In the phasor diagram following:
φ is the phase advance of the displacer with respect to the piston,
δ is the phase advance of the compression space volume with respect to the piston, and
α is the phase advance of the expansion space volume with respect to the compression space volume.

   function 
 
 
   betadrive 
 
 
   % Beta drive engine configuration 
 
 
   % Israel Urieli 1/22/08 
 
 
   global 
 
 
   vclc vcle 
 
 
   % compression,expansion clearence vols [m^3] 
 
 
   global 
 
 
   vswc vswe 
 
 
   % compression, expansion swept volumes [m^3] 
 
 
   global 
 
 
   alpha 
 
 
   % phase angle advance of expansion space [radians] 
 
 
   global 
 
 
   new fid 
 
 
   % new data file 
 
 
   fprintf( 
 
 
   'beta drive engine configuration\n' 
 
 
   ) 
 
 
   if 
 
 
   (strncmp(new, 
 
 
   'y' 
 
 
   ,1)) 
 
 
   xpa = input( 
 
 
   'enter piston amplitude (m): ' 
 
 
   ); 
 
 
   xda = input( 
 
 
   'enter displacer amplitude (m): ' 
 
 
   ); 
 
 
   phid = input( 
 
 
   'enter displacer phase angle advance [degrees]: ' 
 
 
   ); 
 
 
   dp = input( 
 
 
   'enter piston diameter (m): ' 
 
 
   ); 
 
 
   dd = input( 
 
 
   'enter displacer diameter (m): ' 
 
 
   ); 
 
 
   dr = input( 
 
 
   'enter displacer rod diameter (m): ' 
 
 
   ); 
 
 
   vclc = input( 
 
 
   'enter compression space clearance volume [m^3]: ' 
 
 
   ); 
 
 
   vcle = input( 
 
 
   'enter expansion space clearance volume [m^3]: ' 
 
 
   ); 
 
 
   fprintf(fid, 
 
 
   '%.3e\n' 
 
 
   , xpa); 
 
 
   fprintf(fid, 
 
 
   '%.3e\n' 
 
 
   , xda); 
 
 
   fprintf(fid, 
 
 
   '%.1f\n' 
 
 
   , phid); 
 
 
   fprintf(fid, 
 
 
   '%.3e\n' 
 
 
   , dp); 
 
 
   fprintf(fid, 
 
 
   '%.3e\n' 
 
 
   , dd); 
 
 
   fprintf(fid, 
 
 
   '%.3e\n' 
 
 
   , dr); 
 
 
   fprintf(fid, 
 
 
   '%.3e\n' 
 
 
   , vclc); 
 
 
   fprintf(fid, 
 
 
   '%.3e\n' 
 
 
   , vcle); 
 
 
   else 
 
 
   xpa = fscanf(fid, 
 
 
   '%e' 
 
 
   ,1); 
 
 
   xda = fscanf(fid, 
 
 
   '%e' 
 
 
   ,1); 
 
 
   phid = fscanf(fid, 
 
 
   '%f' 
 
 
   ,1); 
 
 
   dp = fscanf(fid, 
 
 
   '%e' 
 
 
   ,1); 
 
 
   dd = fscanf(fid, 
 
 
   '%e' 
 
 
   ,1); 
 
 
   dr = fscanf(fid, 
 
 
   '%e' 
 
 
   ,1); 
 
 
   vclc = fscanf(fid, 
 
 
   '%e' 
 
 
   ,1); 
 
 
   vcle = fscanf(fid, 
 
 
   '%e' 
 
 
   ,1); 
 
 
   end 
 
 
   ap = pi*dp*dp/4; 
 
 
   % piston area (m^2) 
 
 
   ad = pi*dd*dd/4; 
 
 
   % displacer area (m^2) 
 
 
   ar = pi*dr*dr/4; 
 
 
   % displacer rod area (m^2) 
 
 
   vpa = xpa*(ap - ar); 
 
 
   % (piston - rod) volume aplitute {m^3) 
 
 
   vda = xda*(ad - ar); 
 
 
   % (displacer - rod) volume amplitude(m^3) 
 
 
   vea = xda*ad; 
 
 
   % displacer volume aplitute {m^3) 
 
 
   phi = phid*pi/180; 
 
 
   % radians 
 
 
   delta = atan2(vda*sin(phi),(vda*cos(phi) - vpa)); 
 
 
   % compression space volume to piston amplitude phase advance 
 
 
   vca = sqrt(vpa*vpa - 2*vpa*vda*cos(phi) + vda*vda); 
 
 
   % compression space volume amplitude (m^3) 
 
 
   vswc = 2*vca; 
 
 
   % compression space swept volume (m^3) 
 
 
   vswe = 2*vea; 
 
 
   % expansion space swept volume (m^3) 
 
 
   alpha = pi + phi - delta; 
 
 
   % expansion phase angle advance (radians) 
 
 
   fprintf( 
 
 
   '\nbeta drive engine data summary:\n' 
 
 
   ); 
 
 
   fprintf( 
 
 
   ' comp clearence,swept vols %.1f, %.1f [cm^3]\n' 
 
 
   , vclc*1e6,vswc*1e6); 
 
 
   fprintf( 
 
 
   ' exp clearence,swept vols %.1f, %.1f [cm^3]\n' 
 
 
   , vcle*1e6,vswe*1e6); 
 
 
   fprintf( 
 
 
   ' expansion phase angle advance %.1f[degrees]\n\n' 
 
 
   , alpha*180/pi); 
 
 
   %==============================================================