Diesel has an energy density of 36 MJ/l, or 136 MJ/gallon. If you assume 12 MPG, a school bus driven 100 miles a day will consume 8.3 gallons. With a conversion efficiency of 30% (30% of the energy makes it to the pavement and moves the bus, the rest is lost as heat in the engine, transmission, and tires), that's 136 MJ/gal * 8.3 gal * 0.3 = 339 MJ of energy consumed. Or 3.4 MJ per mile.
A full-size school bus is about 2.4 meters wide by 12 meters long, so you could put about 28.8 m^2 of PV panels on top of the bus. Commercial PV panels are rated at around 135 Watts/m^2 (about 18% efficiency), 28.8 m^2 then has a peak generating capacity 3888 Watts. If the bus were driven 1 hour at noon on a sunny day, it would generate 3888 W * 3600 sec = 14 MJ. Or enough to travel 4.1 extra miles.
Capacity factor for the U.S. is about 0.145. That is, for every 1000 Watts of PV you have installed, it'll generate on average 145 Watts throughout the year after factoring in night, weather, angle of the sun, dirt on the panels between washings, etc. So those 28.8 m^2 will actually only generate 3888*0.145 = 536.8 Watts average through the day. 536.8 Watts * 1 day * 24 h/day * 3600 s/h = 36.38 MJ in a day. Or enough to move the bus 10.7 miles per day. You've paid to cover the entire top of the bus in PV panels, and over a day it's harvesting less than 11% of the energy the bus needs for its daily route.
This is what most solar proponents don't seem to get. Solar energy is very, very low density. Even if PV panels reached 100% efficiency, the dream of an electric bus driving 100 mi/day powered entirely by solar panels on its roof can't happen. Sunlight simply doesn't have enough energy density.
If you're going to go solar, you are much better off with fixed panels (either on top of buildings, or on a covering structure for the school bus parking lot). They should plug into the grid and provide electricity where it's needed. And when the the bus comes back from its route, it can plug in and get its electricity from the grid as well (from solar, wind, hydro, nuclear, gas, coal, whatever). This:
- Combines a much larger area of PV panels while using a single voltage regulator and other electronics, reducing cost.
- Has lower construction strength requirements since they don't need to survive constant motion, bumps, and jiggles, also reducing cost.
- Allows the panels to contribute even if a bus happens to sit unused for several days or weeks (beyond the point where its battery is full) due to maintenance or a little thing called summer vacation.
- Vastly simplifies maintenance as your panels are always accessible, and aren't sitting atop of things that move around and rearrange themselves a lot.
- Vastly reduces the risk of damage, not just from vehicle accidents but from all the little rocks and pebbles which get flung up in traffic.
- Allows you to dispose of and replace buses without losing your investment in the PV panels. The panels will probably last 2-3 decades. Buses on average are replaced after about 12 years.
PV panels on top of buses. Bad idea.