichever gun is selected. A cited sinking has its own pin, at sea level. The pin is the cited sinking position, not a surveyed impact point, and the page does not replay the engagement.
Published ranges are the cited figures. The flight is a point-mass shell in a flat east-north-up frame, with constant gravity of 9.80665 m/s². One quadratic drag coefficient is fitted so the published muzzle velocity reaches that one published range at the published elevation. The elevation is laid as if the Earth did not rotate and the air were still. Earth’s rotation is the Coriolis term. Wind is a steady horizontal wind. If that lay cannot reach the aim, the round falls short on the line and the map marks it “Falls short”. The brown mark, “No compensation”, is only how far rotation and wind then move that fall. This is not a firing table.
The ballistic figure is a side view of the shell’s path. A straight aim does not carry the shell to a ship at this distance. The curve is a simplified ballistic path, not a firing table and not a corrected lay. It uses that same gravity, the published muzzle velocity, and the drag already fitted to the published range. The elevation on the figure is a label so the curve can be read. It is not a lay.
Equal heights make the flat line of sight zero. The spherical depression does not. Across about 36 km it is about 0.16°. From 100 m down to the water at 30 km, the flat angle is about 0.19°, and the spherical depression is larger by about half the angle at the earth’s centre.
The flat line of sight and the spherical depression are the sight, and the miss from not compensating is the map mark “No compensation”.
English pins are WGS84 conversions of Kent Historic Environment Record grid references. The records mark the points as estimated. The conversion used the OSGB36 transverse Mercator and the Ordnance Survey seven-parameter Helmert shift. Five decimal degrees is that conversion, not centimetre knowledge of a gun pivot.
French pins are weaker. Batterie Todt is one museum pin. Batterie Lindemann is one Wikimapia site pin, not a survey.

It does not produce a corrected lay. It does not keep score. The time of flight is the simplified path in the figure, not a timed engagement. This is not a firing table, and this is not operational fire control.