Rocket Propulsion
Solid Rocket Motors
AE4451
Solid Motors 1
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
Rocket Propulsion
Solid Rocket Motors
Background
Solid Motors 2
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
AE4451
1
Solid Rocket Motors
• Oldest rocket technology
Fire Arrow launcher from
14th century Huǒ Lóng Jīng
(developed before 1230)
cyber-heritage.co.uk
/rocketrocket/rockets.htm
credit: National
Air and Space
Museum
1941 demonstration of Jet
Assisted Takeoff (JATO)
Boxer Rocket (1855), twostage, used for rescue
operations
– powder based propellants (black
powder, amide* powder for JATO)
AE4451
*no sulfur and ammonium nitrate added
Solid Motors 3
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
Solid Rocket Motors
• Compared to LREs
Advantages
Disadvantages
Simple (less system components) Lower Isp
Reliable (few moving parts)
Harder to test (no subcomponent tests)
and sensitive to environmental temp.
Reduced storage volume (high ) Hard to actively throttle
Storable (especially compared to
cryogenics)
Manufacturing defects (e.g., cracks) and
degradation at extreme storage
conditions
Easier to start (vs. pump fed
LREs)
No restarts
Easily(?) scalable (to high and
low thrust)
Emissions (HCl and chlorinated
compounds) and signature (smoke) for
popular propellants
Solid Motors 4
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
AE4451
2
Solid Rockets - Major Applications
• High thrust
– boosters
– high acceleration missiles
• Simplicity, storability
– hobbyists, weapons systems
– novel programmable micro-thrusters
Solid Motors 5
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
AE4451
SRM Components/Nomenclature
• Basic parts of a solid rocket
motor (SRM)
– casing
Igniter
– insulation
– propellant (grain)
Insulation
– port/bore (not for end
burning)
Port
– igniter
– payload
– nozzle
Solid Motors 6
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
Payload
Casing
Propellant
AE4451
3
SRM Launch Booster Example
Titan IV
From Humble
AE4451
Solid Motors 7
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
SRM In-Space Example
STAR (apogee kick motor):
CTS, GMS, BS, GPS, GOES
satellites from Sutton, Rocket Propulsion
Solid Motors 8
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
Inertial Upper Stage (IUS):
used in Titan, Space
Shuttle launchesFrom Sutton
AE4451
4
Solid Propellants
• Two basic types
• Homogeneous
– reactants (fuel, oxidizer) mixed at
molecular level
– e.g., double-base propellants
• Heterogeneous
– fuel and oxidizer are “macroscopically”
separated
– e.g., composite propellants
Solid Motors 9
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
AE4451
Double-Base Propellants
• Typically combination of explosive liquid and selfburning powder
– e.g., nitroglycerine and nitrocellulose (gun cotton,
flash paper)
– powder absorbs liquid explosive, molecularly mixed
– other additives (opacifier, stabilizers, burn-rate
modifiers, flash suppressors)
• Can be extruded or cast
• Used in early modern rockets, e.g. at JPL
– replaced gun/black powder
– used in WWII JATOs and early Sidewinder
– weapons systems
Solid Motors 10
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
AE4451
5
Composite Propellants (CP)
• “Oxidizer” particles
Coarse Ox
held together in nonParticle
energetic polymer
binder (fuel)
Fine Ox
• Manufacture
Particles
– grind oxidizer
Binder
crystals into powder, add other solids
(e.g., catalysts)
– mix liquid binder with liquid curing agents,
crosslinkers, plasticizers, stabilizers, bonding
agents
– mix solids and liquids, cast and cure
AE4451
Solid Motors 11
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
Cleaved Composite Propellant Sample
Scanning Electron Microscope (SEM) image
10 m
Fine AP
Solid Motors 12
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
• 10m and 400m
ammonium perchlorate
(AP) particles
– self-burning oxidizer
• HTPB binder
– polymer (like a
synthetic rubber)
– fuel
• 92% solids
– relatively high solids
loading
Coarse AP
AE4451
6
Rocket Propulsion
Solid Rocket Motors
Regression Rate and
Internal Ballistics
AE4451
Solid Motors 13
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
Mass “Production” Rate
• Propellant converted to gas due to heat
feedback from flame at rate given by
flame
  r s Ab
(IV.26) m
• (Surface) Regression Rate r
r  dx dt sometimes
rb
Burning
Area, Ab
– standard model (Burning Rate “Law”
or St. Robert’s “Law”)
n
(IV.27) r  apo
with a=f (Tsolid ,…)
– also,
Solid Motors 14
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
m
s
r
q
x
r  c  bpon etc.
AE4451
7
Solid Propellant Burning Rate
r  apon  ln r  ln a  n ln p
From Sutton
AE4451
Solid Motors 15
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
Motor Internal Ballistics
• What governs motor internal conditions?
• Examine mass conservation
0

dmCV
   u  nˆ dA
dt
mstore
0
Vo
d
oVo   m exit  m b
dt
d o
dV
 o o
dt
dt
1 dpo
RTo dt
mstore,p
 o  Ab r 
mstore,V
Solid Motors 16
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
Vo
r s Ab
po
RTo
 2 

  1
 
 1
m exit
CV
2  1
At
m b
Assuming:
1) uniform gas prop’s. in CV
2) TPG, CPG
3) To=constant (e.g., Tad)
4) po, Ab, r given at time t
mstore,p+mstore,V = mb mexit
AE4451
8
Internal Ballistics (con’t)
• Solve for rate of pressure change
 1
  2   1
(IV.28) Vo dpo  rA      p A


b
s
o
o t
RTo dt
RTo    1 
• For steady burning
 1 / c*
A
dpo
 0  po  r b  s   o c* (IV.29)
At
dt
– using standard burning rate law
po  apon
~s in many cases

Ab
 s  o c*  po  aK  s  o c*
At
For steady burning (if a , n , To ,  , and
At constant) then Ab must be constant

1
1 n
(IV.30)
Ab At  K
po ~ K
1
1 n
AE4451
Solid Motors 17
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
Motor Stability
• Recall mass conservation (for fixed To)
m exit  c* po At  po
m store , p  m b  m store ,V  m exit
m incr  Ab  s   o r  pon
 m incr  m exit
• For stable operation (po= const), need mstore,p= 0
• So when are we stable?
m incr n  1
m exit
– only if n  1
m exit  m incr
m
 po 
m incr n  1
– normally use
0.3<n<0.7
m exit  m incr
operating
point
 po 
po
Solid Motors 18
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
AE4451
9
Combustion Limits
m
• If n or po too low
– do not get stable combustion
– after ignition, propellant
soon stops burning (r0)
t
• At too high po
– possibility of erratic, unpredictable burning
– e.g., po > 5000 psi)
AE4451
Solid Motors 19
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
Pressure Histories
• Motor designer can adjust pressure profile
(“history”) of a solid motor by arranging how burning
area changes with time (grain geometry)
• Thrust given by   po At c
– so thrust history of motor essentially follows
motor’s pressure history
• Characterize pressure/thrust histories as generally
– progressive: increase with time
– neutral: constant with time
– regressive: decrease with time
– combinations
Solid Motors 20
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
AE4451
10
Grain Geometries and Thrust History
or “boost sustain”
From Hill and Peterson
Solid Motors 21
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
AE4451
More Solid Motor Grain Geometries
From Sutton
Solid Motors 22
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
AE4451
11
SSRB (Space Shuttle Rocket Booster)
•
•
•
•
•
•
Largest SRM flown and first designed for
reuse
– diameter = 12.17 ft, length = 149.16 ft
Sea Level Thrust: 3,300,000 lb
Weight: 1,300,000 lb (inert: 192,000 lb)
Provide ~ 71% of thrust at lift-off and ascent
Propellant composition (mass fractions)
– AP: 69.6%, Al: 16%,
Fe2O3 (catalyst): 0.4%,
HTPB (binder): 12.04%
epoxy (curing agent): 1.96%
Four segments
– 11 point star (neutral) in forward segment
– double truncated cone (regressive) in 3 aft
segments
http://spaceflightnow.com/2015/03/11/worlds-largest-solid-rocket-motor-fired-in-utah/
AE4451
Solid Motors 23
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
Rocket Propulsion
Solid Rocket Motors
Design Issues and Example
Solid Motors 24
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
AE4451
12
SRM Design
Dt
• Typical Requirements
– thrust, (t)
D
– burn time, tb
or total impulse, Itot
• Design Variables
L
– propellant composition ( c*, a, n)
– grain design
• Other constraints/issues
‒ high volume loading
– motor geometry: D, L
fraction (Vpropellant /Vchamber)
– nozzle geometry: , Dt
‒ low residual propellant
• Unsteady variables
mass
‒ structural integrity
– po(t), m(t), …
‒ limit erosive burning
‒ limit max operating press.
Solid Motors 25
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
AE4451
Design of an End-Burning Motor
•
•
•
•
Start with end burning motor
– easiest to analyze
– constant thrust
Db
– used in some small motors
and gas generators
Requirements
– tb=100 s, vac=500 kN (105 lbf)
lweb
Constraints
– po=4 MPa (assume uniform)
– nozzle: c=1.85 (~30-50)
– propellant: c*=1500 m/s, =1.2, MW=24, s=1800 kg/m3,
r=0.40 [po(MPa)]0.3 cm/s
Design Variables
– Dt, Db, lweb (assume axisymmetric-cylindrical geometry)
Solid Motors 26
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
Dt
po m b
AE4451
13
End-Burning Motor Example
• Nozzle throat size, Dt
from
(IV.12)
At 

Dt

po c
5 10 N
4 106 N m 2 1.85
5

po m b
Db

lweb
 0.0676m2
At   Dt2 4  Dt  29cm~ 1 ft 
AE4451
Solid Motors 27
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
End-Burning Motor Example
• Motor length, lweb
r

dx
dt
steady burning
 web
tb
 web  rtb  0.44 cm s 100s 
0.3
Dt
po m b
Db
lweb
 0.61 cm s 100 s 
 web  61cm
Dt  29cm
Solid Motors 28
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
  web Dt  2
AE4451
14
End-Burning Motor Example
Dt
• Motor diameter,Db
– recall for steady-burn
from
(IV.29)
Ab
 s  o c*
At
Ab
po
po
K

*
At
r  s   o c
r s c*
po  r

po m b
Db
lweb
4 106 N m 2
 243
0.0061m s 1800 kg m3 1500 m s


 Db  24329cm  4.57m  Db  web  7.5!!!!
Huge end-burning motors to produce high thrust
AE4451
Solid Motors 29
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
Internal Burning Motor Design
• Burn time associated with
web thickness, wt
• Length impacts burn area,
Ab(t) = L  S(t) perimeter
• For given initial grain
geometry, need to know
how S evolves with time
– integration of burning
surface location due to
regression acting normal
to surface
Solid Motors 30
Copyright © 2007-2008, 2018, 2020 by Jerry M. Seitzman.
All rights reserved.
wt
Dt
Dp
Ab(t)
L
Dp (t) port diameter
S(t2)
S(t1)
AE4451
15