Did we decide if ballasted pullups are higher????????

Todd Pattist wrote:
I suppose this is true, but either glider can go as fast as
they want - just point the nose down. The ballast isn't
carried for speed. It's carried because the power we get at
any sink rate is weight times sink rate. The heavy glider
gets more power, and has more fuel.

I don't get this. given that the glide angle for a ballasted and
unballasted glider is approximately the same, i.e., in a no-wind zero
lift day the two gliders will touch down at the same spot, what other
advantage is their other than speed? In fact, the heavier glider will
land sooner.

If both gliders H and L start their maneuvers at the same speed v and
same altitude (assume they start at zero altitude), and fly the same
trajectory and pull into the vertical to climb to height h, then the
energy equations for each a

1/2 mv^2 - Fd = mgh

Where Fd is the work done against the glider by drag, over the distance
flown. F is a complex function of speed and lift, which is changing
throughout the profile.

to solve for the height reached, you get

(1/2)v^2/g - Fd/mg = h

The leftmost term is the same for heavy and light glider. The rightmost
differs between the two obviously. for a heavy glider, the term is
smaller, and if you only consider parasitic drag, which would be the
same for both gliders, the heavier would clearly go higher. When you add
in induced drag due to lift, it might get a little muddy. But I doubt
the increase in induced drag due to the pullup is that much more, and it
certainly does not occur for long. so the heavier should go higher. So
sayeth Sir Isaac Newton.