Why only two wheels? Tremulis and Summers suggested that a two wheeled vehicle could be more efficient than its larger four-wheeled counterpart. Smaller and lighter weight means it can use a smaller engine. The Gyro-X was reported to reach speeds of 125 mph using an 80 hp Mini Cooper S engine. Also, the gyroscope’s stored kinetic energy would be harnessed as an additional power source in future gyro vehicles! The aerodynamic body design reduced wind resistance, while half the number of tires reduced road drag. As far as drivability, two wheels made for greater maneuverability, like that of a motorcycle. While a two-wheeled automobile may at first glance seem unsafe and definitely unstable, the Gyro-X made use of a single 22- inch hydraulically-driven gyroscope which stabilized the vehicle, allowing it to “swoop through 40 degree banked turns without tipping.”

(Via Lane Motor Museum.)

Winchell Chung (@nyrath on Twitter and developer of the Atomic Rocket site), reminds us that Doc Smith lovingly described a similar vehicle in First Lensman (1950); he called it a Dillingham eleven-forty:

He got in. The door jammed itself gently shut. The runabout--a Dillingham eleven-forty--shot smoothly forward upon its two fat, soft tires. Half-way to the exit archway he was doing forty; he hit the steeply-banked curve leading into the lofty "street" at ninety.

The first fictional description of a gyrocar - a two-wheeled automobile - was in 1911 in Two Boys in a Gyrocar: The story of a New York to Paris Motor Race by Kenneth Brown.

(Two-wheeled gyrocar)

Most of the cars were between sixty and seventy horse-power; the Amphibian alone being as low as forty-five; while the Capri was eighty, the Gowfer's Goer a hundred, and the huge Liebig a hundred and twenty horse-power.

And it was among these leviathans that the little gyrocar was daring to thrust its puny self, with its two young drivers - and their dog...
(Read more about the gyrocar)

The first prototype Gyrocar, The Shilovski Gyrocar, was commissioned in 1912 by the Russian Count Pyotr Shilovsky, a lawyer and member of the Russian royal family. It was manufactured to his design by the Wolseley Tool and Motorcar Company in England in 1914 and demonstrated in London the same year.[3][4] The gyrocar was powered by a modified Wolseley C5 engine of 16–20 hp, with a bore of 90 mm and a stroke of 121 mm. It was mounted ahead of the radiator, driving the rear wheel through a conventional clutch and gear box. A transmission brake was fitted after the gearbox – there were no brakes on the wheels themselves. The weight of the vehicle was 2.75 tons and it had a very large turning radius. (Wikipedia)