# Power calculation of pressure difference engine (Gravitation propeller)

Pic. 3 shows the piston rotor (end view) consisting of eight cylinders fastened at the rotor circumference. The diameter of each cylinder is one fourth of the piston rotor diameter. All the calculations will be done for this ratio of shapes of cylinders and the piston rotor. The working equation will be equation 4.3 from chapter "Motion formula"

**A****=0,57****πR****²****Spg**

This formula describes work done by a single piston when moving along the half-circle of the piston rotor. But in this case four pistons participate in motion, therefore, work will be four times higher. As is well-known, power is work done in unit time.

Time (t) required for the piston to make a half-revolution is determined by formula **t****=****πR****/****V** where:** V****-**circular speed of the piston

By inserting this expression into the piston work equation, we obtain the power formula for a single piston: **P****=0,57****VRSpg****,** therefore, power for the complete piston rotor will be four times higher:

**P****=2,28****VRSpg**** (4.4)**

Pistons circular speed (as the piston is subjected to the force with free fall acceleration) can be determined from free-fall velocity formula as square root of product hg, where h is fall height. In this case, the fall height is equal to piston length. In turn, the piston length will always be equal to the half-circle length if forces acting in pistons and at circumference are equal. But I did not included this expression in the power equation, as this speed can be higher. For an engine with the piston rotor with diameter equal to 2 meters, circular speed will be about 5.5 m/s. Below you can find an approximate calculation of power for this engine.

Piston area **S****=****πr****²=3,14*0,25²=0,196(m²)**

For a water using engine (p=1,000 kg/m³):

**P****=2,28*5,5*1*0,196*1000*9,8=24086(Вт)=24(kW)**

For an ethyl iodide using engine (p=1930kg/m³):

**P****=46,3(kW)**

For an engine using mercury (p=13600kg/м³)

**P=3****26****,****4****(****kW).**

The results of calculation, except for mercury, may seem very modest, but it should be noted that this calculation is highly simplified and gives an indication of the order of the proposed power.

In particular, the pressure difference factor (1.24) between lower and upper half-circles and kinetic energy of piston motion (1/2MV²) (this energy can be also transformed by the piston rotor) are not taken into account. The rotor rotation velocity can be higher than the design one in many cases, as the rotor will unwind with a constant acceleration, but the real rotor velocity can be determined only in practice.