Magdeburg hemispheres (3D)
About this app
Guericke's experiment of 1657: pump out the air, let horses pull and calculate the holding force of air pressure.
With explain mode: an AI tutor walks you through the app, points out what matters in the scene and answers your questions.
Why the hemispheres hold together
Otto von Guericke used his piston air pump to remove the air from two copper hemispheres placed together. Afterwards they held so firmly that teams of horses could not separate them. The force does not come from the vacuum, because empty space does not pull. The outside air pressure presses on each half, and inside there is no counter-pressure. The holding force is the pressure difference times the cross-sectional area, F = Δp · π r². With a diameter of about 42 cm and a perfect vacuum that is about 14 kN, as much as the weight of roughly 1.4 tonnes.
What the app shows
The app reconstructs the experiment in 3D: two copper hemispheres with a leather ring and a tap, a piston pump, two teams of low-poly horses and a wall. The sphere is cut open. Air particles strike the wall from outside and inside, and pressure arrows show who is pushing. A diagram shows the pump's suction and compression strokes with both valves. The values give the outside and inside pressure, the holding force and the force in the rope. Whatever is uncertain, such as the quality of Guericke's vacuum or the pulling force of a horse, is stated in the app as an assumption with a source.
What you can try
You pump out the sphere and watch the remaining pressure fall with every piston stroke. Then you let two teams of eight horses pull and compare with one team pulling against a wall: the force in the rope is the same. With enough horses on one side the sphere is torn open. In the Place panel you choose a mountain such as the Zugspitze and see that lower air pressure there holds the halves less firmly. An AI tutor can demonstrate the experiment and answer questions in the scene.
Frequently asked questions
- What holds the Magdeburg hemispheres together?
- The outside air pressure. After pumping out, air presses on both halves from outside while almost no pressure pushes back from inside. The holding force is F = Δp · π r²; at 42 cm diameter and a perfect vacuum about 14 kN.
- Why does the second team of horses not count double?
- The second team only holds against the pull, just as a wall could. The force in the rope is that of the weaker team. Eight horses against eight horses give the same rope force as eight horses against a wall.
- Do the hemispheres hold less firmly on a mountain?
- Yes. Air pressure is lower higher up; on the Zugspitze, according to the barometric formula, about 713 hPa instead of about 1013 hPa at sea level. With the same vacuum inside, the holding force drops accordingly.
- What can I adjust in the app?
- The number of horses per team, a wall or a second team, the pump's achievable remaining pressure, the altitude above sea level, the diameter of the hemispheres and the assumed pull per horse. You can toggle air particles, pressure arrows and the cut through the sphere.
Subject: Physics experiments (Deutsches Museum)
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