Em Drive Basic Theory 1 Em Drive Theory
Em. Drive Basic Theory 1
Em. Drive Theory Microwave energy is fed to a specially tapered resonator, which produces a net thrust from the large number of EM reflections in the high Q structure. (typically 5 x 104) Fg 1>Fg 2 as guide velocity Vg 1>Vg 2 Static Thrust given by: 2
Derivation of Basic Thrust Equation From principle of operation now Ref: A. L. Cullen Thus force is inversely proportional to guide wavelength Then where S 0 corrects for Einstein’s equation for the addition of relativistic velocities Relationship between guide wavelength and waveguide geometry is non-linear 3
Axial Component of Sidewall Force F Area A 2 F 2 1 At first sight it might appear that because A 1= A 2+A 3 then F 1= F 2+F 3 Area A 1 Area A 3 However as the relationship between F and A is highly non-linear, the cavity can be designed to maximise F 1/F 2 and minimise F 3/F 1 Detail design requires software developed by SPR Ltd and is included in IPR However intuitively it can be seen that at cut -off : Guide wavelength is infinity Group velocity and force is zero Area A 2 is clearly not zero 4
Conservation of Momentum Vg = 0. 99 c Waveguide velocity = 0. 5 c Vg measured inside waveguide = 0. 99 c Vg measured outside waveguide = 0. 99 c (not 1. 49 c !) This applies if the open end wall is now closed An EM wave propagated inside a CLOSED waveguide is an OPEN system Momentum can therefore be exchanged between the EM wave and the waveguide end walls Momentum is therefore conserved 5
Conservation of Momentum Assume that at velocity c, the EM wave has momentum At initial propagation 1 = 0. 4 and 2 = - 0. 4 Then 1 + 2 = 0 w At end plates 1 = 0. 9 and 2 = - 0. 1 1 2 Then momentum lost by EM wave at end plates = 2( 1 + 2 ) = 1. 6 Momentum gained by waveguide w = - 1. 6 Then w +2( 1 + 2 ) = 0 Vg 2 =. 1 c Vg 0 =. 4 c Vg 1 =. 9 c 6
Conservation of Energy Ff Fr Vg 2 Vr Vg 1 Vf Cavity Acceleration Cavity acceleration produces unequal Doppler Shifts in Ff and Fr during each wavefront transit. Doppler Mathematical model illustrates Doppler shift for both Motor and Generator modes. +ve acceleration gives a frequency decrease and hence an energy loss (motor) -ve acceleration gives a frequency increase and thus an energy increase (generator) 7
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