Sunday, October 23, 2011

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.

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.

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.

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 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 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 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.

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.

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.

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.

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.

Jaxa Website

Encyclopedia Astronautica Website

“Survey of Japanese Space Program With Emphasis on Kappa and Lambda Type Observation Rockets”


  1. I'll bite. I must say it's about time someone other than me has taken a long hard look at the Lamda. Duh! My company Aeronautic Enterprises Inc. Is in the process of designing a modern version of the Lamda L-4. Our version is 47ft tall and uses motors built at our launch facility on Matagorda Peninsula, Tx. At an estimated cost of $350,000 real USD each to put 20kg payloads into LEO on a schedule of 2 per month. This is the most realistic approach for commercial space to begin putting payloads into orbit on a budget affordable enough for anyone that wants to do so. I have been working on the facility and the launcher now for 3 years mostly on my own as there are not many that have enough vision to actually do the work required to make it a reality. I have dedicated my life to the project and I wont give up until it becomes a reality if I have to do it alone. Anything else without tons of money backing it will fail. Why reinvent the wheel?

  2. Well, the L4S was only marginally successful. It failed 5 out of 6 times.

    One could argue that the failures were due to development issues, but it appears obvious to me that the issue was the design. There was hardly any delta V margin and he guidance mechanism left much to be desired.

  3. Well you know we are not talking about an exact duplicate of the design! Just the basic size. There is no need to use the same guidance technique

  4. I found an error in my table and I corrected it. The Isp for stage 0 was wrong and the masses changed a bit.

  5. Oh, also, in reviewing the data on the Lambda 4S rocket, I see that it is *NOT* the smallest land-launched vehicle. The GLOW that I calculate is 28211 pounds but the Vanguard was only about 22,000 pounds GLOW.

    I had taken the word of several sources around the web for granted, but my analysis shows that they're wrong. The number that most people quote as the GLOW is really the Stage 1 weight plus the strap-on-boosters. This weight doesn't even take into account the upper stages.

    It's easy to see how people make the mistake, though, because the table from JAXA []is a bit hard to make sense of.

  6. @ Ed. If the Lambda is not the lightest rocket ever launched to achieve orbit, what is? I have been trying to find this information out.

    1. As far as I know, the Lambda 4S *IS* the lightest orbital rocket. The next lightest is the US's Vanguard launcher.
      There was an error in my earlier calculations of the weight of the Lambda 4S vehicle. I corrected those and it absolutely *IS* the smallest launch vehicle (to date).

      The note at the top of the article points out:

      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)

      I apologize for any inconveniences my error has caused.

      Ed L

  7. Ed,
    I'd like to link back to this page, as well as use that image for a little something I'm writing (in reading that sentence, it sounds remarkably spammish; trust me, it's not!). I find your analysis of the Lambda to be great, certainly the best I've found on the Internet, and I want to give credit where due for a goodly chunk of my research. Okay to proceed?

  8. First of all, I would like to say I love this post (it's a ton more useful than most sites with info on this brilliant rocket). I was wondering if you could elaborate more on how the fourth stage oriented itself in between spin down and spin up motors. It just blows my mind how bare bones and cost efficient this rocket seems. How involved was this orientation in the fourth stage?

    1. It was so hard to piece together what information I had in this article. I don't have any more details. It's been years since I researched the article and I can't find my original sources on the final stage orientation information. Maybe someone in Japan (or who travels to Japan) can research that and post it.

    2. I understand, thank you for the speedy reply


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