This is not so much a mathematical concept as it is simple commonsense. Ignoring potential obstacles, the shortest path between two points is a path directly towards the other point.
Flying cars already exist but their implementation is tricky because of the perceived dangers of them malfunctioning, falling out of the sky & damaging infrastructure. Whereas if a vehicle on the ground malfunctions, it can be stopped on the side of the road or crashed into an arrestor bed.
I've been searching some information on heavy-duty vertical take-off aircraft (helicopters) & found aircraft such as the Mil Mi-26 of the Soviet Union/Russia & the Boeing CH-47 Chinook. Both these aircraft have a cruise speed of over 250 km/h, both can lift over ten tons (i. e. over 70 people & their luggage) & both can travel over 400 km without refueling. They cost ten times less than the Boeing 737 most commonly used in South African fleights & about the approximate price of eight buses. What I am thinking is custom made Mil Mi-26 & Boeing CH-47 Chinook aircraft with passenger seats, passenger windows, some lighter carbon fibre fittings. This could be done to make an air service that works like a bus, using shorter range stops to pick up people at select launching pads as opposed to airports with extended runways. Just several small patches of landing pads with a separate parking lot to make a micro airport setup. This could be as an (air)bus service for people who need to travel 100 km to 300 km. The advantages could be;
1) no traffic,
2) shorter travel time &
3) no road/rail infrastructure (& it's associated infrastructure problems) needed.
Taking into account that these aircraft - the Mi Mi-26 & Chinook cost about US$ 3,5 million a year to maintain including fuel (that's US$ 9600 a day), a ticket for a trip could be US$ 48 per passenger for the air service to cover costs. Provided that the aircraft are carrying a full load of passengers each trip.
If my concept of vertical-axis wind-turbine powered electric vehicles comes to reality & translated into aircraft, we could have aircraft that need less external power whether it be kerosene or electric to make a full trip.
