Easy workaround for Delta-IW heavy problem?

Suppose the Delta-IV heavy problem is indeed caused by a fuel sensor
being uncovered early due to slosh/vortex/etc. .

On the other hand, the CBC seems to work OK in the Delta-IV single.
The differences in operating conditions a The Heavy tries to
throttle closer to depletion, there is less acceleration at this point
(for the center CBC, anyway) and the trajectory is different (may be a
slightly different local "down") in the two cases.

Any sensor uncovering problem will be helped dramatically if there is
more fuel in the tank, and we know the CBC works OK when the thrust
reduction occurs when 24 sec of fuel is left.

So here's the workaround - throttle all CBC engines back when 24 sec of
full thrust remain (like the Delta IV regular) instead of when 6 sec
remain, as the D-IV heavy tried. Assuming a reduced thrust of 60%,
this will add 12 sec to the burn time, both of the outer CBCs, and the
center one.

Of course, the reason they don't normally do this is because it
increases gavity losses, but by how much? Assuming 5G at full thrust,
and 3G at reduced thrust, and a very crude geometrical gravity loss
approximation, we get

18 sec at 3G rather than 5G loses 12.6 m/s or 40 fps
12 extra sec at 3G loses 20.4 m/s or 65 fps

Both of these losses occur on both the outer CBC end of thrust, and the
core CBC end of thrust, for a total of 66 m/s or 210 fps. The actual
loss will be somewhat less, I think, since the velocity is a
substantial fraction of orbital already at this point, which is not
considered in the above arguments.

Now, how much must the payload be reduced so the second stage can
supply an extra 66 m/sec? Assuming demosat = 6000 kg, empty stage 2 =
3500 kg, full stage 2 = 31000 kg, exhaust vel = 4500 m/s, then the
second stage adds 4500*ln(37/9.5) or about 6100 m/s. To get 70 m/sec
more, we need to reduce the final (and initial) mass by about 200 kg.
So reducing the payload by 200 kg should do the trick.

This should be OK for all current practical purposes, since there are
only two payloads, and these were originally designed for the Titan,
which is rated at 5760 kg to GSO.

Lou Scheffer