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This answer describes the timing between the Titan III Stage 0 (SRM's) and Stage 1 events.

The Titan first stage ignited just prior to SRM separation:

Titan Stage I ignition occurs at approximately 112 seconds after liftoff. The actual time is controlled by three majority-voted acceleration switches which command ignition and initiate a staging timer when vehicle acceleration reduces to 1.5 g. Approximately 12 seconds later the SRMs are jettisoned upon command from the staging timer. (emphasis added)

Source

above: from page 2-9

I've highlighted "vehicle acceleration reduces to 1.5 g" because for constant thrust a rocket's acceleration would increase as the mass decreases.

This suggests that the SRM's thrust starts to ramp down significantly in the last tens of seconds of their burn, so much so that acceleration sensing switches could unambiguously interpret the acceleration drop as a major event sequencing trigger.

Is this ramp down in SRM thrust the intrinsic nature of the booster, or was it designed in specifically to allow for the acceleration switches to sense the drop and initiate first stage ignition and then SRM separation?

From the bottom of page 6-15:

The SRM has a regressive thrust-time curve (Figure 6-15) produced in part by the star configuration of the propellant grain in the forward closure of the motor. During the early phases of burning, this portion contributes much of the gas flow necessary to produce the high initial peak in the thrust-time curve.

SRM has a regressive thrust-time curve (Figure 6-15)

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uhoh
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The Shuttle SRB had a similar profile, with a steep reduction in thrust from 110 seconds on:

enter image description here

This profile is what you'd expect when the propellant has a conical void down the middle, so at 110 seconds, at the bottom of the stage the burn pattern reaches the casing and the total area of burning propellant starts to decrease. You need a conical shape to make sure you can remove the mandrel after casting the propellant, so this thrust profile is almost inevitable.

Hobbes
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  • The curve between 110 and 130 seconds is very similar I see. Bottom of page 6-15 says "The SRM has a regressive thrust-time curve (Figure 6-15) produced in part by the star configuration of the propellant grain in the forward closure of the motor. During the early phases of burning, this portion contributes much of the gas flow necessary to produce the high initial peak in the thrust-time curve." so it may in fact burn out first near the top rather than the bottom, but I think the gist of your answer is that a 10 to 20 second "ramp-down" is inevitable for SRBs? – uhoh Jun 20 '19 at 14:29