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Chapter 10 of Chariots For Apollo remarks the following in discussing the pogo problem of Apollo 4 and 6 and the role of the first stage F-1 engines in that:

The mission analysts later discovered that two of the Saturn engines had been inadvertently tuned to the same frequency, probably aggravating the problem. (Engines in the Saturn V cluster were to be tuned to different frequencies to prevent any two or more of them from pulling the booster off balance and changing its trajectory during powered flight.)

What does it mean to "tune the engine to a frequency"? How is the tuning done? Was this only a thing for the F-1 engines or is this common procedure (then and now)?

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    $\begingroup$ Great question. Followed. $\endgroup$ Mar 17, 2022 at 21:40
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    $\begingroup$ "The mission analysts later discovered that two of the Saturn engines had been inadvertently tuned to the same frequency, probably aggravating the problem" I haven't been able to turn up any source for this statement in the postflight reports. $\endgroup$ Mar 17, 2022 at 23:31
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    $\begingroup$ @OrganicMarble there are some potentially useful references on this page at heroic relics.org, but all the links to NTRS are dead... I hoping to find "AS-502 Flight Report Volume 1", presumably about the S-1C stage failure (assuming that it exists; I infer its existence from the fact that Volume 2 & 3) have been available at some point in time). $\endgroup$
    – Ludo
    Mar 19, 2022 at 14:01
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    $\begingroup$ @Ludo I looked through Vol 2 & 3, and MPR-SAT-FE-68-3 (the Saturn V postflight report). The more I think about it, this line from Stages "any two or more of them from pulling the booster off balance and changing its trajectory during powered flight" makes absolutely no sense at all. $\endgroup$ Mar 19, 2022 at 14:07
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    $\begingroup$ This document ntrs.nasa.gov/api/citations/20100024127/downloads/… says the AS-502 problems stemmed from changing the oxidizer suction lines from flexible to rigid. The solutions described in that document don't say anything about tuning engines. $\endgroup$ Mar 19, 2022 at 14:27

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Combustion instabilities (oscillatory combustion) in rocket engines are caused by coupling between the combustion processes and pressure oscillations. Frequencies can vary from 100-20,000 Hz and pressure amplitudes from 10-1000% of the engine’s steady state pressure. Combustion instabilities can produce destructive vibration up to RUD.

Acoustic resonators are commonly installed in combustors to provide passive acoustic damping of high frequency combustion instabilities.

Also, injectors can be tuned to act as half-wave resonators and provide acoustic damping. This is particularly effective for managing intermediate frequency oscillations to prevent them from becoming high frequency oscillations.

https://scholarworks.utep.edu/cgi/viewcontent.cgi?article=1417&context=open_etd

I’m venturing out of my pay grade, but I assume that measuring and tuning the dominant acoustic frequency of an engine would be a part of test firing. Other factors being equal, I would assume the lowest energy oscillations would be tuned in (lowest frequency, lowest pressure amplitude)

When multiple engines are mechanically bolted together, interactions of these frequencies would need to be taken into account. Similar, but slightly different, frequencies could produce beat frequencies very different from the primary frequencies. This could produce unexpected structural loads or interact with other vibration modes such as pogo vibration

Addendum. I'm going to delete my answer. The quote in the OP makes no sense to me and my answer doesn't clear anything up. The vibration problem on Apollo 6 was attributed to pogo, not combustion instability. Hopefully other information will come to light on what "pulling the booster off balance" is all about.

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    $\begingroup$ Do you have any specifics about how it was done to the F-1s? This seems like a lot of generalities. $\endgroup$ Mar 17, 2022 at 23:29
  • $\begingroup$ Maybe relevant reference $\endgroup$
    – Ludo
    Mar 19, 2022 at 14:44
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    $\begingroup$ It says “aggravated”, not “caused”. I think your answer contains relevant information, it’s just not the complete picture. $\endgroup$
    – Ludo
    Mar 21, 2022 at 7:29

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