Concerning the rolling disturbance
caused by the joint work of a rocket
carriers LPR Engines
Boris Rabinovich
2
Concerning the rolling disturbance caused by the
joint work of a rocket carriers LPR Engines
• The problem of the rolling disturbance moment is considered arising
during the joint work of a lot of liquid propellant rocket engines (LPR
Engines). The engines are supposed to be located on the equal
distances along the circle as for example on the A-section of the
heavy rocket carrier N-1. The simple mathematical models are
proposed for the qualitative explanation of some phenomenon being
observed during the flight experiments, namely:
• The arising of the disturbing moment around the longitudinal axis of
the rocket caused by the twist of the joint work of all of the rocket
engines.
• The absence of such a moment in the case of an interval in the
working engines chain (two engines located on the opposite ends of
the diameter are turned off).
3
The position of the LPRE NK-15 on the
A-section of the rocket carrier N-1
4
Equilibrium forms of the jets system
• a) Continuous chain of
the LPRE, the regular
symmetry
• b) The chain of LPRE
having the gates
(N-1 # 3L)
• c) Continuous chain of
LPRE, the screw
symmetry (N-1 # 6L)
5
Equilibrium forms of the jets system
• a) Continuous chain of
the LPRE, the regular
symmetry
• b) The chain of LPRE
having the gates
(N-1 # 3L)
• c) Continuous chain of
LPRE, the screw
symmetry (N-1 # 6L)
6
The model of the LPRE chain
having the gates (N-1 # 3L)
The system of two cores
Non-symmetric equilibrium form
Symmetric equilibrium form
7
The model of the LPRE chain having the gates
1     ,  2     ,
  1/2 (1   2 ),   1/2 ( 2  1),
  - (2   a  2 ),
(1)
1  1,  2  1,   a .
P  const  0, T  c  ( ) sign ,
M1  k 1 , M 2  k  2 .
3
3
(2)
• Potential energy (3)
• Equilibrium conditions (4)
• Stability conditions (5)
• Generalized coordinates (1)
• External forces (2)
 ( , )  1/2(  4   4  6 2 2 ) 
 2P  c / 2(2  a 2 ) 2 . (3)

 0,


 0.

(4)
 2
 0,
2

 2
 0.
2

(5)
8
The model of the LPRE chain having the gates
The equilibrium forms and stability
• Symmetric equilibrium form
• Non-symmetric equilibrium form
P

,
2
2
k  2c
( P  с a 2 )

,
2
2
2
k (  3 )  2c 
  0.
( 2c a  3k )

.
2
k  ca
( 6)
3 k 2  2 ca  0,
3 k  2 c  0.
2
2
( 8)
3k 2  2ca   0, k  ca 2  0,
(7) 3k 2  2 c 2  0.
The existence by k>>cl2
The existence by k>>cl2
is most probable
is impossible
• Equilibrium conditions - (6), (8). Stability conditions - (7), (9 )
(9)
9
The model of continuous LPRE chain (N-1 # 6L).
One of the cores
The plane orthogonal to
the longitudinal axis
The plane passing through
the longitudinal axis
10
The model of continuous LPRE chain
Q  const  0, F  2  Q,
T  c  (  ) sign  ,
(10)
   ( 2l   a ),
2
M   k  3 ,
• External forces (10)
M   k  3 .
 ( ,  )  k/4 ( 4   4 ) 
• Potential energy (11)
• Equilibrium conditions (12)
• Stability conditions (13)
 2Q   c / 2(2   a 2 ) 2 . (11)

 0,


 0.

(12)
 2
 0,
2

 2
 0.
2

(13)
11
The model of continuous LPRE chain
• The regular symmetry
• The screw symmetry
2Q  
 2
,
2 2
k  4 c 
2(Q  сa  2 ) 

,
2
2 2
k   4 c 
  0.
ca   
  2
.
2
k 2ca
(14)
k  2  4 c 2  2  0,
k  4 c   0,
2
2 2
3 k 2  4 c 2  2  0.
(16)
(15)
k  2 c a 2  0.
(17)
The existence by k>>cl2
The existence by k>>cl2
is impossible
is most probable
• Equilibrium conditions – (14), (16). Stability conditions –(15), (17)
12
Concerning the rolling disturbance caused by the
joint work of a rocket carriers LPR Engines
Summary
•
•
The equilibrium forms of the jets system with the right-screw or leftscrew symmetry are stable while absence of the gates in the LPRE
chain. The jets axle are screwing in this case around the longitudinal
axis of the rocket. The regular-symmetric form of the jets system
equilibrium will transform immediately, being non-stable, in one of the
equilibrium forms with the screw symmetry. The last one create the
mighty disturbing rolling moment. This moment has been observed by
the lunch of the N-1 rocket carrier # 6 L.
In the case of the gates in the contrary the regular-symmetric
equilibrium form of the jets system is stable. The jets neighboring to
the gates have the inclination in the direction of the gates. The
existence of non-symmetric equilibrium forms arising while absence of
the gates is impossible in this case. The symmetric form of the jets
system has been appeared probably by the N-1 rocket carrier # 3 L
lunch. The disturbing rolling moment was in this case not observed.
13
Equilibrium forms of the jets system
• a) Continuous chain of the
LPRE, the regular
symmetry
• b) The chain of LPRE
having the gates(N-1 # 3L)
• c) Continuous chain of
LPRE, the screw
symmetry (N-1 # 6L)
14
Concerning the rolling disturbance
caused by the joint work of a rocket
carriers LPR Engines
Boris Rabinovich
Space Research Institute (IKI) Russian Academy of Sciences
Profsoyuznaya 84/32, Moscow 117810, Russia
The electronic version vas fulfilled by Victoria Prokhorenko