How much electricity is needed to power Morpho in 86?
Morpho is a wunderwaffen used by the Legion in the light novel series 86. According to the novel, it is a railgun powered by solar energy. How much electricity will it need then? And how much area of solar panels will that be?
Assuming 20% of energy efficiency for the railgun [1], 10 tonnes of mass delivered per projectile, and an initial speed of 8000 m/s, we arrive at an electricity demand of 1.6 * 10¹² Joule, or 444 MWh. The maximum number of projectiles Morpho can launch is 100 per 15 hours, or 160 per day. So the maximum electricity required per day to operate Morpho is 71 GWh (this is the electricity Germany’s public grid consumed in 1.5 hours in 2020 on average [2]).
How large will the area be required to power such electricity demand with solar panels? It depends, of course, on the solar radiation condition at the location and also the type of solar panel and energy storage technology equipped in Edelfalters.
I will ignore the energy storage technology in Edelfalters to simplify the discussion and assume (as a first order approximation) the electricity produced by them can be completely transferred to Morpho. Needless to say, to stay afloat in the air Edelfalters also will consume some energy produced by themselves, which I will also ignore here. To justify this, a very light photovoltaic material and a storage material with very high energy density will be required. To my knowledge the latter will be more problematic (which is why airplanes are the hardest to electrify in the transportation sector).
I will assume that the solar radiation condition of the location where Morpho operates resembles that of central Europe. The full load hours of photovoltaic in Germany is 980 hours in 2020 [3], which translates to 2.68 hours per day on average (note that strong seasonal variation exists and will be something the legion needs to consider; for simplicity of our calculation we will omit this aspect of discussion here). Assuming full load hours remain the same even if photoelectric efficiency improves, this leads us to the conclusion that at least 27 GW of solar panels will be needed to deploy for the operation of Morpho when the maximum amount of projectiles is to be delivered to the enemy. This is nearly half of the current photovoltaic fleet in Germany, or about 1/10 of the global PV capacity addition per year in the next decade.
If we assume the legion has adopted advanced PV technologies, then a photoelectric efficiency of 30% can be a reference point since it is what some researchers expected to be commercially available in the next decade [4]. In that case, it will require around 88 km² of area of Edelfalters for the operation of Morpho (using 1000 W/m² as the reference ideal solar radiation condition). This is about 1/10 the land area of Kreutzbeck.
Higher photoelectric efficiency up to 47% has been proven in the lab [4] but the order of magnitude of area required remains the same even so. The legion also has the ability to manipulate the weather so the solar radiation condition might be better, and unlike fixed photovoltaic systems Edelfalters should be able to maximize their power output by adjusting their tilt angle at the sun (without the risk of shading each other, unlike tracking systems on the ground), but again the order of magnitude of area required probably will remain the same.
[1] Lumped Parameter Modeling of the Ideal Railgun: Examining Maximum Electromechanical Energy Conversion Efficiency, Victor Sung et al., 2008,
http://ilin.asee.org/Conference2008/SESSIONS/Lumped%20Parameter%20Modeling%20of%20the%20Ideal%20Railgun.pdf
[2] See https://energy-charts.info/charts/energy_pie/chart.htm?l=de&c=DE&year=2020&interval=year
[3] See https://www.bdew.de/service/daten-und-grafiken/jahresvolllaststunden/
[4] Solar photovoltaics is ready to power a sustainable future, Marta Victoria et al., 2021.
