How Semaphore Sends Numbers (and What It Costs)
Flag semaphore encodes letters as arm positions, and it has an awkward problem that Morse solves differently: there is no separate set of positions for the digits. Numbers are sent by reusing the letters, and telling the receiver you are about to do so.
The numeral sign
The convention is a mode switch. A dedicated “Numerals” sign announces that everything following is to be read as digits, with A through I standing for 1 through 9 and J for 0. A matching “Letters” sign switches back.
The semaphore signal reference models this directly. Ask it to send “AB 12” and it reports four characters but five signs, because one mode shift has to be inserted between the letters and the digits.
Mode shifts are not free
At a typical 35 signs per minute, that five-sign message takes about 8.6 seconds. The shift is a fifth of the total — for a message this short, the overhead of announcing the mode change is comparable to the content.
The practical consequence is that alternating between letters and digits is expensive. “A1B2C3” needs a shift before every single character change of type. Grouping — sending all the letters, then all the digits — costs one shift instead of five, and it is the reason well-drilled semaphore procedure puts numeric groups together.
Why not just have number flags
Because semaphore is made of two arms in eight positions each, which yields a limited vocabulary — enough for the alphabet and a handful of control signals, not enough for a separate numeric set.
Maritime flag hoists solved the same problem differently, with dedicated numeral pennants, because a flag locker can hold as many distinct flags as you care to sew. Semaphore is constrained by human anatomy, so it borrows.
Morse made the same trade differently
Morse has no such constraint: dits and dahs can be strung to any length, so the digits got their own five-element codes. That costs time — every digit is five elements where most letters are one to four — but it costs no mode switching at all.
Both systems are paying for the digits somewhere. Morse pays per character, semaphore pays per transition. Which is cheaper depends entirely on how mixed the message is, and that is a real design trade rather than a historical accident.
What the estimate does not include
The reference's timing assumes a steady signalling rate and a receiver who is already watching. It does not include the attention signal used to open a transmission, the acknowledgement, or the repeats that any real exchange over distance involves.
Treat the figure as a lower bound on the message body. A real semaphore exchange between two stations who are not already in contact takes considerably longer than the letters alone suggest, which is the same lesson every mode teaches eventually.