IEEE - Aerospace and Electronic Systems - September 2019 - 15

Doyle and Peck

WATER ISRU IMPACT
MODEL
The ISRU of water for propulsion will have a dramatic
impact on mission planning. The nature of the rocket
equation is such that the available DV is a function of
thruster exhaust velocity ve , spacecraft propellant mass
mp , and the spacecraft dry mass m0 :


m0 þ mp
DV ¼ ve ln
:
m0

(1)

In terms of the spacecraft propellant required
 DV

mp ¼ m0 e ve À 1 :

(2)

This well-known result indicates that the propellant
required to achieve a given DV depends exponentially on
that DV and linearly on the payload mass to be delivered.
Thus, doubling the required DV-such as for a round
trip-more than doubles the propellant required. Therefore, if a spacecraft is able to gather propellant at its destination for the return to Earth, substantial mass savings can
be made.
Additional mass savings are possible if the water
onboard serves multiple purposes. For example, in our
CisLunar Explorers spacecraft, the presence of water for
spin-slosh damping eliminates the need to carry multiple
RCS thrusters or other attitude control devices. On a
crewed mission, gathering water can replenish human consumables as well. Even assuming a very efficient water
reclaiming system where only 0.5 L/day is depleted per
person, for a trip to Mars or Deimos with a 360 day round
trip time in space and 500 day time at the destination, a
mission with a crew of 6 can save over 3 metric tons of
water from the supply mass launched by producing the
necessary water for the primary mission in situ.
If the mission is designed with a free-return trajectory
prior to Mars orbit insertion, it may not be desirable to
rely on ISRU water for crew supplies on the return trip.
This is because if the mission needs to abort for a return to
Earth, the ISRU water would not be able to be collected.
This is unlike the water used for the surface mission,
which could be produced in advance as a precondition for
the crew departure from Earth and would not be needed in
the event of a free-return abort. Water for use as a propellant for the return trip could still be produced in situ,
because it would only be needed in the event of a successful insertion.
Whether ISRU is used or not, it is possible to reduce
the mass requirements in another way by taking advantage
of the versatility of water. Because the same material will
serve multiple purposes, we can reduce the required mass
SEPTEMBER 2019

margin as compared to having separate supplies for propulsion, oxygen production, and crew consumption. In a
system with separate contingency and margin for propellant, crew water, and oxygen supplies, each requires its
own independent bookkeeping. For example, if during the
course of the mission, not all of the propellant reserves are
needed, the remainder cannot be redirected for other purposes, such as to refill crew oxygen in the event of a leak.
In contrast, when the same resource serves multiple purposes, the same margin of reserves can guard against multiple supply overruns. Returning to the propellant/oxygen
example, if an oxygen leak occurs but the propellant margins have not been fully drained, the remainder of propellant reserves can be repurposed to replenish the oxygen.
The probability that all subsystems drawing on a collective resource will use a given percentage of their margins
is less than the probability that any one subsystem will.
For independent margins, we have
mts ¼ mp þ mw þ mo

(3)

where mts is the total mass of separate reserves required for
each of the several independent uses of water onboard: propellant ðmp Þ, water for the crew ðmw Þ, and water as feedstock for oxygen production ðmo Þ. In the general form,
mts ¼

n
X

mi

(4)

i¼1

where mi is the margin for each of the n individual supplies on the spacecraft.
If these supplies all draw from a common source, we
have
mtc ¼

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
mp 2 þ mw 2 þ mo 2

(5)

where mtc is the total mass of combined reserves required.
In the general form
mtc ¼

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
Xn
mi 2 :
i¼1

(6)

Because mtc < mts except for trivial cases where the two are
equal, this approach always results in a mass savings:
Dmt ¼ mts À mtc :

(7)

An architecture can then reduce the propellant mass
required for the mission by accounting for the reduced
mass of supply margins that must be carried. By substituting (7) into (2), the propellant mass savings and then the
total combined mass savings Dm are
 DV

Dmp ¼ Dmt e ve À 1

(8)
DV

Dm ¼ Dmt þ Dmp ¼ Dmt e ve :

IEEE A&E SYSTEMS MAGAZINE

(9)
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