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According to this answer the minimum and maximum they could be were:

Pilots: Height between 62 and 75 inches. (1.57 to 1.90 meters)

Mission Specialists: Height between 58.5 and 76 inches. (1.49 to 1.93 meters)

It is quite understandable that there would be a maximum height so that they could fit into the capsule and so that there was not too much weight. Why was there a minimum height?

The Rocket fan
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Everything that must interface with the human body must be designed to fit a certain range of body sizes. For example, in the early days of shuttle when airline-like operations were envisaged, the requirement was to design all crew equipment to fit 90% of the US adult population.

The normal complement of crew equipment will provide supplies for a standard crew of four for a mission of 7 days. The equipment is designed to be used in the Orbiter shirt-sleeve environment by 90 percent of the male/female population (the 5th to 95th percentile).

Space Shuttle Press Reference Manual (preflight version) (emphasis mine)

Examples of equipment affected:

  • launch and entry suits
  • EVA suits
  • toilet equipment
  • crew seating
  • escape equipment
  • emergency medical supplies

An example of small body size impacting mission ops occurred during STS-086. Astronaut Wendy Lawrence was planned to serve as a long-duration US crewmember on Mir. However, due to failures experienced on the Mir shortly before the mission was launched, the timeline of her stay was replanned to include an EVA repair. Unfortunately, Lawrence was too small to fit into the Russian EVA suit and so could not participate. This forced her to be replaced as the long duration crewmember by David Wolf.

awrence, Wolf, and Scott Parazynski standing side by side This NASA KSC photo shows STS-086 crewmembers Lawrence, Wolf, and Scott Parazynski standing side by side during pad escape training for that mission.

Organic Marble
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    I was quite amused when I worked in NMR imaging (now known as MRI), and the machine I was working on was designed to the same 5-95% of the US adult population. It turned out that many more than 5% of patients could not fit in the tube, as the people who could afford to pay for an MRI formed a very skewed subset of the adult population who were rather bigger than the 95 percentile. Ooops! – Neil_UK Jan 12 '23 at 15:53
  • @Neil_UK re: "rather bigger than the 95 percentile". Bigger in what dimension, if I might ask? – mustaccio Jan 12 '23 at 20:40
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    ... presumably in the direction that makes them not fit in the tube ... – davidbak Jan 12 '23 at 21:33
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    Plus the need for things like being able to see out the windows (to a prescribed field of view) while in the seat, which I think is why there's a narrower range for pilots. – hobbs Jan 12 '23 at 22:48
  • @hobbs Valid, but I would imagine that reaching controls is a bigger issue than seeing out the windows. A knob being just 5cm out of your reach becomes very, very problematic when you are strapped to your chair at 3g. – Lodinn Jan 13 '23 at 07:57
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    Could you label who is who in the photo? Lawrence can be guessed by her height, but it's hard to tell who is Wolf and who is Parazynski without clicking on external links. – jaskij Jan 13 '23 at 08:43
  • Are taller people on average richer or why do you think it has to do with their wealth @Neil_UK? – SirHawrk Jan 13 '23 at 11:01
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    @SirHawrk The tube was 3 metres long with open ends, so it was more about girth than height. People that can't afford to eat are generally thinner than people who can. – Neil_UK Jan 13 '23 at 11:18
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    @Neil_UK In the devloped world it is actually the other way around. Poverty and obesity are strongly correlated: https://bmjopen.bmj.com/content/8/1/e019862 – SirHawrk Jan 13 '23 at 12:01
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    @jaskij they literally have nametags sewed on their clothes. You will see that Scott is labeled "Too Tall" and Wendy "Too Short". – Organic Marble Jan 13 '23 at 13:06
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    @OrganicMarble I did not think of that, but at least on my PC the photo is so small when displaying here on SE that I didn't realize the tags were there. When opening the photo in a separate tab and zooming in they are visible and readable though. – jaskij Jan 13 '23 at 13:54
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    @OrganicMarble Just a small detail, but work uniforms like this will generally have one side of a Velcro fastener patch sewn onto the uniform where the nametag goes. The nametag has the complementary side attached to the back of it to allow one to quickly and easily change the nametag without tailoring when one needs a new work uniform. It also allows for jokes or pranks based around nametag contents to easily happen. – CitizenRon Jan 13 '23 at 15:53
  • @CitizenRon thanks! I guess you're taking issue with my use of the word "sewed"? oops. You're right, it was Velcro. – Organic Marble Jan 13 '23 at 16:00
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    @Lodinn For large aircraft, including the Shuttle, the pilot's eyes must be located in a small box for proper visual references. This is especially important for optical guidance systems, including the PAPI system and the HUDs the Shuttle used. For a pilot, the vision dictates the seating position, and flight controls are then adjusted to match. – user71659 Oct 16 '23 at 20:58