The emerging float was the final evolution of the submersible float, invented by Imhotep for the pyramid of Saqqara after more than a century of R&D and after the construction of four pyramids.

It should be remembered that floats were implemented to lift stone blocks too large to be hauled up by a rope along the face of the pyramid; this process used to place millions of filling and casing stone blocks. These floats were expected to deliver 50 tons per hour, while emerging floats were expected to lift a 72-ton beam to a height of 60 meters.

Unfortunately, this device is difficult to imagine as it is very long and narrow. In the Cheops’ Pyramid, the float of the first floor measures 37 m high and is 4 m² in section; it slides inside a vertical well shaft of same dimensions. This well shaft goes from 3 m above the base to a depth of 34 m under the base, where a large volume of water, 126 m², is stored in the subterranean chamber to prevent the displacement of the float to modify the water level of the well shaft.

It is extended by a 3x4m cage, which starts from the loading station (at the 3 m level) to a height of 60 m from the base.

The submersible float used in the Saqqara pyramid was made to have a large section and a low draught. To properly operate, it had a low freeboard (the height to sink the deck). To increase its tonnage capacity, its section had to be enlarged as well as its size (weakening it) to make room for a large, empty, hollowed, and airtight volume.

The emerging float, on the other hand, had a full section of smaller size and a high freeboard. Its wetted length could be lengthened to increase its load capacity, and as a result, its span was increased as well. This type of float presented an advantage regarding the lifting height. From its static equilibrium point, workers could make it oscillate by several meters, increasing its span.

In Cheops’s Pyramid, the float of the first floor measured 37 m (121.39 ft.) long, had a 4M² cross-section and weighted 32 t; unloaded its draught was 32/4 = 8 m (26.24 ft.), its “deck” would therefore raise by 37-8 = 29 m (95.14 ft.) in relation to the waterline, in other words to the water level in the well shaft.

Loaded with a 16-ton stone block, it sank an additional 4 meters. At its new static equilibrium, the deck was only 25 m above the water level but could be swung by +/- (16/4) = 4 m; at its highest oscillation point, it could have a span of 29 m (95.14 ft.).

Loaded with a 32-ton stone block, it sank additional 8 meters (26.24 ft). At this new static equilibrium point, its deck was at 21 m (68.89 ft.), but could be swung by +/- 8 m and still had the same span as when unloaded.

As a result, the emerging float had a maximal span regardless of its load within certain construction limit.

But this performance advantage had a cost: as it sank into water, the float moved such a significant volume of water that it would raise the water level, overflowing the well shaft. To resolve this issue, a large surface of open water had to be provided in the well shaft’s water circuit to absorb the volume of water displaced by the float, so that as it sank, it would only change the water level slightly.

The harrows chamber, remains of the well shaft of the third floor, is 1.5 m2 in cross-section. The upper chamber that supplied it has a surface area of 50 m2; therefore, the builders chose a relation of 50/1.5 = 33. When the float sinks by 33 meters (108.26 ft.), the water level inside the well shaft rises by 1 meter. To not overflow it, builders had to accept losing 1 meter of span.

By complying with this relation, the lower chamber with an open water surface of 80 m2 (the total sum of the chamber’s, the horizontal gallery’s, and the niche’s surfaces) could supply a well shaft of 2.4 m2 in cross-section, and the subterranean chamber of 126 m2 could supply a well shaft of 4 m2.

Builders had to be able to lower the first floor float’s platform to the level of the loading station, meaning sinking it by 29 m (95.14 ft.), static equilibrium point height, either by decreasing the water level by 29 m by emptying the subterranean chamber, or by loading the platform with (29 x 4) 116 ton of copper bars with a volume of 13 m3. In both cases, the same volume of water was displaced, either by means of a chain of buckets in the descending gallery to empty the subterranean chamber, or by means of a course winch loading the 116 tons of bars onto the platform.

Everything we see inside the pyramid tells us that the water levels were keep stable with accuracy, at least when it came to the ordinary procedure. We can conclude that weighting down the float to lower it to its loading station was the solution retained by builders.

This option functions like a shaduf: displacing relatively low masses, but multiple times to arrive at a significant mass in the end.

The platform was left at the loading station, at the 3 m level, loaded with 116 tons of copper bars, and placed in a way to leave a space oriented east-west, large enough to accommodate the biggest stone blocks mounted on their roller skids.

Let’s examine two examples to illustrate the operation:

The 22-ton entrance lintel, at 15 m high, and the 32-ton chevron of the lower chamber, at 25 m high.

Lintel, L = 0.86 m; W = 2.82 m; H = 3.7m; Wt = 24 t; the float traveled 15–3 = 12 m.

The platform carrying the lintel and the ballast measured 3 x 4 m. In order to accommodate the stone block, the load had to be evenly spread over the platform for its stability as it was lifted by the float of 4 m2 in section. For instance, the lintel rested on one of its faces of 0.86 x 2.82 m (2.82 x 9.25 ft.) and was mounted on its four roller skids in the center of the platform, oriented east-west. On each side of the lintel, there were two spaces of (3- 0.86)/2 = 1 x 4 m available to accommodate 13 m3 of ballast, i.e., two stacks of 1.6 m high. The ballast could be done with 116 bars of 1 ton (1 x 0.33 x 0.33 m or 3.2 x 1.08 x 1.08 ft.), easy to maneuver with the course winch.

The lintel was loaded with its skids onto the platform at the loading station. Once this was done, the ballast bars were removed one by one from the course, employing a winch to raise the platform, pushed by the float, by 12 m (39.37 ft.).

When the 24th bar was removed, the platform didn’t move yet; it would start raising by 1/4 = 0.25 m (0.82 ft.) once the 25th bar was removed. It would keep rising by 0.25 m with each bar removed.

The platform would reach the 15-meter (49.21 ft.) level after the removal of 48 bars; these were then stored on the course, on the edge of the cage, sticking out a little bit into the cage.

That way, when the lintel would be pushed out of the platform before being placed in its final position, the platform would stay stuck. To go back to the loading station, it had to be loaded again.

The dimensions of the vault chevrons in the lower chamber are only partially known, but we can expect them to be cut to the same dimensions as the entrance chevrons: thickness = 0.8 m (2.62ft.), width = 2.4 m (7.87 ft.), length = 7 m (22.96 ft.), and weight = 36 tons, to raise to a height of 25 m (82.02 ft.).

To statically lift the chevron to this height, as was the case for the entrance lintel, the platform would have to be completely unloaded of its ballast; the float would have weighted 36 + 32 = 68 tons and would have sunk by 68/4 = 17 m (55.77 ft.). It would therefore have been raised by 37 – 17 = 20 m (121.39 – 55.77 ft = 65.62 ft.) above the water level (at 3 m, or 9.84 ft.). This represents a total height of 20 + 3 = 23 m (65.61 + 9.84 = 75.45 ft.), whereas the targeted height was 25 m (82.02 ft.).

This is where the benefits of this architecture come in: from the new static equilibrium of 23 m (75.45 ft.), a combination of ballast and worker movements could be used to set the float in oscillation, eventually reaching the level of 25 meter (82.02 ft.), at which point it would remain locked on check-valves.

Following which, the chevron could be unloaded from the platform, but some ballast bars were left astride on the cage to prevent the platform from going up under the float’s thrust during the unloading.

Through this example, we understand that the solution offered by the emerging float, implemented in Cheops’s Pyramid, allowed, theoretically through oscillations, a span equals to the float’s length; here, 37 m + 3 m = 40 m (or 121.39 + 9.84 =131.23 ft.), but let’s say a span of 37 m (121.39 ft.) to maintain a safety margin to prevent the float from dislodging itself on reaching the high point!

This 37 m level would have been reached with a static equilibrium point at 20 m (65.61 ft.); the float oscillated with a maximal amplitude of 17 m (55.77 ft.).

When it came to lifting the 72-ton beam to the 50-meter (164.04 ft.) level to top the upper chamber, the float would weight 32 + 72 = 104 tons, with a draught of 104/4 = 26 m (85.3 ft.), and the platform’s static equilibrium point would be at 37-26 = 11 meters from the water level at 11 + 3 = 14 meters (45.931 ft.); when oscillating, the float would reach the maximal height of 14 + 11 = 26 m (85.3 ft.). 24 meters (78.74 ft.) would still miss reaching the targeted height.

We will examine in details in the megaliths’ procedure how, using check-valves and extensions, the builders could have hauled this monster to a height of 50 m (164.04 ft.) in successive stages.

To deliver these performances, the float obviously had to be correctly guided within the well shaft and the cage.