I tried a calculation. It appears there is an optimal gas velocity in between 0 and V_train. It depends on a lot of factors that I didn't spend much time tryi

I tried a calculation. It appears there is an optimal gas velocity in between 0 and V_train. It depends on a lot of factors that I didn't spend much time trying to come up with realistic values. If I weight things heavily in my favor, you can save over 50% power requirements by moving the air at around ~120m/s. If I weight things in your favor there is a pretty paltry power savings at around ~10m/s. If you care, here was my method: f=0.006; %wall friction factor inside tube, also skin friction outside a train rho=1.2; %air density [kg/m^3] R=1.5; %tube radius [m] Vg=0:200; %velocity of tube gas [m/s] Vt=250; %velocity of train [m/s] L=500e3; %length of tube [m] Cd=0.8; %drag coefficient, form drag trainfill=0.1; %percent of tube filled by train airfill=1-trainfill; %percent of tube filled by air ncars=1000; %number of cars in tube Pg=pi/4fVg.^3LairfillR; %power required to move gas through tube Pt_fm=ncars0.5rhopiR^2Cd(Vt-Vg).^3; %power required to overcome form drag on each car Pt_sk=pi/4f(Vt-Vg).^3LtrainfillR; %power required to overcome skin friction drag Pg_annulus=0; %since the mass of air is so small between the train and tube wall, assume 0. Pt=Pg+Pt_fm+Pt_sk; %total power requirements