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I was reading the wikipedia article about the SRBs, which were retrieved, refurbished, updated and re-used. I understand that if they were taken apart and pieces were replaced, that there was a 'new two' for each flight.
However, I'm looking for a rough idea of how many SRBs there were - surely it wasn't the same two, and obviously the four that weren't recovered - so how many were made? If they're famously recoverable, I would understand that they didn't make all 270 of them.
The answer to the question is an ancient philosophical question: Ship of Theseus. As Organic Marble mentioned in his comment which could have been an answer:
The SRBs were made up of segments, and the reuse was at the segment level.
The obvious lower bound for number of SRB segments produced would be eight: four SRB segments per side per launch. We can double that to 16 as this photo shows two STS stacks on the pad together.
Each SRB segment was rated for 20 launches. This document for the SLS Qualification Motor shows booster segment serial numbers in use on that test:
O32, O89, O43now, L82, L89n, L109, L98n, L92, L95n, O59
I'm sure that I've misread or misinterpreted that slightly, but for purposes of estimating population the numbers will do.
If we apply the German tank problem to that data, then we can estimate 120-130 total segments that were given serial numbers, as the higher serial numbers are better represented. Divide 120 by 4 segments per SRB, and I would say that enough SRB segments were produced to build about 30 SRBs, given enough nose caps, nozzles, and other components.
The following table lists the number of booster segments flown by type.
All shuttle missions and Ares-1X are included, no ground tests are included.
Here is a picture to help interpret the results. The red letters are the nomenclature I used for each booster segment.
(original diagram from Collectspace here)
So, if one took every segment ever flown, and ignored segments that were lost or scrapped, there would have been enough segments to build 53 boosters, with the upper cylinder segments being the limiting factor. (160 were flown, it would take 159 to build 53 boosters). Note that this is a purely hypothetical situation.
Booster segment data from the paywalled http://www.spaceshuttlealmanac.com/
Caveat: Please treat this as a "best-guess". My attempts to validate the data from the paywalled site have not been completely successful. I am seeking additional shuttle flight segment data to continue the validation.
Production for SRB segments was as follows:
$$\Tiny\begin{array}{lllllllllll} \textbf{Production Batches} & \text{STD FWD} & \text{STD} & \text{newCF} & \text{LWT} & \text{newCF} & \text{STD} & \text{LWT} & \text{STD } & \text{LWT } & \text{STD AFT} \\ & \text{Dome } & \text{CYL} & \text{SCYL } & \text{CYL} & \text{LCYL } & \text{ATT} & \text{ATT} & \text{STIFF} & \text{STIFF} & \text{Dome} \\ \text{Actual} & 61 & 94 & 77 & 124 & 101 & 15 & 62 & 73 & 97 & 65 \end{array}$$
Segments came in several flavors. STD=Standard Weight (original production run) LWT=Lightweight (MTI shaved the case down to reduce weight, with the consequent increase in ovality) newCF=new configuration (the RSRM with capture feature as a newly manufactured segment)
All existing segments were remilled to include the capture feature.
newCf were manufactured in both:
SCYL= Standardweight Cylinder LCYL=Lightweight Cylinder.
As far as the placement of the cylinders there is 4 segments in a SRB.
FWD segment made up of a fwd dome and two STD cylinders
FWD CNTR segment made up of two cylinders
AFT CNTR made up of two cylinders
AFT segment made up of the ET ATT cylinder, two stiffener cylinders and the AFT Dome
