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There's a kind of urban legend that the Space Shuttle boosters diameter could have been larger if it was not restricted by the limitations imposed by the railroads, specifically the railroad gauge. I can't find any convincing detailed analysis of how fair the claim was about the boosters diameter being dependent on the railroad gauge.

Did the boosters have exactly that diameter because the larger the better and the current one is the largest one that could be afforded with transporting the boosters by railroad?

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The claim may be based on a misunderstanding. The solid rocket boosters were made in Utah and transported to the launch site in 4 segments by rail, which did limit their size. But it was not the track gauge that influenced this limit, but the loading gauge, which is only very indirectly related to the track gauge.

However, the diameter of the shuttle boosters (12 feet) exceeds the width of all loading gauge standards in the USA (which differ mostly in height, the width is generally 10 feet 8 inches). Shipments that exceed the standard loading gauge in width are not all that uncommon, more mundane industrial parts often exceed them, but it requires careful planning and is very expensive as it often involves temporarily dismantling blocking structures, and of course at some point (such as with a tunnel) you run into hard limits.

So it doesn't look like transport by railroad dictated the booster designs, but it probably influenced them. I'm pretty sure that if making them wider would have yielded some large advantage and been otherwise feasible, then a solution to the transportation problem would have been found.

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There's a forum post here that has some interesting information:

Well, there was SOME justification for the decision to cast the propellant in Utah-- the cool dry climate there, especially the low humidity, helped considerably in getting a CONSISTENT propellant casting, especially in casting multiple segments for a solid rocket motor.

Aerojet had created the world's largest solid rocket motor, a 260 inch behemoth which was static tested as a possible (cheap? or so the thinking went) replacement for the Saturn IB first stage (cluster's last stand) instead of the nine clustered tanks, thrust structure, and eight clustered liquid engines used on that stage. They cast it in Florida (IIRC) because the 22 foot diameter and massive weight precluded moving it very far if at all. They test fired it in a 'silo' test stand (which is there to this day, but abandoned) and there were some difficulties encountered with the casting of the grains and the motor itself which were basically 'traced back' to variable temperature and humidity messing up the pours. The engine didn't perform as expected, and basically broke the test stand from the vibration, etc. so they abandoned the idea.

A few years later when shuttle decided to go with solid rocket boosters, Morton Thiokol, who had extensive experience with solid rockets from their ballistic missile work for Air Force, won the contract. Their facilities were in Utah, and really sold the idea that their products (large ICBM solid rocket motors for missiles like Minuteman) had given them considerable experience in this area, and they wouldn't have the problems casting the much-larger shuttle SRB segments because the dry climate in Utah made casting pours more consistent and easier. BUT, because of the weight of the fully-fuelled segments, the only realistic way to transport them was by rail-- they would be too heavy and too big for road transport, and MUCH too heavy for air transport, and Utah doesn't have any water shipping ports capable of shipping them by barge. This meant that the SRB's were ultimately limited in diameter, which of course in a core-burning solid rocket, determines the burn duration (more or less).

The Aerojet 260" booster was an attempt to get around size limits of solid rockets. According to the forum post, this attempt failed.

Note that ESA decided to use a segmented booster design for Ariane 5, as well. The top segment is fueled in Italy, the two lower segments are fueled at the Kourou spaceport. They are joined by a construction that is similar to the Shuttle SRBs.

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