Solar-powered space flight
3b. Power required to reach earth orbit
ignoring atmospheric drag: Assuming that we launch vertically upwards, but with
variable exhaust velocity
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3.7 However, the
required power per unit final mass falls considerably if 
can
vary, as does the maximum acceleration. The optimal choice of with
this sort of trajectory is to maximise 
which occurs when 
. Flight metrics for
various ratios of 
using this approach
are set out in Table 2. The acceleration experienced by the vehicle is
constant throughout the flight (and equal to 
),
see Figure 2.
Table 2. Flight characteristics to reach 
for a
range of 
, if propellant is
ejected vertically downwards at optimally varying speeds
|
 (kW/kg)
|
Ratio of propellant
to lifted mass
|
 (kW
per kg lifted mass)
|
Flight time to
reach orbital velocity (s)
|
Maximum
acceleration ms-2
|
|
100
|
1.6
|
256
|
780
|
10
|
|
50
|
3.1
|
206
|
780
|
10
|
|
30
|
5.2
|
186
|
780
|
10
|
|
15
|
10.4
|
171
|
780
|
10
|
|
10
|
15.7
|
167
|
780
|
10
|
|
8
|
19.6
|
165
|
780
|
10
|
|
6
|
26.1
|
163
|
780
|
10
|
Figure 2. Plot of
vehicle velocity as a function of time, if propellant ejected at a constant
speed vertically downwards, if = 30 kW/kg
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