Pullups and Pushes

[David Bingham]

The equation relating potential energy to
kinetic energy is:

mdg=mvv/2

where m=mass
d=height
g=gravitation const.
v=velocity

NOTE: THAT m(MASS) CANCELS OUT!!!!!!

height=velocity squared/2*gravitational const

OK an example: Say we throw a glider vertially
in the air. How high will it go if its initial
vertical speed is 140mph. Approximately 660feet.

OK. Now lets throw the same glider vertically at
the same speed and measure how high it rises for
its vertical speed to have diminished to 50mph,
575 feet!

So if you fly your glider at 140mph and you
efficiently pull the stick back and climb
until you reach 50mph you will gain over 500
feet. Conversely if you are flying at 50mph
and push the stick forward until you accelerate
to 140mph you will lose about 600 feet. Why
500 feet and 600 feet and not 575 feet? Because
you don't have a 100% efficient flying machine!

OK. Same glider with and without water. Should
you expect the same result going from one speed
to another? No! But the difference will be small
usually and will depend on the glider's polar.
If the 2 speeds are on the linear part of the
polar (ie close to best glide) the difference
will be negligible. If you select the 2 speeds
at the high end of the polar water wins. At
the low end water loses. VNE to full stall -
your guess is as good as mine!

I encourage all of you to use the above equation
with your own numbers. Remember the v squared
term is the differance of 2 squares. Example:
140*140-50*50. Also be consistent in your use
of terms - metric/English/whatever.

Dave

[Scott Correa]

"David Bingham" > wrote in message
om...
> The equation relating potential energy to
> kinetic energy is:
>
> mdg=mvv/2
>
> where m=mass
> d=height
> g=gravitation const.
> v=velocity
>
> NOTE: THAT m(MASS) CANCELS OUT!!!!!!
>
> height=velocity squared/2*gravitational const
>
> OK an example: Say we throw a glider vertially
> in the air. How high will it go if its initial
> vertical speed is 140mph. Approximately 660feet.
>
> OK. Now lets throw the same glider vertically at
> the same speed and measure how high it rises for
> its vertical speed to have diminished to 50mph,
> 575 feet!
>
> So if you fly your glider at 140mph and you
> efficiently pull the stick back and climb
> until you reach 50mph you will gain over 500
> feet. Conversely if you are flying at 50mph
> and push the stick forward until you accelerate
> to 140mph you will lose about 600 feet. Why
> 500 feet and 600 feet and not 575 feet? Because
> you don't have a 100% efficient flying machine!
>
> OK. Same glider with and without water. Should
> you expect the same result going from one speed
> to another? No! But the difference will be small
> usually and will depend on the glider's polar.
> If the 2 speeds are on the linear part of the
> polar (ie close to best glide) the difference
> will be negligible. If you select the 2 speeds
> at the high end of the polar water wins. At
> the low end water loses. VNE to full stall -
> your guess is as good as mine!
>
> I encourage all of you to use the above equation
> with your own numbers. Remember the v squared
> term is the differance of 2 squares. Example:
> 140*140-50*50. Also be consistent in your use
> of terms - metric/English/whatever.
>
> Dave



Dave.
This is a good post but omits the fact that the lighter glider
will have a greater rate of decent in FPS at any given airspeed
above max L/D. So you need to subtract the energy required to
get to the heavy gliders sink rate from the light glider before you
figure the climb. At VNE a ballasted glider might be going 20/1
while the unballasted glider might be around 16 or 17. BIG
difference in sink rates.

Scott

[nafod40]

David Bingham wrote:
> The equation relating potential energy to
> kinetic energy is:
>
> mdg=mvv/2
>
> where m=mass
> d=height
> g=gravitation const.
> v=velocity
>
> NOTE: THAT m(MASS) CANCELS OUT!!!!!!
>
> height=velocity squared/2*gravitational const

Hi David,

The full equation is mdg + work_due_to_drag = mvv/2

The work due to drag (a negative term) is a complex function of speed
and AOA, but in general the MASS DOES NOT CANCEL OUT!!!!!!!

If all of the drag is parasitic, i.e., due to just the shape of the
bird, then the heavy plane is favored. Not by a lot, for sure. Percent
diffs.

For your example where you throw the glider vertically in the air, the
only drag will be parasitic drag, since the wings will be generating
zero lift. The heavier plane will then absolutely go slightly higher.

>
> OK an example: Say we throw a glider vertially
> in the air. How high will it go if its initial
> vertical speed is 140mph. Approximately 660feet.
>
> OK. Now lets throw the same glider vertically at
> the same speed and measure how high it rises for
> its vertical speed to have diminished to 50mph,
> 575 feet!