References

Rocket Propulsion Analysis (Lite Edition) v.1.2.5 by www.propulsion-analysis.com

Note on ISP

You might wonder how the RL-10B-2 which has an ISP of 464 seconds, can have a higher ISP than the commonly quoted theoretical maximum of 451-455 seconds for LOX/LH₂ found on the internet.

Or how documents which list theoretical ISPs for different types of fuels can have wildly differing numbers, e.g. Document A says LOX/LH₂ has a vacuum ISP of 454, while Document B says it’s 462.

The answer is that the maximum theoretical ISP of a propellant is heavily dependent on engine-specific numbers like chamber pressure (P_C), nozzle expansion ratio (Ɛ), and the Oxidizer/Fuel Ratio (O/F). If you use different numbers, you get different theoretical vacuum ISPs.

In the example above, Document A had a P_C of 1000 psia, Ɛ=40 and O/F=4.83, while Document B had a P_C of 1000 psia, Ɛ=60 and O/F=5.0

Expansion ratio (Ɛ) in rocketry is the area of the nozzle exit divided by the area of the nozzle throat. If your engine does all of it’s work in an atmosphere, you want a low expansion ratio to provide good sea-level ISP (the F-1’s Ɛ=16 and the RS-68’s Ɛ=21.5), while if your engine lives in vacuum, you want a large expansion ratio (the RL-10A-1’s Ɛ=40 and the J-2X’s Ɛ=90).

At the far edge of currently proved nozzle technology is the RL-10B-2’s astounding Ɛ=285, which is achieved through a carbon-carbon nozzle extension which is stowed in a “retracted” position to take up less space during launch (Cutaway photo of RL-10B-2 in stowed mode). After stage separation, the Nozzle Extension Deployment System (NEDS) uses a series of ball-screw drives to lower the nozzle extension over the core engine nozzle.

Chamber Pressure (P_C) has very little effect on theoretical vacuum ISP, but a large effect on sea level ISP. To illustrate this point; we’ll use the Space Shuttle Main Engine (SSME). It has Ɛ=77.5; which with an O/F ratio of 6.03, gives us the following theoretical maximum specific impulse:

P_C: 1000 psia = Sea Level 196.52 seconds, Vacuum 463.77 seconds
P_C: 3000 psia = Sea Level 374.88 seconds, Vacuum 464.69 seconds

You can see how a very high P_C allows for a significant improvement in sea level performance for nozzles with a large Ɛ; albeit at increased cost and complexity. Currently, the highest production P_C is found on Russian staged combustion kerosene engines such as the RD-180 and RD-191, which reach 3,500 to 3,800 psia.

Oxidizer/Fuel Ratio (O/F): By varying the ratio of oxidant, you can control ISP and chamber temperature as needed. A good example would be this graph which was calculated through Rocket Propulsion Analysis (Lite Edition) v.1.2.5.

As your expansion ratio changes, so does the O/F mixture needed to achieve optimum performance, as shown by this graph which was also calculated through RPA (Lite Edition) v1.2.5.

It’s worth noting that these graphs were calculated with the assumption of a perfect combustion process; e.g. every molecule of fuel is perfectly combusted with it’s counterpart oxidant molecule, which doesn’t happen in reality. This is most notable with liquid hydrogen fuelled engines.

Calculating Overall Propellant Density

PropDens = (OFR + 1) / [ (OFR / Oxidizer_Density) + (1/Fuel_Density) ]

Where:

OFR: Oxidizer/Fuel Ratio. If it is 6 [to 1], then put in 6.
OxidizerDensity: Density of oxidizer in kg/m3
FuelDensity: Density of fuel in kg/m3
PropDensity: Density of propellant in kg/m3

Calculating Metallized Gel Propellant Density

PropDens = 1 / [ (1 – ML – GL) / LPD + (AL / AD) + (GL / GD) ]

Where:

LPD: Liquid Propellant Density
AD: Additive Density
AL: Additive Loading
GD: Gellant Density
GL: Gellant Loading

EXAMPLE: The density of a metallized gel propellant that used liquid hydrogen as a base (71 kg/m3) with 60% by weight Aluminum additive (2,768 kg/m3) and 10% by weight of Methane (CH4) gellant (520 kg/m3) would be:

1 / [ (1 – 0.6 – 0.1) / 71 + (0.6 / 2768) + (0.1 / 520) ] = 213 kg/m3

Standard Propellant Combinations
(Widely understood, and easily handleable)

NOTE: The optimum O/F ratio depends on the surrounding environment – the optimum propellant mix for a engine is different between vacuum and sea level – and generates different levels of ISP. The mixtures below were formulated for optimum vacuum ISP, at the loss of some sea level ISP.

Hydrogen (LH₂) / Liquid Oxygen (LOX)

Actual Reference O/F Ratios: 6.0 (SSME), 5.85 (RL-10B-2), 5.50 (J-2X).
Actual Engine Efficiencies: 97.7% (SSME), 96.6% (RL-10B-2), 95.7% (J-2X)

Kerosene (RP-1) / Liquid Oxygen (LOX)

Actual Reference O/F Ratios: 2.72 (RD-180), 2.27 (F-1), 2.25 (MA-5A), 2.23 (H-1)
Actual Engine Efficiencies: 94.2% (RD-180), 92.1% (MA-5A) 91.8% (H-1), 90.1% (F-1)

Monomethyl Hydrazine (MMH) / Nitrogen Tetroxide ( NTO)

Notes: This is currently the “standard” storable hypergolic propellant, though attempts are underway to replace it with ‘green’ non-toxic propellants.

Due to it being used heavily for space storable systems, and also because the Soviet Union designed a 3,140~ psia P_C storable propellant engine, the RD-264 for the R-36 (SS-18) ICBM, the table has been expanded to add 150 P_C.

The 150 psia P_C compares quite well to the 100 psia found on the Apollo Service Propulsion System, 116~ psia on the Lunar Module Descent engine, and the 125 psia on the Space Shuttle’s Orbital Maneuvering System.

Actual Reference O/F Ratios: 1.65 (Shuttle OMS)
Actual Engine Efficiencies: 93.4% (Shuttle OMS)

Exotic Propellant Combinations
(Not understood well, and/or extremely dangerous to handle)

Notes: Due to the largely experimental nature of these propellants, you are encouraged to be strongly conservative in picking these for your hypothetical spacecraft via using conservative engine efficiency ratios (around 94% or so).

Aluminum/Hydrogen Cryogel / Liquid Oxygen (LOX)

Notes: The cryogel’s density is 170.9 kg/m3; of which the aluminum additive is 60% by weight.

While this system actually is slightly less dense than straight LH2/LOX, there’s a massive beneficial spiral of weight decreases due to the massively increased density of the fuel (71 to 170.9 kg/m3) and the lower oxidizer to fuel ratio.

A crude estimate of a S-II sized system holding 72,780 kg of fuel has a total system mass of 525.13 tonnes for the ‘straight’ LH2 version, and 195.24 tonnes for the Aluminum/Hydrogen Cryogel version, while delta-v remains largely the same.

Reference: NASA TM-1998-206306: Preliminary Assessment of Using Gelled and Hybrid Propellant Propulsion for VTOL/SSTO Launch Systems.

Hydrogen (LH₂) / Fluorine (LF₂)

Notes: You might wonder why Liquid Fluorine isn’t used more. The answer is that Fluorine is violently unstable and likes to spontaneously combust on contact with such sundry things as the air, or rocket engineers.

Monomethyl Hydrazine (MMH) / Fluorine (LF₂)

Notes: This mixture was the “last man standing” out of JPL/NASA/USAF studies conducted from the 1960s to the late 1970s for a next generation space-storable propellant. The losing mixtures were Oxygen Difluoride (OF2) / Diborane (B2H6), which was studied from 1966-1971 and various fluorine-oxygen mixtures (FLOX) combined with MMH.

Due to this essentially being designed for a space storable system, and also because the Soviet Union designed a 3,140~ psia P_C storable propellant engine, the RD-264 for the R-36 (SS-18) ICBM, the table has been expanded to add 150 P_C.

The 150 psia P_C compares quite well to the 100 psia found on the Apollo Service Propulsion System, 116~ psia on the Lunar Module Descent engine, and the 125 psia on the Space Shuttle’s Orbital Maneuvering System.

Typical efficiency of this kind of mixture in a practical engine would be about 93%.

References:
Experience with Fluorine and its Safe Use as a Propellant – NASA JPL Publication 79-64 (30 June 1979)

Oxidizers (By Density)

Fluorine (LF₂)

Density (Liquid): 1,510 kg/m3
Freezing Point: -219.6 C
Boiling Point: -188.1 C

Oxygen (LOX)

Density (Liquid): 1,140 kg/m3
Freezing Point: -219 C
Boiling Point: -183 C

Nitrogen Tetroxide / NTO (N2O4)

Density (Liquid): 1450 kg/m3
Freezing Point: -9.3 C
Boiling Point: 21.15 C

Fuels (By Density)

Monomethyl Hydrazine / MMH (CH₃NHNH₂)

Density (Liquid): 866 kg/m3
Freezing Point: -52.4 C
Boiling Point: 87.5 C

RP-1 Kerosene

Density (Liquid): 806 kg/m3
Freezing Point: -73 C
Boiling Point: 147 C

Hydrogen (LH₂)

Density (Liquid): 71 kg/m3
Freezing Point: -259 C
Boiling Point: -253 C

Solid Propellants

TP-H1148

Type: PBAN
Burn Rate: 0.42 to 0.47 inches per second at 1000 psi
Density: 1,757.67 kg/m3
I^osps: 261.9 using HPM nozzle
ISP (vac): 268.5 using HPM nozzle

Composition:
      PBAN/Epoxy Binder: 14%
      Iron Oxide (Fe₂O₃): 0.28% (varied throughout mix to control burn rate)
      Aluminum Powder: 16%
      Aluminum Perchlorate: 69.72% (varied throughout mix to control burn rate)
      Total Solids: 86%

Toxic Exhaust Products
      HCl: 0.5860 moles per 100 grams
      Al2O3: 0.2965(S) moles per 100 grams
      CO: 0.8555 moles per 100 grams

Notes: Used in Space Shuttle High Performance Motor. Meets the Space Shuttle HPM Specification, which requires it to maintain integrity over a five year storage period between 35-95F.

References:
Block II Solid Rocket Motor (SRM) Conceptual Design Study (NAS 8-37295) Final Report Vol 1: Appendices by Atlantic Research Corporation (31 Dec 1986) (PDF excerpt)
Block II SRM Conceptual Design Studies Final Report: Conceptual Design Package: Volume I, Book 1 – by Morton Thiokol (19 Dec 1986) (PDF Excerpt)

DL-H396 Propellant

Type: HTPB
Density: 1,801.4 kg/m3
ISP (vac): 280.04 at 7.72 Expansion Ratio and 1000 psia

Composition (by percentage of weight):
      R-45HT/HTPB Polymer: 11.02%
      HX-752 Aziridine Bonding Agent: 0.15%
      Iron Oxide (Fe₂O₃): 0.2%
      Aluminum Powder: 19%
      Aluminum Perchlorate (200/20 microns): 68.92%
      IDPI Curing Agent: 0.71%
      Total Solids: 88%

Notes: Modified Peacekeeper Stage I formulation using lower cost ingredients such as non-spherical aluminum and RT-45HT/HTPB polymer, which costs about 50% less than PBAN or R-45M/HTPB polymer.

References:
Block II SRM Conceptual Design Studies Final Report – Conceptual Design Package: Volume I, Book 1 – Morton Thiokol (19 December 1986) (PDF excerpt with specifications)
Block II SRM Conceptual Design Studies Final Report – Preliminary Development and Verification Plan: Volume I, Book 2 – Morton Thiokol (19 December 1986) (PDF excerpt)

DL-H397 Propellant

Type: HTPB

Composition (by percentage of weight):
      HTPB/Isocyanate Binder: 10%
      DOA: 2%
      Iron Oxide (Fe₂O₃): 0.25% (varied for burn rate control)
      Aluminum Powder: 19%
      Aluminum Perchlorate: 39.50%
      Sodium Nitrate (NaNO₃): 0.25% (varied for burn rate control)
      Aluminum Oxide (Al₂O₃): 0.25% (varied for burn rate control)

Notes: Designed for very low HCl exhaust products (less than 1%).

References:
Block II SRM Conceptual Design Studies Final Report – Conceptual Design Package: Volume I, Book 1 – Morton Thiokol (19 December 1986) (PDF excerpt with specifications)
Block II SRM Conceptual Design Studies Final Report – Preliminary Development and Verification Plan: Volume I, Book 2 – Morton Thiokol (19 December 1986) (PDF excerpt)

TP-H3340 Propellant

Type: HTPB
Density: 1,815.8 kg/m3
ISP: 280.11 (unknown what is used as baseline to establish this)

Composition:
      HTPB/Isocyanate Binder: 11% (HX-752 Aziridine bonding agent)
      Aluminum Powder: 18%
      Aluminum Perchlorate: 71%
      Total Solids: 89%

Notes: Used in Star 37X Motor.

References:
Block II SRM Conceptual Design Studies Final Report – Conceptual Design Package: Volume I, Book 1 – Morton Thiokol (19 December 1986) (PDF excerpt with specifications)
Block II SRM Conceptual Design Studies Final Report – Preliminary Development and Verification Plan: Volume I, Book 2 – Morton Thiokol (19 December 1986) (PDF excerpt)

ARCADENE 360A

Type: HTPB
Density: 1,813.03 kg/m3
I^osps: 260.7 lbf-sec/lbm

Composition (by percentage of weight):
      R-45 HT Binder: 10%
      DOA: 2%
      Aluminum Powder: 18%
      Iron Oxide (Fe₂O₃): 1.5
      Aluminum Perchlorate (60/40 200 μ/MA): 68.5%
      Total Solids: 88%

Notes: Variant of 1980s MLRS propellant proposed for use as SRB Igniter.

References:
Block II Solid Rocket Motor (SRM) Conceptual Design Study (NAS 8-37295) Final Report Vol 1: Appendices by Atlantic Research Corporation (31 Dec 1986) (PDF excerpt)

ARCADENE 360B

Type: HTPB
Binder: R-45HT/IPDI
Density: 1,799.19 kg/m3
I^osps: 263.1
ISP (vac): 269.7

Composition:
      Iron Oxide (Fe₂O₃): 0.1% to 0.3%
      Aluminum Powder: 18%
      Total Solids: 88%
      Aluminum Perchlorate Mix: 70% Coarse, 30% Fine

Toxic Exhaust Products
      HCl: 0.5837 moles per 100 grams
      Al2O3: 0.2989(S) moles per 100 grams
      CO: 0.7697 moles per 100 grams

Notes: Was being produced at rates of 70,000 lb/day for the Vought MLRS program around 1986. ISP is designed around using the Space Shuttle High Performance Motor as a baseline.

References:
Block II Solid Rocket Motor (SRM) Conceptual Design Study (NAS 8-37295) Final Report Vol 1: Appendices by Atlantic Research Corporation (31 Dec 1986) (PDF excerpt)