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How does change in energy density over time affect the viability of the energy source?

Going by your numbers, jet fuel maintains 46MJ/kg as it is depleted—the last kg has the same energy density as the first kg. I would exclude the weight of the enclosing tank because I think that’s usually the airframe itself.

Batteries start at 1MJ/kg for the first MJ and fall to 0MJ/kg when depleted (I don’t know what the curve looks like, but I’d expect it to be worse than linear).

What is the practical impact of this difference, if any?

If energy is consumed uniformly over time, and all fuel is consumed during a flight, it would mean a factor of 2. Using a lot of fuel during takeoff would mean a slightly higher factor, but keeping a fuel reserve would decrease the factor, so it would probably come out even?

An important characteristic of liquid fuels are that as you extract the energy from them you reduce the total weight. In particular for flight this helps increase overall range and efficiency.

Batteries weigh the same full or depleted. So after you deplete 50% of your battery power you’re still carrying 100% of the weight.

In cars this is less of an issue. But for planes, where you are defying gravity, it can make a large difference.

Interestingly, if you ignore air drag for cars, the equation is basically the same. Lift to drag is just the reciprocal of rolling resistance. But yeah, that does change the answer a bit. One possible solution is to stage off some of the battery mass.

The wheels on my Tesla hold up the batteries from gravity easily but in a plane you have to continuously lift them, does that change the dynamic?

Not as much as you might think. A huge amount of energy is required to gain the altitude for long distance flight. Cruising much less so.

It certainly does. To fly, an airplane has to push air down, it creates wing tip vortices, these vortices are wasted energy. The heavier the plane, the more air it has to push, the stronger the vortices and the more energy is wasted.

Cars push on the ground, and the ground gives back all the force applied to it, so no losses here, planes that fly very close to the ground can also take advantage of the ground effect (that's the name) for more efficient lift.

To how much extent, I don't know, but one thing for sure, manufacturers strive to make their planes as light as possible.

As a side note, heavier gliders actually fly a bit better (faster) but unlike powered airplanes, they don't lift themselves.

Edit: added ground effect

The way that airplane wings work allows planes to sort of float on a cushion of air, so modern planes, for example a 747 at cruising speed, have a lift to drag ratio of 17. So one pound of thrust gives you 17 pounds of lift.

>conventional aircraft still leave a huge amount of efficiency on the table

Go on. I’m listening and I’ll bet Airbus and Boeing are too

Cost is the missing element there. They know how to make more efficient planes (e.g. Dreamliner) but the industry can't afford to apply that efficiency to the entire fleet.

Not the GP, but I'll take a stab.

Roughly speaking, you can increase the efficiency of an airplane in 2 ways: increase the thermodynamic efficiency of the engine, and make the engine push more air at a slower speed.

For the first one you need to make the engine burn hotter. Since metals melt at a certain temperature, you need to use ceramics if you want to exceed that temperature. Such as Silicon Carbide [1] which "melts" (or decomposes) at 2830 degrees Celsius. The efficiency of an ideal Carnot engine is 1-T_cold/T_hot, so if T_cold = 300K and T_hot = 3000K, you end up with 90% efficiency. Of course the jet engine is not quite the Carnot engine, but the idea stands that higher burning temperature leads to higher efficiency. Now, if manufacturers decide to use Hafnium Carbide one day, that one melts at 1000 degrees Celsius higher.

The second method is due to the relationship between momentum and energy. Energy is m v^2/2, which means that for a given energy (think quantity of jet fuel burned in the engine), you can either push a certain amount of air at a given speed, or 4 times as much air at half the speed. But momentum is m v, so the second choice gives you twice the momentum. In other words, twice the thrust. To push more air, you want to grab more air, so you want turbines with higher diameter, and a higher bypass ratio.

General Electric and Pratt&Whitney do exactly that with their engines. Engines with higher bypass ratios and using ceramics (more precisely, ceramic matrix composites). In fact GE's engine is so fantastic, that Boeing decided to put it on the 730-Max, and the rest is history ...

So, yes, Boeing and Airbus know what needs to be done, but it's just not that trivial.

[1] https://en.wikipedia.org/wiki/Silicon_carbide

You missed the big one: improve the lift to drag ratio. A Cessna does like 10. State of the art airliner does like 20. But the Virgin Globalflyer did 35-40 and modern sailplanes do 50-70+, and it’s possible to do up to 100.

I did skip that one, as the topic was engines (gas fueled or electric), not overall efficiency. But since you mentioned this, here's yet another big one (known by very few people): just go faster. Much faster. The lift-to-drag ratio goes down, but the time spent in the air goes down more, so you might end up burning less fuel overall. In cruise mode, a Concorde quite efficient, but it was horrible at takeoff and climbing; because you need fuel to carry fuel, the problem was compounding and overall Concorde was not economical. If someone can solve the takeoff problem (e.g. by using catapults) and climbing (maybe using detachable and reusable boosters?) then a Mach 5 jet could be very competitive. I think this is what the Boom guys had in mind when they say they aim to get to where anyone can travel to any destination on Earth in 4 hours for only $100 [1].

[1] http://edition.cnn.com/travel/article/boom-supersonic-four-h...

> This is the same reason why gasoline is ~15 times better than lithium ion, and typical gas car ranges are 400 miles but you can get a Model S with the same 400 miles range

I think the real reason is there is that no need for bigger gas tanks.

Particularly when refueling is so fast and fuel stations so widespread.

But I'd need >1100 km range to make my road trip between family cities without stops, and each stop substantially increases travel time, even if refueling and paying are all I do.

Still waiting for a ground vehicle that I can pilot* on ordinary roads and highways, go a bazillian range units without stopping, and thereby usually avoid the dramatic'ly worse flying aggravations compared to when I was grammar school. (^_~)

* not technic'ly "driving" when you're not behind the thing that you're causing to move. Although really, any linguist would acknowledge that in reference to ground vehicles, the verb "drive" has acquired the additional meaning of the verb "pilot", so I'm just being silly.