How are the equations in terms of total energy, roughly guestimating?
Earth receives a solar flux of ~1370 W/m2. Which is about roughly 340 W/m2 average on the surface. Say that for a lattitude of 40-45 degrees the average value is about 0.5 kW/m2 for easy ballpark figures. Cars typically use 10-50 kW driving, I estimate. But in between the two is the efficiency of the photosynthesis, the loss to other, unusable masses, the transport and distribution of the fuel and the efficiency of the car itself. Suppose (wild guess) that 10% of the solar flux is captured in the photosythesis, which is transferred to fuel with a loss of 50% rougly estimating including all the other processes, except that the fuel efficiency of the car is about 40% which means that 2% of the 0,5 kW/m2 is used effectivily for propulsion (5 W). So to generate the 10-50kW we need 1000 - 5000 m2 production area.
Of course cars don't drive continuously, while the production can be considered continuously. So if I drive average 15,000 miles a year in 400 hours that's roughly one hour per day, so the 1000 - 5000 m2 can support 24 cars continuously. So you'd need some 40-200 m2 fuel production area per car. How far am I off? Is this feasible as prominent fuel source for the future?