White Paper - Number of Engines - Design Criteria Relation to Reliability and Other Factors

Edgar Zapata, NASA KSC

October 23, 1998

With costs per pound currently ranging in the tens of thousands of dollars per pound (examples⁽¹⁾ include Delta II apx. $10K/lb to low earth orbit (LEO), Pegasus XL apx. $25K/lb to LEO, and Ariane 44LP apx. $12.5K/lb to LEO) major decisions are currently being made to achieve low cost operations. This decision making, all directly determining capabilities (or not) in the coming decades, can be categorized as follows:

• Technology investment decisions already made or being decided: NASA, with efforts such as X-33, 34, and Future-X, Pathfinder and Trailblazer class demonstrators.
• Start-up business decisions right now: Entrepreneurs such as Kistler Aerospace Corp., Pioneer Rocketplane Corp., and Kelly Space and Technology Inc. and many others are in the midst’s of decision making toward the formation of profitable commercial ventures.
• New approach expendables, decisions already made: Ventures such as Sea Launch by Boeing are one of the more near term attempts to seize a part of the growing expenditures in satellite constellations using new combinations of existing technologies and approaches. Also, upgrade decisions to Atlas and most Delta plans have already been made.
• Reusables, near term: Shuttle upgrade studies continue focused on larger "go-no-go" large investment decisions to be made at the turn of the millennia.

Among the criteria that may be applied to a space transportation system in order to assess costs, and to better make investment decisions, especially for a reusable space transportation system, are "number of engines". This criteria, at the single engine level, has been identified as a medium priority for improvement by previous studies⁽²⁾. From the broader criteria of addressing the integration and simplification needs of future systems, the criteria has been rated as a high priority feature⁽²⁾ to be considered and improved upon in future systems.

The Worksheet

The purpose of this worksheet is to show some basic inter-relationships, on the fly, between the reliability, R, of a liquid rocket engine, the numbers of these engines (Y) used in a concept, and the duration of the stage event (X), such as burning for 3 minutes.

It is generally considered that liquid propulsion is more reliable, against catastrophic failure, than solid propulsion systems, principally due to greater control of events, such as being able to shut-down a faulty liquid engine before harm occurs. This is not possible for today’s solids.

This reliability statement must carry disclaimers of course, such as "all other things being equal" which may be neglected in casual comparisons. At an individual engine or SRB level, Shuttle PRA - Probabilistic Risk Analysis (by SAIC)⁽³⁾ shows a current estimate of about 1/146 chance of loss of vehicle/crew for the Shuttle system. [Fig.1.0, B]

At an SSME engine or SRB level, contributions to this probability are actually quite similar - as shown about just over 1/1500 chance per engine or per SRB of these being the cause. [Fig.1.0, A]

Fig. 1.0 - Sample Screen, Engine Reliability spreadsheet

As current consideration is being given to the upgrade of the Solid Rocket Boosters by replacing them with reusable liquid rocket boosters or LFBB’s, Liquid Flyback Boosters, the inter-relationships of Reliability against catastrophic failure of the liquid rocket engines, the numbers of these in the liquid booster configuration, and the time of the staging all come into play.

The goal would be to be at least as good as the SRB’s - about 1/775 chance of catastrophic failure by current estimates based on probabilistic risk assessment.

The flyback staging makes the job easier on each engine - less burn time is less opportunity for failure or exposure to the possibility of the event.

Using the spreadsheet it can be seen that even though the same engine, an SSME, might be considered as a baseline Reliability number, that for a 3 minute burn, the chances of failure become more remote per engine, about 1 in 4080 chances versus the usual 1 in 1530 chance of catastrophic failure - per engine. [Fig.1.0, C]

Another factor is engine count.

In the previous example, a 6 engine liquid flyback booster replacement with a 3 minute staging or burn time, and engines of equal reliability to an SSME did not decrease the chances of catastrophic failure of the Shuttle system. On the contrary, such a combination INCREASES the chances of a catastrophic failure.

Other factors come into play. For example, the Reliability may be increased per engine to be better than SSME reliability. [Fig.1.0, Use D]  

A third major factor is burn time - exposure to the possibility of an event. Although event potential varies with the moment under consideration, such as transients at startup and shutdown versus steady state conditions, it can for this basic calculation be assumed to have a linear effect.

Short variations in burn time can allow a less reliable engine to perform as well from a probability of catastrophic failure viewpoint as an equal number of engines burning only seconds more.

Adjust the time to 2.75 minutes and notice the variation in R increase required to get a TRUE for the element being safer than an SRB- much less R increase is required than for a 3 minute exposure. [Fig.1.0, Use F]

One neglected factor in this spreadsheet is "THE REST OF THE LIQUID FLYBACK BOOSTER". Of course, this would add to the probabilities.

Therefore - caveats:

Any numbers for the engines must actually be better [Fig.1.0, F] than calculated to account, or leave space, for all the other system failure modes from the booster, in many ways similar to an orbiter, albeit with a much shorter mission duration.

  References

1. NASA JSC Cost Estimating Group "Parametric Cost Estimating Reference Manual, US Expendable Launch Vehicle Data for Planetary Missions" at "http://www.jsc.nasa.gov/bu2/ELV_US.html"
2. Space Propulsion Synergy Team "Guide for the Design of Highly Reusable Space Transportation," August 29, 1997.
3. Data from SAIC Shuttle Probabilistic Risk Assessment (PRA), Fragola et al.

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Edgar Zapata, NASA Kennedy Space Center

Shuttle Process Engineering Directorate, Fluid Systems Division