Naive Fallacy

Buoyancy calculus

Berechnung Auftrieb        

Some of my readers are real enthusiasts. One of them has created a calculation sheet based on Excel, which allows you to calculate the maximum achievable buoyancy power in the simplest way – calculation base are the dimensions of a "power plant" of the type GAIA / ROSCH. Just try it yourself!

Download Calculation Sheet

Note: The calculation provides only the achievable performance of the buoyancy. The energy consumption for filling the container with air is not taken into account which is always higher than the calculated power that can be obtained by the buoyancy in any case.

The tattered drive chain

An attentive reader has wondered why the upper drive chain is not shredded immediately in the Video of ROSCH, showing the prototype in Belgrade during operation.

If it is assumed that the generator delivers a power output of 12 kW as indicated by ROSCH, this power must also be transmitted to the drive shaft.

In the video you can see that the top shaft is spinning very slowly. It requires 38s for a full revolution!

The formula for the torque on the shaft with an output of 12,000 watts is given by

M = torque [Newton meters]
P = transmitted power by the shaft [Watt]
n = speed of the shaft [revolutions per second]

72600 Nm! – For comparison, a VW Golf 7 diesel with 105 hp produces a torque of 250 Nm on the drive shaft!

I'll eat a broom along with the cleaning lady if there was no chicancery ...!


A frequency meter is visible in the same video indicating a very stable frequency of 50 Hz. Control engineers, please contact me! Which one of you can keep this system stable from the input (pressure air injection) to the output (generator voltage) as a normal mains frequency? I'm already hungry for the dog of the cleaning lady, if that is possible without using highly complex control systems ...!


The following simple calculation – which is at all the more plausible one because of its simplicity (any high school student should be able to reproduce it easily) – was sent to me by Gerhard Daniel Kadisch via email. It has only been slightly reformulated and completed by myself.


GAIA states that the space required for the plant is approximately an area of 0.5 x 0.5 m and a height of 5 m. Excluding any walls of or transport elements this results in a total water volume of 0.5 m * 0.5 m * 5 m = 1.25 m3.

The available space for the buoyancy containers is only half of this volume (in the other half the filled containers fall back down). This results in 1,25 / 2 = 0.625 m3. Since the volume cannot of course be fully used (the containers are rounded and are mounted with a little distance from each other), one can approximately guess that the usable volume for the buoyancy process is only about 0.5 m3. The maximum lifting force is thus 500 kg (it corresponds to the weight of the volume of water displaced, namely the weight of 0.5 m3 of water). In the videos of GAIA and ROSCH can be seen that the containers move at a speed of about 15 cm per second (= 0.15 m/s).

If you want to yield a power of 5 kW (as was promised for the "power plant"), then you need to calculate as follows: You need to move a mass of 500 kg (equivalent to 0.5 m3 of water) continuously at a speed of 1 m/s against gravity to the top of the tank!

In order to raise 500 kg within a second to 1 m height, one needs an output of 500 kg * 9.81 m/s2 * 1 m/s = 4905 Nm/s = 4905 W. So this corresponds almost exactly to the guaranteed value of 5 kW.

(Note: The value of 9.81 m/s2 is to overcome gravity.)

In our case the 500 kg only move at a speed of 0.15 m/s upwards ... i.e. one receives
500 kg * 9.81 m/s2 * 0.15 m / s = 735.75 watts of mechanical power at maximum which is available for the generator to produce electricity.

Well, now the obvious things: So far I have neglected that blowing the air into the containers by a compressor does not require any energy ... To hell with GAIA! Where should this energy come from then when we already receive less energy than promised ??!

In addition, the adopted dimensions of the system are idealized, i.e. they are clearly rounded up in favor of GAIA. Also, no friction or heat losses were considered that are far from negligible!

Conclusion of this impressively simple calculus: This "power plant" can never ever produce the promised output power!!!

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