## Microsoft word - 502-509 _219_.doc

Fernando de Souza Costa and Ricardo Vieira

**Preliminary Analysis of Hybrid **
**Fernando de Souza Costa **
**Rockets for Launching Nanosats into **
fernando@lcp.inpe.br
12630-000 Cachoeira Paulista, SP, Brazil

*This work determines the preliminary mass distribution of hybrid rockets using 98% H2O2 *
*and solid paraffin mixed with aluminum as propellants. An iterative process is used to *
*calculate the rocket performance characteristics and to determine the inert mass fraction *
**Ricardo Vieira **
*from given initial conditions. It is considered a mission to place a 20 kg payload into a 300 *
*km circular equatorial orbit by air launched and ground launched hybrid rockets using *
rvieira@lcp.inpe.br

*three stages. The results indicate total initial masses of about 7800 kg for a ground *
*launched hybrid rocket and 4700 kg for an air launched hybrid rocket. *
**Keywords**: hybrid rocket, paraffin, H2O2, nanosats, low Earth orbit (LEO)
12630-000 Cachoeira Paulista, SP, Brazil
The hydrogen peroxide (H2O2) is a well-known oxidizer and has
been used for decades in rockets, gas generators, helicopter rotors
and rocket belts (Davis Jr. and Keefe, 1956; Wernimont et al.,
1Hybrid rocket technology is known for more than 50 years; 1999). It was used, for example, as an oxidizer in the British rocket
however, only in the 1960's its safety characteristics motivated a
Black Knight. Heister et al. (1998) cite some advantages of using
significant research. Nowadays, the need for green propellants hydrogen peroxide as oxidizer: high density, easy of handling, non-(propellants with low toxicity and low pollutant characteristics), the
toxicity and mono-propellant characteristics. Turbo-pumps and
requirements of safe operation and storability, low cost missions,
pressurization systems can utilize the energy released during
and the interest for launching small payloads and nanosats into LEO
peroxide decomposition and its products in order to simplify the
made hybrid rockets more attractive.
tank pressurization systems. Walter (1954) describes the
Hybrid propulsion systems employ propellants in different decomposition and detonation characteristics of peroxide and
phases, being the most usual hybrid systems with a solid fuel and a
mentions that peroxide at concentrations lower than 82% is not
liquid oxidizer. Since they use only one liquid propelllant, they detonable and that pressure does not affect the peroxide require only one liquid line and a relatively simple injection system,
decomposition velocity. Williams et al. (2004) state that HTP (High
as compared to liquid bipropellant systems which require two Test Peroxide), a high concentration peroxide, above 84% in water, separate liquid lines and a complex injection plate in order to collide
is similar to nitroglycerin in terms of shock sensitivity and explodes
and mix the fuel and oxidizer jets. The control of the oxidizer flow
with the same strength as the same quantity of TNT
rate in hybrid systems allows several starts and an accurate control
(Trinitrotoluene). Ventura et al. (2007) present supporting evidence,
of the thrust level.
analysis, historical technical data, recent test data, prior and current
The safe operation of hybrid propulsion systems is related to the
experience, modern and literature test data which can be used to
separation of fuel and oxidizer, differently from solid systems which
make informed decisions on peroxide applications. They also report
mix fuel and oxidizer in the grain. Another important safety that changes in the propellant manufacturing process may have characteristic is the independence of the regression rate with respect
significantly improved peroxide properties in the last decades.
to the chamber pressure, making hybrid systems safer than solid
The objective of this work is to make a preliminary analysis of
systems if pressure peaks do occur.
mass distribution of hybrid propulsion systems and to compare the
The main disadvantage of hybrid rockets is the low thrust level
performance of air launched and ground launched hybrid rockets.
attainable, due to the relatively low regression rates of conventional
The propellants are an aqueous solution of 98% H2O2, in mass,
solid fuels, making necessary the use of a large number of ports, i.e.,
burning with solid paraffin mixed with 10% aluminum, in mass. The
flow passages through the grain. Some methods to increase the effects of mixture ratios, thrust/weight ratios and chamber pressures regression rate are known, such as i) insert screens or mechanical
are analyzed. Three stage rockets are considered for placing a 20 kg
devices in the ports to increase the turbulence level; ii) use of nanosat into a low Earth circular equatorial orbit at 300 km.

metallic additives; iii) use of oxidizers mixed within the solid fuel;

iv) increase of the surface rugosity adding small solid particles.

**Nomenclature **
However, these solutions have also undesirable characteristics such as increase in weight and complexity, non-stop burning and nozzle

*= area, m2 *
erosion by solid particles.

*= experimental constant, (mm/s)(m2s/kg)n *
Recently, it was developed in Stanford University and in the

*CF = thrust coefficient, dimensionless *
Ames-NASA Research Center, both in the USA, a new paraffin-

*= mass fraction, dimensionless *
based fuel whose regression rate is approximately three times higher

*= safety factor, dimensionless *
than conventional hybrid fuels (Karabeyoglu et al., 2003a,b, 2004).

*= diameter, m *
Promising results were obtained by several researchers (Brown and

*F = thrust, N *
Lydon, 2005; Karabeyoglu et al., 2004; Santos et al., 2005;

*go = gravity acceleration at sea level, m/s2 *
McCormick et al., 2005; Authors, 2006; Authors, 2007) using

*Go = mass flow rate of oxidant per unit area, kg/s/m2 *
paraffin with different oxidizers – liquid oxygen (LOX), gaseous

*Isp = specific impulse, s *
oxygen (GOX), nitrous oxide (N2O) and hydrogen peroxide (H2O2).

*= length, m *
*= mass, kg *
*m*&

* = mass flow rate, kg/s *
**Paper accepted October, 2010. Technical Editor: Eduardo Belo. **
*= experimental constant, dimensionless *
**502** / Vol. XXXII, No. 4, October-December 2010

Preliminary Analysis of Hybrid Rockets for Launching Nanosats Into LEO

*OF = oxidizer/fuel mass ratio, dimensionless *
In this work, hybrid rockets with three stages are studied,

*= pressure, Pa *
assuming a uniform distribution of characteristic velocities among

*rp = blowdown ratio, dimensionless *
stages. Sutton (1992) shows that, for simplified cases and

*= gas constant, J/kg/K *
disregarding trajectory effects, a uniform distribution of

*r*&

* = regression rate, mm/s *
characteristic velocities is an optimum solution.

*= time or thickness, s *
Initially, in order to determine the rocket mass distribution, it is

*temperature, *
required to estimate the inert mass fraction of all stages. The inert

*Ve = exit velocity of combustion products, m/s *
mass is the total initial mass minus the propellant and the payload

*= volume, m3 *
masses. The inert mass fraction,

*finert,j*, of the

*j-*stage (

*j *= 1, 2 or 3) is

*W = weight, kg *
**Greek Symbols **

Δ

*inert*,

*j*
*inert*,

*j*
(

*prop*,

*j inert*,

*j *)

*V = characteristic velocity, m/s *
Δ

*P = pressure loss, Pa *
*= nozzle expansion ratio, dimensionless *
where

*mprop,j* is the propellant mass and

*minert,j* is the inert mass of the
θ

* = convergence semi-angle, degrees or radians *
ρ

* = density, kg/m3 *
Tables 1 and 2 show data presented by Isakowitz et al. (1999),
σ

* = yielding tensile, Pa*
concerning the mass distribution, in kg, of rocket engines using
solid and liquid propellants, respectively. Tables 1 and 2 show the

**Subscripts **
inert fractions of the solid propellant engines,

*finert,s*, and the inert
fractions of the liquid propellant engines,

*finert,l*. The complete rocket
relative to burning

* *
inert mass, including the engine inert mass, rocket casing,
relative to chamber
electronics, control, valves, and other components for all stages will

*cat * relative to catalytic bed
be estimated later with aid of Eq. (38).

*con * relative to convergent section
Humble and Altman (1995) showed that the propellant mass of

*div* relative to divergent section
the

*j*-stage, for constant specific impulse and constant gravity, can
relative to exit or exhaustion
be calculated by:

*ext* relative to external
relative to fuel or final

*j Isp j go*
*V j Isp j go*
*prop*,

*j*
*pay*,

*j *(

*inert*,

*j *) (
) (

*inert*,

*j*
relative to grain

*He* relative to Helium
relative to initial
where

*mpay,j* is the payload mass,

*Ispj* is the specific impulse,

*go* is

*int* relative to internal
the gravity acceleration at sea level, and Δ

*Vj* is the characteristic

*ins* relative to insulation
velocity of the

*j*-stage.
relative to stage
The specific impulse can be related to the exit velocity of
relative to liquid propellant
combustion products,

*Ve,j* =

*goIspj*, and is obtained from the NASA
relative to oxidizer
CEA 2004 code written by McBride and Gordon (1994, 1996), and

*pay* relative to payload
available in the internet (CEA, 2007). The CEA 2004 code adopts the Gibbs free energy minimization method and solves the mass, energy and atom conservation equations with a generalized Newton

**The Mass Distribution of Hybrid Rockets **
method to calculate the equilibrium conditions of the reactive flow
The optimization of a propulsion system to perform a given in the rocket chamber and along the nozzle. Alternatively, frozen
mission is a complex task, since there are several coupled variables
flow conditions can also be considered along the nozzle.
which depend on time and on rocket trajectory. The mass
The payload mass of a given stage is the total initial mass of all
distribution analysis will also depend on the component level upper stages, and the payload mass of the last stage is the nanosat considered, i.e, a more detailed mass distribution analysis would
mass. The inert mass is calculated in terms of the assumed inert
consider the masses of each small part in the rocket, including fraction: electronics and control system components, screws, nuts, etc.
To place a satellite into a specified orbit around Earth, the

*inert*,

*j*
*inert*,

*j*
*prop*,

*j*
(

*inert*,

*j *)
launching vehicle must attain a characteristic velocity, Δ

*V*, to
overcome the Earth gravitational field, the air drag, to make and the total initial mass,

*mT*,

*j*, is calculated by
maneuvers and to attain a prescribed orbital velocity.
Humble et al. (1995) used historical data of several launching

*T *,

*j*
*inert*,

*j*
*prop*,

*j*
*pay*,

*j*
vehicles and presented typical Δ

*V* values between 8800 and 9300 m/s,
as required to place satellites into a low Earth orbit. In this work it was
The

*F*/

*W* ratio relates to the thrust,

*F*, and the weight,

*W*, of a
adopted a conservative Δ

*V* = 9300 m/s for ground launched rockets
rocket, and is generally expressed in

*g*-number. This ratio
and a Δ

*V* = 8700 m/s for air launched vehicles, based on data from the
(acceleration) is limited to a range. It can not be high in order to
American air launched rocket Pegasus.
avoid damages to the equipment, or not to harm an eventual crew.
Usually, a rocket must have several stages to transport a payload
Obviously, it cannot be smaller than unit, but should be small
fraction, i.e., the ratio of payload and total initial mass, above 1%
enough to optimize the performance, especially in the first stage,
into an orbit around Earth. The increase in payload fraction with a
which has to overcome a significant air drag. The thrust to obtain a
larger number of stages is significant up to 3 or 4 stages, but above 4
specified

*j*-stage thrust/weight ratio, (

*F*/

*W*)

*j*,

* *is obtained from
stages, the propulsion system complexity grows considerably, with
consequent reduction in reliability and no significant increase on

*F *=

*F W m g *. (5)
payload fraction.

*T *,

*j*
**J. of the Braz. Soc. of Mech. Sci. & Eng. **
**Copyright **** 2010 by ABCM **
October-December 2010, Vol. XXXII, No. 4 /

**503 **
Fernando de Souza Costa and Ricardo Vieira

**Table 1. Mass distribution of solid propellant engines (masses in kg). **
Engine Propellant
Nozzle Ignition Miscellaneous Inert
GEM 11767 312 372
242 7.9 291 1224.9
50 3024 75.6 133.4
342.9 0.898 0.102
38 770.7 21.9 39.4
Source: Isakowitz et al. (1999).

**Table 2. Mass distribution of liquid propellant engines (masses in kg). **
*f,j* is the fuel density and ρ

*o,j* is the hydrogen peroxide
density, which varies with temperature, pressure and peroxide
Engine Propellant

*fprop,l finert,l *
concentration. In the next sections the subscript

*j* will be

**Fuel Chamber and Nozzle **
The chamber mass depends on the paraffin grain geometry. The
initial port diameter of the fuel grain,

*Dint,g*(0), is calculated by
RL10B-2 16820 2457
AJ10-118K 6004 950 0.86
= (

*m*& π

*G*
11D58M 14600 2720
where

*Go*(0) is the initial mass flow rate of oxidant per unit area in
the fuel chamber, assumed as 250 kg/m2/s for peroxide fed by a
Source: Isakowitz et al. (1999).
vortical injector, to avoid blowout. The regression rate of hybrid
fuels (Humble and Altman, 1995) is adjusted experimentally by
The total mass flow rate of propellants,

*m*&
, is related to the

*prop*,

*j*
thrust and to the specific impulse by
=

*aG *(

*t*) (13)

*Isp g *. (6)
where

*t* is time and

*a* and

*n* are experimental constants. Equation

*prop*,

*j*
(13) is derived assuming a turbulent reactive-diffusive boundary
layer adjacent to the fuel grain, differently from a solid propellant
The fuel mass flow rate,

*m*& , limits the thrust levels, due to the

*f *,

*j*
rocket. For a constant oxidizer mass flow rate,

*m*& , the oxidizer flow
relatively low regression rates of hybrid fuels. It is related to the
rate per unit area,

*G*
total mass consumption rate of propellants and to the

*OF*
*o*, and the regression rate,

*r*& , decrease with time,
since the fuel port area increases during the burning period.
(oxidizer/fuel) mass ratio, by the relation:
Assuming a single circular port, integrating Eq. (13) from

*t* = 0
to

*t* =

*t*
1 +

*OF *. (7)

*b*, yields the fuel grain external diameter,

*Dext,g*:

*f *,

*j*
*prop*,

*j*
*m*& π

*t *+

*D *+
The oxidizer mass flow rate,

*m*& , is calculated by

*o *,

*j*
and the grain length,

*Lg*, is given by

*m*& =

*m*&
1 +

*OF *=

*m*&

*o*,

*j*
*prop*,

*j*
*prop*,

*j*
*f *,

*j*
*L *= 4

*V*
⎡⎣ (

*D *−

*D *(0) ⎤
The burning time,

*tb,j*, is obtained from
The fuel chamber internal diameter is

*Dint,c* =

*Dext,g* + 2

*tins*, where

* *
*b*,

*j*
*prop*,

*j*
*prop*,

*j*
*tins* = 0.003 m is assumed as the insulation thickness, a minimum
value for support and molding of the grain. The fuel chamber
The fuel and oxidizer volumes,

*Vf,j* and

*Vo,j*, are calculated, external diameter is

*D*
+ 2

*t *, where

*t*
*w,c* is the chamber
respectively, by
wall thickness, given by
ρ , with

*m *=

*m*
1 +

*OF * (10)

*o*,

*j*
*prop*,

*j*
*o*,

*j*
*o*,

*j*
*o*,

*j*
= 1+

*f P D*
*s *)

*c*
1 +

*OF * (11)

*f *,

*j*
*prop*,

*j*
*f *,

*j*
*f *,

*j*
*f *,

*j*
*c* is the chamber pressure,

*σc* is the yielding tensile of the
chamber material and

*f*
*s* is a safety factor for the chamber wall
stress, assumed as 100%.

**504** / Vol. XXXII, No. 4, October-December 2010

Preliminary Analysis of Hybrid Rockets for Launching Nanosats Into LEO
The fuel chamber comprises the catalytic bed, injection plate,
wall thickness and the mass of the spherical oxidizer tank are,
fuel grain section, pre-combustion section, post-combustion section
and nozzle convergent. The catalytic bed decomposes the hydrogen
peroxide, by an exothermic reaction which generates H2O and O2 at
= 0.25 1+

*f P D*
*s *)

*o*
high temperatures, to ignite and burn the fuel grain. The pre-
combustion, post-combustion and catalytic bed (including injection

*m *= (1+

*f *) ρ (π 6

*D*
plate) lengths are assumed as

*Lpre* = 0.5

*Dint,c*,

*Lpos* = 0.7

*Dint,c* and

*Lcat*
= 0.5

*Dint,c*, respectively, which are estimated to allow oxidizer
atomization, complete burning and full catalytic decomposition. The
where σ

*tk,o* is the yielding tensile of the tank material,

*ftk* =
length of the nozzle convergent section is

*mweld+sup*/

*mtk* ≈ 0.2 is a tank mass fraction used for welding and
support, and

*D*
is the external diameter of the
= 0.5(

*D *−

*D *) tanθ
A cylindrical tank with two hemispherical domes is used in the
where θ

*con* = 45o is the convergence semi-angle. Thus, the fuel first stage. The total length,

*Ltko*, wall thickness,

*tw,tko*, and mass,

*mtko*,
chamber length of a stage is
of the cylindrical tank are, respectively:

*L *=

*L *+

*L*
+

*L *+

*L *+

*L*
*L *=

*D*
and its mass is, approximately,
= 0.5 1+

*f P D*
*s *)

*o*
*m *≅ 0.25(1+

*f*
πρ ⎡

*L D*
*ex *t,

*c*
*m *= (1+

*f *) ρ (π 6 ⎡

*D*
*t *(

*D*
−

*D *) tanθ ⎤

*c*,

*tko *⎦ (27)
where ρ

*c* is the fuel chamber wall density and

*fcat* =

*mcat*/

*mc* ≈ 0.2
is a mass fraction corresponding to the catalytic bed

*.*
= 4(

*V *+

*V *− (π 6

*D*
is the length of
) 3

*int,tko *) ( 2
The throat area is calculated from

*A *=

*F C P *, where

*C*
the cylindrical section of the oxidizer tank.
the thrust coefficient, obtained from NASA CEA 2004 code, for a given nozzle expansion rate, ε, and chamber pressure,

*Pc*. Therefore, the nozzle exit area is

*A *= ε

*A * and the throat diameter is

**Pressurizing System **
*D *= (

*A *π )1/2
The oxidizer is pressurized by a gas generator using H2O2 at 70
% in mass decomposed at a catalytic bed. The pressurizer mass is
Considering a conical nozzle, the nozzle divergent length and
mass are approximated, respectively, by

*V *+

*V*
*R T * (28)

*pres *(

*u*
*L *= 0.5

*D *−

*D*
where

*fpres * ≈ 0.05 is a pressurizer mass fraction (pressurizer mass
in the lines / pressurizer mass in the tank) for filling the feeding

*m *= 0.5ρ

*t*
π (

*D *+

*D *)((

*D *−

*D *) 4 +

*L*
(21) lines and

*Rpres* is the gas constant of the decomposed pressurizer.
The liquid pressurizer (70% H2O2) is assumed at constant pressure

*Ppres* = 1.2

*Po*, to overcome pressure losses in the valves and avoid
where θ

*div* is the divergence semi-angle,

*De* is the nozzle exit flow instabilities, with density ρ

*pres* and volume

*Vpres* =

*mpres*/ρ

*pres*.
diameter and

*t*
= 0.5

*t * is the average nozzle wall thickness.
The internal diameter, the wall thickness, with

*fs* = 1, and the
mass of the spherical pressurizer tank are, respectively:

**Oxidizer Tank **
Spherical oxidizer tanks are used in the second and third stages,
with internal diameter,

*Dint,tko*, given by
= ( (

*V *+

*V *) π )1 3
(1+

*f *)(π 6

*D*
int,

*tkpres *)
where

*Vu* ≈ 0.05

*Vo* is the initial

*ullage* of the oxidizer tank to allow
A small helium tank with a blowdown ratio

*r*
space for the pressurizer gas and thermal expansion of the liquid

*p* =

*PHe,i*/

*PHe,f* = 5 is
used to pressurize the liquid 70% H
2O2. The final pressure at the
helium tank is assumed

*P*
The oxidizer pressure in the tank is

*P*
*He,f* = 1.2

*Ppres*, to overcome pressure losses

*o* =

*Pc* + Δ

*Po*, where

* Pc* is
in the valves, and the initial helium volume, assuming an isothermal
the combustion pressure and Δ

*Po* ≈ 0.2

*Pc* MPa is the total pressure
expansion process, is

*V*
(

*r *− 1) , which is equal to the
loss in lines, injection and valves. The pressure loss is mainly due to
injection and it is relatively large to avoid flow instabilities. The
helium tank volume,

*VtkHe*.

**J. of the Braz. Soc. of Mech. Sci. & Eng. **
**Copyright **** 2010 by ABCM **
October-December 2010, Vol. XXXII, No. 4 /

**505 **
Fernando de Souza Costa and Ricardo Vieira

**1st stage **
H2O2 70% catalytic bed
valve paraffin nozzle

**3rd stage **
**2nd stage **
He valves paraffin
He catalytic beds
H2O2 70% catalytic beds

**Figure 1. Three stage hybrid rocket configuration scheme. **
Then, the mass of helium is
= ρ

*L *(π 4

*D*
*int,case *)

*m *= 1.2

*r P V*
*R T * (32)
Therefore, the total inert mass of a stage is, approximately,
and the internal diameter, wall thickness and mass of a spherical
≅ 1.1

*m *+

*m *+

*m *+

*m*
helium tank are, respectively,
+

*m *+

*m*
which also includes a 10 % increase corresponding to the masses of
= 0.25(1+

*f *)

*P D*
the control system, telemetry, valves, feeding lines, stage coupling
and other devices. Figure 1 shows a scheme of a typical hybrid
(1+

*f *)(π 6

*D*
rocket configuration.

*int,tkHe *)
is the external diameter and ρ

**Results and Comments **
the material density of the helium tank.
Table 3 shows the initial conditions and Table 4 shows the
mechanical properties of materials used for the mass distribution analysis. Titanium was used in all tanks, stainless steel was used in

**Stage Case **
the chambers and nozzles, and carbon fiber was used in the cases
The total stage case length is, approximately,
and fairing. Ground and air-launched hybrid rockets with three
stages were compared in order to place a 20 kg payload into a low
≅ 1.1

*L *+

*L *+

*D*
Earth circular orbit at 300 km height.
(

*c tko ext*,

*tkHe ext*,

*tkpres div *)
Propellants are 98% H2O2 and C20H42 paraffin mixed with 10%
aluminum in mass. Aluminum increases the specific impulse and
which includes, as a first estimate, depending on available reduces the optimum

*OF* ratio. The paraffin regression rate
equipments and technology, a 10% increase corresponding to constants were based on Brown and Lydon (2005) data which
spacing for control system, telemetry, valves, feeding lines, stage
obtained

*a* = 0.0344 (mm/s)(m2s/kg)

*n* and

*n *= 0.9593 (non-
coupling and other devices.
dimensional) for paraffin burning with 84% hydrogen peroxide. The
In the third stage it is included a fairing, assumed as cylinder
regression rate was multiplied by 0.98/0.84, for the richer peroxide
with 0.8 m height and 0.6 m diameter, to carry a nanosatellite with a
solution used, since the reaction rate in the turbulent reactive-
volume of, approximately, 0.4 × 0.4 × 0.4 m3. The internal diameter
diffusive boundary layer is proportional to the oxidizer mass
of the stage case,

*Dint,case*, is assumed equal to the external diameter
of the oxidizer tank plus 0.04 m for tank support rings, which are
Figure 2 shows the theoretical specific impulse and the thrust
used to increase stiffness, connection with the rocket case and allow
coefficient obtained with the NASA CEA 2004 code, assuming

*P*
electric wiring and cabling passage. The external diameter of the
30 atm, equilibrium flow and adapted nozzles. It is verified that
stage case,

*Dext,case*, depends on material compression strength and chamber pressures have no significant effects on

*Isp* and that the
on the applied compression force due to the rocket acceleration:
maximum

*Isp* values are obtained with

*OF* ≈ 6.5.
Assuming

*Pc* = 2.5 MPa,

*OF* = 6.5,

*F*/

*W* = 2.5,

*CF* efficiencies of
+ 4

*m g *(1+

*F W *πσ ⎤
93% and initial

*f*
⎣

*int,case*
*inert* = 0.2 in all stages, the masses and sizes of the
main components and stages were calculated. A new inert fraction
was calculated for each stage and compared to the previous one. If

*int,case* is the case internal diameter and σ

*c* is the compression
strength of the case material. The compression strength of the case
the difference was less than 0.01% the calculation was stopped, if
was assumed to be equal to its yielding strength. Nevertheless, a
not a new iteration was made. In general, 6 iterations were enough
minimum thickness of 2 mm was considered for all stages, for for convergence. Table 5 shows the final mass distributions and manufacturing purposes. The stage case mass is calculated by
additional data of air and ground launched hybrid rockets to perform
the assigned mission, using three stages.

**506** / Vol. XXXII, No. 4, October-December 2010

Preliminary Analysis of Hybrid Rockets for Launching Nanosats Into LEO

**Table 3. Initial conditions for 3-stage hybrid rockets. **
**Ground launched **
**Air launched **
Δ

*Vtotal* (m/s)
1st 2nd 3rd 1st 2nd 3rd
Δ

*V* (m/s)
3100 3100 3100 2900 2900 2900
Expansion rate (ε) 10 40 60 10 40 60
F

* ***(-)**
257 290 297 257 290 297

**Table 4. Materials and mechanical properties. **
Fuel chamber/nozzle

*A e */

*A t*
**Figure 2. Specific impulse, Isp, and thrust coefficient, CF, versus expansion **
* E* = bulk modulus; σ = tensile yield strength.

**rate, **ε

**, for 98% H2O2 burning with paraffin 90% C20H42 and10% Al, at Pc = 30 **
Source: www.matweb.com

**atm, assuming equilibrium composition and adapted nozzles. **
Figures 3 and 4 compare the effects of

*OF* mass ratio on stage
mass and on inert fraction, respectively, for ground and air launched rockets. Figures 5 and 6 show the effects of the

*F*/

*W* ratio and
chamber pressure, respectively, on mass and inert fraction of air
launched rockets. Figures 7 and 8 show the effects of the

*F*/

*W* ratio
and chamber pressure, respectively, on length and diameter of air
launched rockets.
It can be seen in Table 5 that the masses and sizes of air-
launched rockets are significantly smaller, about 60% of the masses
and 82% of the sizes of ground launched rockets. The payload
fraction and total lengths of ground and air launched rockets are
about 0.26% and 18 m, and 0.43% and 14.7 m, respectively. Figures 3 and 4 depict that the minimum total mass is found with

*OF* = 6.5,
corresponding to the maximum

*Isp*, whereas the inert fractions are
lower with

*OF* = 7. Inert fractions for first stages are below 20%,
whereas third stages present inert fractions above 25%. The large
inert fractions and low payload ratios obtained using the preliminary
mass distribution model can be explained by the conservative

**Figure 3. Effects of OF mass ratio on stage mass of ground launched (GL) **

parameters adopted. Lower

*F*/

*W* ratios and lower chamber pressures

**and air launched (AL) hybrid rocket stages, with Pc = 2.5 MPa and F/W = 2.5. **
yield smaller sizes and masses for all stages. First stage tanks could
have larger diameters in order to reduce the total lengths. Using
more advanced materials would also allow to obtain lower masses and sizes.
It is seen that the inert fraction is strongly affected by the
oxidant pressures, especially in the first stages, whereas variations
on

*F*/

*W* and

*OF* in the ranges considered do not show significant
effects on inert fractions and sizes, for all stages.
The 10% mass increase adopted in Eq. (38), considered for
control system, telemetry, wiring, etc., may be reduced in a second
mass distribution analysis, depending on a deeper knowledge of the
available technology. As a consequence the payload fraction could be correspondingly increased.
It should be noted that the mass distribution of existing systems
showed in Tables 1 and 2 refer only to the solid and liquid engines
and do not include additional masses, such as fairing, rocket casing,
connections, rings, control devices, etc., for the entire rocket and
stages which were considered to generate the data in Table 5.

**Figure 4. Effects of OF mass ratio on inert fraction of ground launched **
**(GL) and air launched (AL) hybrid rocket stages, with Pc = 2.5 MPa and **

F/W = 2.5.
**J. of the Braz. Soc. of Mech. Sci. & Eng. **
**Copyright **** 2010 by ABCM **
October-December 2010, Vol. XXXII, No. 4 /

**507 **
Fernando de Souza Costa and Ricardo Vieira

**Table 5. Preliminary mass distribution and other data for hybrid rockets. **
**Ground Launched **
**Air Launched **
**Item Unit **1st

kg 7812.676 1048.527 179.351 4690.856 763.526 150.016
kg 1048.527 179.351 20.000 763.526 150.016 20.000

*mT – mpay *
kg 6764.149 869.176 159.351 3927.330 613.510 130.016
kg 4792.319 603.136 101.778 2779.250 422.989 81.935
kg 737.280 92.790 15.658 427.577 65.075 12.605
kg 1234.550 173.249 41.950 720.504 125.447 35.475
kg 460.129 52.573 8.816 259.244 36.778 7.119
kg 29.514 7.474 1.049 14.677 4.838 0.818
kg 318.923 27.101 4.573 184.581 19.006 3.682
kg 6.760 0.851 0.144 3.921 0.597 0.116
kg 117.558 14.795 2.497 68.176 10.376 2.010
kg 0.677 0.085 0.014 0.392 0.060 0.012
kg 8.644 1.088 0.184 5.013 0.763 0.148
kg 134.99 48.046 19.878 93.211 37.767 17.579
m 10.35 4.414 3.195 8.563 3.885 2.221
m 1.188 0.992 0.568 0.992 0.886 0.531
s 72.747 77.009 77.857 70.266 74.167 74.941
N 191538 25706 4398 115002 18719 3678
0.1825 0.1993 0.2630 0.1835 0.2045 0.2729

*F */

*W*
**Figure 5. Effects of ***F***/***W*** ratio on stage mass and inert fraction of air **
**Figure 6. Effects of chamber pressure on stage mass and inert fraction of **
**launched hybrid rockets, with ***Pc*** = 2.5 MPa and ***OF*** = 6.5. **
**air launched hybrid rockets, with OF = 6.5 and F/W = 2.5. **
**508** / Vol. XXXII, No. 4, October-December 2010

Preliminary Analysis of Hybrid Rockets for Launching Nanosats Into LEO
The authors acknowledge FAPESP (São Paulo State Foundation
for Science Support) for financial support to this research through
grant 2007/03623-8.

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**J. of the Braz. Soc. of Mech. Sci. & Eng. **
**Copyright **** 2010 by ABCM **
October-December 2010, Vol. XXXII, No. 4 /

**509 **
Source: http://plutao.sid.inpe.br/col/dpi.inpe.br/plutao/2010/12.02.14.25/doc/v32n4a12.pdf

terapia de Tener paz no es estar sin crisis, sino estar presentes en el centro terapia de A lo largo de la Historia, la humanidad realización y la trascendencia. muchas alteraciones de la salud ha utilizado diferentes propuestas de La sintergética supone toda una son producto de modificaciones salud, todas ellas válidas, todas ellas

Clinical dermatology • Original article Hyperbaric oxygen therapy for nonhealing vasculitic ulcers S. Efrati,*† J. Bergan,* G. Fishlev,* M. Tishler,‡ A. Golik† and N. Gall* *The Institute of Hyperbaric Medicine and Wound Care Clinic, †Department of Medicine A, and Department of Medicine B, ‡Assaf Harofeh Medical Center,Zerifin, Israel (affiliated to Sackler School of Medicine, Tel Aviv University, Israel)