samara state aerospace university (ssau) samara 2015 selection of design parameters and optimization...

Samara State Aerospace University (SSAU)

Samara 2015

SELECTION OF DESIGN PARAMETERS AND OPTIMIZATION TRAJECTORY OF MOTION OF ELECTRIC PROPULSION SPACECRAFT WITH

LOW THRUST

Prof. O.L. Starinova

Optimization of low thrust Earth-to-Mars transfer

Samara State Aerospace University 2

- All the spacecraft maneuvers (acceleration and transfer to the departure trajectory, heliocentric transfer and the braking maneuver to ascent the orbit of the artificial satellite of Mars) are supposed to be held by the electric propulsion system;- The minimum initial mass of the spacecraft on the parking orbit is used as the optimization criteria.

The statement of the design and ballistic optimization of the Earth-Mars transportation mission problem:

Figure 1 – The ballistic scheme of Earth – Mars mission

The design model of the space tug

Initial mass of the space tug can be represented as the sum of the masses of it’s general systems, fuel and payload.

(1) In a first approximation, the system masses depend on velocity exhaust of propellant and nominal thrust as follows:

- the power plant mass; (2)

- the propulsion system mass; (3)

- the tank mass, including the propellant system; (4)

- the construction mass. (5)


ctfpspppl mmmmmmm 0

pspppppp

cPm

20

0Pm psps

ft mkm

00

2P

cPm c

psppcc

N Engine name, the mode of use

Exhaust velocity, m/sek

Engine efficiency

Thrust of one engine, N

1 HiPEP mode 1 96000 0,80 0,6702 HiPEP mode 2 82700 0,78 0,4603 HiPEP mode 3 80000 0,74 0,7804 NEXIS DM 1 75000 0,75 0,4755 ID-500 (Russia) 70000 0,78 0,7806 NASA-457M mode 1 27500 0,63 2,2007 PPS-20kML 27500 0,65 1,0508 NASA-457M mode 2 20000 0,58 2,400

The characteristics of the high power propulsions

Figure 2 – The general view of engines HiPEP, NEXIS DM1, NASA-457M


The fuel mass estimated

For electric propulsion space tug, the output power and the thrust depend on the phase coordinates (a distance from spacecraft to the Sun, a power decreasing due to the Earth radiation belts, and possible shading of solar arrays, work duration of a nuclear reactor, etc.). To estimate the design parameters of the spacecraft we can find with low accuracy the fuel consumption on segments using the Tsiolkovsky rocket equation:

, (6)


0exp1 mc

Vm f

Vwhere is a reference velocity needed to make a parabolic velocity increase maneuver in the sphere of influence of the Earth, the heliocentric Earth-Mars transfer and the braking maneuver in the sphere of influence of Mars.

The algorithm of optimization

1. The required reference velocity is defined for all segments of the trajectory: • The parabolic velocity increase and the Earth escape maneuvers:

(7)

• The heliocentric Earth-Mars transfer:

(8)

• The braking maneuver in the sphere of influence of Mars:

(9)

2. The type and quantity (n) of the electric rocket engines for the power interplanetary spacecraft unit is chosen. Their parameters are defined according to the table on slide 3: - exhaust velocity of the engine; - thrust of the engine.


121

EE

Ex HRV

M

E

MEMEE

M

MEx r

r

rrrrr

r

rrV

222

123

MM

Mx HRV

c

eP


3. The total thrust and the power plant mass are calculated by the formulas:

(10)

(11)

4. The required power of the energy unit and the energy unit mass can be found as follows:

(12)

(13)

5. The mass of the spacecraft construction is calculated:

(14)


nPP e 0

nPPm epspsps 0

pspppp

cPN

20

pspppppppppp

cPNm

20

00

2P

cPm c

psppcc


6. The Tzyolkovsky numbers are defined for all segments of the trajectory: • The increase of the velocity in the sphere of influence of the Earth:

(15)

• The Earth-Mars transfer:

(16)


(17)

7. The first approximation for the spacecraft initial mass without the fuel and tank mass is calculated:

(18)


c

Vz x1

1 exp

c

Vz x2

2 exp

c

Vz x3

3 exp

2.100 cpspppl mmmmm


8. The working body mass is calculated for segments in i approximation: • The increase of the velocity in the sphere of influence of the Earth:

(19)

• The Earth-Mars transfer:

(20)


(21)

To prove the results the total working body mass is calculated:

(22)

VERY IMPORTANT !THE RESULTS RECEIVED BY (21) AND (22) SHOULD FULLY AGREE !


10

1

11

1

iif m

z

zm

ifiif mm

z

zm 1

10

2

22

1

ifi

fii

f mmmz

zm 21

10

3

33

1

10

321

11

ii

f mzzz

m


9. The storage system and the fuel-feed system masses are calculated:(23)

and the adjusted initial mass of the spacecraft is defined as follows:

(24) 10. The initial masses received within the i and i –1 approximations are compared.

IF THE ERROR OF THE INITIAL MASS CALCULATION DOES NOT EXCEED 5% THEN IT IS POSSIBLE TO GO TO STEP 11.

IF THE ERROR EXCEEDS 5% THEN IT IS NECESSARY TO MAKE ONE MORE APPROXIMATION I=I+1. TO DO THIS ONE SHOULD REPEAT STEPS 8-10 USING THE FORMULAE (19 - 24).


if

it mkm

it

ifcpspppl

i mmmmmmm 0

%1000

1

i

io

io

m

mm


The initial data

The initial data are:

m3/s2 – gravitational parameter of the Earth,

m3/s2 – gravitational parameter of the Sun,

m3/s2 – gravitational parameter of Mars,

m – average radius of the Earth,

m – average radius of Mars,

m – altitude of the initial geocentric orbit,

m – altitude of the final areocentric orbit,

m – average radius of the Earth orbit,

m – average radius of the Mars orbit.

1410986.3 E2010327.1

1310283.4 M610371.6 ER610396.3 MR

5105EH5105MH

1110496.1 Er

1110279.2 Mr

Conclusion


IN YOUR TRAINING CASE

CONTAINS AN EXAMPLE OF THIS

CALCULATION.

EXAMINE IT CAREFULLY AND

REPEAT FOR THEIR VERSION OF

THE ORIGINAL DATA.

ANALYZE THE REZULTS.

Get and analyze the

results

Repeat the calculation

for your option

Examine carefully

the example

samara state aerospace university (ssau) samara 2015 selection of design parameters and optimization...

Documents

fuel mass

hipep mode

electric propulsion

starinova slide

required power

mode of use exhaust

tank mass

construction mass