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Comment by dghlsakjg | Hacker News Reader

Nit: When they did the actual flight I did the math on the $5 worth of power claim, and it just doesn’t pencil out even at the lowest power rates in North America. Just to illustrate: at $.05 per kWh (which is less than half the price of electricity where they flew), you get 100kwh for $5. 100kw is what it takes to takeoff a 1200 pound Cessna. Probably about 75kw for an efficient cruise in that same plane.

Still an incredible feat, but no idea where the $5 comes from. Maybe that’s just the power they use to get from the threshold of the runway to wheels up.

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You can't convert between kWh and kW. 100 kWh = 6 MW for one minute... so there is plenty of power if the flight is short enough. They said the plane has 4 Tesla's worth of battery power, let's assume they are 80KWh packs then that's 320kWh that they could use for a short flight. That's a fair amount of juice, they definitely won't be flying long in a 25 ton aircraft without starting up the auxiliary motor but I have no doubt it will be able to get off the ground on $5 worth of electricity.

To be fair though it is more likely to be 50 kWh just for the take-off, so that's probably where their $5 figure came from (at $0.10 / kWh). For comparison: a single gallon of Jet-A = ~150MJ. 320 kWh = 320,000 W for one hour so 3600 * 320,000 = 1150MJ, or about 40 gallons and I suspect that these electric motors are quite efficient.

So it does pencil out, I think. Or maybe my pencil is broken and no doubt HN will correct my math.

The specific claim from the company is that the entire 27 min flight was done with $5 worth of power using an all electric power system with a power output exceeding one megawatt.

https://www.heartaerospace.com/newsroom/heart-aerospace-comp...

I still think it is an amazing achievement. I just don’t see how they were able to get it done on $5 worth of power, or they just quoted the wrong price.

I still don’t see what the problem is. The entire flight was likely just a few patterns and your earlier figure of 100 kWh (let’s assume they get their electricity for cheap) is already a serious amount of energy. It takes 100 kWh of energy to lift a 10.4ton object by about 3.2 km, so we’re obviously in the same ballpark for the maiden flight, and the rest is just drag. For drag, I’ll approximate the plane fuselage as two EVs that I drive. A 737 has a lower drag coefficient than my car, but a plane also has wings, so let’s say that evens out. Out of that 100 kWh, we probably only needed like a half for pure altitude, so we have 50 kWh for drag. An EV can sustain 200 km/h with about 60 kW of power, so let’s say 120 kW for the plane, and the flight was less than half an hour. Also, the plane got to convert all the potential energy back to kinetic energy on descent, so that was “free”.

Again, I believe that the napkin math checks out.

The 100kwh number was based on a rate of electricity that is 1/6th the average cost of electricity in the area they did the flight. Even the absolute cheapest rate in that region is 4x the price I used. The price I quoted was a little less than the cheapest published electrical rate in North America, which isn’t in the United States.

So you can barely make it work if you price electricity at a rate that doesn’t exist in the country they did it, using an amount of power that much, much smaller planes usually require to stay aloft (A Cesnna 172, which will struggle with 4 adults, uses 145hp/115kw for takeoff and climbout at a much lower speed). A plane of comparable size and capacity uses 1500-2000 hp turbine engines. That lines up with their own megawatt plus claim.

Regular rates in the area they operate in get them less than 25kwh. They would have had to negotiated a hell if a discount to have pulled it off. And even so, it would be a deceptive claim. It’s like claiming that you doubled the cost efficiency of a 737 (by getting a sponsorship from Shell).

Sorry, but you’re still weirdly switching from power (kilowatts) to energy (kilowatt hours). The electric plane could easily pull 1.5 megawatts for two minutes (on takeoff) and consume 50 kWh of energy, then spend the next 45 kWh cruising around and descend on the rest. (Or similar numbers, of course.)

I understand that energy and instantaneous power draw aren’t the same. I’m working with the numbers given: over a megawatt of power draw, and the price of energy in kilowatt hours. I’m not saying that they are flying on 100kw. I’m saying that using absurdly optimistic - unrealistic, really - pricing they have alln energy budget of 100kwh to use for the entire flight of 27 min. That means that average power consumption for the entire flight is just over 200kw if they are paying slightly less than the lowest power rate on the continent (which isn’t available in the country they did this test in). We both understand that energy is power * time.

100kwh was an extremely generous amount of energy to allow for $5. Actual, real world, best case scenario industrial pricing in the region they are in would give them 50kwh for $5.

Look at your numbers again with the fantasy pricing. You are saying that they took off with a normal amount of power for a plane that size, then cruised around using an amount of power (45kw) that wouldn’t keep a two person plane 1/20th the weight airborne. Now cut that budget in half.

Even the most efficient planes on earth - single person powered gliders - need about 15-25kw to maintain level flight at much lower speeds. Keep in mind that drag increases with the square of speed, and this plane is traveling significantly faster than any of the low power planes I’m citing. Citing drag from a Tesla is kind of irrelevant because the whole way an airplane works is by creating lift via drag. The Tesla has wheels to hold the weight, so incurs a much lower penalty for weight.

The reason I’m so skeptical is that I have done the engineering calculations to convert my own very small (sub 1k pound gross) plane. It would need about 30kw/h to maintain level flight with just 1 person in it.

Again, I am incredibly impressed with the engineering and what they have accomplished. I just think that one of their marketing figures was pulled out of someone’s ass.

> You are saying that they took off with a normal amount of power for a plane that size, then cruised around using an amount of power (45kw) that wouldn’t keep a two person plane 1/20th the weight airborne.

No, I’m not saying anything about 45 kW, you’re, again mistaking kW for kWh.

> Citing drag from a Tesla is kind of irrelevant because the whole way an airplane works is by creating lift via drag.

That’s already included in the drag coefficient that I quoted, and I know what induced drag is. Airliners are incredibly slippery because of their shape, a Skyhawk (or any other small GA plane) is a brick compared to that.

I’m not arguing about the $5 figure, it might as well be $20, I don’t know where they buy their electricity, but it’s still a very low number compared to anything burning Jet-A or avgas, and it’s absolutely a “low hundreds of kilowatt hours” number.

You were arguing for the 100kwh derived from $5 a few comments up. Now you are arguing for low hundreds of kWh?

So you are now in agreement that $5/100kwh is unrealistic? That was my whole point the entire time.

> A 737 has a lower drag coefficient than my car

Drag coefficient is about the shape and needs to be multiplied by area to get drag. Your car is a lot smaller when viewed from the front than a 737.

And there's no way a plane flying at the speed it does has the same drag losses as two EVs.

That’s why I approximated the fuselage as two EVS (the frontal area) and I only looked up the drag coefficient of a 737 because it’s a well-known narrow-body airliner.

I don’t know what speeds they flew, but AFAIK most maiden flights are very tame. My point stands, low hundreds of kilowatthours of energy seems like the right ballpark.

> That’s why I approximated the fuselage as two EVS (the frontal area)

Have you ever seen a car and a plane? The Tesla model x has a frontal area of 2.6 sqm and a 737 fuselage alone, without any wings is already 11 sqm. With all attachments it’s at least 20 sqm.

And half of the energy for altitude gain and half for drag is way too optimistic.

The flight cost more than $5 in energy.

The electric plane isn’t a 737, the fuselage looks quite slender.

> more likely to be 50 kWh just for the take-off

1.6 MW power [1]. Would be 2 minutes for take-off realistic?

[1] https://youtu.be/nM86DBOqgPM?t=475

Depends on how high you go ;)

The takeoff roll is only a minute or so to lift-off, so it's possible. But also somewhat meaningless, as an airplane can take off for free in high-enough headwinds.

"hybrid system (electric + conventional turbo prop)" there's your answer

so for an hour flight it costs $5?

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