G - forces imparted by launchers

How can one know the G forces imparted from the technical data presented on the websites of launch vehicles? I am interested in finding a way to theorise the max G-forces imparted by researching mission profiles and engine data, or anything else that may be public.
I have tried going through some manuals but that did not help me.

• Look up TWR, then subtract 1 for G-force added by the launcher. Or don't subtract, for the G-force experienced by the astronaut (acceleration + Earth gravity). If you don't have TWR, you have thrust and mass, it's the simple (thrust to weight) ratio. Obviously both change over time, so you can't just happily insert launchpad data; you'll need tables/graphs over time.
– SF.
Aug 13 '18 at 15:11
• @SF. TWR (thrust to weight ratio) is unitless so subtracting 9.81 m/s^2 doesn't work. Subtracting 1 g from thrust doesn't work either. You'd need to know the ratio of maximum thrust to mass, but mass is constantly changing. And for part of the launch there is quite a significant drag force that you'd have to subtract from thrust first.
– uhoh
Aug 15 '18 at 3:10

The best way to know is to check the payload planning guide for a particular launcher. Many modern launchers throttle down over the course of a flight to limit g-loading, so a simple rated-thrust divided by mass-at-burnout calculation will not give the correct answer.

For example, the 2010 version of the Atlas V Launch Services Guide says (of the 400-series configurations):

Near the end of the booster phase, the RD-180 engine is continuously throttled so that axial acceleration levels are not exceeded. These g-levels may be a function of payload weight and do not exceed 5.0 g steady state.

• Thank you for your Answer, but there are payload guides which dont talk about G - forces experienced. I was looking to see if there was any way to figure it our using engine data and mission profile Aug 13 '18 at 15:46
• That seems improbable, as forces the payload is subjected to is one of the most fundamental and important things a payload operator needs to know. It may be described as "acceleration limits" rather than g-force, but it should be in there; do you have an example of a payload guide which doesn't include that information? Aug 13 '18 at 16:40
• I found a document for the GSLV, which isn't a payload guide, but I'm looking for the G-forces for the GSLV Mk-II . I have no way to find the G-forces imparted by it. CHeck here isro.gov.in/sites/default/files/pdf/gslv-brochures/gslv-d5.pdf Aug 14 '18 at 7:31
• GSLV II has modest peak accelerations, because it retains the mass of the solid-fuel core stage (which burns out first) through the entire burn of the liquid fueled boosters. I believe the Vikas engines do not throttle down, so @Jack's method, taking the stage thrust and dividing by the remaining mass of the rocket in a given situation, is valid. With a 2.5 ton payload, I get a peak of about 5.3g at core burnout, 2.7g at booster burnout, 3.7g at second-stage burnout. Computing core burnout is trickiest; you have to pro-rate the booster fuel remaining based on the stage burn times. Aug 14 '18 at 17:13
• @RajathPai I recommend you choose a specific example where applying answers here don't seem to work, and ask that as a new question. Something like "I've applied answers to my previous question to Rocket X and still can't figure out what the maximum acceleration loading on the payload could be."
– uhoh
Aug 15 '18 at 3:14

This is easy to calculate using our old friend $F = ma$ and knowing the thrust and mass at any given point in the launch:

1. Take the combined thrust of all the engines $F$ in Newtons, remembering that some of them may be throttled down.
2. Take the mass of the entire vehicle $m$ in kg.
3. Use $a = \frac{F}{m}$ to find the acceleration in ms$^{-2}$.
4. Divide by $g \approx 9.81ms^{-2}$ to get the scalar gees.

For example, let's take rough values of the Saturn V just after liftoff:

$$gees \approx \frac{5 \times 7000000N}{3000000kg \times 9.81ms^{-2}}g \approx 1.2g$$

For a later point in the flight, you just need to know how much fuel has been spent and whether the thrust has changed. If no engines have been discarded or throttled, the acceleration will increase as fuel is burnt. Also note that atmospheric drag will influence the acceleration felt by the vehicle.

Alternatively, you can often find graphs in the vehicle documentation which give acceleration profiles of the launches. For example, this one from the Apollo 11 launch vehicle evaluation:

• Thank you for helping with the valuable input. There are a few manuals which show the mission profile but no acceleration chart, which makes it hard to figure out a max G at any point. The mass profile is also not so obvious. Aug 13 '18 at 15:45
• +1 for science and math!
– uhoh
Aug 15 '18 at 3:11