I was looking at the fantastic data plots provided by OneSpeed and had a question for the rocket scientists in the forum. This may have been discussed at another forum. If so, I apologize in advance. My question is: As I recall, during the manned Dragon II launch Bob and Doug mentioned that the second stage ride seemed much rougher than first stage. The acceleration data in OneSpeed's chart seem to show a gradual increase in "noise" starting about halfway through the second stage burn. The noise, or vibration, gets progressively worse toward the end of the burn and the data from the latest launch (L11) even shows signs of periodic acceleration spikes. Does this relate to the "rough ride" noted by the astronauts?
That's quite possible. Small fluctuations in thrust will product small fluctuations in acceleration. As the fuel is consumed, the mass of the vehicle decreases and the amplitude of the acceleration fluctuations increases.
That being said, I would not read too much into the noise in these plots. We do not have the raw telemetry, only the video stream, which displays altitude above ground and velocity in the rotating earth reference frame in km/h at the frame rate of the video, which is being processed by on-screen OCR to read out these values.
At this point this data is already preprocessed with some filtering by SpaceX, then rounded in the velocity domain to km/h and in the time domain to 1/30s Sometimes there's gaps in the data or small jitter due to transmission delays and buffering effects on the SpaceX media side.
However, the acceleration is the derivative of velocity so the change in speed per time. Due to the rounding to full km/h this is inherently noisy, and the jitter adds additional noise, which also increases the faster the rocket accelerates.
So - although you would expect the actual noise in the acceleration to also increase as the rocket gets lighter and as such small thrust fluctuations have larger impact, I would expect this noise to be at higher frequencies than the 1/30 s resolution we can see in the stream. The noise in these plots is most likely dominated by the noise introduced by the way this is read out.
A hint at the actual noise is given by the Falcon9 payload user guide (current version:
https://www.spacex.com/media/falcon_users_guide_042020.pdf ) which lists the maximum axial acceleration noise under 30 Hz at 0.8 g and the maximum axial acceleration noise at frequencies above 100Hz at 0.9g - with a noise maximum at around 160Hz