Fuzzy Thrust Staging Kinematics for the NERVA Strap-on Boosters

Fuzzy Thrust Staging Kinematics for the NERVA Strap-on Boosters
Radu D. Rugescu1, a, Stefan Staicu1,b
and Seyed Mohamadreza Mahmoudian2,c
1University “Politehnica” of Bucharest, Spl. Independentei 313 sector 6, Romania
2Private Org. Tehran, Iran
arugescu@yahoo.com, bstaicunstefan@yahoo.com, cmci_mahmoudian@yahoo.com
Keywords: space safety, launch on the Black Sea, rocket launchers, NERVA launcher
Abstract. NERVA small space launcher under development in Romania by Politehnica University is
based on the solution of hard take-off with three strep-on SRM boosters. Due to the very high thrust
enhancement a lift-off loading of more than 40 g-s appears, which is quite challenging. The main
challenge is connected with the possible uneven thrust and burn duration of the three SRE-s of the
first stage, which we call fuzzy thrust. Experimental data show variations of up to 0.5 seconds in the
duration of the powered phase of SRE-s, from a total of 3.0 seconds of a mean burn. Yet undetermined
variations in the total ignition delay between individual motors are a stronger concern. While for the
unique booster of the standard SA-2 vehicle the ignition delay has no impact, when those engines are
forced to work in parallel the individual differences become catastrophic. Severe imbalance between
the two lateral engines may occur, ending in a potentially severe damage of the launching rail,
possible loss of flight stability along the boost phase and damage of the second stage structure. The
problems regarding the efficiency of the propulsion system that accompany this project are considered
and solutions are proposed for the high thrust augmentation of the booster stage. Cryogenic vs
storable propellants are studied for thrust augmentation of the boosters.
Introduction
Due to the hazardous character of the rocket staging, intensive research has been devoted to the design
[1], [11] and prediction of rocket staging behavior [13], [15], with emphasize on collision avoidance
during the staging process [1], [14]. The problem is important as an entire line of failures were
encountered with improperly developed staging systems. Two groups of problems appear, one for the
atmospheric staging [18], [21] and another for free space staging [12], [13], [14], [16], [17], [19],
addressed by different means [15], [20], [22], [23]. Due to the short burn, booster staging of NERVA
vehicles occurs at low altitude and at high speed, thus the aerodynamic effects are high. To avoid as
much as possible development difficulties, the main rule in NERVA design is to only accept minor
modifications to the existing SRM and LRE systems of the SA-2 missile, with proven reliability and
efficiency. This means so far that the solution is to cluster three identical SRMs in order to augment
the take-off thrust. The strap-on booster solution is practical and most commonly used [2], [3], still it
drives three typical problems:
Un-even (non-synchronous) ignition, especially of the LRM members of the cluster;
Un-even steady-state thrust of the members of the cluster, equally LRM and SRM, with the
consequence of a potential thrust misalignment;
Non-synchronous thrust decrease between the members of the cluster, especially in the SRM case.
The design is based on the exploitation of the existing SRM-s on the missiles, which present the
mean thrust of 310÷530 kN (ti=-50C…+50C) for a new engine and of 230÷390 kN respectively for an
aged motor, performing under a quasi-neutral burning law (Fig. 1 and 2). The only modification is the
10 degrees tilted nozzle of the side boosters for thrust couple mitigation.
Advanced Materials Research Vols. 463-464 (2012) pp 1611-1615
© (2012) Trans Tech Publications, Switzerland
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Characteristics of the Solid Boosters
The thrust diagram recorded on the test stand shows the real shape of the tail thrust to be considered
(Fig. 6). The mean thrust of 353.0494 kN for a duration of 3.1873 seconds, with the maximal thrust
value of 360.9228 kN, were recorded, delivering 1934.1 m/s of mean sea level specific impulse,
which means total losses of 9.79% from the theoretical values. From the level of 90% of the mean
thrust up to the final stop the duration of 0.3 s appears. Right before the thrust decay, the temporary
thrust raising is due to grains fragmentation prior to burn-out. It is estimated that differences as high as
0.1 seconds in burning duration may occur between different engines, value to be considered in
numerical simulation of the cut-off behavior. The solid propellant consists of twelve tubular grains,
arranged in a triple-triangular package, more compact than the hexagonal mount. However, this is not
the most compact arrangement possible.
Fig. 1: Bank booster SRM of the NERVA launcher. Fig. 2: Thrust history
A neighboring configuration, four millimeters more compact in radius only, produces a slightly
unstable position of the grains. It follows that after a very short time of burn, while the missile is still
running on the launcher rails, the solid charge is no more supported by the chamber walls and only
remains driven, in a fast accelerated motion, by the bottom grid that closes the chamber at nozzle
entrance. Therefore the decreasing mass of the solid grains remains bound to the aft grid up to the end
of combustion, where the propellant mass is concentrated regarding the mass center. This produces a
considerable displacement of the mass center, around two meters forward from the initial, take-off
position. The nozzle tilt is oriented towards the final station of the mass center, which means by 10
degrees to the longitudinal axis of the rocket.
The maximal outer diameter of the SRM at the welding zones measures 655 mm, while the
cylindrical part is of 652 mm in diameter. There are four circumferential welding strips (Fig. 1). The
convenient location of the front connecting rod is at the front end plane of the four support legs that
transfer the boosters’ thrust to the sustainer stage. The rear connecting rod is conveniently located at
nozzle throat, within the fins supporting rings, unused on the bank boosters and free for exploitation
(Fig. 3).
Fig. 3: Installment of the NERVA staging mechanism.
1612 Advanced Materials Research II
To simultaneously deploy both bank boosters with minimal delay between them, the unlocking
must be commanded from a single point by a mechanical controller.
The main task of the design team is to completely compensate the potential non-synchronization in
the thrust schedule of the bank boosters, which could produce otherwise highly hazardous effects.
Besides the uneven deployment of the side boosters, the unstable flight phenomena may manifest in
other two concerning phases: uneven ignition delay, and unbalanced steady thrust. While a solution
for balancing the steady-state thrust was easy found, de-synchronization during start and stop are
much tougher. Adding the variable ignition time of the SRM-s to the de-synchronization of up to 0.1
seconds in the burning duration, total laps of up to 0.5 seconds may be considered for a solution to the
design problem of thrust unbalance. In the present case with a solid propellant charge comprising of
twelve cartridges, the variance of the size and burning duration on individual grains is considerably
mediated by their high number. The variability of the burn duration of the whole booster is thus
expected to be quite small and the ignition delay to remain as the primary concern for the design of the
NERVA staging mechanism.
Fig. 4: Deployment during staging, forces and moments.
Fig. 4 shows the main force system, which produces the deployment of the bank boosters at the
release of connecting rods, under the action of the thrust itself. The uneven work of booster motors at
tail thrust will produce transversal effects. Their amplitude and duration is simulated through the
ADDA flight dynamics code and depend on the delay between the thrust decay within the motors. The
effects may be critical.
Kinematics of Interstage Deployment
Transient effects are considered in the full, unsteady form of the gas-dynamical thrust of the “k”
engine:
( )
0
( )
( )
( )
( ) 2
2
[( 2 ) ]
k
k ek
k
k
ek k
k k
ek k
k k
jk
A k
k k nk
V
A
a k k k
V
k
k k nk A k k A
V
k
k k A k k k nk
dV v dA
t
p dA dV
t
v dA dV m
v dA
σ
σ
σ
σ
ρ
ρ
ρ
ρ ρ
ρ
∂
= − + +
∂
∂
+ − − ∧ +
∂
+ ∧ + − − ∧ −
− ∧ ∧ + + ∧ +
∫ ∫
∫ ∫
∫ ∫
∫
n
n
v
T v
p n ω r
ω r f a ε S
ω ω S v ω r p
(1)
x1
O2
O3
Q
φ10
φ21
φ32
O1
x0
x2
x3
Advanced Materials Research Vols. 463-464 1613
where the local transport acceleration of local origin Ak in respect with the global mobile referential M
is
Ak M MAk ( MAk ) a = a −ε ∧r +ω∧ ω∧r (2)
Based on this knowledge and designating the elements as 1, 2 and 3, the relative motion of the
deploying mechanism in respect to the main body “0” is described by the velocities of the joints
2
21
O 0 10 21 ( ) [ ] ( ) z v =ϕ
u A r { } 3
21 32 32
O 0 10 21 32 21 32 ( ) [ ] ( ) ( ) [ ] ( ) z z z v =ϕ
u A r + A r −ϕ
u A r (3)
For the accelerations of the mobile joints O2 and O3 the computational relations are:
{ } 2
2 21
O 0 10 10 21 ( ) [ ] ( ) z a = ϕ

u −ϕ
E A r
{ }{ }
{ }
3
2 31 32
O 0 10 10 21 32
2 32
21 21 10 21 32
( ) [ ] ( ) ( )
[ ] 2 [ ] ( )
z z
z
a u r r
u u r
ϕ ϕ
ϕ ϕ ϕ ϕ
= − + −
− + +
E A A
E A










(4)
The three absolute rotational velocities of the elements are given by the anti-symmetrical matrices
10 10 [ω ] = [u]ϕ

20 10 21 [ω ] = [u](ϕ
−ϕ
)
30 10 21 32 [ω ] = [u](ϕ
−ϕ
−ϕ
) (5)
The notation [u] designates the constant matrix
0 1
[ ]
1 0
u
 − 
=  
 
The velocity and acceleration of any point on the elements of the mechanism are now available
with the aid of relations that give the distribution of velocities and accelerations along a rigid body.
Conclusions
The development of the staging mechanism in the form here adopted, due to the specific design
constraints, proves a considerable challenge. Potential de-synchronization in the time schedule of the
bank boosters is the main concern that requires further theoretical and experimental investigations
and massive numerical simulation. The kinematics of the relative motion of the deploying mechanism
is the first part of this investigation and represents the present development stage of the NERVA
space launcher.
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