mliben
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.
In the aircraft world, Magnix has been doing some really awesome work. Their motors + inverters are about 4 kW/kg continuous. Our multiple areas of technology development should put us >12 kW/kg, which would be a 3x improvement. We are excited to build and iterate on a rapid pace to get there as soon as possible (hardware is, of course, hard :)
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
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
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.
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 characteristic current of the machine is roughly the same as the maximum inverter current, so at maximum power the power factor is between 0.7-0.8. This also means the flux weakening capability (CPSR) of the machine is very good, although that isn't particularly useful in these propeller-load applications. In many applications the machine would spend most of the time at ~0.6pu speed and ~0.5pu torque (cruise), where the power factor is > 0.9.
I can't discuss the specific rotor design, but I will say it is a very high flux machine.
The inverter and motor are on opposite sides of the coolant, and so heat from each flows into the coolant. The mechanism by which the motor would heat the power electronics is via increasing the coolant temperature, which to some extent is mitigated by maintaining an appropriate flow rate given the loading conditions.
I can't go into much detail, but we are working on addressing this in a couple different ways in our insulation system design.
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.
That being said, typically the effective thermal conductivity of the winding (perpendicular to the axis of current flow) is limited by the insulation (strand and/or turn) and the encapsulation/varnish. As a result, changing the thermal conductivity of the conductors themselves will have much less impact on the total thermal resistance (from winding hotspot to coolant) than changing the insulation and encapsulant thermal conductivities.
At these very high power densities, the thermal RC time constants inside the motor are very short (small motor = small thermal capacity, low thermal resistance by design). Therefore, even for a "short" 10 minute takeoff, most of the motor will have already hit thermal steady state. As such, the motor needs to be able to run at takeoff power continuously. There has been a lot of fun discussion elsewhere in this thread about how to tackle that aspect of the problem (given that takeoff power is typically 3x cruise power).
I will say that we are working on developing a high thermal conductivity (> 1 W/m-K) and high temperature (> 300 C) insulation system.
I can't be too specific, but you can probably get an idea of the rotor size from the preliminary datasheet (and/or CAD model) that you can download from our website. We have dimensions of the outside of the unit. Remember that the inverter is in there as well!
Our technology demonstrator is a 250 kW machine, but we have plans to scale up to the megawatt class in the next few years. Like Jason mentioned elsewhere in the thread, tens of megawatts are required for a narrow-body jet like the 737. There is significant aerodynamic benefit from having multiple distributed propellers/fans as opposed to two-four big ones, and likely this is the path forward for electrification of these larger planes, i.e. a lot more than 2-4 units, with single-digit megawatt capability per unit.
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.
We want to start simple with cooling, hence the water/glycol. There certainly could be some opportunity to use something different (maybe with certain fuel cells and liquid hydrogen already onboard?). Regardless, the thermal resistance from hotspot to coolant is dominated by conduction resistances inside the motor, and is less a function of the convection resistance from the housing to the coolant.
We will be sending out a newsletter occasionally, there should be a link at the bottom of our website.
Thanks for the questions!
From there, we identify the best high-level design traits and begin some optimization work to get most of the way to a fully-optimized solution (this is more FEA-based, both mechanical, magnetic, and thermal). This gets us climbing up the right "mountain" on the continent.
At this point, we put the pens down and start building something, because we will learn more building a prototype and iterating than we will spending too much time in simulation-land.
In parallel, we have been putting together a workflow to co-optimize the design across mechanical, magnetic and thermal simultaneously. Thus far the jump across each discipline has been a bit more on the manual side, but automatic co-optimization is a long term project, and would get us to the "peak" of the mountain.
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.
We have received significant interest for high performance ground and marine applications, which we plan to leverage in the short-term as a way of getting lots of in-situ run-time for our technology without the hurdles of certification. We will be pursuing the long road to certification in parallel.