This is an excellent question. For narrow body aircraft we've studied, they require high propulsive power during the takeoff and climb phases, and a fraction of the peak propulsive power during the cruise phase. One aircraft we looked at required 30-35MW during takeoff and ~10MW during cruise.

So, thrust power and system level power density (kW/kg) are critical during takeoff/climb and cruise efficiency is important for minimizing energy consumption.

Like Audunw mentions, its very application dependent as well. It all boils down to the propulsion system mass fraction. For lower PSMF, efficiency matters more once you are above a certain power density. For higher PSMF, power density matters more. There is an optimal balance of efficiency vs. specific power for every aircraft. We can "tune" our technology relatively easily depending on what that balance is to maximize range.

I'll let my cofounder Max chime in since he does a lot of vehicle-level architecture and optimization. He's been doing some studies for rotorcraft and planes to look at how specific power and efficiency impact range/endurance so I'm sure he can expand on my answer a bit.

The other part is that there's a straightforward trade-off between specific power and efficiency. Two motors on the same shaft can each be run at half the current, and since power loss due to resistance is: P=I^2*R, your losses due to resistance would halve. (There are, of course, other loss mechanisms.)

So it's good to start out with a really high specific power because you can often trade that back for efficiency.

But that big max/cruise delta disappears as soon as you ditch the wings and go 'copter, which seem to dominate all use cases where electric is anywhere close to viable.

Where motors excelling in W/g could absolutely shine is the still empty area of hybrid planes that downsize their combustive propulsion to cruise requirements and carry batteries only for those short periods of peak power demand.

Would you use a generator or a directly connected ICE?

Certainly not a generator, at least not unless there was some miracle fuel cell fuel. The "electric boost" would need to be completely idle most of the flight (which creates some interesting challenges regarding conversion of electric torque to air movement).

This is a fascinating analysis of hybrid electric planes

https://link.springer.com/article/10.1007/s13272-017-0272-1

I think the idea is worth exploring. Esp with superconductors an electric powertrain could have lower losses than mechanical.

Oh, that's sobering. All the referenced modeling seems to start with hypothetical batteries many times lighter than we have, and even then they only give minor emissions reduction hardly beyond what we are used to from e.g. succeeding generations of 737. And only under the assumption that the electricity used is completely emission-free.

And why even bother modeling constant power split? You might just as well linearly interpolate between conventional and an all-electric design and call it a day. Everything interesting about hybrid propulsion happens when the ratio is varied with power demand.

What's interesting is how much mass they account on the electric side in addition to the battery. This kind of validates H3X.

> One aircraft we looked at required 30-35MW during takeoff and ~10MW during cruise.

Do you envision some airframes to include assisted take-off technology? (JATO and the like, even catapults)

A simpler alternative could be to just have an electrified runway. The plane draws power from power rails embedded in a runway, or something like that. So, it doesn't switch to batteries until it's in the air.

You could even have a long cable that hangs behind the plane and keeps an electrical connection until you're a few hundred feet up. (I'm picturing it connected to something like a slot-car that travels in an electrified track that could extend a mile or so past the end of the runway.) When you get to the end of the track, the cable (which could probably belong to the airport rather than be part of the plane) releases from the plane.

(This would help marginally with range, but doesn't really help with power density, unless you're limited by the voltage and current available from the batteries rather than the power of the motor.)

I keep wondering if there could be a way to re-charge in flight so that battery range/weight wasn't such an issue, but that's a hard problem.

As a rule, whenever one feels tempted to say "just do <x>", it's time to wait and think. Because, if it's "just" about doing something, why isn't it being done already?

In this case: let's say it's feasible to retrofit runways to use this system (it probably isn't) and look at a few issues.

For instance: "the cable releases from the plane". No system is fail safe. What happens if the cable does NOT release from the plane? What happens if it snags during the takeoff roll? What happens when there's wind gusts?

If there's no cable, and it's "just" a rail, presumably the plane is taking off aligned to the rail. What happens if the alignment is off? Or is the 'rail' supposed to keep the plane straight? If so, what about the force distribution on the plane's landing gears or (if a specialized system is installed), in the fuselage?

So say you have such a system and everything has been retrofit. What happens if there's an issue with the land-based generator during the take off roll? Would the aircraft still have enough power to perform the take-off from the onboard batteries? If so, this is just about range and the system would never be installed, as aircraft would be certified with the lower range instead. If not, it's a disaster in the making.

> I keep wondering if there could be a way to re-charge in flight so that battery range/weight wasn't such an issue, but that's a hard problem.

There isn't unless you can transfer power from elsewhere. In-flight "refueling" from another plane is out of the question. You are essentially left with beamed power from ground stations (or orbital if we are really forward thinking). That might theoretically be feasible (planes don't have a very large surface area so the power delivery system would probably look like a weapon and mostly behave like one). Engineering it is another matter, not to mention practicality.

We’ve been launching airplanes with steam catapults for many decades, albeit in an environment where we’re willing to take more risks than to go see Grandma, but many of the catapult concerns are areas where we have decades of experience and hundreds of thousands of successful cat shots.

But the catapult isn't for saving on energy that needs to be carried on the aircraft. It's simply that you can't build engines and propulsion systems on a plane with the desired takeoff weight when you have as short a runway as you do on an aircraft carrier

Regardless of the underlying driver to implement it, we've solved some of the concerns that GP mentions for ground-assist launches, so there is a body of experience/work we can easily build upon.

It is the same thing. The high power for takeoff shortens the runway from 7km to 400m.

We could do the same thing with cars and equip them with a super aerodynamic body and a 7kw engine, it could do 80kph.

> As a rule, whenever one feels tempted to say "just do <x>", it's time to wait and think. Because, if it's "just" about doing something, why isn't it being done already?

In this case, the simplest counter to that question is just that electric aircraft barely even exist at this stage, due to battery weight issues.

That isn't to say this is a great idea (a small boost in range probably isn't worth the additional complexity), but we just don't know at this point what electric aircraft will be like down the road when they're more common and people have figured out what works and what doesn't.

> For instance: "the cable releases from the plane". No system is fail safe. What happens if the cable does NOT release from the plane? What happens if it snags during the takeoff roll? What happens when there's wind gusts?

We already have this figured out for gliders and tow planes, and that's a cable designed to withstand the full thrust of the puller plane without breaking. A power cable can be designed to disconnect if it's yanked too hard. It can also be made to just plain break if it snags.

> So say you have such a system and everything has been retrofit. What happens if there's an issue with the land-based generator during the take off roll? Would the aircraft still have enough power to perform the take-off from the onboard batteries? If so, this is just about range and the system would never be installed, as aircraft would be certified with the lower range instead. If not, it's a disaster in the making.

I'm assuming the plane has batteries and intends to go somewhere. If it has enough batteries to actually go anywhere useful, it should have more than enough batteries to circle around and land immediately if there's a problem with the power cable. This is no problem. Gas planes generally should be prepared to emergency-land at any point during takeoff and ascent (in a field if necessary) in case of complete engine failure, and this would just be more of an "oh, I guess we have a couple minutes less range than I thought I was going to have, and I'll have to land sooner" sort of situation.

> There isn't unless you can transfer power from elsewhere. In-flight "refueling" from another plane is out of the question.

It's not out-of-the-question in the sense that we couldn't do it if we wanted to, it's just incredibly inconvenient and probably not a problem that's worth trying to solve with current technology because the result wouldn't be useful. In-air refueling currently exists with gas planes, and it could be done with electric aircraft with a power cord instead of a fuel tube. It wouldn't be energy efficient and the tanker would probably have to be gas-powered, so it doesn't make sense environmentally. It would also take a very long time to recharge, given current battery technology. You'd be better off just flying a gas plane that has ten times the range or so to begin with.

Alternatively, you could swap batteries mid-air, but how would that even work?

Like I said, transferring energy to in-flight aircraft would be best, but I'm not aware of a way to do it that would be practical (i.e. doesn't involve technology we don't have, or building megastructures across the landscape, or wasting energy in other ways). Maybe we'll get the energy density of batteries up high enough that it doesn't matter before we figure out high-power long-distance wireless energy transfer. Or maybe we'll be using liquid fuel in planes indefinitely. For right now I think figuring out a sustainable way to make liquid fuel from electricity is probably the easiest route, if we're just trying to get off of fossil fuels for aviation in the short term.

> You could even have a long cable that hangs behind the plane and keeps an electrical connection until you're a few hundred feet up.

I can assure you this will never ever happen. It’s wildly impractical, improbable, and sounds extremely unsafe. Sure, it’s theoretically possible, but that’s about it.

The NFPA is not going to add a code section in the NEC for hundreds of feet long live electrical conductors being pulled into the air by a plane and then disconnected in mid-air, and the FAA isn’t going to allow it either.

Tow planes and gliders routinely fly with a disconnecting cable between two aircraft, and that seems at least as impractical and unsafe (or it would if you were proposing it as a new idea). Though maybe that's the sort of thing that's "grandfathered in" from earlier, more permissive days of experimental aviation.

I think the strongest argument against using a power cable during takeoff is just that it's not worth the effort and complexity just for a slight increase in range, except in rare situations or planes that normally make very short flights and don't want to be weighed down with extra batteries (like the aforementioned glider tow planes).

> Tow planes and gliders routinely fly with a disconnecting cable between two aircraft

This is true. However, the cable is not carrying KW or megawatts of electricity, it's just there for tension, to transfer forces from something else to get the glider airborne.

Technically, you don't even need the tow plane, some places perform winch launches (or car launches!) exclusively. This is very common where general aviation is not as common.

Should the cable not detach (extremely rare), it can be cut at the other end. Cutting a live cable should be much more interesting. Other issues, the glider can release it. The glider will most likely be fine, even if the flight is now cut short.

Gliders are very light and still the cable weights a lot. That's probably the limit of what's practical. There are some gliders with electric motors, they don't need all that much power, by definition. Some can even self-launch.

> Tow planes and gliders routinely fly with a disconnecting cable between two aircraft, and that seems at least as impractical and unsafe (or it would if you were proposing it as a new idea). Though maybe that's the sort of thing that's "grandfathered in" from earlier, more permissive days of experimental aviation.

A tow cable does not have live electrical conductors in it.

They allowed 737 MAX 8, so maybe, who knows?

Or for an even simpler alternative, just get towed into the air as motorgliders are (the ones with sustaining motors but not auto-takeoff).

I wonder if this tech might be better suited to self-launching motorgliders than GA.

It certainly seems like something that will be towed.

None of the things you mention would have a significant effect on range, and all could be replaced with a nominal increase in runway length. If an aircraft cannot produce sufficient power to take off, it cannot produce sufficient power to climb.... And to be efficient, it must climb as high as possible, ideally to 30k feet or more. You are talking about the first 30 seconds... But it needs to keep it up for 30 minutes.

Take off assists are for ultradshort runways.

Or how about a large battery pack that drops back to the ground after take off, eliminating it’s weight from the airframe?

I think most forms of assisted takeoff technology would reduce electrical power requirements for takeoff, but not put much of a dent in the climb power (unless you can catapult/ JATO all the way up to cruising altitude, which would be challenging). Since climb power is still significantly higher than cruise power, and is effectively thermal steady state for these components (10-20min), it would still drive the propulsion system sizing.

You still need enough reserve power at the end of a flight to do a rejected landing/go around, or you won't get certified. If you are relying on some kind of catapult, rail gun, or rocket assist to take off, not sure how that happens.

An early rejected landing still requires less power than a static takeoff, so you could get by with a mix of craft and assistive power.

You could have another aircraft tow you, like gliders sometimes do. Doesn't seem terribly practical though.

That could be a great use case for lighter/smaller electric motors, since a tow plane could take off, assist with takeoff, turn around and land, charge, and repeat. The tow plane wouldn't need as large of a battery pack, but having good power to weight for towing other plants to whatever altitude is very important.

I feel like this is something that drones/100% automated ops can really help with.

Power satellites (basically giant solar arrays transmitting power) are also interesting (https://www.geekwire.com/2020/space-force-will-test-solar-po...).

We could have these complex automated systems to make electric aircraft much more viable, which is cool in theory.

Power satellites are interesting. But here's the thing:

For most aircraft (except some gliders), covering them fully with solar panels is not even close to the power they need in cruise, correct?

So a power satellite would have to generate _at least_ the same W/m2 as the sun (around 1.4kw/m2( just to break even with a solar panel, but most likely much, much more, by orders of magnitude.

For a 747, I've seen figures from 90 MW to almost 200MW. If the receivers were at the wings only, that would be almost 6MW per square meter if you take the lower figure.

For a target as small as a plane, this would look like an energy weapon from science fiction.

Even something like this would not cut it:

https://en.wikipedia.org/wiki/MIRACL

For general aircraft the numbers look better. Then again, they are much smaller.

I can't wait for power satellites to be deployed, but they will mostly be servicing ground stations.

Not exactly what Talyn Air is doing, but along the same lines- separating out the "lift/climb" vehicle from the "cruise" vehicle. It can actually be a very compelling design!

Keep in mind that an electric motor isn’t limited by the amount of oxygen in the air. As a result it can fly significantly higher where there is far less air resistance.

Since air density is proportional to the square of the elevation this can lead to significant efficiency gains. Believe it or not, partly as a result of this, the SR-71 had it’s best mpg at peak speeds.

A simple physics-based plane model (like the one we made to understand vehicle-level impact of our technology development) dictates that the range-optimal cruise speed is proportional to 1/sqrt(air density), so it makes sense that the blackbird was more efficient at high speed when at high altitudes (admittedly, this simple model is subsonic, and there are a lot of other factors for supersonic flight).

Since having lower air density also means you need a higher lift coefficient (angle of attack) to produce the required lift, and then you have more lift-induced drag (which goes with the square of the lift coefficient). I think air density more or less washes out when it comes to its impact on range. That being said, you cover the full vehicle range at a higher velocity at higher altitudes, so it certainly seems like there would be significant benefit from a travel-time perspective.

All that being said, there are significant high voltage insulation challenges at higher altitudes, which is something we are working on.

That's really not too accurate. The most efficient aircraft are sailplanes (the high end ones usually have a motor, BTW), and they operate at lower altitudes typically. Lift-to-drag of 70 has been achieved. The SR-71's L/D is probably classified still, but probably around 7 or so.

The issue is a certain aircraft has an optimum cruise altitude. If you try to fly fast at low altitude, it'll be horrendously inefficient. If you try to fly higher, you'll often be beyond the maximum lift coefficient so you'll be less efficient or you'll stall.

To first order, efficiency is independent of cruise velocity.

The range for an electric aircraft (this is basic physics) is: Range = (battery specific energy) * efficiency * (L/D) * (mass_battery/mass_total)/gravity.

Altitude and air density and velocity do not directly figure into the calculation as you pick your cruise altitude to maximize your (L/D). And maximum L/D depends somewhat loosely on Reynolds number (which, granted, does depend on speed) and especially Mach Number. If you can keep totally subsonic flow (i.e. usually up to about Mach 0.5), your maximum (L/D) doesn't directly depend on speed.

Sailplanes increase their speed (at optimal glide ratio) by putting on ballast. You can achieve the same effect by cruising at higher altitudes.*

We are definitely saying the same thing in very different ways.

Just using the drag polar approach and neglecting second-order effects (assume negligible dependence on Re, sufficiently subsonic so negligible impact of M, and linear lift coefficient region aka no stall), we get the following (I'm skipping a lot of intermediary steps):

Cd = Cd0 + k*Cl^2 -> Cd0 is the parasitic drag coefficient -> k is the lift-induced drag coefficient -> Cd is the overall drag coefficient

Range is maximized when Cd0 = k*Cl^2 (parasitic drag = lift-induced drag) -> Cl is a function of speed: since the required lift is constant, more speed = less Cl required = less lift-induced drag -> maximum L/D is achieved at this range-optimal speed

This speed can be calculated exactly from the total weight (W), air density (rho), lifting area (S), and drag coefficients:

range-optimal speed = sqrt((2*W/(rho*S))*sqrt(k/Cd0))

As long as you always operate at this range-optimal speed (aka speed for maximum L/D) which is a function of air density (and therefore altitude), the equation for range reduces significantly:

R = endurance*velocity, where endurance = battery energy / drag power, and we know the equation for drag power...

Simplifies to:

R = E*eta/(2*sqrt(Cd0*k)*W) -> R is range -> E is battery energy -> eta is total system efficiency

Dimensionally, this equation is of course the same as yours, with an energy being divided by a force to get a distance. The key point I am trying to make is that if you just look at that equation with no context, speed and air density are not present anywhere. But what is hidden in the assumptions is that you are assuming that you are operating at the maximum L/D speed given the air density at any particular altitude. Going back to my other comment, range at the range-optimal speed does not depend on air density or velocity directly, but lower air density at higher altitudes will result in a higher range-optimal speed, and hence less travel time for a given range.

Oh, yes, precisely. That’s one thing about air travel that people don’t really understand. They think fast = inefficient, but as long as you’re supersonic, speed is roughly independent of efficiency. You can have you cake and eat it, too!

This is not really true for any other transportation method. Cars and buses and boats and even trains have an efficient vs speed trade off especially at higher speeds.

And there is an efficiency advantage of speed in that you can get by with just a cramped seat because your trip time is short, a few hours. A similar trip in a conventional train, cruise ship, zeppelin, or sailboat may require bringing along basically a small apartment (or “sleeper car”) which is much heavier and can destroy the efficiency advantage you might have otherwise had. And the same vehicle can be used many more times for the same route if its speed is much greater, which (combined with the lower vehicle weight per person) reduces the effective embodied emissions of the vehicle per passenger mile significantly.

> there are significant high voltage insulation challenges at higher altitudes

What are these challenges? How does having a near vacuum cause trouble with ~1kV potentials?

The phenomenon is due to Paschen's law (there is a good wikipedia article on it). The breakdown potential of a gas is minimized at some pressure, and in the case of air, that pressure is < 1 atm, and corresponds to a specific altitude.

I can't go into much detail, but we are working on addressing this in a couple different ways in our insulation system design.

Unless I am missing something obvious, lift-induced drag is largely independent of altitude. However, parasitic drag is significantly reduced by lower air pressure. Thus the advantage from high altitude flight.

Less dense air -> higher angle of attack required to produce required lift -> true lift vector is more offset from vertical -> horizontal component of lift is actually producing drag

Like I said in the other comment, if the plane is operating at the range-optimal speed, I think the air density does not impact the range capability (it cancels out) but it does increase the range-optimal speed, allowing for faster travel.

Drag required to make lift is only a subset of total drag.

A car for example doesn’t need to produce lift, but it still displaces air which causes drag. The same is true of an aircrafts fuselage, which is generally not used to generate lift but still increases total drag. https://en.wikipedia.org/wiki/Parasitic_drag

Also, an aircraft is generally designed so that at cruse speed and altitude the wing incidence angle provides appropriate lift. https://en.wikipedia.org/wiki/Angle_of_incidence_(aerodynami.... Which means at optimal curse distance the cabin would almost perfectly level independent of optimal cruse speed or altitude.

Yes, the range-optimal speed is where the parasitic drag is equal to the lift-induced drag.

If you go through the analysis, the air density drops out of the range equation if you assume are operating at the range-optimal speed (which is higher at lower air densities).

> the range-optimal speed is where the parasitic drag is equal to the lift-induced drag

Not quite true -- range-optimal speed is where the sum of those terms is minimal. With some assumptions, this is where the derivative is 0, dDrag/dv = 0, and since derivative is linear, this means: the range-optimal speed is where the (infinitesimal) increase of parasitic drag (with speed) is equal to the decrease of lift-induced drag (in other words, opposite derivatives).

Using the simple drag polar approach,

D = A*v^2 + B/v^2 (D is total drag, first term is parasitic drag, second term is lift-induced drag)

dD/dv = 0 where v = (B/A)^(1/4)

Plug in v = (B/A)^(1/4)

D = sqrt(AB) + sqrt(AB), aka dD/dv = 0 exactly when parasitic drag is equal to the lift-induced drag

I stand happily corrected :)

That’s only relevant up until you approach the speed of sound. Passenger aircraft are designed to stay subsonic for a host of very good reasons.

Definitely, for sure. Like I said in the other thread, supersonic is a whole other thing, and I don't think anyone is trying to electrify anything supersonic any time soon :)

Propeller efficiency decreases at high altitude though.

> Given that the batteries weigh a lot more than the motors, I would have thought that motor efficiency (which scales battery size) was much more important than motor weight.

I guess that depends on what kind of airplane you are making. If you're just making the same kind of airplanes we've been making with ICE, but with electric motors and batteries instead, you're probably right.

But if you're making an electric airplane from scratch, there's a lot you can do if you have a really light motor, which can drastically reduce drag.

Look at Maxwell X-57 for instance: https://www.youtube.com/watch?v=-HvZ7c0F9ik

If you're going to have lots of motors on the wings, they better be as light as possible.

I'm guessing the increased efficiency from a design like that can easily be as important as the efficiency of the motor itself.

These are all great points- everything is very interconnected in these vehicles, and there is a lot of potential upside in high power density distributed propulsion (like on the Maxwell).

In characterizing the vehicle-level benefit of power density, it is definitely important to consider the X kg of structure required to support 1 kg of motor/inverter/gearbox/etc.

Excellent points about associated structures! However for the motors, isn't it the case that the support structure design is dominated by the thrust loads, which should vastly exceed the motor mass? For sure, there is some non-thrust-related structure to react the motor's mass, e.g., inertia from a harsh landing, but how much extra is it? This is much more the case with power/mass optimized motors like yours.

Consider an ideal case - you achieve the same power with negligible mass, say 1kg. How much structure in my aircraft using your motor could I really eliminate vs your current model?

And the real case, switching from a competitor's similar-power motor to yours, how much additional structure weight can I save by switching, beyond the obvious great advantage of your motor's weight savings?

(Obviously, these answers massively depend on other factors, but... )

Yeah, there are a lot of factors that play into this. A couple things come to mind:

1) Considering megawatt-class machines are necessary for many future applications, the mass of the motor+inverter+gearbox (especially using best current technology) definitely adds up.

2) With a very distributed propulsion system, motors that end up near the wing tips have a big moment arm compared to the ones typically tucked under the wing root

Excellent point about the moment arm and control issues! I'm definitely all about maximizing power-weight and strength-weight ratios...

I am wondering about the ratios you are achieving, and about the issues of scale.

Do things get better as you scale up? I notice you mentioning the state-of-the-art at 3-4 kW/kg, and you shooting for 12 kW/kg.

This is even substantially better than small scal T-motor UAV motors at around 7w/g [1]. The chart shows them peaking at 3181W and weighing 453g.

So, I'm wondering what scale factors may be working in your favor at your scale vs the single-digit kW scale.

Also, any plans to scale slightly smaller (I'm involved in such a project)?

[1] https://uav-en.tmotor.com/html/2021/Antigravity_0119/668.htm...

From an active mass (electromagnetic parts, power switches, etc) perspective, our specific power is relatively consistent from 100 kW up to 1 MW. TBD on lower or higher than that.

The biggest difference is the total mass specific power (including housing, bearings, etc) usually gets worse at much lower powers (1s-10s kW), because these components become a more significant fraction of the total mass.

The 12 kW/kg number is continuous output power / total system mass (active + inactive, including motor, inverter, gearbox, housing, bearings, etc). If you isolate just the motor to compare, it is much higher than 12 :)

We do have plans to develop a ~100 kW (maybe a bit smaller) unit in the future, but when is TBD.

> - A 1% increase in motor efficiency could eliminate 0.1 kg of batteries, which would let you double the weight of the motor.

Wouldn't it be much simpler to state that a 1% increase in motor efficiency could eliminate 1% of battery weight? (trying to get the theory clear)

---

Obs: This is only approx. valid if efficiency is already high. If efficiency was very low, e.g. 2%, then 1% more (going to 3%) would enable eliminating 1/2 - 1/3 = 1/6 = 16.7% of the batteries.

An equation to describe this situation, assuming constant energy need, is Eb = Em / n, where Eb is energy provided by batteries, Em the work of the motor, and n efficiency.

Also, the energy need should indeed decrease with decreasing battery weight, amplifying this effect even more, but at high efficiency the correction isn't too large. Equations omitted because there are too many assumptions (acceptable battery mass fractions, energy usage vs weight, ...).

(A starting model would be: Maircraft = Mbatteries + Mconst; Mb = aEb; Em ~ Ma^p ; Em = ( k(aEb+Mc) ) ^ 1/p; Is p~=1?; Eb = kMc/(n-a*k); )

So in principle an 1% increase in motor efficiency gives even more than 1% of less battery weight!

A complication however is that batteries have power constraints as well as energy constraints (how power constrained . If the peak power only has to be sustained over a very small period, this would allow complementing energy-dense sources (batteries) with power-dense sources (capacitors). However, some power-dense sources do not last long enough to cover the peak-power intervals, so they would not fit.

If the following diagram is to be trusted:

https://commons.wikimedia.org/wiki/File:Power_vs_energy_dens...

Then for my guess of 5 minute take-off constant peak power time lithium-ion still has the greatest power density, which means other sources should not be combined.

You can use variations in chemistry among Li-ion cells to achieve this tradeoff, but those limitations provide a slight negative correction (greater efficiency giving less mass gain).

Those effects would need to be combined.

Anyway, there is a lot of interesting performance and Operations Research (Linear programming) optimization here.