# Upper stage structural loads on ascent?

In another question, this came up:

For example, if a Falcon 9 launches 20 tons of fuel to dock in LEO, how can the same upper stage be used to launch 40 tons of fuel to the same orbit? Doesn't it need to be larger and maybe sturdier to support the much heavier payload?

And I realized I'm not sure how structural strain on upper stages actually works.

Sitting on the ground, the second stage structure is supporting the weight of that 20 or 40 ton payload under Earth gravity, which we can express as a force in Newtons.

Once out of the atmosphere and staged, though, the operative force is that of the second stage engine - some 95 tons for the Merlin Vac at peak thrust - so is that the force on the structure of the second stage? Or assuming the stage plus payload is accelerating together uniformly, does the force need to be pro-rated between the stage mass and payload mass? Does that mean the effective weight of the payload increases as propellant is used?

How would structural strain on the second stage during the early part of ascent be calculated, with aerodynamic drag opposing the thrust from the first stage engines?

• The old adage has it that the 90/10 rule prevails: 90% of the weight of a rocket is required to carry 10% of the total weight to orbit. That includes all the structure to keep it from falling apart on the way, plus the fuel to get it there. Commented Apr 13, 2017 at 3:16

Edit: this answer was based on a mis-interpretation of the question. Leaving it since it attracted some interest.

I can explain in general terms how this was done for Shuttle. From attending interorganizational working group meetings, I can say that this same general process is carried out for expendable launch vehicles, albeit with newer technology.

For the shuttle, instead of trying to compute structural loads in real time (considered impractical with 70's/80's technology), constraints were generated ahead of time. Then, using the mass properties, throttle settings, SRB bulk temperatures, winds, etc, of the day, simulated trajectories were run on the day of launch and steering parameters were generated to ensure that the vehicle would stay within the constraints.

Many constraints were checked, but those relating to structural loads were the Q-planes or squatcheloids, a set of three-dimensional volumes in alpha, beta, and q (angle of attack, sideslip angle, and dynamic pressure), indexed by Mach number.

If dispersed trajectory lay within the Q-planes at all times, the check was passed.

Other constraints were the Structural Load Indicators, "calculations derived from higher fidelity structural analytical limits to determine element structural loadings". Forty-two Structural Load Indicators were evaluated for each trial trajectory. All had to have positive margin to pass the check.

There were many other checks done before a trajectory design was accepted, but these are the major ones dealing with structural loads.

For more detail I suggest reading the very accessible and interesting information at these two links.

• Interesting, but I'm asking more about the idealized physics - how does the math work assuming payload and first stage are both spherical cows of uniform density, zero AoA, constant thrust force, etc. Commented Apr 11, 2017 at 20:16
• Sorry. I was trying to answer this "How would structural strain on the second stage be calculated during ascent,". I took "during ascent" to mean in realtime. I see now you're really asking "how are ascent structural loads calculated." Commented Apr 11, 2017 at 20:43
• Gotcha. I've rearranged that sentence to help with that ambiguity. Commented Apr 11, 2017 at 21:50