The Japanese Lambda 4S Launcher

NOTE: It was kindly pointed out by Stephen Pietrobon that I had made an error in my interpretation of the mass table. The following is the corrected version of the analysis. (CORRECTED 12 August 2012)

Is it possible to put a payload into orbit on a multistage rocket without a guidance system? The answer is "yes." In 1970, Japan launched its Lambda 4-S (or L4-S) launcher with the Osumi satellite and placed its payload into orbit. This vehicle had no on board guidance system and is, to date, the smallest ground based launch vehicle to place a satellite into orbit. This vehicle provides some interesting lessons to those with small launch vehicle orbital aspirations.

The history of the Lambda L4-S is in solid propellant sounding rockets where most of the four stages were developed. The first stage was composed of the L735 sounding rocket motor with 2 SB-310 strap on booster motors. The second stage was a shortened version of the first stage known as the L735-1/3 (it was about 1/3 the length of the first stage). The third stage was a sounding rocket motor known as the L500. The fourth stage was a small spherical solid motor known as the L480S.

The payload placed into orbit was the Osumi satellite which was composed of the fourth stage motor plus the satellite instrumentation. It was placed into an orbit with a perigee of 200 miles and an apogee of 1500 miles. Launched in 1970, its orbit finally decayed in 2003 and it entered the atmosphere.

THE ANALYSIS
Information on this rocket is scarce but, piecing together a cryptic table of masses and performances from the Japan Aerospace Exploration Agency (JAXA), finding some other documentation at the NASA Technical Report Server (NTRS), and fitting everything into the rocket equation, I was able to get a reasonable model of the stages, their weights and performances.

STRAP ON BOOSTERS
The first stage to consider is the strap-on boosters and their involvement in launching the rocket onto its trajectory. Two SB-310 motors were strapped on to enhance the boost rate and delta V of the vehicle. These motors are each 12.2 inches (310 mm) in diameter, 19 feet (5772 mm) long, weighed about 1100 pounds and produced about 21,000 lbs ( 1824 N) of thrust each, burning for 7.1 seconds with an Isp of 220 seconds. These motors continued seeing use in the later Mu family launchers.

STAGE 1
The first solid stage motor, designated L735, was about 2.4 feet (735 mm) in diameter, and 27 feet (8280 mm) long. It had four fins to stabilize it and weighed about 20721.22 lbs (9399 kg). It produced 92170 lbs (410 kN) of thrust, burned for about 29 seconds and had a sea level Isp of about 215 seconds.

STAGE 2
Stage 2 was a shortened version of the Stage 1 motor and was called the L735-1/3 because it was 1/3 of a first stage solid motor. It was 2.4 feet (735 mm) in diameter, about 12 3/4 feet (3900 mm) in length and weighed about 5400 lbs (2450 kg). It produced about 26,527 lbs ( 118.00 kN ) of thrust burning for about 38 seconds with an Isp of 242.9 seconds.

STAGE 3
Stage 3 was a solid rocket motor designated L-500. It was about 1.64 feet in diameter (500 mm), 8.2 feet (2500 mm) in length, weighed about 1700 lbs (800 kg) and had an Isp of 249.3 seconds. It weighed about 1760 lbs ( 800 kg ). Stage 3 also had spin up motors to cause gyroscopic stabilization.

STAGE 4
Stage 4 was a spherical solid rocket which stayed in orbit with the satellite; it was designated the L-480. It had a diameter of 1.3 ft (480 mm), weighed about 220 lbs ( 100 kg ) full and had a vacuum Isp of 254 seconds. Stage 4 also included spin up and spin down motors which were used in preparation for the horizon sensing and azimuth setting activity.

PERFORMANCE TABLE SUMMARY
Because of the strap-on boosters, we must break down the time when both the boosters and the first stage are firing and treat this as one "stage" after the strap on boosters are ejected, what's left of the first stage is another "stage." I therefore include the thrust of the boosters plus that of the first stage during their coincident burn duration. This is designated in the performance table as "Stage 0." After the strap-on boosters burn out and are ejected, the stage 1 rocket tube plus the remaining propellant in the first stage motor constitutes "Stage 1." The upper stages require no other coincidence considerations and follow the published stage figures from JAXA.

GUIDANCE AND TRAJECTORY
Although details are sketchy and hard to come by, the best available details suggest that stages 1 and 2 used fixed aerodynamic surfaces and a gravity turn to direct the vehicle trajectory. Then the third stage used spin motors to gyroscopically stabilize itself. The fourth stage despun itself, pointed in the correct orientation and then fired its motors to set itself on the desired trajectory and respin itself for stabilization. Apparently the reason for this approach to "guidance" was that Japan's constitution forbade technology that could have military purposes so the guidance system had to avoid military applications. This system wasn’t properly a “guidance system,” but more of a one-shot pointing system.

AERODYNAMIC AND GRAVITY LOSSES
My simulation shows about 218 fps of aerodynamic losses. But, this number is hard to establish with certainty because I don't have a good way of calculating coefficients of drag for shapes which are not bodies of revolution.

The simulation also showed about 870 feet per second for gravity losses through the 1st stage burnout.

LESSONS LEARNED
Some of the most obvious things that can be learned from this launcher are the kinds of weight ratios that each of the stages had. This can be useful in estimating weight ratios for our own rocket designs (or at least suggesting reasonable ranges for similar rockets).

Another lesson that can be learned is that the launch vehicle total delta V had a small margin above what was required for orbit (about 20%). Looking at the number in the analysis table, we see that this launcher had a total delta V of about 29526 fps.

Another thing worth pointing out is that it is possible to orbit a satellite with only a final stage orientation mechanism, leaving the other stages only to follow gravity turn trajectories.

A final thing to notice is that the length to diameter ratio (fineness ratio) is about 22. As rockets get smaller, it is more beneficial to go with larger fineness ratios to counteract the increased effects of aerodynamics which don't scale equivalently with the mass.

REFERENCES
Jaxa Website
http://www.isas.jaxa.jp/e/enterp/rockets/vehicles/l-4s/index.shtml

Encyclopedia Astronautica Website
http://www.astronautix.com/

“Survey of Japanese Space Program With Emphasis on Kappa and Lambda Type Observation Rockets”
NASA NTRS, http://ntrs.nasa.gov/search.jsp