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In this article about max Q https://en.m.wikipedia.org/wiki/Max_Q the shuttle launch is discussed. Since there are four distinct large objects - two boosters, one shuttle and one giant tank - there could be several ways to define an effective max-Q.

There are three different aerodynamic pressures on leading surfaces, and two distinct average shear forces on struts connecting the components. Since both the boosters and the shuttle produce thrust, and since each had a different mechanism for reducing thrust around the one-minute mark, this must have been quite an interesting problem compared to a single body cylindrical rocket.

In this case, which was more critical - pressures on the objects and their internal structure, or drag-induced shear forces between objects due to imbalances of sums of drags and thrusts?

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Max Q is simply the maximum of the dynamic pressure of the external flow, ${1\over 2}\rho v^2$. It has nothing to do with the vehicle, except for the vehicle's speed relative to the undisturbed fluid.

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  • $\begingroup$ Got it - thanks! So this leads to a more differentiated question $\endgroup$
    – uhoh
    Commented Jul 10, 2016 at 6:45
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    $\begingroup$ @Steve I think Mark may be saying that the term "Max Q" actually refers to the point where the term ${1\over 2}\rho v^2$ is maximum, period. Maximum aerodynamic pressure will probably occur nearby, but it depends on many real-world effects. But the term "Max Q" does not actually mean the same thing as "maximum aerodynamic pressure". $\endgroup$
    – uhoh
    Commented Jul 10, 2016 at 11:24
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    $\begingroup$ Both q and the attach loads betwen the elements were predicted and checked for excedances when the STS trajectory was designed on launch day. As was the product of q x alpha and q x beta. $\endgroup$
    – Organic Marble
    Commented Jul 10, 2016 at 11:38
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    $\begingroup$ @OrganicMarble I originally thought "Max Q" meant exactly maximum aerodynamic pressure. Since that maximum may occur at different times on the three very differently shaped objects due to aerodynamic details, I thought I had a "gotcha" moment. But it doesn't, so I don't. Instead, I'd like to know more about all of the major forces in this aerodynamically complicated superstructure. Thus the question Shear forces between Shuttle, tank, and boosters - what pushes what? However, now I'm wondering what alpha and beta and q mean also! $\endgroup$
    – uhoh
    Commented Jul 10, 2016 at 11:53
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    $\begingroup$ @Steve the value of q was just the dynamic pressure at any instant. Max q was the largest value. You seem to be asking "what is the q limit?" which is a different question. Although I agree that this "In this case, which was more critical - pressures on the objects and their internal structure, or drag-induced sheer forces between objects due to imballances of sums of drags and thrusts?" and the question in the title are really two different questions. The accepted answer, answers the question in the title, and not the question in the body. $\endgroup$
    – Organic Marble
    Commented Jul 10, 2016 at 17:23
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Supplemental answer:

The equation given in Mark Adler's answer is what was actually used in the calculation of shuttle dynamic pressure. Max Q would trivially be the maximum value reached. Don't over think it. What goes into the equation is the freestream velocity and a table lookup of density vs. altitude.

Here is a page from the DADS Training Manual with the proof.

enter image description here

DADS was the program used to design the ascent trajectory for shuttle. This was done on the day of launch (reference includes links). A major constraint on the trajectory design was to keep the dynamic pressure as close as possible to the structural limit without exceeding it.

This equation was used to calculate the dynamic pressure throughout the generation of the first stage trajectory including the supersonic regime.

Source: DADS Training Manual

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  • $\begingroup$ So this comment - at least for the case of the Space Shuttle - seems to be correct? btw thank you for coming up with this excellent source that nails it! Actually, I guess this is the most complete/correct answer (...so far) $\endgroup$
    – uhoh
    Commented Sep 15 at 1:52
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    $\begingroup$ @uhoh yes on the comment. Somewhere on this site I'm pretty sure I wrote an answer about max q for shuttle being a calculated not a measured thing. Looking for it now. $\endgroup$
    – Organic Marble
    Commented Sep 15 at 1:54
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    $\begingroup$ @uhoh here is what I was remembering space.stackexchange.com/a/49480/6944 $\endgroup$
    – Organic Marble
    Commented Sep 15 at 1:56
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    $\begingroup$ OK my coffee is just starting to kick in; I'm wondering if this is the basis of a new question: "While V and M (looks like V is in ft/sec/1000?) are smooth, Q is wiggly. Is the wiggling coming mostly from wind speed variations, or from density (temperature) variations, vs altitude? Are both of those quantities coming from balloon data?" update: oh, you've answered that in comments there already. $\endgroup$
    – uhoh
    Commented Sep 15 at 2:07
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    $\begingroup$ @uhoh If the winds had been nice and smooth that job would been have a lot more straightforward. $\endgroup$
    – Organic Marble
    Commented Sep 15 at 2:36
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According to the discussion here, to find the point where $q$ is maximised, we need to use formulae applicable to the speeds in question.

This dynamic pressure formula: $$q = {1\over 2}\rho v^2$$ is only valid for subsonic speeds. For supersonic speeds we need to use the compressible flow formula: $$q=p_s\left(1+\frac{\gamma-1}{2}M^2\right)^{\frac{\gamma}{\gamma-1}}-p_s$$

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  • $\begingroup$ @uhoh I have no idea, but that's a great question! $\endgroup$
    – Kami
    Commented Sep 14 at 5:19
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    $\begingroup$ @uhoh The point of my answer is that the formula given in the other answer is not applicable when the shuttle reaches a supersonic speed. I think this information is useful, even if I don't have answers to your follow-up questions. I have provided a reference to the place where I learnt about it. BTW, there is the same issue with the first formula: does $\rho$ refer to the air density of the undisturbed cold atmosphere nearby, or to the much hotter compressed gas at the noses of the shuttle, tank, and boosters, each which may be a different temperature? $\endgroup$
    – Kami
    Commented Sep 14 at 6:38
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    $\begingroup$ You're right, deleting, sorry, thanks, etc. $\endgroup$
    – uhoh
    Commented Sep 14 at 6:44

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