Take a peek on this video to see the principle.

Who is going to build a record fairing that is very narrow and slim in the front?  Not me , been there, done that :-),

Up til now the cylindrical or oval movement of the feet determined the (large) size of the front half of the record fairings.
With the lineair movement the space required for the moving feet is very much smaller. Even the same space the left foot dives in at the end of the stroke can be used by the right foot at the end of the stroke. This allows a smaller frontal area and better streamline than the round pedaling machines.
The propulsion and gearing can be done much more effective by means of Snek propulsion; the rowingbike stepless gearing system by Dyneema®  cable in stead of the primitive chain :-)
No need for an intermediate axle and/ or energy eating gearing systems but straight from the pedals with Dyneema®  cords on very small Sneks at the wheel axis with end Ø 16 mm.  On a 27” wheel this gearing allows speeds over 150 km/h!!!
There is almost no speed limit on the stepless gearing by Snek transmission.