Rocket Motors, Hybrid

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Encyclopedia of Physical Science and Technology EN014G-835 July 31, 2001 16:56

Rocket Motors, HybridDavid AltmanSpace Propulsion Group, Inc., and Stanford University

I. IntroductionII. Burning RateIII. Motor BallisticsIV. Propulsion SystemV. Propellant Combinations

GLOSSARY

Blocking parameter A measure of the reduction in heattransfer due to blowing; represented by CH /CHO orCf /Cfo.

Blowing coefficient Ratio of gas flow from a surface tothe axial flow; denoted B.

Entrainment The injection of liquid droplets into a gasstream.

Fuel mass flow The rate at which fuel is gasified from aunit area of surface; denoted mf.

Heat of gasification Total heat required to gasify a solidfrom its ambient temperature; denoted hv.

Heat transfer Rate at which heat is transferred from theflame to a surface; denoted Q.

Mass flux Mass rate of flow of a fluid per unit area ofcross section in the port; denoted G.

Mixture ratio Ratio of oxidizer to fuel burned; denotedO/F.

Regression rate Linear rate at which a solid fuel re-gresses due to gasification; denoted r .

Stanton number Coefficient that relates the heat

transfer rate to the heat of combustion; denotedCH.

A HYBRID ROCKET uses both a liquid and a solid aspropellants. In the typical classical hybrid, the fuel is asolid and the oxidizer is a liquid (see Fig. 1). However, itis possible to use solid oxidizers with liquid fuels; suchcombinations have been called “reverse hybrids.” Unlessotherwise specified, the classical hybrid with the solid fuelgrain will be assumed.

Although many components are common to liquid andsolid rockets, the operation of a hybrid is distinctly dif-ferent. In the solid rocket, the oxidizer and fuel are inti-mately mixed in the single solid phase and combustionoccurs when the exposed surface is heated by the com-bustion flame to the ignition temperature. In the liquidrocket, both oxidizer and fuel are intimately mixed in thevicinity of the injector to form a combustible mixture. Inboth cases, therefore, everywhere in the combustion cham-ber there is a uniform mixture of both oxidizer and fuel.The hybrid, however, burns as a macroscopic diffusion

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304 Rocket Motors, Hybrid

FIGURE 1 Schematic of a hybrid rocket.

flame where the oxidizer-to-fuel ratio (O/F) continuallydecreases down the length of the chamber.

I. INTRODUCTION

A. Why Hybrid?

The fundamental difference between a hybrid and the liq-uid or solid rocket leads to a number of distinguishingcharacteristics. The advantages are:

• Safety. The fuel is inert and can be manufactured,transported, and handled safely in accordance with stan-dard commercial practice. The system is nonexplosivesince an intimate mixture of oxidizer and fuel is notpossible.

• Simplified throttling and shutdown. The engine canbe throttled by modulating the liquid flow rate, which issimpler than in a liquid rocket, where two flow rates mustbe synchronized while being modulated. In the hybridrocket, the fuel flow rate, which results from vaporiza-tion from the solid surface, automatically adjusts to thechange in oxidizer flow rate. Consequently, thrust termi-nation is simply accomplished by turning off the liquidflow rate, a feature of significance in an abort procedure.

• Grain robustness. Unlike solid rockets, fuel graincracks are not catastrophic because burning only occursdown the port where it encounters the oxidizer flow.

• Propellant versatility. The selection of propellants ismuch greater than with either liquids or solids. In con-trast to liquids, solid constituents such as dense, energetic

metals can be added to enhance both performance anddensity without resorting to slurries. In contrast to solids,the oxidizers provide much higher energy levels.

• Temperature sensitivity. Since the temperature effecton burn rate is negligible (as in liquids), no margin needbe applied to the thrust chamber weight to account for ahigh ambient launch temperature, which would increasethe maximum expected operating pressure (MEOP).

• Low cost. The total operational cost for hybrid sys-tems benefits greatly from the safety features and inertpropellant. Manufacture of the fuel can be done in a com-mercial facility that does not require the large acreageand many buildings for solid propellant manufacture. Asa consequence, the fuel plant can be located at or near thelaunch site. Furthermore, the system can tolerate largerdesign margins, resulting in a lower fabrication cost.

These advantages, however, are not enjoyed withoutsome disadvantages, such as:

• Low regression rate. The small resulting fuel webmeans that most combustion chambers over 1 ft in diam-eter require multiple ports. But this characteristic is desir-able for long-duration applications such as target drones,hovering vehicles, and gas generators.

• Low bulk density. A consequence of the low regres-sion rate is that a large grain surface area must be providedto supply the required thrust. This is generally done withmultiple ports that lead to a relatively low volumetric fuelloading and results in a moderate fuel sliver loss. However,recent efforts to increase the regression rate have reducedthis disadvantage.



Rocket Motors, Hybrid 305

• Combustion efficiency. The nature of the large diffu-sion flame results in a lower degree of mixing and hencelower impulse efficiency. This loss is generally 1–2% morethan in either liquids or solids. In comparison with solids,however, the delivered specific impulse Isp is greater.

• O/F shift. The opening of the port during burningcauses an O/F shift with burning time, which can lowertheoretical performance. With proper design of the initialO/F, however, this loss is usually minimal.

• Slower transients. The ignition transient is slower,as is the thrust response to throttling. In most practicalapplications, where reproducibility is more important thanspeed of response, this aspect is not significant.

B. History

Despite the fact that hybrid rockets have not enjoyed thesame extensive development background as solid and liq-uid motors, hybrid combustion involving a solid and afluid has been nature’s way of burning fuels and oxidiz-ers. Examples are (1) a wax candle or oil lamp burning inthe presence of atmospheric oxygen, with the wick beingthe flame holding device, (2) a fireplace, where the bel-lows serves as a means of increasing the “oxidizer massflux” and therefore the burning rate, and (3) on a granderscale, a forest fire involving the turbulent mixing of airand the vaporized fuel exuding from the trees. Here again,the augmenting effect of wind velocity is well known.

Because of its nonexplosive character, safety of opera-tion, and low cost, the hybrid rocket has been a favoriteof amateur rocketeers. The earliest work on hybrid rock-ets was conducted in the late 1930s in Germany at I. G.Farben and in the United States at the California RocketSociety. Leonid Andrussow, in conjunction with O. Lutzand W. Noeggerath, tested a 10-kN hybrid in 1937 us-ing coal and gaseous nitrous oxide (laughing gas). Duringthe same period, Oberth, in Germany, did some work onthe more energetic LOX–graphite propellant combination.Neither of these last two efforts was successful becausethe very high heat of sublimation of carbon results in anegligible burning rate.

In the early 1940s, a more successful effort was con-ducted by the California Pacific Rocket Society, employ-ing LOX and several fuels such as wood and rubber. Ofthese combinations, the LOX–rubber combination was themost successful and a rocket using these propellants wasflown in June 1951 to an altitude of about 9 km. Althoughthe Society did not report any ballistic analyses, they didhave an accurate concept of the fundamentals of hybridburning as evidenced by the following statement: “Thechamber pressure of a solid–liquid rocket engine is pro-portional to the oxidizer flow and not to the internal surfacearea exposed to the flame. Thus, there is no danger of ex-

plosions due to cracks and fissures in the charge as withsolid propellant rockets.”

In the mid-1950s, two significant hybrid efforts oc-curred. One was by G. Moore and K. Berman at GeneralElectric, involving the use of 90% hydrogen peroxide andpolyethylene in a rod and tube grain design. The com-bustion was very smooth, resulting in a high combustionefficiency. The authors drew several very significant con-clusions: (1) the longitudinal uniformity of burning wasremarkable, (2) grain cracks had no effect on combustion,(3) hard starts were never observed, (4) combustion wasstable since the fuel surface acted as its own flame holder,and (5) throttling was easily accomplished by a singlevalve. The authors observed, however, that the burningrate was low and could not be varied significantly. Thesecond significant effort was by William Avery at the Ap-plied Physics Laboratory, who investigated a “reverse hy-brid” composed of a liquid fuel (JP) and a solid oxidizer(ammonium nitrate). The primary motivation for this pro-pellant selection was low cost. Technically the programwas not successful because of the rough combustion andpoor performance.

During the 1960s, two European countries engaged inhybrid studies leading to flight tests of sounding rock-ets. These organizations were ONERA (in conjunctionwith SNECMA and SEP) in France and Volvo-Flygmotorin Sweden. The ONERA development used a hypergolicpropellant based on nitric acid and an amine fuel. Thefirst flight of this vehicle occurred in April 1964, followedby three flights in June 1965 and four flights in 1967. Alleight flights were successful, reaching altitudes of 100 km.The Volvo-Flygmotor rocket was based on a hypergoliccombination using nitric acid and Tagaform (polybutadi-ene plus an aromatic amine). It was flown successfully in1969 to an altitude of 80 km carrying a 20-kg payload.

United Technologies Center (Chemical Systems Divi-sion [CSD] of United Technologies Corp.) and Beech Air-craft developed a high-altitude supersonic target drone inthe late 1960s called the Sandpiper, using MON-25 (25%NO, 75% N2O4) and polymethyl methacrylate (PMM)-Mg as the fuel. The first of six flights occurred in January1968 and these rockets flew for over 300 sec and with arange in excess of 100 miles. The HAST, a second version,carried a heavier payload and was based on an IRFNA-PB/PMM propellant combination. This 13-in.-diametermotor was throttleable over a 10/1 range. A later versionof this vehicle, the Firebolt, was developed by Chemi-cal Systems Division (CSD) and Teledyne Aircraft, usingthe same propulsion configuration as the HAST. Thesethree programs were successfully conducted over a 15-year period until the mid-1980s. These target drone rocketswere the only hybrid propulsion systems built to militaryspecifications.




FIGURE 2 Hybrid motor firing with FLOX oxidizer (F2 + O2).

An investigation of the use of high-energy hybrid pro-pellants based on a lithium-containing fuel and FLOX(F2 + O2) as the oxidizer was conducted by CSD in themid-1960s. This led to a hypergolic propellant system thatwas throttleable and demonstrated a vacuum Isp of 380 secat 93% Isp efficiency. A firing of this 42-in.-diameter mo-tor in 1970 is shown in Fig. 2, which is taken from thecover of the January 1970 issue of Aviation Week.

The largest hybrid rockets built to date had a thrustlevel of 250,000 lb and used LOX/HTPB propellant. Theywere made by American Rocket Company (AMROC) andwere designed for use in a space vehicle and a high altituderocket (HYTOP). Another hybrid rocket at about the samethrust level built by a consortium of Lockheed Martin,Thiokol, and CSD and sponsored by NASA was fired inthe late 1990s. However, neither of these rockets was flighttested.

II. BURNING RATE

A. The Combustion Model

The combustion process in the hybrid motor is distinctlydifferent from that in either the liquid or solid motor,where the oxidizer and fuel are intimately mixed. Inthe hybrid motor, combustion occurs as a macroscopic

diffusion flame, where the oxidizer is injected at the headend and the fuel is uniformly vaporized down the port.Although this fundamental distinction appears at firstas a potential complexity in hybrid ballistic design, it isprecisely this feature of separation of oxidizer and fuelthat accounts for the nonexplosive characteristic of thehybrid and its consequent greater safety in manufacture,storage, handling, and operation.

In the hybrid combustion chamber an atomized liquidflows down the port reacting near the surface of the solidfuel. Experimental investigations have shown that the con-trolling factors in the combustion process are the rate ofheat transfer to the solid surface and the heat of decom-position of the solid-phase fuel. The mass flux, which isregulated by the rate of flow of the liquid phase, deter-mines the rate of heat generated in the combustion zoneand hence determines both the heat transfer and the thrustmagnitude.

The combustion phenomenon is similar to that of a tur-bulent diffusion flame, where the flame zone is establishedwithin the boundary layer. Experimental measurementsof gaseous oxygen reacting with Plexiglas fuel have con-firmed this basic model, as is shown in the Schlieren pho-tograph in Fig. 3. It is convenient to represent this processby an idealized model in which the flame zone is treatedas the region where the opposing flows of oxidizer fromthe port and vapor from the fuel surface meet, as shownin Fig. 4.

In the real case of finite combustion kinetics, the flamezone is thickened, with continuous gradients in both tem-perature and composition. The combustion zone is estab-lished at that point where an approximate stoichiometricmixture ratio has been achieved. The important feature ofthis model shows that the combustion zone occurs withinthe turbulent boundary layer at a distance from the solidwall yb which is less than the momentum boundary layerthickness. The axial velocity at the flame ub is also lessthan that at the outer edge of the boundary layer ue. Thisis the basic model used to develop the mathematics of thecombustion process as discussed in the following sections.

B. The Regression Rate Equation

In the literature on hybrid motors, it has become commonto refer to the burning rate of the fuel as the regressionrate since, as can be seen in Fig. 4, combustion is dis-placed from the fuel surface and actually occurs withinthe momentum boundary layer. The heat transfer from thecombustion zone to the fuel surface causes it to regress as itvaporizes to feed the combustion layer. The common termfor regression rate, r , stems from early derivations, wherer referred to the radius of a circular port in the grain and rto its rate of change. In solid propellants, however, early




FIGURE 3 Schlieren photographs of the hybrid combustion boundary layer at Go = 0.0216 lb/in.2-sec.

burning rate theories considered flat “cigarette burning”surfaces and the term r is commonly used as an abbrevi-ation for the rate of burning.

1. Convection Model

The energy equation that expresses the balance betweenthe heat transfer and the heat of gasification is

Qw = mfhv, (1)

where Qw is the rate of heat transferred to the wall (fuel),mf is the rate of fuel gasification, and hv is the total ef-fective heat of gasification, i.e., the heat content of the

FIGURE 4 Hybrid combustion model. The combustion zone is within the boundary layer at a region where the counterdiffusion flows of oxidizer and fuel are approximately equal. The thickened combustion zone is due to turbulence andfinite kinetics.

gaseous fuel at the surface less the heat content of thesolid fuel at the ambient temperature. In general, hv in-cludes three terms: (1) the heat to warm the solid to thesurface temperature, (2) thermal changes prior to gasi-fication (such as depolymerization), and (3) the heat ofvaporization. If the fuel contains a solid which does notvaporize at the surface, then it includes the heat to simplyraise the particle temperature from ambient to the surfacetemperature.

The convective heat transfer to the wall can be expressedin terms of the Stanton number CH:

Qc = CHρbub�h, (2)




where ρ b and ub are, respectively, the density and velocityof the gas in the flame zone within the boundary layer and�h is the specific enthalpy difference between the flameand the wall. The evaluation of CH is similar to that inconventional pipe flow in that it is given in terms of thefriction factor Cf, but with two major corrections. Oneaccounts for the fact that the heat source is located in thecombustion zone within the boundary layer, resulting inthe formula

CH = (Cf /2) ρeu2

e

ρbu2b

. (3)

The other correction accounts for the fact that the heat flowmust travel upstream against a counterflow of fuel vapor.This latter correction, known as “blowing,” is expressedin a term that relates the fuel flow from the surface to themain core flow along the axis of the port and is designatedas B:

B = (ρv)w

(Cf /2)ρeue= r ρ

(Cf /2)G , (4)

where the axial flux ρeue is replaced by the total mass fluxG and (ρv)w by r ρ = mf, the mass flow of gas from thesurface.

Equations (1)–(3) may now be combined to yield forthe regression rate

mf = r ρ = Cf

2G

(ue

ub

�h

hv

). (5)

Comparing Eq. (5) with Eq. (4), we can see that whereconvection is dominant, the blowing term B is also givenby the term in the parenthesis:

B =(

ue

ub

�h

hv

)= Bt . (6)

The term Bt, also known as as the mass transfer num-ber, can now be evaluated in terms of thermodynamicquantities. An approximate value of ue /ub has beenfound to be in the range of 1.5–1.7 for several sys-tems and is less variant than �h /hv. The evaluation ofthe friction coefficient is made from the turbulent em-pirical law in the absence of blowing (Prandtl numberPr = 1): Cfo /2 = 0.03(µ/Gx)0.2, where µ is the viscosityand G is the mass flux at the distance x . The remainingparameter to be evaluated is the ratio Cf/Cfo (=CH/CHO)reflecting the blocking effect on the heat transfer coeffi-cient as shown in Eq. (3). The general equation for theregression rate is now

rρ = (Cf/Cfo)0.03(µ/x)0.2G0.8 Bt. (7)

This equation shows the combined effectiveness of blow-ing through the blocking parameter Cf/Cfo and the effec-tive heat of gasification hv which appears in Bt. Figure 5

FIGURE 5 Plot of the blocking parameter versus the blowingterm B. As shown in the text, the simple expression Cf/Cfo =B−0.68 gives an excellent fit in the range 5 < B < 20 coveringmost hybrid fuels. It has the virtue of resulting in the simplifiedregression expression shown in Eq. (8). (�) Exact, (+) [ln (1 + B)/B ]1.088, (♦) B−0.68.

shows a graph of Cf/Cfo versus the blowing term B. Theexact equation is

Cf

Cfo=

[ln(1 + B)

B

]0.8 (1 + 1.3B + 0.364B2

(1 + B/2)2(1 + B)

)0.2

,

This can be approximated by Cf/Cfo = [ln(1 + B)/B]1.088 and shows that the blocking can appreciably re-duce the heat transfer. In the typical B range of 5–20 forclassical hybrid fuels, the Cf/Cfo ratio is empirically givenvery closely by B−0.68, resulting in the final simplified re-gression rate equation

rρ = 0.03(µ/x)0.2G0.8 B0.32t . (8)

Note that the important fuel property that determines ris hv, which is incorporated in Bt as shown in Eq. (6).Equation (8), however, shows that this term is only raisedto the 0.32 power, which reflects the impact of blowingon the heat transfer. Thus, the regression rate is not verysensitive to the vaporization heat of the fuel, an observationthat holds true for a wide variety of fuels.

The practical equation used in engineering developmentis a condensation of Eq (8):

r = aGn xm, (9)

where the constants a, n, and m are empirically deter-mined. Equation (9) shows in principle that r varies downthe port, which could therefore result in a nonuniform ax-ial burning. This is so because the total mass flux G is thesum of the oxidizer flux Go and the fuel flux Gf, which in-creases down the port. Countering this effect, however, is




the boundary layer growth term expressed by xm , wherem is theoretically −0.2. The combination of these twoeffects tends to cancel, which results in a fairly uniformaxial regression rate. This is illustrated by conducting astepwise computer solution on Eq. (9) in conjunction withthe following two equations:

G(x) = Go + Gf(x) (10a)

Gf(x) = 4ρ

π D2

∫ x

0r (x, D) dx . (10b)

Computer simulations of port diameter versus x at differ-ent times in a circular port motor using Eq. (9) show thatexcept for the region close to the origin, the port diameterremains quite uniform. This result has indeed been ob-served experimentally and is of considerable significancein practical motor designs since it leads to the use of aspace-average regression rate.

If a suitable space average D can be assigned, then itcan be moved outside of the integral in Eq. (10b). Equa-tions (9), (10a), and (10b) can now be combined and afterseparation of variables and a Taylor expansion, the resultis

r = a′Gno xm

(1 + 2na′ρx1+m

DG1−no

), (11)

where a′ = a/(1+m). The advantage of this expression isthat it only contains input parameters and therefore doesnot require iteration. In practice, it is further found thatthe term in the parentheses does not vary much, and to afair approximation, the simple expression

r = aGno xm (12)

is very useful in preliminary design. Investigators in thefield will use any of the three equations (9), (11), or (12)based on the desire for precision or ease of use.

2. Radiation Correction

The radiation transfer from a gas at temperature Tr to awall at temperature Tw is given by the equation

Qr = σεw(εgT 4

r − T 4w

), (13)

where σ is the Stefan–Boltzmann constant and εw andεw are the emissivities of the wall (fuel surface) and gas,respectively. The term T 4

w is usually neglected since it issmall relative to Tr

4. The problem in applying this classicalequation to the hybrid motor is the nonuniform radiationenvironment, where the hot combustion gas occupies arelatively thin zone in the port. To take this feature intoaccount, it is customary to assign a typical average tem-perature in the combustion region. Although the equationdoes not provide an accurate quantitative prediction of theradiation transfer, it has a reasonable mathematical form

for the correction, which can then be useful for assigningempirical constants from experimental data.

Assuming a reasonable estimate of Qr is obtained andthe optical absorptivity in the solid is large, we can obtainits impact on the regression rate from the modified energyequation as shown:

mfhv = rρhv = Qcr + Qr, (14)

where Qcr is the conductive heat transfer in the presenceof a radiation field. It is important to make this distinc-tion because the increased mf increases the blowing andhence decreases the convective heat flow. Clearly, if radi-ation is added to convection, the increased heat transferwill increase r , but not in proportion to the increase inQr because of the increased blockage. The equation thatreflects this coupling effect is approximately given by

r/rc = exp(0.37Qr/Qc), (15)

where rc and Qc refer to values in the absence of radia-tion. As an example, if the radiation input is 50% of theconductive contribution, the increase in r is only 20%.

3. Pressure Effects

Some hybrid propellants have evidenced a pressure depen-dence of the regression rate in certain regions of operation.This dependence can occur for two reasons: (1) radiationemissivity is pressure sensitive through the optical densityterm, i.e.,

εg = 1 − e−bpz, (16)

where p is the pressure, b is a constant depending on flametemperature, composition, and percentage of metal, and zis the optical path length from the flame to the wall; and (2)combustion kinetics when the reaction time, which is pres-sure dependent, becomes comparable to or greater than thediffusion time of reacting species in the boundary layer.

The pressure effect due to radiation can be representedby a simple formula by combining Eqs. (12)–(15) to give

r = rc + k(1 − e−bpz) ∼= rc + kbzp. (17)

The last part of the equation is an expanded version forlow emissivity when bpz < 1. In a typical port, the opticalpath z will depend on the port diameter. Thus, the radiationcorrection will be influenced not only by the pressure p,as shown, but also by the motor scale through z. Thisbehavior has been observed experimentally where, at verylow flux rates (where G → 0), the regression rate tendsto flatten out, being dependent now on Qr, the radiationenvironment. The term (bz) can vary slightly during arun with changes in O/F and port diameter. The equationshows the right intuitive behavior for the radiation pressure




effect, i.e., no effect for large emissivity when the radiationis saturated, but an effect at low G when rc becomes smallrelative to the radiation term.

The kinetic pressure effect arises out of the pressuredependence of the kinetics of combustion, where the ratedepends on the concentration of reacting species, whichis directly related to pressure. Typically, in diffusion com-bustion, where the reactants are not premixed, the rate ofreaction is much faster than the diffusion of the reactants.In this case, the rate of combustion is diffusion limited.In the hybrid combustion model, the diffusion rate is gov-erned by the mass flux G. We may expect, however, thatat high flux levels and low pressure, the kinetics can berate determining, in which event a pressure dependencecan exist in r .

The combination of both radiation and kinetic effectson the regression rate is shown in Fig. 6 as a function ofthe mass flux G. Since the pressure effects due to radiationand kinetics occur at opposite ends of the mass flux, thischaracteristic provides a clue to the origin of the pressuresensitivity. The large bulk of hybrid fuels under typicaloperating conditions falls in the central diffusion-limitedregion. Some aluminized fuels have shown a pressure de-pendence that generally has been attributed to the higheremissivity of a particle-laden gas.

4. Temperature Sensitivity

The temperature sensitivity refers to the increase in burn-ing rate and therefore chamber pressure with ambient tem-perature. This quantity is especially important in solidrockets, which are not throttled, because of its impact onthe maximum expected operating pressure (MEOP) where

FIGURE 6 Radiation and kinetics effects on regression rate. Atlow G, radiation dominates heat transfer and the optical path Pz isinfluential. For large motors, z is determined mainly by D. At highG, turbulence diffusion rates can dominate and reaction rates,which are influenced by P, become rate determining.

the motor case has to be designed to sustain the highestpressure that can be realized during operation. In typicalhybrid fuel compositions, the latent heat of vaporization(or decomposition) of the solid is large compared to thevariation in heat content due to the expected extremes ofambient temperature. Therefore, the initial temperature ofthe solid material only slightly affects the rate of regres-sion. From Eq. (5), we can express r as a function of thesolid ambient temperature T , where hvo is evaluated at thereference temperature To. The result is

r ∼ [hvo − c(T − To)]−0.32. (18)

The temperature sensitivity of burn rate σp is defined as

σp = 1

r

∂ r

∂T= 0.32c

hvo − c(T − To). (19)

Because the main influence of ambient temperature onthe flow rate of combustion gases is through the burningrate equation, the temperature sensitivity of pressure forhybrids (πk) is simply

πk = 1

p

∂p

∂T= σp

1 + O/F. (20)

In solids, the term (1 + O/F) is omitted because the en-tire propellant including oxidizer and fuel is temperaturesensitive. In a hybrid, however, the important considera-tion is the effect σp has on the variation in fuel consumeddue to an ambient temperature change. For a typical hy-brid (c = 0.4 cal/g◦C and hvo = 300 cal/g at To = 273 K)σp ∼ 0.044%/K which reflects the percent variation of fuelweight. This is well within usual weight margins.

C. Regression Rate Measurements

1. Experimental Methods

The mass flow rates in Eqs. (10a) and (10b) show that r isa function of the local axial position and mass flux. How-ever, as mentioned earlier, the reasonably uniform axialburning contour justifies the use of a space-average re-gression rate that simplifies engineering design at a smallcompromise in precision. As a consequence, the large bulkof experimental data reported in the literature has beenobtained as space-average values. However, investigatorswhose prime interest is in studying basic mechanisms havepursued local methods of regression rate measurement.The typical local measuring techniques have involvedthe use of ultrasonic methods and embedded thermocou-ples that locally display the regression rate at a givenlocation.

A simple method for measuring the space-average re-gression rate is to make a weight measurement of the fuelgrain before and after the test. Although the change in




web thickness or grain diameter for a circular port can bemeasured directly, a more accurate evaluation is done bya weight loss measurement of the fuel. This is shown asfollows, where �m is the weight loss of the grain, D2 andD1 are the final and initial values of the diameter, respec-tively, ¯r is the average rate, ρ is the fuel density, and L isits length:

�m = π

4

(D2

2 − D21

)ρL

= π

4(D2 + D1) (D2 − D1)ρLt (21a)

¯r = D2 − D1

t= 4�m

π (D2 + D1)ρLt . (21b)

Since the measurement represents an average value overthe time interval t , it is desirable to have the runs fairlyshort so that the average values are close to instantaneous.

The measurements are made over a range of average ox-idizer mass flux Go and a logarithmic plot of r versus Go

gives the values of a and n in the regression rate equa-tion (12). The problem with this approach, which is espe-cially pronounced in small motors, is that if the burnedweb is small, measurement errors can be appreciable.On the other hand, if thicker webs are used to reduce theweight measurement error, an uncertainty occurs in theproper definition of Go. There are three averages forthe mass flux, which is defined as m/port area. The firstapproach selects a simple average D = (D1 + D2)/2 forcalculating the port area. The second employs an averageD2 = (D2

1 + D22)/2, and the third averages the initial and

final values of Go, i.e. Go = (1/2)(G01 + G02). These def-initions are shown in the following equations, where mo

is the constant oxidizer flow rate:

Go1 = 16 mo

π (D1 + D2)2 (22a)

Go2 = 8 mo

π(D2

1 + D22

) (22b)

Go3 = Go1 + Go2

2= 2 mo

π

(1

D21

+ 1

D22

). (22c)

It can be shown by integrating the regression rate Eq. (12)for a circular port that the minimum error incurred is onein which a linear average is used in Eq. (22a). As an exam-ple, if the ratio of final to initial port diameter is 2, the errorincurred is about 2% for a linear average, about 7% forthe average area, and about 20% for the average mass flux.Figure 7 shows a typical calculation with the three aver-ages compared with the accurate equation. The significantconclusion is that with Go1, relatively large diameter ratios(i.e., large burned webs) can be used to incur only smallerrors. This conclusion, which may seem counterintuitive,

FIGURE 7 Regression rate constant, based on Go average.The simple linear average for initial and final port diameters re-sults in minimum error. This somewhat surprising conclusion isbased on the mass flux power law. (�) Go1 = 4mo/π D2, (+)

Go2 = 4mo/πD2, (♦) Go3 = 12 (Go1 +Go2).

assumes that the conventional equation (12) is valid. It alsoapplies to Eq. (9), which employs total G = Go + Gf. Inthe latter case, mo in Eqs. (22a)–(22c) should be replacedby mo + mf/t as a close approximation when mf < mo, acondition satisfied by most common hybrids.

Some investigators have attempted to obtain the regres-sion rate parameters in a single motor test with a circularport. As the burning proceeds and the port diameter opensup, the mass flux decreases as well as the pressure. Therates of change of these parameters are related to the re-gression rate constants. By tabulating the pressure at var-ious times during the run and knowing theoretical c∗ as afunction of O/F, one can in principle obtain regression ratevalues during the course of the run. The auxiliary equationneeded is

ηc∗ = CD Pc At

mo + mf, (23)

where η is the combustion efficiency, CD the dischargecoefficient, and mf = π DρLr . A stepwise integration ofmf gives the values of �mf burned at a time t , and theport diameter D is then obtained from the mass balance:�mf = π (D2 − D2

1)ρ L/4. The fuel mass flow mf is in-tegrated over the course of the run and is then comparedwith the measured fuel burned. Care must be taken duringthe integration to record the change in c∗ with O/F. Theunknown parameter is the combustion efficiency η, whichis then adjusted by trial and error until the calculated andmeasured values of fuel burned are equal. Although thisapproach is mathematically neat, experience has shownthat it is fraught with uncertainty due to (1) the combustionefficiency adjustment, (2) the possibility of the change in




nozzle throat area At during the course of the run, and (3)calculation uncertainties in a stepwise integration.

2. Summary of Working Relations

The regression rate equations that have been used are sum-marized as follows:

r = aG0.8 L −0.2 (24a)

r = aGn Lm (24b)

r = aGno L

m (24c)

r = aGno L

m

(1 + 2ρanL1+m

DG1−no

)(24d)

r = aGn Lm[1 − exp(−D /Do)] (24e)

r = aGno L

m Dd p p . (24f)

Equation (24a) is the classical theoretical expression basedon the model shown in Fig. 4. The values of the expo-nents are obtained from the boundary layer theory. Equa-tion (24b) allows these exponents to be assigned empiri-cally based on modifications to the model which normallyoccur. It also has been shown to be an excellent technicalrepresentation of experimental data, but it has the draw-back of requiring an iterative calculation on the computer.For preliminary design estimates, it is convenient to useEq. (24c), which only involves input data. Because of itsconvenience, this equation has received the most exten-sive use in the experimental literature. As discussed ear-lier, Eq. (24d) is a modification of (24c) to incorporatethe effects of the fuel mass flux on G as derived earlier inSection II.B.1. Mathematically it approximates Eq. (24b)with the virtue of containing only input data. It has beenfound in many small-motor experiments that the port di-ameter has an impact on the regression rate, which mayinvolve a refinement of the theory to account for bothboundary layer interaction and radiation through the op-tical path. To take these effects into account, Eq. (24e)

TABLE I Regression Rates for LOX–HTPBa

Eq. r a n m Error (%)

(24a) aGn Lm 0.21 0.80 −0.20 5.6

(24b) aGn Lm 0.16 0.75 −0.13 4.0

(24c) aGno L

m 0.22 0.75 −0.14 5.5

(24d) aGno L

m (1 + 2 ρanL1 + m /DG1 −no ) 0.19 0.76 −0.14 4.1

(24e) aGn Lm [1 − exp(−D/Do)] 0.28 0.76 −0.24 2.9

(24f) aGno Lm D−0.06 p0.05 0.17 0.72 0.05 3.7

a Do is an empirical constant, about 1 in. for this propellant. The data are based on 35tests in which the diameter ranged from 2 to 11 in. The 24 small motors have average portdiameters of 2 in. most of which are circular, whereas the 11 large motors have triangularports with Dh values from about 7 to 11 in .

has sometimes been employed, where Do is an empiri-cal constant. This value is usually fairly small, so that inscaling to larger motors, the exponential approaches zero.Finally, the completely empirical equation (24f ) has beenproposed because it follows a classical chemical engineer-ing treatment. It is useful in describing variations withina mass of data where only interpolations are required.However, because of the arbitrary relation between thevariables, extrapolations are hazardous. In summary, theequations most extensively employed are (24b) and (24c).

Table I shows a summary of experimental data on aLOX–HTPB system covering 35 data points with a widerange of port diameters from 2 to 11 in. The followingobservations are of interest: (1) All expressions give asatisfactory representation of the data based on the aver-age error, (2) the average error is decreased with Eq. (24e),although the improvement is small, and (3) the simple the-oretical equation (24a) with assigned n and m exponentsprovides an acceptable small average error and is usefulin initially estimating regression rates with sparse data.

D. High-Regression-Rate Fuels

The conventional hybrid fuels are characterized by lowregression rates as compared to solid propellants. As aconsequence, relatively thin webs are required in most typ-ical applications, leading to poor volumetric fuel loadings.The various efforts to increase the regression rate gener-ally fall into two categories. The first approach involvesattempts to increase the heat transfer by generating tur-bulence through swirl motion or roughening the surface.This technique, however, has had limited effectiveness be-cause the increased gasification rate acts to decrease theheat transfer. The second approach involves incorporat-ing additives in the fuel which create an exothermic re-action at the surface, thus effectively reducing the heatof vaporization. Typical additives include solid oxidizerssuch as NH4ClO4, NN4NO3, and nitro compounds suchas RDX and HMX. In principle, these additives are added




in amounts just short of maintaining sustained burning.In that sense, they resemble low-energy solid propellants.However, in common with solid propellants, their burningrates show a pressure dependence. These propellant sys-tems have also been referred to as liquid-augmented solidswhere the incentive was to both impart throttleability andincrease the Isp with a more energetic oxidizer. Althoughthese additives have been effective, the amounts added toappreciably increase the regression rate elevate the ship-ping classification to explosive, and requires a more expen-sive manufacturing facility, similar to solid propellants. Itshould also be noted that since such partially oxidized fuelgrains border on sustained burning, they can compromisethe shutdown capability, especially in larger motors.

A more recent concept, which has proven to be muchmore effective, is based on utilizing fuels that developa melt layer of low viscosity which can entrain liquiddroplets under the influence of the shear force of the axialgas flow in the port. It has been shown that if the melt layeris sufficiently fluid, i.e., with low viscosity and surface ten-sion, then under a high gas flux environment (G), the shearstress can create an instability in the liquid layer, result-ing in the formation of liquid droplets that are expelledfrom the surface. This behavior is typical of cryogeniccompounds, which crystallize on solidification and ex-hibit high fluidity on melting. Also included are a class ofnonpolymerizable fuels, such as the alkanes, whose meltlayers are quite fluid. When liquid entrainment occurs, theresulting propellant flow from the surface is composed ofa mixture of vapor and liquid droplets. This occurrencecan have a profound effect on the regression rate, increas-ing it by many factors. There are two reasons for thiseffectiveness:

1. The droplets that are formed do not require a heat ofvaporization, but only a heat of fusion, which isgenerally several times less than vaporization.

2. Since the gas flow from the surface is reduced, theblowing term B is diminished, resulting in a reducedblocking of the convective heat transfer.

The effect of blowing on heat transfer (Fig. 5), showsthat with classical polymeric hybrid fuels (5 < B < 20),the heat transfer is reduced by a factor of about three tosix, whereas with entrainment, the reduction is typicallyless than a factor of two. The impact of this reduction isshown in Eq. (7). This effect exemplifies the effectivenessof porous wall cooling in combustion chambers whereblocking is desired. By the same token, it explains why,when gas emanates from a body moving in a fluid, thedrag is reduced.

The cryogens that have exhibited this behavior insmall lab-scale motors are the solid forms of CO, O2, H2,

C2H2, CH4, and pentane (C5H12). The higher alkanes, in-cluding many of the paraffins, can also form liquid lay-ers of sufficiently low viscosity to exhibit entrainment ofliquid droplets.

For a hybrid with a melt layer, a certain degree ofentrainment will occur depending on the fluidity of themelt and the mass flux. The quantitative calculation of theamount of entrainment is quite complex theoretically, butsome empirical relations have been developed. However,we can formulate the energy equation and the form of theregression rate in terms of the mass fraction of dropletsin the gaseous mixture emanating from the surface. If re

represents the regression rate due to entrainment and rv

that due to vaporization, then r = rv + re. If we define thefraction entrained as θ = re /r , then the total heat of gasi-fication of the two-phase mixture is

hθ = (1 − θ )hv + θ (hv − Lv) = hv − θ Lv , (25)

where θ Lv is the reduction in heat required due to theformation of the liquid droplets. With entrainment, there-fore, the term hv in the mass transfer number Bt in Eq. (6)is replaced by hθ and the blowing term B in Eq. (4) ismultiplied by (1 − θ ) to reflect the fact that it is the gasemanating from the surface that accounts for the blocking.

By incorporating these corrections into Eq. (5), we cannow express the ratio of rates for entrainment relative tono entrainment when θ = 0, i.e., R(θ ) = r (θ )/r (0). Withthese corrections to both B and Bt, we can now calcu-late the effect of the entrainment ratio θ on the regressionrate ratio R(θ ). The Cf /Cfo ratio in Eq. (7) (equivalent toCH /CHO) is shown in Fig. 5 as a function of the blowingparameter B. This curve, which is based both on theoryand experiment, can be represented very closely over theentire range by the expression [ln (1 + B)/B]1.088. Table IIshows the values of the amplified regression rates as afunction of the entrainment ratio θ and at two values ofLv/hv. Note that for the reference B value of 10, regres-sion rate increases up to factors of 10–15 are theoreticallypossible. Magnifications in this range were indeed sug-gested in the deep cryogenic solids such as solid methaneand oxygen, whereas for the more moderate cryogen solidpentane, the increase is of the order of 3. This suggests anentrainment ratio of 60–70% for pentane and over 90%for CH4.

Although this method of augmenting regression ratesappears very promising, there are several drawbacks. Theuse of cryogens can be expensive and incurs significantweight penalties because of the insulation required. Forthe noncryogens that have fluid melt layers, such as cer-tain paraffins, the class of fuels available is limited sincea low-viscosity melt is required at the surface tempera-ture to allow entrainment. One further caution is that thissystem can evidence sloughing if the solid conductivity is




TABLE II Regression Rate Ratio R(θ) versus Fraction En-trained for Two values of Lv /hv

a

R(θ)

θ B Cf /Cfo Lv /hv = 0.5 Lv /hv = 0.7

0.00 10.00 0.211 1.00 1.00

0.20 8.00 0.245 1.29 1.35

0.40 6.00 0.294 1.74 1.93

0.60 4.00 0.371 2.51 3.03

0.70 3.00 0.432 3.14 4.00

0.75 2.50 0.472 3.57 4.69

0.80 2.00 0.521 4.11 5.60

0.85 1.50 0.585 4.81 6.83

0.90 1.00 0.671 5.77 8.58

0.95 0.50 0.796 7.17 11.24

0.98 0.20 0.904 8.38 13.62

1.00 0.00 0.999 9.45 15.75

a θ is the fraction entrained, B is the blowing = m(g)/(Cf /2) G ,r = const ∗ Cf /C f o/(1 − θ Lv /hv), and R(θ ) = r (θ )/r (θ = 0).

too high. Nevertheless, laboratory and small-scale exper-iments appear promising.

III. MOTOR BALLISTICS

In contrast to the solid and liquid motors, hybrid combus-tion occurs as a diffusion flame that extends the length ofthe grain. As a consequence, many of the operational pa-rameters, such as the oxygen-fuel ratio (O/F), thrust, andfuel flow rate, will depend on the grain dimensions andtherefore change with time as the fuel port opens up. Onemust understand these variations in order to minimize theperformance decrements that might result from the associ-ated Isp variations due to the O/F change. In discussing thisbehavior, the equation in common use, r = aGn

o Lm , will

be used for simplicity. In the case of a noncircular port, ahydraulic diameter DH = 4A /P will be used, where A isthe cross section of the port and P is its perimeter.

A. O/F Shift

The O/F in rocket combustion is defined as mo / mf, whichis the reciprocal of the fuel–air ratio common in air-breathing engines. In liquid rockets, this parameter is de-termined solely by the rates of oxidizer and fuel injection,which are input variables. In solid rockets, the oxidizer andfuel are intimately premixed and so the O/F is unchangedregardless of operating conditions. In hybrids, the O/F isdetermined by the fuel flow rates, which depend on theoxidizer flux.

The mass flow of fuel per unit area of surface in acircular port is given by

FIGURE 8 Plot of O/F shift versus port diameter ratio at severaln values.

mf = r π DLρ = a

(mo

π D2 /4

)n

Lm π DLρ = K mno L

1+m

D2n −1,

(26)where K = 4naπ1−nρ, a constant depending only on mate-rial properties. For a noncircular port, mf = r P Lρ =a(mo/A)n P L1+mρ. The O/F for a circular port is given by

O/F = m1−no D2n−1

/K L1+m (27a)

and the corresponding formula for a noncircular port is

O/F = m1+no An

/ρa P L1+m . (27b)

From Eq. (27a) we can see that O/F will increase duringburning according to D2n−1. Typical O/F shifts in a circu-lar port are shown in Fig. 8 for diameter ratios from 1.2to 2.0 corresponding to volumetric loading efficiencies of30–75%. When n = 0.5, there is no shift and for a typi-cal n value of 0.7 at a volumetric efficiency of 69%, theO/F shift is 27% at constant oxidizer flow. As further seenfrom Eqs. (27a) or (27b) this shift can be reduced with a re-gressive oxidizer flow. This fortunately is a typical designrequirement to limit vehicle acceleration during flight.

B. Stoichiometric Length

The stoichiometric length is that position in the grainwhere the integrated fuel burned satisfies the required O/F.In chemical terms the stoichiometric point (O/F)st occursat complete oxidation, when all carbons, hydrogens, andmetals react. In a high-energy system such as rockets,however, the optimum specific impulse usually occurs onthe fuel-rich side. This is true for hybrid propellants em-ploying liquid oxygen as the oxidizer and especially whenthe fuel contains aluminum. In these cases, Lst refers tothat length where O/F provides maximum Isp. The relation




between the stoichiometric length and O/F is obtained interms of Go:

Lst =(

G1−no D

4aρ(O/F)st

)1/(1+m)

, (28)

where DH substitutes for D in the noncircular case. Thisquantity is significant because in the motor design, Lst

specifies the length of a port, which determines the mo-tor envelope. Since m is usually a small negative number(m = −0.2 theoretically), a first good guess for (L /D)st isobtained from the relation (ao = aLm)

(L /D)st = G1−no

/4ao ρ(O/F)st . (29)

For typical polymeric fuels, L /D varies between 20 and30 for maximum Isp. In cases where the envelope is re-stricted in length, multiple ports are required to shorten theoverall grain length accompanied by an increase in mo-tor diameter. For the high-regression-rate fuels discussedin Section II.D, thicker webs are possible, resulting in(L /D)st < 10.

C. Pressure/Thrust Variation

The pressure and consequently the thrust will vary duringa run at constant mo mainly because of the mf variationshown in Eq. (26). Figure 9 shows how the pressure variesduring a run depending on the n exponent. The equationgoverning the pressure is

P = mc∗/At (30a)

F = mgIsp , (30b)

where m = mo + mf , At is the nozzle throat area, c ∗ is thecharacteristic velocity, g is the gravitational constant, andIsp is the specific impulse. For a system operating near stoi-chiometric ratio, the dominant term in the above equationscausing the pressure variation is mf, with c ∗ providing asecondary effect. The curves in Fig. 9 were obtained byallowing both mf and c ∗ to vary with time, using c ∗ val-ues for a typical HTPB fuel. For each n value, the initialO/F was selected on the fuel-rich side of stoichiometric tominimize the c ∗ variation during the run. The thrust vari-ation will closely follow the pressure variation since theIsp change will closely parallel the c ∗ variation.

A summary of formulas for the various parameters use-ful in preliminary design is given in Table III. The formu-las are based on the simple expression r = aGn

o Lm and aregiven for circular and noncircular ports.

FIGURE 9 Pressure versus time for various n values; circular portwith D2 /D1 = 2. In this example, the oxidizer flow rate mo and theinitial O/F are fixed, but the O/F varies with time in accordancewith Eq. (27a). The c∗ values were permitted to vary with O/F.

IV. PROPULSION SYSTEM

The propulsion system consists of two main parts, the liq-uid tank with its feed system, and the combustion chamberthat houses the fuel. The liquid tank with the feed systemcomponents is essentially identical to that of the liquidsystem. The feed system typically consists of any of thefollowing: (1) inert pressurized gas such as N2 or helium,(2) hot gas derived from a separate gas generator, typi-cally H2–O2 diluted with He, (3) pump run by a gas gen-erator, and (4) a low-boiling-point liquid such as nitrousoxide (N2O), which has a vapor pressure in the vicinity of700 psi at ambient temperature. Although N2O is not anenergetic oxidizer, it has the virtue of simplicity and lowcost, and therefore has been a favorite of amateurs andthose developing low-cost sounding rockets.

A. Combustion Chamber

The combustion or thrust chamber can be considered asdivided into five major components: the injector assembly,

TABLE III Summary of Ballistic Parametersa

Parameter Circular Noncircular

O/F m1−no D2n−1

K L1+m

m1−no An

ρa P L1+m

Lst(

G1−no D

4aρ(O/F)st

)1/(1+m) ( G1−n

o DH

4aρ(O/F)st

)1/(1+m)

L /D (approx.) G1−no

4ao ρ(O/F)st

G1−no

4ao ρ(O/F)st

mf K mno L

1+m /D2n −1 aρ( mo/A)n P L1+m

a K = 4na π1−nρ, a0 = aLm .




the grain compartment, the aft mixing chamber, the noz-zle, and the thrust vector control, which typically, but notnecessarily, is part of the nozzle. For flights in the atmo-sphere, it is usually more efficient to simply use fins orwings with actuators.

B. Injector Assembly

The types of injectors used may include all of those usedin liquid propellant rockets plus several that are uniqueto hybrids. There are two basic injector design philoso-phies: one entails direct injection of the oxidizer down theport and the second involves injection into a precombus-tion chamber where the oxidizer is largely gasified andheated prior to flowing down the port. The direct injectiontechnique was historically used because the early work in-volved small motors with single circular ports and directinjection appeared obvious. With large-diameter motors,however, where multiple ports are necessary, a precom-bustion chamber to vaporize the oxidizer and provide auniform entrance condition to all the ports is desirable.

In the early work with multiple ports, individual in-jectors were used, as shown in Fig. 11. In that case, itwas necessary to verify that all injectors had identicalflow characteristics to guarantee uniform burning downthe ports. A further disadvantage of this arrangement isthat if a hypergolic fuel is required for ignition, each in-dividual injector will need its own means of injecting thehypergolic fuel. Despite these issues, the use of individualinjectors did work well, giving relatively high combustionefficiency (91–93%) with N2O4 as the storable oxidizer.

When a precombustor is used, one of the more conven-tional liquid injectors is used which provides a uniformatomized spray. The hypergolic liquid is injected in muchthe same fashion as the fuel in a liquid rocket, except, ofcourse, in much smaller quantities. The injector types thatcan be used include the showerhead, impinging jets (dou-blets, etc.), use of splash plates, and swirl sprays involvingboth hollow and full cone patterns. A detailed discussionof some of these injectors can be found in texts on liquidrockets. In the early French and Swedish programs, wherenitric acid was used as the oxidizer, the main solid fuel wasselected to be hypergolic with the oxidizer and thereforeno separate ignition fuel was needed. Hypergolicity wasimparted to the fuel by incorporating an amine compound.When a precombustor is used, its configuration is selectedso that there is sufficient residence time to vaporize theoxidizer.

C. Grain Design

The simplest grain configuration is the one with a singlecircular port. In this case, the web thickness is typically

in the range of one-fourth the diameter, leading to a volu-metric loading of 75% in the fuel section of the case. Forlarger motors, however, the web must increase to maintaina reasonable loading density. With typical regression rates,this would lead to unacceptably long burning times. Thesolution to this dilemma is to select a multiport design thatprovides an increased burning surface in a shorter lengthbut larger diameter motor. Each port satisfies

Figure 10 shows six typical grain designs. The single

the L /D re-quirement as shown in Table III. As the motor diameteris increased, the number of ports is increased as dictatedby the web thickness, which in turn is determined by theregression rate and the burning time.

cylinder has the advantage of being highly efficient anddesirable for applications requiring long burning times.An example is the case of the target drone, described ear-lier, which required burning times of up to 5 min with alow thrust sufficient to overcome atmospheric drag. If ahigh-regression-rate fuel is employed (as discussed in Sec-tion II.D), then a thicker web can be used for high-thrustboost applications. The seven-cylinder cluster representsa means of retaining the simplicity of the single port inan optimum packaging configuration. This approach alsosimplifies manufacturing and motor loading since stan-dard identical units can be employed. The design trade-off here is a more efficient packaging envelope at the ex-pense of additional free volume between cylinders, whichamounts to about 22%.

The wagon wheel design is very popular and has beentested in configurations of up to 15 ports (AMROC 250-klb-thrust motor). The double wagon wheel has not beentested but is a conceptual design suitable for very largemotors. Figure 11 shows a 12-port wagon wheel designbefore and after the test. An important consideration ofthe multiport design is the grain support toward the endof burn. To avoid shredding of the webs when they be-come thin toward the end of a burn, it has been customaryto employ a low-density web support that is fairly rigid.A disadvantage of the multiport designs is that the sharpcorners in the ports lead to residuals at the end of burning,which increase the inert rate. This penalty can be reducedby using low-density “sliver savers” or by allowing a low-thrust tailoff, which is allowable in certain applicationssuch as space motors. Another consideration of the wagonwheel design is whether to allow burning to occur in thecenter circular port. It is obviously more efficient volu-metrically if this occurs, but care must be taken to matchthe hydraulic diameters of the circular port with the tri-angular or quadrilateral ports of the wagon wheel. If thisis not done, the gas flow will prefer the larger hydraulicdiameter, thereby starving the other ports.

Grain loading in the motor case is usually accomplishedin two ways. The first, which is common in solid rockets, is




FIGURE 10 Examples of grain shapes.

by bonding the grain to the case wall. This is done by fillingthe empty motor case with the uncured liquid fuel and ap-propriate mandrels to create the port holes. This approachrequires the fuel to have adequate physical properties towithstand the ignition loads due to case expansion and ac-celeration loads in flight. The second approach involvesloading the fuel in a cartridge that is then inserted in themotor. By providing the proper support for the grain andallowing a small clearance between the cartridge and casewall, the grain can be disengaged from the expansion ofthe case wall during pressurization. As a consequence, theelongation property requirement on the grain is consider-ably reduced.

Both approaches require adequate properties to avoidgrain slumping during storage and potential shear stress

FIGURE 11 Multiport grain before and after firing. [Courtesy ofthe Chemical Systems Division of United Technologies.]

failure during accelerated flight. In the case of cartridgeloading, aft end support of the grain must be considered.These considerations are generally of little importance forsmall motors, but can be critical for large motors in flight.

D. Aft Combustor/Nozzle

1. Aft Chamber

Because of the turbulent diffusion flame, the combustiongas exiting the grain will generally exhibit striated beamsof both high and low O/F values. Flow in the center ofthe port will be more oxidized than near the fuel surface,which contains a fuel-rich layer. Aside from the turbu-lence in the boundary layer, additional mixing is desired.Several approaches that have been found effective includethe following:

(a) Provide an aft combustion chamber with an L/Dratio sufficient to give increased mixing residencetime.

(b) Use mechanical mixers (turbulent generators) at theaft end of the grain to stimulate turbulent mixing.

(c) Use a submerged mozzle to generate aft end mixingfrom the protruding forward end of the nozzle.

(d) Provide for aft end injection of part of the oxidizer tostimulate mixing. The additional benefit here is thatoxidizer makeup can be provided during low-O/Foperation, usually during the early portion of the




flight. The objection to this approach, however, is theadditional plumbing complexity.

(e) Use a multiport design to decrease the averagediffusion length between high- and low-O/F regions.

The simplest approach that has been found to be effec-tive is the use of a submerged nozzle at the end of themixing chamber, usually with a multiported grain. Thetypical combustion efficiency c ∗ is about 95%, which is2–3% below that of the premixed liquid and solid motors.

2. Nozzle

The nozzle design generally follows the same ablative ap-proach as the solid motor but with one caveat. An alu-minized solid propellant usually operates in a low-O/Fregime where Isp is maximized. In this region, where thecombustion gases contain a low concentration of oxidizingspecies (such as O2, OH, H2O, CO2), graphite nozzles per-form well, showing low erosion. However, most hybrids,unless aluminized, operate in a region where the oxidiz-ing species are in a higher concentration. Consequently,except for short-duration runs or for those designed torun fuel-rich, a ceramic-containing nozzle insert or onecontaining silica fortification has been found to providemore resistance to oxidation than graphite. Typical valuesfor erosion rates for aluminized solids are in the range of3–7 mils/sec, whereas typical nonaluminized hybrids fallin the range of 10–25 mils/sec depending on the nozzlematerial selected and the range of O/F and pressure oper-ation. In general, nozzle erosion is governed by the samelaws as hybrid burning and erosive burning in solid pro-pellants. One can expect Eq. (7) to be applicable to the

TABLE IV Performance of Hybrid Propellantsa

mf ofSpecific gravityIsp (std.) oxidizing

Propellant O/F Fuel Oxidizer Average 500 psi species Tc (K)

HTPB–LOX 2.25 0.98 1.14 1.09 277 0.51 3635

HTPB/Al–LOX 1.21 1.25 1.14 1.19 275 0.12 3795

PE–LOX 2.50 0.92 1.14 107 281 0.51 3530

HTPB–N2O4 3.30 0.98 1.43 1.29 257 0.42 3420

HTPB/Al–N2O4 1.70 1.33 1.43 1.39 259 0.10 3770

HTPB/Al–RFNA 1.80 1.35 1.55 1.47 252 0.20 3500

HTPB–N2O 7.33 0.98 0.77 0.79 247 0.30 3370

HTPB/Al–N2O 2.80 1.56 0.77 0.89 253 0.04 3930

PE–H2O2 (90%) 7.70 0.92 1.38 1.31 247 0.85 2600

HTPB/Be–LH2–LOX 0.80 1.57 1.14 0.32 408 <0.01 2690

PE/Li–FLOX 2.60 0.62 1.44 1.05 350 <0.02 4970

aAluminized propellants contain 15% Al in the total propellant. FLOX (with PE/Li) contains 85% F2. The Be in the “tribrid”is 80% of the solid fuel and 25% of the total propellant. The hydrogen acts essentally as a working fluid because of its lowmolecular weight. The term mf is the mole fraction of oxidizing species, which is defined as 2 × O2 + O + H2O + CO2 (otheroxidizing species are usually negligible). PE is polyethylene with the formula (CH2)x.

behavior of an ablative nozzle in a combustion gas, withthe Go term now referring to the mass flux of oxidizingspecies. By Reynolds’ analogy, the diffusion of reactiveoxidizing species would follow the same law as heat con-duction. As a consequence, one would expect the erosionrate to depend both on the fraction of oxidizing speciesand the pressure that determines the mass flux G. Theseeffects have indeed been observed in practice. Table IVshows the mole fraction of oxidizing species for sometypical propellants. Of interest is the fact that the additionof aluminum reduces the oxidizing species since thosepropellants optimize performance on the fuel-rich side.

These considerations assume that the combustion tem-perature is sufficiently high that the rate-determining stepin nozzle erosion is governed by diffusion of reactivespecies. For “cool” propellants, this is not the case anderosion effects are minimal. Similarly, during the earlytransient of motor operation before the nozzle has heatedup to its steady temperature, erosion is low. For this reason,nozzle erosion is of lesser concern in short-duration runs.

V. PROPELLANT COMBINATIONS

Because the hybrid employs both a liquid and a solid,it enjoys the largest selection of candidate propellants.These range from storable to cryogenic to metallizedcombinations.

A. Storable Propellants

Where storability is required, any of the oxidizers that havebeen employed by liquid propellants is suitable. Theseinclude nitrogen tetroxide (N2O4), nitric acid (HNO3),




red fuming nitric acid (HNO3 + N2O4), hydrogen perox-ide (H2O2), and certain fluorine compounds such as ClF3.Combinations of some of the oxidizers have also beenused, such as NO dissolved in N2O4 (to lower the freezingpoint) and an aqueous solution of hydroxylamine nitrate(N2H4O4). The former was used in the CSD drone flightprogram and the latter has only been tested to date in thelaboratory.

Also included in this class are the “reverse” hybrids,where the solid is the oxidizer and the liquid is thefuel. Typical oxidizers include ammonium perchlorate(NH4ClO4), ammonium nitrate (NH4NO3), and the ni-trates of sodium and potassium. Higher energy oxidiz-ers, such as nitronium perchlorate (NOClO4), hydrazinenitrate (N2H5NO3), and hexanitroethane [C2(NO2)6],have also been considered but not developed because oftheir unstable character. The typical fuels used with ANand AP have been kerosene (or JP) and the hydrazines(N2H4 and UDMH).

B. Cryogenic Propellants

The most extensively employed oxidizer in this class is liq-uid oxygen, or LOX. It delivers high performance sinceit is not diluted with other inert elements, and is suitablewith a wide variety of fuels, principally the polybutadi-enes. The higher energy form of oxygen, namely ozone,has been considered but not employed in practice becauseof its cost and instability.

A higher energy oxidizer in this class is fluorine. Thisoxidizer is typically used as a solution in liquid oxygen(FLOX, containing 60–70% F2) for three reasons. One isthat with a typical hydrocarbon (like HTPB), the maxi-mum energy output is obtained when the carbon is oxi-dized to CO and the hydrogen to HF. The energy level canbe further improved by incorporating lithium in the fuelto deliver a vacuum Isp in excess of 380 sec. The secondadvantage in using FLOX is that its corrosivity is reducedrelative to pure F2. The third reason is the high density ofliquid fluorine (1.5 g/cm3), which results in an improvedmass fraction in a vehicle. Despite these advantages, al-though this oxidizer has been tested at thrust levels of40,000 lb, it has not been seriously considered for opera-tional use because of its toxicity. It remains, however, asa serious option for certain space engines.

Finally, there is the class of cryogenic solids discussedin Section II.D. These include solidified O2, CO, OH4, H2,and C5H12 and have only been tested on a laboratory scale.Their advantage of high Isp and high regression rate makesthem suitable in special circumstances. However, for prac-tical applications, this advantage is overshadowed by theexpense, insulating weight penalty, and inconvenience ofhandling these cryogens in the solid state.

C. Other Propellants

Because the hybrid fuel can sustain modest cracks andvoids with no disastrous effects, the physical property re-quirements, compared to solids, are greatly reduced. Thisexpands the field of eligible candidates. Indeed, early test-ing included fuels such as wood, coal, lucite, and evencompacted “garbage fuels” held together with 5–10%binder. An example of this latter fuel that has been testedis shown in Fig. 12. Because of its useful performance, asshown in the figure, it has been considered for auxiliarypower in space stations.

The highest performing propellant not involving eso-teric ingredients is a “tribrid” involving the bipropellantH2–O2 with beryllium incorporated in a polymeric fuelbinder. The H2–O2 is burned in the precombustor andthe hot gas flows down the port, burning the beryllium-containing fuel. This propellant combination provides acalculated vacuum impulse in excess of 500 sec. Figure 13shows a graph of the performance of this hybrid as com-pared to H2–O2 under the same operating conditions. Wereit not for the toxic nature of BeO, this propellant wouldbe a serious candidate for space applications.

D. Summary

A compilation of hybrid propellant combinations is shownin Table IV. Performance data are displayed both understandard conditions and in space for the higher perform-ing propellants. The most popular propellant has been theLOX–PB (such as HTPB) combination because of its highperformance and reasonable cost. For storable combina-tions, the most practical have been those using N2O4 andH2O2 as oxidizers. The target drone programs that en-joyed 15 years of successful flight experience used bothN2O4- and HNO3-based oxidizers. These oxidizers havehigh density and are hypergolic with amine fuels, such asthe hydrazines, which provides a convenient means of ig-nition. The highest density propellant combination in thislist is aluminized HTPB with RFNA as oxidizer. High-density propellants are generally desirable because theyresult in higher mass fraction propulsion systems. Thenext to the last column lists the mole fraction of oxidizingspecies, which provides an indication of the corrosivenessof the combustion gases on carbon nozzle throat inserts.Note that all the metallized combinations have low con-centrations of oxidizing species. Indeed, experience hasshown that the aluminized solid propellants show lowererosive behavior to carbon or graphite nozzles than thenonaluminized combinations. This is true despite the factthat the metallized propellants have high flame tempera-tures because of their energy. To resolve this problem, thenonmetallized propellants have sometimes used ceramic




FIGURE 12 The “trash” rocket. Left: Grains formulated with 2% and 4% HTPB binder. Right: Waste vacuum specificimpulse potential as a function of oxidizer composition. NAR, North American Rockwell. [Courtesy of the ChemicalSystems Division of United Technologies.]




FIGURE 13 Performance of Be/H2/HTPB–O2 tripropellant com-pared to that of H2–O2 under the same operating conditions;pc = 500 psi, area ratio = 50.

or silica-filled plastics instead of carbon-based materials.It may be surprising to observe that the highest flame tem-perature propellant, FLOX plus a lithium-containing fuel,ran for over 50 sec in a relatively large motor without un-due erosion. This may be attributed to the exceedingly lowoxidizer content since the gases were principally CO, HF,Li, H2, and H.

SEE ALSO THE FOLLOWING ARTICLES

COMBUSTION • CRYOGENICS • ELECTRIC PROPULSION

• FUELS • HEAT TRANSFER • ROCKET MOTORS, LIQ-UID • ROCKET MOTORS, SOLID • SPACECRAFT CHEMICAL

PROPULSION • SPACE NUCLEAR PROPULSION

BIBLIOGRAPHY

Altman, D. (1991). “Hybrid rocket development history,” Presented atthe 27th Joint Propulsion Conference, AIAA.

Altman, D., and Humble, R. (1995). “Hybrid rocket propulsion systems,”In “Space Propulsion Analysis and Design” (R. Humble, G. Henry,and W. Larson, eds.), pp. 365–441, McGraw-Hill, New York.

Barrere, M., and Moutet, A. (1963). “La Propulsion par FuseesHybrides,” International Astronautical Congress.

Boardman, T. A., and Carpenter, R. L. (1997). “A comparative study ofthe effects of liquid-versus gaseous-oxygen injection on combustionstability in 11-inch-diameter hybrid motors,” Presented at the 33rdJoint Propulsion Conference, AIAA, Seattle, WA.

Calabro, M. (1991). “European hybrid propulsion history,” Presented atthe AIAA Hybrid Propulsion Lecture Series, 29th Aerospace SciencesMeeting, Reno, NV.

Green, L., Jr. (1964). “Progress in astronautics and aeronautics.” In“Heterogeneous Combustion,” Vol. 15, p. 451, Academic Press, NewYork.

Karabeyoglu, M. A., and Altman, D. (1997). “Transient behaviorin hybrid Rockets,” Presented at the 33rd Joint Propulsion Confer-ence, AIAA, Seattle, WA.

Karabeyoglu, M. A., Cantwell, B. J., and Altman, D. (2001). “Devel-opment and Testing of Paraffin-Based Hybrid Rocket Fuels,” AIAAPaper No. 2001-4503, Joint Propulsion Conference, July 8–11, SaltLake City, Utah.

Larsen, C. W., Pfeil, K. L., De Rose, M. E., and Carrick, P. G. (1996).“High pressure combustion of cryogenic solid fuels for hybrid rock-ets,” Presented at the 32nd Joint Propulsion Conference, AIAA.

Marxman, G. A., and Gilbert, M. (1992). “Turbulent boundary combus-tion in the hybrid rocket.” In “Ninth Symposium (International) onCombustion,” pp. 371–383, Academic Press, New York.

Netzer, D. W. (1972). “Hybrid rocket internal ballistics,” CPIA Publica-tion 222.

Rocketdyne. (1962). “Research on hybrid combustion,” SummaryReport, January 30, 1962, Contract Nonr 3016(00).

Smoot, L. D., and Price, C. F. (1965). “Regression rates of metallizedhybrid fuel systems,” Presented at the 6th Solid Propellant RocketConference, AIAA, Washington, DC.

St. Clair, C., Rice, E., Knuth, W., and Gramer, D. (1998). “Ad-vanced cryogenic solid hybrid rocket engine developments: Conceptand testing,” Presented at the 34th Joint Propulsion Conference,AIAA.

Wooldridge, C. E., and Muzzy, R. J. (1964). “Measurements in a turbulentboundary with porous wall injection and combustion.” In “Tenth Sym-posium (International) on Combustion,” pp. 1351–1362, The Combus-tion Institute.

Wooldridge, C. E., and Muzzy R. M. (1966). “Internal ballistics consid-erations in hybrid rocket design,” AIAA Paper No. 66–628, ColoradoSprings, CO.

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