arla-lt1.htm Tri-Mode ARLA

Amateur Rocket Launch Assist (ARLA)

Additional Notes on Launch Tubes, Part 1

GASSES AND GAS CONTROL SYSTEMS

Several gasses were reviewed for possible use with the launch tube. For a number of reasons it was desirable to keep the vehicle and gasses from exceeding 90% of the local speed of sound within the tube. Therefore the review was limited to gasses that had speeds of sound of at least 2,200 fps. Other concerns were cost, safety, availability, and etc.

Storage of large quantities of gasses is a significant engineering issue. For small amateur rockets standard K-bottles should be satisfactory. Otherwise there would be a tradeoff between pressure, volume, and phase. The higher the pressure the smaller the volume but the cost of the storage tank and compressor go up. Novel storage vessels include buried tanks, sealed mines and caves, and even underwater tanks. At a depth of 230 ft the water pressure is 100 psi.

Low vapor pressure liquids such as cryogenic liquid nitrogen, propane, and water have several advantages. Liquids take up much less volume than compressed gasses and require smaller and less expensive containers. Because they are low pressure they are generally safer to handle. The disadvantages are the requirement for considerable amount of heat addition in a very short amount of time (as little as 0.1 second). This means a very high BTU furnace or a heavy thermal storage system.

Air was the first gas considered. It had the advantages of being inexpensive and safe to handle. The biggest disadvantage was a room temperature speed of sound of only about 1,000 fps. At 1,700 degrees fahrenheit, a relatively moderate flame temperature, the speed of sound is about 2,280 fps. This temperature can be achieved by combusting the air with a liquid fuel, such as kerosene, as it enters the tube but this intruduces exhaust products directly into the tube. This temperature can also be achieved by running the air through a heat exchanger inside a furnace but this adds expense and complexity. The use of such temperatures introduces tube material strength, erosion, and corrosion concerns. Compressed air in 2,200 psi bottles is readily available from the local welding supply house along with regulators. This makes it a good portable gas supply for the amateur rocketeer.

Nitrogen is readily available in 2,200 psi bottles and as a cryogenic liquid. It's speed of sound is about 13% higher than that of air for the same temperature, is non-combustible, and inert at all temperatures of interest. It is slightly more expensive than air and cannot be combusted directly, though it can be heated safely.

Chemical propellants, such as gun powder, have the advantage of being storable, inexpensive, and compact. The disadvantages of these are safety, regulatory requirements, and deposition of combustion products on the inside of the barrel leading to additional operating expense. On the scale of amateur rockets, with a very small number of launches per year and where similar chemicals are already in use in the rocket itself, this may be acceptable.

Hydrogen peroxide was considered and found to be storable and, when run through a catalyst, produces an oxygen rich gas at 1,700 degrees F without additional complexity. It's speed of sound is similar to that of air and steam. When combusted with a small amount of fuel, such as kerosene, the temperature can easily exceed 2,000 degrees fahrenheit. The high temperatures and free oxygen could limit the types of launch tube materials used. Handling of hydrogen peroxide can be complex and dangerous if safety procedures are not strictly adhered to. Hydrogen peroxide with 30% water is readily available and relatively safe to handle. Combusted with kerosene it would have the temperature needed for an adequate speed of sound. This would be equivalent to mounting a peroxide rocket engine to the bottom of the tube except that the engine could be built very robust for greater reliability and operating life. This may be the best solution in some cases, particularly where hydrogen peroxide is already being used for other purposes.

Water could be used but, like other liquids, would have to be vaporized and superheated by the addition of heat. Water is very safe (though steam is not), easily portable, low cost, and readily available. It's speed of sound is similar to that of air. The principle disadvantage of water is that it would have to be flash heated from 382 F (200 psi, ref baumeister, pg 4-4-41) to 1,700 F in less than one second. This could be accomplished by preheating an iron particle bed through which the water and vapor would flow. For longer tubes (and longer delivery times) a flash furnace could be built. Either of these methods add to the expense and operating difficulties.

Carbon dioxide (CO2) has properties similar to air though is a little more dense. It can be purchased as a compressed gas or a solid (dry ice). As a solid it is storable (for days), easily transportable, widely available, low cost, and relatively safe. Flash heating to gassify and heat the CO2 would be similar to that for water.

Helium was considered and found to be relatively inexpensive, very safe, and had a room temperature speed of sound of about 3,100 fps. It also has the lowest viscosity of any gas found and the second lowest density. Helium bottles can be purchased from a local welding supply house in 2,200 psi bottles. In large quantities it can also be purchased as a cryogenic liquid. On the scale of amateur rockets this would make an excellent portable propellant. Helium was chosen as the gas most likely to be used generally.

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          PROPERTIES OF SELECTED GASSES

Gas                    G     M      C1      C2

Dry Air               1.40   29   1,138   2,276
Ammonia (NH3)         1.32   17   1,427   2,854
Cargon Dioxide (CO2)  1.30   44
Helium (He)           1.66    4   3,316   6,635
Hydrogen (H2)         1.41    2   4,415   8,826
Methane (CH4)         1,32   16   1,479   2,955
Nitrogen (N2)         1.40   28   1,148   2,296
Oxygen (O2)           1.41   32   1,086   2,171
Propane (C3H8)        1.15   44
Steam (H2O)           1.30   34           2,384

G = Ratio of Specific Heats
M = Molecular Weight
C1 = Speed of Sound at 80 F (ft/sec)
C2 = Speed of Sound at 1,700 F (ft/sec)
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         Stagnation Properties
                (approx)

Mach Temp     Temp Pressure  Density
 No    F      T/To   P/Po     D/Do

  0       0    1.0     1.0     1.0
  1     100    1.2     1.9     1.6
  2     300    1.8     7.8     4.3
  3     600    2.8    37      13.2
  4   1,100    4.2   143      36
  5   1,900    6.0   500      91
  6   2,700
  7   3,800
  8   4,900
  9
 10           21    50,000   200

Notes:
  1.  Temp F is in temperature rise
  2.  Temp T/To is the ratio of temperature rise (Kelvins)
  3.  Pressure is the ratio of pressure rise
  4.  Density is the ratio of density rise 
  5.  The characters used for density, etc, are non-standard 
      but useful for this simple web page


  US Standard Atmosphere

Alt (ft)  Temp (F)  P/Po

      0      59     1.00
  5,000      41     0.83
 10,000      23     0.74
 20,000     -25     0.53
 30,000     -48     0.37
 40,000     -70     0.25
 50,000     -70     0.15
 60,000     -70     0.09
 70,000     -67     0.06
 80,000     -62     0.04
 90,00      -56     0.02
100,00      -51     0.01

Po (sea level) = 14.7 psi


Possible Flight Profile and Operating Parameters
            Ram Effective Pressure

   Mach       Altitude     Effective   Pressure
 No  P/Po    ft    P/Po      P/Po        psi

 2    7.8     0    1.0        7.8        115
 3    37     30K   0.297     11.0        162
 4   143     70K   0.044      6.3         93
 5   500    100K   0.011      5.5         81


             Ram Effective Density

   Mach       Altitude     Effective
 No  D/Do    ft    D/Do      D/Do

 2     4.3    0    1.0        4.3
 3    13.2   30K   0.37       4.9
 4    36     70K   0.058      2.1
 5    91    100K   0.014      1.3


                  Mass Flow

Mach  Altitude  Ram Effective
 No      ft         D/Do

 2       0           4.3
 3      30K          4.9
 4      70K          2.1
 5     100K          1.3


Note:  The above calculations are crude but show
       that by careful selection of the altitude and velocity 
       (which may require other than vertical flight):
  a.  The maximum pressure on the vehicle (stagnation) can 
      be kept under control.  This is similar to the Maximum 
      Q talked about with the space shuttle.
  b.  The combustion chamber pressure can be kept fairly 
      constant, like the Q.
  c.  The density can be kept within a fairly narrow range 
      making design of the flame holder and combustion chamber 
      relatively straightforward.
  d.  The mass flow, and therefore thrust, does not go to 
      extreme highs or lows allowing a relatively constant thrust 
      throughout the flight regime.  With the profile shown above 
      thrust should peak at about Mach 3 and 30,000 ft but still 
      be almost the same at 100,000 ft as at sea level.
=========================================

Speed of Sound in a Perfect Gas
  v (speed of sound) = sqrt (GRT/M)
  R (gas constant) = 8.314 J/mol-K
  T (absolute temperature)
  ex:  v (He) = sqrt [(1.64)(8.314)(300)/(0.004) 
              = 1,011 m/s = 3,317 fps


Speed of Sound Relative to Some Baseline
  v(1) = v(0) * sqrt[1 + T(1)/T(0)]
  ex:  gas = Helium
  T(0) = 300 K = 540 R
  T(1) = 1200 K = 2160 R
  v(1) = 1100 m/s * sqrt [1 + (1200/300)] = 2461 m/s = 8077 fps

Temperature Conversion Factors
  F = 1.8 C + 32 = 1.8 K - 460 = R - 460  (ex: 300 K = 80 F)
  K = C + 273 = 0.555 F + 255 = 0.555 R  (ex: 1200 K = 1680 F)
  C = 0.555 (F - 32) = K - 273 = 0.555  R - 273
  R = F + 460 = 1.8 C + 492 = 1.8 K  (ex: 1200 K = 2160 R)

Physical Conversion Factors
  1 m (meter) = 3.28 ft  1 ft (foot) = 0.305 m
  1 m/s = 3.28 fps  1 fps = 0.305 m/s

Gas Properties Affecting Tri-Mode Design


This Page Last Updated 13 Dec 98