CALC-099

How much storage an eclipse costs, and how much of the year it costs

Calculation · Cited by CLM-0895

What this is

This is the project's own arithmetic, published in full so it can be checked rather than taken on trust. It is not a source. Every input it uses is cited to a record, and the conclusion it reaches only carries as far as those inputs do.

Feeds CLM-0895. Answers QST-004. Basis: GWh of storage, and hours per year.

Why it was needed. The register holds exactly one on-board storage figure, CLM-0211's 12.186 MWh, and that record is explicit that it is for klystron cathode heaters during occultation and not for bulk power. Nothing says what an SPS does about eclipse otherwise, and nothing sizes the gap.

Inputs. Physical constants, not register claims - no number here is taken from any source's assertion.

Quantity	Value
Earth equatorial radius	6,378.137 km
Geostationary radius	42,164 km
Satellite's rate relative to the Sun	15 degrees per hour (360 degrees per 24 h solar day)
Output to be sustained	2 GW, the scale of a single satellite in the register

Working.

Earth angular radius from GEO   asin(6378.137 / 42164)      = 8.7005 degrees
crossing, Sun as a point        2 x 8.7005 / 15            = 1.1601 h = 69.6 min
storage for 2 GW through it     2e9 W x 1.1601 h           = 2.3201 GWh
against CLM-0211's 12.186 MWh                                = 190.4x
annual, ROUGH                   2 seasons x 44 d x 34.8 min = 51.0 h = 0.582 per cent

Result. About 70 minutes at worst, about 2.3 GWh to ride through it, and about 0.58 per cent of the year.

What is approximate and why it is left that way. 69.6 minutes treats the Sun as a point (CALC-140): it ignores the penumbra and the Sun's angular size, which is why published figures give about 72 minutes. The 44-day season and the half-maximum average are this record's own roughs. THE 0.58 PER CENT IS AN ORDER-OF-MAGNITUDE FIGURE AND IS NOT A CAPACITY-FACTOR DERIVATION.

What it does not say. No held source states that an SPS is expected to sustain output through eclipse at all. This sizes the requirement if it were; it does not establish that anyone has adopted it.

Cite this

energyaperture.com/calc/calc-099

CALC-099. The working above, not a source document.