In the Solid Rocket Boosters of the Space Shuttle, the following reaction happened:

$\mathrm{NH_4ClO_4 + Al \rightarrow H_2O + N_2 + Al_2O_3 + AlCl_3}$

Using carbon instead aluminium, we would have the reaction

$\mathrm{NH_4ClO_4 + C \rightarrow H_2O + N_2 + CO_2 + CCl_4}$

Carbon is much better in the per-mass number of the free valence electrons (12/4 = 3, while in aluminium it is 27/3 = 9). Furthermore, $\mathrm{CO_2}$ and also $\mathrm{CCl_4}$ are gases (on the temperature of the outgoing product), while the products of the aluminium aren't. Thus, their pressure could have served as additional acceleration of the rocket.

My impression is that a rocket using carbon instead aluminium would produce much more specific impulse.

Why then was aluminium used?

  • 2
    I'm not sure your reaction equations are fully correct. HCl is a known component of the SRB exhaust, and it's not present in your reactions. – Tristan May 11 '17 at 17:00
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    @Tristan I think it may be because the burning is not perfect (probably on the temperature + reaction speed + other optimization issues). – peterh May 11 '17 at 18:03
  • 3
    This is correct. Even hydrocarbon engines put out quite a fair amount of incomplete combustion products. Believe it or not, for example, it can actually help the specific impulse to put out carbon monoxide instead of just carbon dioxide, as the exhaust velocity is going to be inversely related to its molecular weight. – Tristan May 11 '17 at 18:06
  • 8
    Possibly because Carbon Tertachloride is (according to Wikipedia) "one of the most potent hepatotoxins", and chronic exposure can cause liver and kidney damage and could result in cancer, while Aluminium chloride is 'merely' corrosive. Lesser of 2 evils ... – brhans May 12 '17 at 4:13
  • 1
    @brhans Beside that its heat of formation is 1/4 of the aluminium burning, also thus could have been a reason. – peterh May 12 '17 at 9:56
up vote 41 down vote accepted

Specific impulse is not the only measure of a rocket. For the case of the SRBs, high thrust is much more important than high specific impulse. In this case, you want to look at the heat of formation for carbon dioxide vs aluminum oxide.

Carbon dioxide has a heat of formation of roughly -390 kJ/mol, compared with roughly -1670 kJ/mol for aluminum oxide. Even adjusting for the heavier molecular weight, the energy difference is enormous. Thermal oxidation of aluminum is a vigorous reaction.

You might be interested in the tool called cpropep. This allows us to gain basic performance indications for different fuels by solving the physics behind it: chemical equilibria and expansion/compression.

So how does $NH_4ClO_4 + Al$ perform against $NH_4ClO_4 + C$? First we feed it the approximate conditions:

Chamber temperature:    anything (calculated by cpropep for the calculation we're gonna do)
Chamber pressure:       60 atm (approx chamber pressur of SRB at the start)
Type of exit condition: pressure
Exit condition:         1 (sea level performance)
Units:                  mol (we're gonna calculate at stoichiometric for simplicy)
Type of problem:        Shifting performance evaluation

Shifting performance evaluation means cpropep is gonna calculate the chemical equilibrium for chamber, nozzle and exit which is reasonable for big engines. Frozen would mean to assume chemical equilibrium is achieved in the chamber and then fixed while going down the nozzle (very short nozzles would work like this).

Here are the important numbers for us:

$NH_4ClO_4 + Al$

                       CHAMBER      THROAT        EXIT
Pressure (atm)   :      60.000      34.930       1.000
Temperature (K)  :    3699.861    3533.767    2622.728
H (kJ/kg)        :   -2049.729   -2483.328   -4817.662
U (kJ/kg)        :   -2873.367   -3263.109   -5366.296
G (kJ/kg)        :  -32622.134  -31683.279  -26489.586
S (kJ/(kg)(K)    :       8.263       8.263       8.263
M (g/mol)        :      37.350      37.679      39.747
(dLnV/dLnP)t     :    -1.04313    -1.03830    -1.01314
(dLnV/dLnT)p     :     1.69444     1.64642     1.29711
Cp (kJ/(kg)(K))  :     4.42029     4.30003     3.14702
Cv (kJ/(kg)(K))  :     3.80757     3.72394     2.79963
Cp/Cv            :     1.16092     1.15470    *1.12408*
Gamma            :     1.11292     1.11211     1.10950
Vson (m/s)       :   957.41428   931.23567   780.19846

Ae/At            :                 1.00000    10.26082
A/dotm (m/s/atm) :                23.97248   233.17936
C* (m/s)         :              1438.34885  1438.34885
Cf               :                 0.64743     1.63579
Ivac (m/s)       :              1768.59728  2586.02157
Isp (m/s)        :               931.23567 *2352.84221*
Isp/g (s)        :                94.95961   239.92313

$NH_4ClO_4 + C$

                       CHAMBER      THROAT        EXIT
Pressure (atm)   :      60.000      34.650       1.000
Temperature (K)  :    3014.701    2852.316    1876.151
H (kJ/kg)        :   -2234.870   -2685.717   -4966.844
U (kJ/kg)        :   -3083.077   -3480.380   -5468.867
G (kJ/kg)        :  -29392.113  -28380.149  -21867.721
S (kJ/(kg)(K)    :       9.008       9.008       9.008
M (g/mol)        :      29.551      29.844      31.073
(dLnV/dLnP)t     :    -1.01662    -1.01377    -1.00112
(dLnV/dLnT)p     :     1.34985     1.30609     1.03630
Cp (kJ/(kg)(K))  :     3.78068     3.58783     1.86674
Cv (kJ/(kg)(K))  :     3.27640     3.11902     1.57970
Cp/Cv            :     1.15391     1.15031    *1.18170*
Gamma            :     1.13504     1.13469     1.18038
Vson (m/s)       :   981.19852   949.57591   769.79086

Ae/At            :                 1.00000     9.25862
A/dotm (m/s/atm) :                24.15204   214.76841
C* (m/s)         :              1449.12231  1449.12231
Cf               :                 0.65528     1.61305
Ivac (m/s)       :              1786.43717  2552.27758
Isp (m/s)        :               949.57591 *2337.50917*
Isp/g (s)        :                96.82979   238.35960

You can see here that Cp/Cv (Ratio of specific heat) is indeed much higher (1.12408 vs 1.18170) which means $NH_4ClO_4 + C$ uses its energy way more effectively.

But what is really interesting for a rocket is in fact (opposed to what @Tristan says) the specific impulse ($I_{SP}$) not the energy stored in it. Even though the energy stored in aluminium is much higher, due to the lower Cp/Cv, its $I_{SP}$ is only a bit higher: 2352.84221 m/s compared to 2337.50917 m/s. Thrust is not based on the energy released, thrust is equal to the mass flow rate (which can be almost freely designed) times the $I_{SP}$ (which is a function of Cp/Cv and the energy) but Al still results in a bit higher $I_{SP}$.

Anyway the difference is actually quite low: less than 0.7%. But there's something that additionally favors $Al$ — its density is higher: $2,7 g/cm^3$ vs around $2,0 g/cm^3$. That means the same booster can fit a bit more fuel in.

You should also note that in reality solid rocket boosters use both: $NH_4ClO_4$, $Al$ and a resin (usually HTPB) composed of $C$ and $H$ to keep it together. this achieves a higher impulse because $C$ and $H$ (especially $H$) raises the Cp/Cv while $Al$ raises the chamber temperature. From my experience adding Aluminium can improve the $I_{SP}$ by up to 10% for CxH2x fuels like plastics.

Results for $NH_4ClO_4 + Al$ (33%) + $C$ (67%):

                       CHAMBER      THROAT        EXIT
Pressure (atm)   :      60.000      34.781       1.000
Temperature (K)  :    3250.729    3090.041    2217.389
H (kJ/kg)        :   -2169.548   -2617.841   -4963.957
U (kJ/kg)        :   -3016.829   -3415.442   -5510.728
G (kJ/kg)        :  -30729.859  -29766.380  -24445.532
S (kJ/(kg)(K)    :       8.786       8.786       8.786
M (g/mol)        :      31.900      32.212      33.719
(dLnV/dLnP)t     :    -1.02439    -1.02104    -1.00427
(dLnV/dLnT)p     :     1.45514     1.41622     1.11496
Cp (kJ/(kg)(K))  :     4.06798     3.93869     2.38904
Cv (kJ/(kg)(K))  :     3.52922     3.43165     2.08380
Cp/Cv            :     1.15266     1.14775    *1.14648*
Gamma            :     1.12521     1.12410     1.14161
Vson (m/s)       :   976.40724   946.88257   790.06150

Ae/At            :                 1.00000     9.99677
A/dotm (m/s/atm) :                24.21831   231.28393
C* (m/s)         :              1453.09835  1453.09835
Cf               :                 0.65163     1.62692
Ivac (m/s)       :              1789.22682  2595.35188
Isp (m/s)        :               946.88257 *2364.06795*
Isp/g (s)        :                96.55515   241.06784
  • 1
    Wonderful data. Thanks! – peterh May 12 '17 at 15:20
  • "Even though the energy stored in aluminium is much higher due to the lower Cp/Cv its ISP is only a bit higher..." -- uh, this seems like it's missing punctuation. Could you, please, clarify the ambiguity? – Dan Mašek May 12 '17 at 19:42
  • @DanMašek I will try: Burning aluminium releases a lot more energy than burning carbon does. But the exhaust gases when burning carbon have a higher Cp/Cv which allows it to use the energy way more effective. Therefore the difference in impulse is not as high as one would expect. If you have an idea how to improve my answer feel free to suggest ! – Christoph May 13 '17 at 10:19

First off, a link to an existing answer: http://www.aerospaceweb.org/question/propulsion/q0246.shtml

A little bit of history knowledge goes a long way. Adding aluminum to solid rocket fuels to increase their specific impulse was a breakthrough achieved in 1956 by two of Atlantic Research Corporation's engineers: Keith Rumbel and Charles Henderson. Simplifying for the sake of ITAR, what matters is the optimum size of aluminum particles.

Please be aware that during World War Two major powers experimented with adding aluminum powder to explosives, which kinda gave superior oxygen balance and yield. It is but one logical step from high-order detonation in explosives to deflagration in solid rockets.

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