Question of the day

A given glider is at level flight, IAS= 100 knots.After a pull-up, will it
achieve more height gain with 100 liters (100 kgs) of ballast than with
empty ballast????
Réjean

The difference in height will be negligible.

The glider's energy, both potential & kinetic is proportional
to Mass so the height gain for a given loss of velocity
will be the same.

However the ballasted glider will have a better sink
rate at 100kts than the unballasted one so during the
few seconds of the pull-up it will 'lose' less height.

On the other side of the equation the un-ballasted
glider will be able to pull up to a lower speed, so
it's change in velocity will be greater so the resulting
height gain may be more.

(My money - if I had any - would be on the un-ballasted
one)

Kevin Neave k wrote in message ...
The difference in height will be negligible.

Not true. A full load of water makes a HUGE difference in pullup
altitude gained

The glider's energy, both potential & kinetic is proportional
to Mass so the height gain for a given loss of velocity
will be the same.

Again, wrong - check your basic physics. You even say that the energy
is proportional to mass. Therefore, more mass, more energy, more
altitude gained. You appear to be confusing velocity with mass.

However the ballasted glider will have a better sink
rate at 100kts than the unballasted one so during the
few seconds of the pull-up it will 'lose' less height.

True, but the crossover point is quickly reached so this effect is
probably negligable.

On the other side of the equation the un-ballasted
glider will be able to pull up to a lower speed, so
it's change in velocity will be greater so the resulting
height gain may be more.

If you pull up below the ballasted sink rate crossover speed, sure a
heavy glider will gain less. But at those speeds neither glider will
gain much anyway. The real test is what you can gain at redline.

(My money - if I had any - would be on the un-ballasted
one)

Too bad, I love a sure thing!

Kirk Stant
LS6-b (which loves ballasted pullups!)

On 8 Sep 2003 13:08:22 -0700, (Kirk Stant)
wrote:

On the other side of the equation the un-ballasted
glider will be able to pull up to a lower speed, so
it's change in velocity will be greater so the resulting
height gain may be more.

If you pull up below the ballasted sink rate crossover speed, sure a
heavy glider will gain less. But at those speeds neither glider will
gain much anyway. The real test is what you can gain at redline.

(My money - if I had any - would be on the un-ballasted
one)

Too bad, I love a sure thing!

Kirk Stant
LS6-b (which loves ballasted pullups!)


Let's define the problem a little better - a pull up from 100KIAS to
50 KIAS, level flight in both cases.
Pull to a flight trajectory of 30 degrees up relative to the horizon.
This gives a vertical velocity of 50 knots immediately after the
pullup. That 50 knots requires an extra 1 g for about about 2.5
seconds(some simplification and approximation here)or a suitable other
combination of G load and time). At the high speed the extra induced
drag is quite small for a short time so can be neglected to a first
approximation. The pullup will take only a few seconds,10 so that
difference in height gain is the difference in ballasted and
unballasted sink rates for a few seconds. At the low end the sink rate
difference is very small and at the high end the ballasted glider has
lower sink rate. This difference might be as high as 200 feet/min but
we are only talking for a small fraction of a minute so we get maybe
30 feet difference in favour of the heavy glider, maybe only 10 to 15
feet.

Please note in the kinetic/potential energy equation the mass cancels
out so to a really rough first approximation neglecting the effect of
ballast on the polar the height gain is the same.

This is used in the design of total energy probes which DO NOT require
changing for different ballast amounts.

With a little mathematical jiggery pokery it can be shown that the
kinetic/potential energy equation is equivalent to the equation for
the pressure produced by the TE probe.

Mike Borgelt

Borgelt Instruments

In article ,
(Kirk Stant) wrote:

| Kevin Neave k wrote in
| message ...
| The difference in height will be negligible.
|
| Not true. A full load of water makes a HUGE difference in pullup
| altitude gained
|
| The glider's energy, both potential & kinetic is proportional
| to Mass so the height gain for a given loss of velocity
| will be the same.
|
| Again, wrong - check your basic physics. You even say that the energy
| is proportional to mass. Therefore, more mass, more energy, more
| altitude gained. You appear to be confusing velocity with mass.

Total energy = kinetic energy + potential energy

kinetic energy = 1/2 mass * velocity squared

potential energy = mass * gravitational constant * height

total energy (altitude 1) = total energy (altitude 2) [conservation of
energy]

Since mass is a constant factor on both sides of the equation, it
cancels out. Therefore there should theoretically be negligible
difference in the pullup altitude gained between the ballasted and
unballasted cases.

-- Tim Olson

Tim Olson wrote:
Total energy = kinetic energy + potential energy

kinetic energy = 1/2 mass * velocity squared

potential energy = mass * gravitational constant * height

total energy (altitude 1) = total energy (altitude 2) [conservation of
energy]

Since mass is a constant factor on both sides of the equation, it
cancels out. Therefore there should theoretically be negligible
difference in the pullup altitude gained between the ballasted and
unballasted cases.

-- Tim Olson

Adding energy lost due to drag into the soup:
m = mass
v1 = initial speed
h1 = initial altitude
v2 = final speed
h2 = final altitude

total energy(alt 1) = total energy (alt 2) + energy lost due to drag
1/2*m*v1^2 + m*g*h1 = 1/2*m*v2^2 + m*g*h2 + Ed

dividing both sides by m:
1/2*v1^2 + g*h1 = 1/2*v2^2 + g*h2 + Ed/m

Now compare two gliders, starting with same speed, same altitude, level
flight. Both pull up and level out with same final speed (just to keep
things even). The above holds for both gliders, so:
(1) 1/2*v1^2 + g*h1 = 1/2*v2^2 + g*h21 + Ed/m1
(2) 1/2*v1^2 + g*h1 = 1/2*v2^2 + g*h22 + Ed/m2
substracting (1)-(2):
0=g(h21 - h22) + Ed(1/m1 - 1/m2)
where h21 is final altitude for glider 1 and h22 for glider 2
and masses m1 for glider 1 and m2 for glider 2.
We get:
h22-h21 = Ed/g(1/m1 - 1/m2)

So if m2 m1, h22 h21. The heavier glider will get more altitude.
But not very much... Approximating Ed from sink rate (energy lost is
m*g*(sink rate)*time) the altitude difference for masses 360kg and 460kg
is a bit over one meter. But then again, to be exact, Ed is bigger for
the heavier glider (same speed, more mass, need bigger AOA - more drag).

Please point out any mistakes (well since it's the Usenet, I'm sure you
will

Jere
jere at iki.fi

I think Kevin's right. (at least to the first order).
In a pullup you trade kinetic energy for potential
energy, so (neglecting friction effects) the physics
are (mV^2)/2=mgh -- kinetic equals potential energy.

Or (solving for h): h=(V^2)/2g (the mass cancels out).

You can try to add the drag parts back in, but the
time is so short, I don't think it will not add up
to much.

I think maybe ther reason people associate ballast
with taller zoomies is because the cruise speeds with
ballast are higher. For my ship a McCready 10 pullup
yields 700 feet with full ballast, 530 feet dry, but
the speed is 15 knots higher.



At 21:00 08 September 2003, Kirk Stant wrote:
Kevin Neave wrote in message news:...
The difference in height will be negligible.

Not true. A full load of water makes a HUGE difference
in pullup
altitude gained

The glider's energy, both potential & kinetic is proportional
to Mass so the height gain for a given loss of velocity
will be the same.

Again, wrong - check your basic physics. You even
say that the energy
is proportional to mass. Therefore, more mass, more
energy, more
altitude gained. You appear to be confusing velocity
with mass.

However the ballasted glider will have a better sink
rate at 100kts than the unballasted one so during
the
few seconds of the pull-up it will 'lose' less height.

True, but the crossover point is quickly reached so
this effect is
probably negligable.

On the other side of the equation the un-ballasted
glider will be able to pull up to a lower speed, so
it's change in velocity will be greater so the resulting
height gain may be more.

If you pull up below the ballasted sink rate crossover
speed, sure a
heavy glider will gain less. But at those speeds neither
glider will
gain much anyway. The real test is what you can gain
at redline.

(My money - if I had any - would be on the un-ballasted
one)

Too bad, I love a sure thing!

Kirk Stant
LS6-b (which loves ballasted pullups!)

One trivial point for Jere's post is that the stalling
speed for the unballasted glider will be lower, so
this guy can pull up to a slower speed & therefore
regain more altitude.

Anyone out there want to know why there's a discrepancy
between the maths (which say that there's not gonna
be a measurable difference between the two) and 'popular'
experience which says that the heavy glider wins?

At 17:12 09 September 2003, Jere Knuuttila wrote:

Adding energy lost due to drag into the soup:
m = mass
v1 = initial speed
h1 = initial altitude
v2 = final speed
h2 = final altitude

total energy(alt 1) = total energy (alt 2) + energy
lost due to drag
1/2*m*v1^2 + m*g*h1 = 1/2*m*v2^2 + m*g*h2 + Ed

dividing both sides by m:
1/2*v1^2 + g*h1 = 1/2*v2^2 + g*h2 + Ed/m

Now compare two gliders, starting with same speed,
same altitude, level
flight. Both pull up and level out with same final
speed (just to keep
things even).

the altitude difference for masses 360kg and 460kg

is a bit over one meter. But then again, to be exact,
Ed is bigger for
the heavier glider (same speed, more mass, need bigger
AOA - more drag).

Please point out any mistakes (well since it's the
Usenet, I'm sure you
will

Jere
jere at iki.fi

Anyone out there want to know why there's a discrepancy
between the maths (which say that there's not gonna
be a measurable difference between the two) and 'popular'
experience which says that the heavy glider wins?

I dunno. According to my math, the heavier one does win. Also, according to
my experience, the heavier one does win.

Jim Vincent
CFIG
N483SZ

On 9 Sep 2003 17:44:24 GMT, Kevin Neave
k wrote:

One trivial point for Jere's post is that the stalling
speed for the unballasted glider will be lower, so
this guy can pull up to a slower speed & therefore
regain more altitude.

Anyone out there want to know why there's a discrepancy
between the maths (which say that there's not gonna
be a measurable difference between the two) and 'popular'
experience which says that the heavy glider wins?


Could this be due to speed difference at cruise or fast cruise speeds?

One point that hasn't been considered by those arguing that the
ballasted glider is faster forget that this is NOT the case at Vne,
which doesn't change with glider weight.


--
martin@ : Martin Gregorie
gregorie : Harlow, UK
demon :
co : Zappa fan & glider pilot
uk :