wiki/ RocketScience/ astrobee d

Astrobee D

Astrobee D on a launch rail

The Astrobee D was a small single stage sounding rocket build by Aerojet General Corporation specifically for low cost meteorological soundings in the 'D zone' of the upper atmosphere (80–140 km MSL). It was one of the first (solid) rockets to use an HTPB binder. It never gained much popularity or as low of cost as the program had originally hoped. But there were at least 48 launches between 1970 and 1980.

  1. Astrobee D
    1. Rocket Specs
      1. Table 1. Astrobee D General Specifications
    2. Motor Details
      1. Table 2. Astrobee D Motor Characteristics
      2. Figure 1. Astrobee D Thrust Curve
    3. Compairson to LV2
    4. Discusion of Optimizaion
      1. The Goddard Problem
    5. Flight 30.250-3
      1. Figure 2. Altitude Plot
      2. Modeling in Open Rocket
      3. Open Rocket Overlays
      4. Figure 3. Altitude with Open Rocket Overlay
      5. Figure 4. Velocity with Open Rocket Overlay
      6. Flight Analysis
      7. Figure 5. Open Rocket Boost Acceleration
    6. Data
      1. Open Rocket
      2. Thrust Curve
      3. 30.205-3 Telemetry
      4. Astrobee D Historical Launch Log
    7. References

Rocket Specs

The total rocket length is about 4 meters counting the sweep of the fins. Most of the rocket is made up of the motor section. Unlike most commercial high power rocket systems which have a 'reloadable' motor casing that fits into the rocket body, this rocket was essentially one giant motor. The skin of the vehicle also serves as the motor casing. There was no recovery system so the rocket was not reused.

Astrobee D major dimensions

For such a small rocket it had an incredible maximum altitude. It was flown as high as 146 km — 46 km above the line of space! All on a single stage, single motor.

Table 1. Astrobee D General Specifications

Metric Value
Total Length 4.02 m
Width 15.24 cm
Fin Span 22 cm*
Nose Cone Length 64.8 cm
Payload Length 53.3 cm
Dry Weight 33 kg*
Propellant Weight 60.3 kg
Fuel Type Solid, HTPB AP
Motor Classification Q
Mass Ratio 0.7*
Max Altitude 140 km
Payload Mass 2–20 kg*

*Approx; Extrapolated from drawings or other spurious data.

The key to its performance lie in its 'dual thrust' slow burn motor. Through carefully chosen grain geometry Aerojet was able to make a solid motor that burned very fast and hard for a couple of seconds then went into a 'sustain' mode that burned very slowly for a long time.

The 'boost/sustain' strategy is optimal for rockets in an atmosphere.

Motor Details

The motor section of the Astrobee D was the dominate rocket structure. It consisted of a simple thin walled motor casing with integrated fins.

Table 2. Astrobee D Motor Characteristics

Metric Value
Motor Length 279.4 cm
Motor Diameter 15.24 cm
Propellant Weight 60.3 kg
Motor Weight 82.1 kg
Total Impulse (Vacuum) 151,000 N·s (Q)
Boost Thrust 17 kN
Boost Duration 2 sec
Sustain Thrust 8 kN
Sustain Duration 16 sec
Total Burn Time 18 sec
Boost Acceleration Max. 25 g
Sustain Acceleration Max. 20 g

Apparently the boost/sustain modes are done through grain geometry. Something fast burning like a star grain burns through first, followed by a very slow core burner.

In addition to the sustain phase taking being slow, it's progressive: slowly building up thrust towards the end of the burn.

Figure 1. Astrobee D Thrust Curve

Astrobee D Thrust Curve

Here we can see the boost burn followed by 16 seconds of progressive sustain burn. The shape of this curve is close to the optimal solution for a flat Earth and exponentially diminishing atmosphere as in the Goddard Problem.

Compairson to LV2

Astrobee D compared to PSAS vehicles

For PSAS, the most intersting thing about the Astrobee D is the fact that it's no larger than our current rocket, LV2.3. What's astonishing is despite the fact that our vehicles are the same size, we have only flown to 5 km while the Astrobee D makes it 140 km!!

Clearly there is room for improvment in our design.

Discusion of Optimizaion

The obvious reason Astrobee D goes so much higher than LV2.3 is it has consiterably more fuel. A large Q motor is almost 16 times as much total impulse as an N. However there have been amateur Q motors flow before. Specifically Derek Deville's Qu8k rocket in 2011. That rocket was very similar in size to an Astrobee D, however only managed 36 km -- about a quarter of 140 km!

The real secret sauce is in the dual mode, boost/sustain grain geometry. While Qu8k and Astrobee D have almost identical amounts of fuel, the Qu8k burn time is only 8 seconds. Because most of the burn is done in the lower atmosphere a large proportion of the energy is lost to atmospheric heating.

With a much longer burn the Astrobee D is able to delay some of the energy of the motor until after most of the atmosphere is left behind. This significatly effects the apogee.

The Goddard Problem

The optimal (for altitude) thrust curve for a simple rocket in an atmosphere is sometimes called the Goddard Problem — after Robert Goddard. The Goddard problem suggests a 1 degree of freedom model constrained to the 'up' direction. The Earth is assumed to be flat (and therefore g is defined as g0 at all time). If there were no air resistance then it can be shown that the optimal thrust curve is simply to burn fuel at the maximum rate. This is suggested by the classic rocket equation in this form:

v_{bo} = v_e \ln\left(\frac{m_0}{m_f}\right) - gt_{bo} + v_0

Where burnout velocity is inverse linear with burn time tbo.

However, the Goddard Problem adds in a simple atmosphere. Since a real complex atmosphere would make the physics non analytical, a simple drag model is assumed with a fixed drag cooeficient and an atmosphere in the form

\rho = \rho_0 e^{kh}

Which is an exponential atmosphere. The density of the atmosphere decreases with the log of the constant k.

The solution to the Goddard Problem suggests the optimal thrust curve for a rocket near a planet in a exponetial atmosphere — i.e. a sounding rocket — follows a boost/sustain model.

Flight 30.250-3

Radar telemetry of at least two flights are available (See Data section). In particular we consider Flight 30.205-3 on March 6th 1972. Launched at 0:14 am local time from Poker Flats Research Range, this particular Astrobee D had an cooled IR aurora sensing experiment onboard. Telemetry for the flight shows an apogee of 89.33 km.

Figure 2. Altitude Plot

Astrobee D 30.205-3 Altitude Telemetry

The telemetry does not cut in until 28.1 seconds after launch. About 10 seconds after motor burnout.

Modeling in Open Rocket

Despite not having boost phase telemetry, we can build and test an Open Rocket model and match it to the rest of the flight. Using known numbers for the overall rocket size and mass we start with a simple 4 part rocket model: nose, payload, motor, and fins. There are some known numbers for the motor weight, those are used to set the mass and CG of that part. The rest of the model mass is guessed assuming it was relatively heavy by today's standards.

A generic mass component is used as the payload and a tiny (~20 cm) parachute is added to model the extra drag from having the nosecone removed at the end of the flight.

An .rse motor file is created from the known propellant mass and thrust curve. This is imported into Open Rocket and added to the model as well.

From here we can adjust the payload mass and launch angle to try and match the telemetry of the real flight.

Open Rocket Overlays

With a launch rail angle of 9.5° and a payload mass of 14 kg — both very reasonable numbers based on what is known about sounding rockets — we get very convincing, matching trajectories.

Figure 3. Altitude with Open Rocket Overlay

Astrobee D 30.205-3 Altitude Telemetry vs Open Rocket

Telemetry in red, Open Rocket data is the thin black line. We overshot a few percent, but the overall shape and timing are nearly identical to the real flight.

Figure 4. Velocity with Open Rocket Overlay

Astrobee D 30.205-3 Velocity Telemetry vs Open Rocket

Telemetry in red, Open Rocket data is the thin black line. If the rocket were moving straight up, the velocity would reach exactly zero. We can match up the launch angle with the amount of horizontal velocity at apogee. At 9.5° launch angle (that is, launching 9.5° from vertical) we get a good match with the velocity curve.

Flight Analysis

Now that we have a model of the entire flight we can look at the numbers. Maximum velocity comes in at 1.404 km/s — 4.7 times the speed of sound at that altitude! At that speed the stagnation temperature is nearly 1,700 °F.

Figure 5. Open Rocket Boost Acceleration

Open Rocket Boost Phase Acceleration

If we believe our Open Rocket model then we can start to make inferences of the acceleration during the boost phase of flight (when the motor is burning) since this data was not provided in the telemetry file.

The maximum acceleration is about 15.5 g (150 m/s/s). The bi-modal thrust curve also has an evident effect on the rocket acceleration, with a strong peak towards the end of the boost.

Data

Open Rocket

Open Rocket with an Astrobee D modeled

Thrust Curve

30.205-3 Telemetry

Astrobee D Historical Launch Log

Launch Date Launch ID Apogee Altitude Launch Site Agency Launch Purpose
1970 Jun 08 ??:??:?? Test 1 98 km White Sands Missile Range (New Mexico) USAF Test
1970 Jun 08 ??:??:?? Test 2 98 km White Sands Missile Range (New Mexico) USAF Test
1971 Jan 19 19:40:47 Robin AFCRL 71-1 146 km Wallops Flight Facility (Virginia) USAF Aeron
1971 Jan 21 18:14:23 Robin AFCRL 71-2 130 km Wallops Flight Facility (Virginia) USAF Aeron
1971 Jan 21 18:57:36 Robin AFCRL 71-3 129 km Wallops Flight Facility (Virginia) USAF Aeron
1971 Jan 21 19:40:47 Robin AFCRL 71-4 132 km Wallops Flight Facility (Virginia) USAF Aeron
1971 Jan 21 20:24:00 Robin AFCRL 71-5 132 km Wallops Flight Facility (Virginia) USAF Aeron
1971 Jan 21 21:07:11 Robin AFCRL 71-6 127 km Wallops Flight Facility (Virginia) USAF Aeron
1972 Jan 28 21:07:11 CRL A30.116-1 117 km White Sands Missile Range (New Mexico) AFCRL Plasma
1972 Jan 29 05:02:23 CRL A30.116-2 122 km White Sands Missile Range (New Mexico) AFCRL Plasma
1972 Mar 06 12:14:23 CRL A30.205-3 86 km Poker Flat Research Range (Alaska) AFCRL Aeron
1972 Mar 09 10:48:00 CRL A30.205-4 90 km Poker Flat Research Range (Alaska) AFCRL Aeron
1972 Dec 06 06:28:48 CRL A30.205-1 27 km Churchill Research Range (Manitoba Canada) AFCRL Ionos/Aeron
1972 Dec 09 01:26:24 CRL A30.205-2 70 km Churchill Research Range (Manitoba Canada) AFCRL Ionos/Aeron
1973 Mar 21 10:04:47 CRL A30.205-5 78 km Poker Flat Research Range (Alaska) AFCRL Aeron
1973 Apr 06 08:38:23 CRL A30.205-6 78 km Poker Flat Research Range (Alaska) AFCRL Aeron
1973 Jun 30 20:24:00 NASA 23.01GT 93 km Wallops Flight Facility (Virginia) NASA Test
1973 Oct 03 01:40:47 CRL A30.311-1 53 km White Sands Missile Range (New Mexico) AFCRL Aeron
1973 Oct 03 02:24:00 CRL A30.311-2 100 km White Sands Missile Range (New Mexico) AFCRL Aeron
1973 Oct 03 06:00:00 CRL A30.311-3 102 km White Sands Missile Range (New Mexico) AFCRL Aeron
1974 Feb 08 04:19:12 CRL A30.311-4 91 km Poker Flat Research Range (Alaska) AFCRL Test
1974 Apr 11 23:31:11 CRL A30.413-1 83 km Poker Flat Research Range (Alaska) AFCRL Ionos
1974 Apr 12 23:31:11 CRL A30.413-2 129 km Poker Flat Research Range (Alaska) AFCRL Ionos
1974 Oct 10 16:33:35 NASA 23.05UE 90 km White Sands Missile Range (New Mexico) NASA Ionos
1975 Feb 26 22:48:00 CRL A30.413-3 104 km Poker Flat Research Range (Alaska) AFCRL Aeron
1975 Mar 01 00:57:36 CRL A30.311-6 111 km Poker Flat Research Range (Alaska) AFCRL Aeron
1975 Jul 15 15:07:11 NASA 23.02UE 76 km White Sands Missile Range (New Mexico) NASA Plasma
1975 Dec 02 12:57:36 CRL A30.311-8 120 km White Sands Missile Range (New Mexico) AFCRL Aeron/Tech
1975 Dec 02 13:55:12 CRL A30.311-5 124 km White Sands Missile Range (New Mexico) AFCRL Aeron/Tech
1975 Dec 02 17:02:23 CRL A30.311-7 125 km White Sands Missile Range (New Mexico) AFCRL Aeron/Tech
1975 Dec 03 00:28:48 CRL A30.413-5 125 km White Sands Missile Range (New Mexico) AFCRL Aeron/Tech
1975 Dec 03 00:57:36 CRL A30.205-7 125 km White Sands Missile Range (New Mexico) AFCRL Aeron/Tech
1975 Dec 03 01:55:12 CRL A30.413-4 127 km White Sands Missile Range (New Mexico) AFCRL Aeron/Tech
1976 Jan 18 19:26:24 NASA 23.03UE 76 km Wallops Flight Facility (Virginia) NASA Plasma
1976 Jan 23 19:26:24 NASA 23.04UE 76 km Wallops Flight Facility (Virginia) NASA Plasma
1976 May 13 02:52:48 NASA 23.06UE 90 km White Sands Missile Range (New Mexico) NASA Plasma
1976 Aug 11 15:50:24 NASA 23.07UE 90 km White Sands Missile Range (New Mexico) NASA Plasma
1977 Jan 08 19:40:47 NASA 23.08UE 83 km Wallops Flight Facility (Virginia) NASA Plasma
1979 Feb 20 ??:??:?? NASA 23.11UU 90 km Churchill Research Range (Manitoba Canada) NASA Aeron
1979 Feb 26 16:48:00 NASA 23.09UE 85 km Red Lake: McMarmac Site (Ontario Canada) NASA Plasma/Eclipse
1979 Feb 27 12:00:00 NASA 23.10UE 85 km Red Lake: McMarmac Site (Ontario Canada) NASA Plasma/Eclipse
1979 Jun 07 ??:??:?? NASA 23.12UU 90 km Wallops Flight Facility (Virginia) NASA Aeron
1979 Sep 16 ??:??:?? NASA 23.16UE 90 km Wallops Flight Facility (Virginia) NASA Plasma
1979 Sep 20 ??:??:?? NASA 23.13UU 90 km Wallops Flight Facility (Virginia) NASA Aeron
1979 Oct 01 ??:??:?? NASA 23.14UU 90 km Wallops Flight Facility (Virginia) NASA Aeron
1979 Dec 18 ??:??:?? NASA 23.15UU 90 km Wallops Flight Facility (Virginia) NASA Aeron
1980 Feb 16 08:24:00 NASA 23.17UE 78 km San Marco Launch Complex (Formosa Bay Kenya) NASA Plasma
1980 Feb 16 20:24:00 NASA 23.18UE 76 km San Marco Launch Complex (Formosa Bay Kenya) NASA Plasma

Direct data download

References

  1. Bollerman, B. May, 1971. Study of 30 km to 200 km Meteorological Rocket Sounding Systems Volume II - Recent Advancements. NASA-CR-1790.
  2. http://ntrs.nasa.gov/search.jsp?R=19710017216
  3. Jensen, L.L. & Kemp, J.C. and Bell, R.J. Nov, 1972. Small Rocket Instrumentation for Measurements of Infared Emissions - Astrobee D 30.205-3 and Astrobee D 30.205-4. Interim report, Utah State University: Logan Space Lab