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Launch vehicles often use vibrational isolators to reduce g-forces to protect delicate payloads. How are g-forces reduced on the payload while both the payload and the launch vehicle maintain the same velocity?

If the launch vehicle and payload are experiencing different g-forces, does that not mean they are experiencing different accelerations and therefore cannot be moving together?

Here is a link to flight data of acceleration of a payload on a launch vehicle

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The g-forces from the rocket's acceleration remain unaffected, of course.

What the vibrational isolators do is isolate the payload from vibrations.

Without them, the payload would experience both the rocket's average acceleration from thrust, but also accelerations (both side-to-side and other directions) resulting from oscillations from the vibrations. These vibrational accelerations are of very short duration, but can be very strong indeed.

Compare when you are drilling concrete with a hand drill on impact drilling mode. It vibrates so hard that it can hurt your hand, yet the drill is going nowhere.
The vibrational isolators are like wearing a heavy glove while doing the drilling, it dampens the shortduration cyclic vibrations, protecting your hand (or the rocket payload, in your question).

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The situation is a bit similar to driving up hill on a bumpy road.

The car's suspension definitely transfers the "average force" from the road up to the passengers, but let's talk about what "average force means.

There's no good way to do this without talking about high frequency, low frequency and DC/constant.

If the road were a perfectly smooth inclined ramp, the force would be DC and the vertical climb velocity of the passenger would be the same as the wheels.

If the road were rough with lots of little bumps, then the wheels would go up and down but the passenger wouldn't (if the suspension was good).

But if the road now had a lot of dips, say 50 cm deep and a few meters long, then the suspension couldn't respond fully to that and the car and passenger would dip right along with the wheels.

So the suspension of the car or the vibration isolation system for the rocket payload will absorb a lot of the high frequency stuff but start passing more and more of the low frequency stuff and all of the zero frequency stuff.

The rocket and the payload will get to space at the same time, but they will experience the bumps and dips differently.

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Other than the "DC" (or low frequency part) of the g-forces, all the "AC" (or high frequency components) of the g-forces create both positive and negative contribution to velocity with each positive and negative half cycle.

So isolators just need to compress for one half cycle of the vibration and relax during the other half cycle. The vehicle velocity increased by a small amount, but that was not transmitted to the payload since the isolator parts compressed. In the next half cycle of the vibration, the vehicle velocity decreased by a small amount and that slack is taken up by the isolator part by decompressing.

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If the absorbers weren't there all the forces causing the spaceship to accelerate would be transmitted to the delicate load, causing it to accelerate in non-wanted ways. If fluid nitroglycerin is part of the load a force shaking the load would give a a considerable bang.

Compare it with a small phial containing liquid. You can shake the phial with your hands. KABOOM! If it contains nitro. If you attach the phial with the right springs to the container the motion is absorbed by the springs. You can adjust the spring constants to take the various kinds of forces into account. When the forces are big and fast-changing you can use springs with a high constant (stiff springs). Small constants are better suited for small slowly changing forces, though in this case not much damage will be done in the first place.

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