# Static Balancing of a Payload

by Bill Claybaugh, Reaction Research Society

Dislocations in the Center-of-Gravity (Cg) of a rocket with respect to the vehicle centerline can lead to “coning” in flight.  This coning is visually characterized by a corkscrew exhaust trail when it occurs during thrusting. Whenever it occurs—and it is likely in all rockets that are not axisymmetrically balanced—it increases drag and lowers performance.  In cases of “extreme” unbalance (which can occur for axial offsets of Cg of as little as a few tens of thousandths of an inch for small diameter rockets) the vehicle can be torn apart in flight by the aerodynamic forces created by the Cg imbalance.

For rockets that are carefully designed to be axisymmetric, the only important issue to address in assuring balance of the rocket is to make certain that the fins all have the same weight within a small margin (removing mass from the heavier fins is best done at the fin Cg).  If all other components are axisymmetric—including the propellant grain—then the only part of the vehicle that will require formal balancing is the payload:

I Longitudinal Balancing

The image below shows the set up for longitudinal balancing of a payload:

Two identical scales are slightly modified to support the payload so that the longitudinal axis is parallel with the base of the scales and level.

After carefully measuring the distance between the centers of the two scales (6.760” in this example) the weight of the payload supported by each scale is noted in two orthogonal planes.  Using a moment balance calculation, the center of gravity is determined in each plane:

Averaging three measurements in plane 1, the scales showed 6.953 lbsm on the left side and 4.523 lbsm on the right scale.  Creating an arbitrary starting datum for calculation that is 0.7125” to the right of the right scale center point (that is, at the bottom of the payload base plate) allows the following center of mass balance:

Cg = (4.487 lbsm * 0.7125 in.) + (6.967 lbsm * 7.4725 in.) / (4.487 lbsm + 6.967lbsm)

​​​​= 4.824” from the datum.

Rotating the payload by 90 degrees and weighing again allows calculating the Center of Gravity in that plane, in this case, that value was:

​​​Gg = 4.881” from the datum.

Thus, the Cg appears—on average—to be offset by 0.057” between the two planes.

Balance can be achieved either by subtracting weight from the top of and in the plane that shows the longer Cg distance (Plane 2, in this case) or by adding weight to the top of the plane that has the shorter Cg.  Conversely, weight could be added at some bottom location of Plane 2 or deducted from a bottom location on Plane 1. Note that any of these actions have effects on the rotational balance, which we will address in a future article.

Subtractive Balancing

We can estimate the amount of weight that needs to be deducted from the firstplane by deciding that the weight will be removed at 9.375” from the datum (a location at the top of the conical aluminum section, just below the fiberglass structure that supports the flight computer / transmitter in the image).

The mass required to move the Cg by 0.057” is then:

Mass Lost (or Gained) / New Total Mass = Change in Cg / Distance to New Mass

Adjustment Mass / (11.451 – Adjustment Mass) = .057 / (9.375” – 4.881”)

This mass must be removed at equidistant locations from the rotational axis, that is, we will require two 0.071 lbsm axisymmetric holes in opposite sides of the payload at the required location.

We can estimate the drill depth assuming the use of a mill cutter.  The required cutting depth is then the cross-sectional area of the mill times the drill depth times the density of aluminum:

​​Mass to be removed = 0.098 lbsm. / cu. in. * (pi * r^2) * h

For a 0.5” mill cutter that depth is:

​​​0.071 = 0.098 * 3.1416 * (0.5 / 2)^2 * h

​​​​​h = 3.69”

Obviously, this is impractical as the depth of aluminum at the subject location is only 0.125”.

The relatively large cutting operation required for subtractive balancing is due to the low density of aluminum.  Alternatively, we can estimate the additional mass required in the shorter of the two planes (Plane 1). Because we can use, for example, tungsten for the weight adjustment, it is possible to move the shorter Cgforward with much smaller but higher density balance weights.

Adding mass at a greater distance from the Cg will lower the mass required to achieve the needed shift.  If we consider adding mass at a location 13.375” from the datum location (on the cross bar near the top of the fiberglass structure that supports the flight computer / transmitter) we can calculate:

Adjustment Mass / (11.454 + Adjustment Mass) = .057 / (13.375” – 4.824”)

Noting that one-half of this is 0.03815 lbsm or 17.3 grams, we can observe that a standard tungsten weight used in “pinewood derby” cars of 0.25” diameter and 0.5” length weighs about 14 grams. Thus, drilling two axisymmetric holes at the required location and gluing the tungsten counterweights in place will produce a Gg offset close to the 0.057” adjustment required (see the comments below on the resolution of this system for locating the Cg).  Note that the two balance weights, in final form, need to weigh the same within a small margin or they will introduce a mass imbalance in rotation. We should also note that we are not here accounting for the mass removed to make the holes for the counterweights.

Verification

The final step is to remeasure the Cg in both planes and verify that they are within the resolution of the measurement system.  If not, another, smaller, adjustment in mass in the longer plane or an adjustment of the balance weight in the shorter plane may be required.

A Note on Accuracy

The relativity low cost scales used in this example resolve weight to 0.10 grams. However, multiple measurement in the same plane (achieved by gently pressing on the payload to reset the scales) shows that the scales are in fact accurate to about +/- 10 grams, about 0.3% of the total weight of the subject payload.

This means that the true resolution of this system with regard to differences in Cg between planes is about 0.015”, thus, once the Cg between the planes is within 0.15”, further adjustment is unlikely to increase accuracy using these relatively low-cost scales.

# MTA Launch Event, 2021-10-16, First Update

by Bill Claybaugh, RRS.ORG

In a remarkable demonstration of persistence and luck, RRS President Osvaldo Tarditti was able to find the spent booster rocket. A few photos were captured of the recovered rocket.

Based on the impact location, it was possible to reconstruct a possible flight trajectory by assuming the motor performed as designed and further assuming the front of the vehicle was a flat plate and that the mass did not include the mass of the payload.  We know from video, telemetry, and recovery of the payload that the payload separated from the booster about one second into the flight.

This analysis suggests a burnout velocity of about 1550 feet/second with a peak altitude of about 21,200 feet given the known range of about 14,300 feet. This analysis gives a flight time of about 74.5 seconds and an impact velocity of about 820 feet/second.

Given the observation that the vehicle stopped in about 2 inches (based on the depth of the depression in the hardpan) before falling on its side; we can estimate the impact deceleration.  Given an average velocity during impact of about 410 feet/second because the final velocity is zero and it took only 0.167 feet to come to rest, it follows that the impact occurred over 0.000407 seconds.  This, in turn, indicates an average deceleration of about 31,250 g’s.

The reason for the vehicle turning to the Northeast starting at about 0.20 seconds into the flight remains unclear. There is no evidence either in video or in images of the recovered hardware of any hot gas leak nor of any transient thrust vector anomaly.  The wind was less than 5 miles per hour and from the Northwest; if it had caused a turn, we would expect it to be toward the Northwest, not the Northeast as observed.  The only plausible theory at this time is that part of the belly-band became embedded between the nose of a fin and the rocket body causing the turn via differential drag and then fell away from the vehicle, causing the resumption of normal flight.  Once the recovered hardware is available for inspection, we will test each fin nose to see if a gap exists that might have caught the 0.020-inch thick belly-band.

It also remains unclear as to why the payload separated about 1 second after launch.  The recovered payload showed that both initiators had fired (by design, if one fires the other is ignited; thus, only one signal is required to fire both) but did not show any evidence of having been “swaged” or otherwise subject to being forced off the rocket by aerodynamic or other forces. Neither does the matching front end of the rocket show any evidence for the payload having been forced off. We thus conclude that one of the flight computers ordered the firing of the initiators.

However, the main flight computer stopped working just after 0.80 seconds into the flight for an unknown reason after recovery it was still connected to its battery, which showed the expected 3.87 volts. Further, the limited data recovered from that computer shows that it did not initiate separation of the payload: the firing circuit shows continuity throughout the period that the computer was operating and separately records that no signal was sent by that computer.

This points to the backup flight computer.  That hardware is currently at the manufacture for repair, after which we hope to extract continuity data with regard to its firing status.  Hopefully, once that and other data is available from the backup computer we will be able to establish when it ordered the separation of the payload, and why.

A second update to this firing report is expected. The booster has been packaged up for a more detailed inspection.

# January 2018 meeting

The RRS met for its monthly meeting, Friday, January 12, 2018, at the Ken Nakaoka Community Center in Gardena. We got a late start (8:04pm), but we covered a lot of ground.

Anniversary issue of the Astro-Jet is now available for purchase (\$10/copy)

Everyone is reminded that the anniversary issue of the ASTRO-JET newsletter of the RRS is now available for \$10 a copy. This special issue will be available in print only and proceeds go to benefit the society and our upcoming symposium event. Bill Janczewski and I have worked hard to bring this milestone issue together and we will have them ready for printing and distribution next week. To order, you can contact me by email (secretary@rrs.org) and send me your mailing address. Payment can be made by check to the “Reaction Research Society” sent to our P.O. Box 90933, in Los Angeles, CA, 90009-0933, found on our website.

Payment to the RRS for the ASTRO-JET newsletters can also be made by clicking our “DONATE” button on the website which directly links to our Paypal site. Please note your are paying for the ASTRO-JET and the number of copies.

Frank brought one of George Dosa’s liquid rocket chambers to the meeting for inspection by the society. This single element coaxial injector has not been fired, but George had this made several decades ago. There was talk about what modifications could be made to get this article into hot fire.

George Dosa’s coaxial injector and chamber

Richard Garcia also brought his own liquid rocket chamber as part of the on-going RRS standard liquid rocket project he has been championing.

Richard Garcia’s pintle injector and chamber design

After the usual reading of the treasury report, we began to discuss the agenda topics. The meeting began with announcing our new members who have recently joined us: Michael Lunny, Bryan Calungcagin, Nancy Squires, Barsoum Kasparian and Jack Oswald. The RRS is glad to welcome our new members.

The discussion had turned to membership cards. Bill Janczewski has worked up a new card design and Frank was working with Bill on a few changes. The RRS does not issue membership cards except on an on-demand basis. RRS member, Alastair Martin who runs a printing business had several ideas for different types of card stocks and discussed them with the RRS.

Our discussion then turned to the upcoming RRS symposium to be held Saturday, April 14, 2018. We will try a new format of having our speakers present in the ballroom among our exhibitors. The collared white shirts we gave to our membership running the event was a good idea. We discussed getting these again with iron-on or screen-printed RRS logos to help identify those of us who will be running the event. Frank wanted to have posters showing a decade-by-decade look of the RRS over our 75 year history. This is a great idea and we’ll be working hard to collect old photos to have them on display at the symposium. Easels and other supporting equipment were in short supply as the brick walls of the Ken Nakaoka Community Center made wall-mounting very difficult.

For next meeting, we will discuss more of the details of the symposium including working on our list of presenters and exhibitors. Frank and I have already began to approach some of our prior speakers and exhibitors. We have already confirmed several from industry, government and academia including the LAPD CSP program and the Aerospace Corporation. We expect this year’s symposium to be even greater than last year’s event where we hosted over 200 people.

For the next agenda item, Frank and Larry will begin our next educational event with the students of Florence Joyner Elementary school in conjunction with the LAPD CSP program. This 5-week event will begin sometime in February with an expected launch event in late March. Alastair had indicated he’d like to participate, film and document this event. An update on this event will be given at the next month’s meeting.

Michael had indicated his interest in running an RRS educational event with his old high school, Redondo Union High School. Larry and Frank had offered to help him figure out how best to set this up based on the experience the RRS has had thus far. I had sent him the PowerPoint file I had made which can serve as the basis for the program he can give to an older group of students. This would be the first of several events that Michael and Bryan would like to hold on behalf of the RRS.

Our next agenda topic discussed establishing an account with the regional liquefied natural gas (LNG) supplier, Clean Energy in Boron, California. Richard Garcia has acquired a methane dewar which will be used for liquid rocketry experiments at the MTA. Richard was able to have one of our contacts at the Friends of Amateur Rocketry (F.A.R.) group modify the dewar such that it is ready for use. Our president, Osvaldo, said he would contact Clean Energy and give them the necessary information for the RRS to begin buying quantities of methane.

The next agenda topic was the quarterly briefing of the SuperDosa project. Osvaldo and I have identified chemical suppliers to produce the RRS standard solid propellant mixture recipe. We will meet offline to discuss prices and what is the best approach to proceed. Richard was going to work out some more simulations of our proposed vehicle to get an idea for sizing. The ballistic evaluation motor (BEM) that I designed is still in work. This is an important piece of hardware to characterize the burn rate of our propellant to help finalize and set the grain design. I hope to complete the assembly before the symposium which would also be the next quarterly reporting date (April 13, 2018).

The last agenda item was to discuss how to formalize the proposal process for RRS projects that we would like to seek funding from outside groups. One of the most important things to getting projects funded is to have a clear plan on what the scope of the project is, what purposes it will serve, what exact materials and quantities will be required and what the expected cost of this project will be using real quotes and defensible estimates. The RRS was in agreement and the executive council will meet later to discuss some of these documented proposals I have assembled. Projects include things like making more alphas and beta rockets, 3D printer for RRS use, spare electric generator for the MTA, getting a new launch rail built as backup, obtaining a liquid oxygen dewar…. etc.

The night ran late and our meeting concluded at 9:10pm.

There’s a lot of preparation that must be done in advance of our 75th anniversary symposium on Saturday, April 14th, so we’ll be putting this recurring item on the agenda for next month’s meeting.

For next month’s meeting, Frank will finish his paper rocket air launcher device that he has been making. This was inspired by the last educational event with Grape Street Elementary where the students visited the Space and Missile Command Center at Los Angeles Air Force Base in El Segundo, CA. With luck, we hope to demonstrate it outside the community center and take some video for our YouTube channel.