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Old April 20th 10, 08:56 PM posted to rec.aviation.soaring
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Default physics question about pull ups

Interesting problem... Seems like you've defined the concept of
energy height. Energy is height is just how you have described
already...
E= mgh + 0.5mv^2
OR
E = wh + (w / 2g)v^2

The effect of drag on height recovery isn't too bad, but is enough to
matter. In general the shallower the climb and the bigger the speed
change the greater effect drag will have overall.
As an approximation, a glider initiating a 30deg climb from 120kts to
40kts would only take about 8sec (without drag decel, only gravity).
Assuming an average L/D of 24:1 over the entire maneuver the glider
would loose only about 5.6 feet of altitude per second due to drag. So
that means about 45 feet of altitude would be eroded due to drag. Of
course that's just an approximation. I'm sure there's a more correct
way...

The only way I could think to explain the extra height gain with a
heavier glider of the same model is the relationship of L/D vs speed.
For most gliders at a given speed their L/D will be higher with more
weight. Looking at polars you'll see, on average, the ballasted
glider will hold a better L/D at the same speed almost all the way
back to thermalling speed. The difference is small but is enough to
matter. On top of that the heavier glider at the same speed has more
energy height available due to its mass...
www.valleysoaring.net/pk/x-c/polar24c.jpg

One thing I wonder is whether a heavier glider initiating a 1.5g climb
would loose more energy through induced drag than a lighter glider,
assuming the same speed. Since a heaver glider would require more
force (lift) to induce a 1.5g climb then I'd think that would require
a greater angle of attack change thus more induced drag.