Question of the day

Kevin Neave 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.

That's right. I left that thing out just to make the calculation simpler.

Lots of discussion about different initial and final speeds and their
effects. Having two gliders with different masses, different initial
speeds and different final speeds makes things complicated. Adding drag
to that makes it even worse. We would need the polar curves for
different loads. Taking the dynamic behavior (1g pull-up and possibly
0g flight path) into account would require the polar curve (or surface)
from 0g to Ng. It would also take some simulating as well I guess.

I'm not going that far. But leaving the drag out of the question we can
get some simple results. Starting with the good ol' conservation of energy:
1/2*m*v1^2 + m*g*h1 = 1/2*m*v2^2 + m*g*h2
This time, dividing by m cancels it out completely, as we've seen
multiple times. So:
1/2*v1^2 + g*h1 = 1/2*v2^2 + g*h2
For the two gliders that is:
(1) 1/2*v01^2 + g*h0 = 1/2*vf1^2 + g*hf1
(2) 1/2*v02^2 + g*h0 = 1/2*vf2^2 + g*hf2
v is speed, where subscript 0 means initial, f final and number is the
glider.
substracting (1)-(2):
1/2(v01^2 - v02^2) = 1/2(vf1^2 - vf2^2) + g(hf1 - hf2)
that is
hf1 - hf2 = 1/2g * (v01^2 - v02^2 - vf1^2 + vf2^2)
But it's kind of hard to see what's happening there. So say the initial
speed of glider 2 is a times the speed of glider 1:
v02 = a*v01
and similarly for final speeds:
vf2 = b*vf1
So we get:
hf1 - hf2 = 1/2g * ((1 - a^2)*v01^2 + (b^2 - 1)*vf1^2)
Then, say the speed change for glider 1 from initial to final is c:
vf1 = c*v01
So:
hf1 - hf2 = 1/2g * ((1 - a^2) + (b^2 - 1)*c^2)*v01^2
that is:
hf1 - hf2 = v01^2/2g * (c^2*b^2 - a^2 - c^2 + 1)
Reality check:
If c=1 (glider 1 has constant speed) increasing a (glider 2 faster in
the beginning) makes the altitude difference negative (glider 1 is
lower). Increasing b (glider 2 faster in the end) makes the difference
positive (glider 1 is higher).
Seems OK.
When c 1 (so at least glider 1 pulls up to a slower speed) a^2 has a
bigger factor (1) than b^2 (1).

What that means:
20% more speed initially has more effect than 20% in the end.
So if glider 1, starting with speed 150 km/h, pulling up to 70 km/h and
glider 2, starting with 180 km/h (150 km/h +20%), pulling up to 84 km/h
(70 km/h +20%) are competing, number 2 gets higher.

Some people have been comparing two gliders flying at Vne. In that case
the lighter wins since it's able to pull up to a slower speed. Plus, I'm
not sure about what different glider manufacturers say about flying at
Vne with full ballast. Might be OK, since the weight and the lift are
both in the wings...

Jere
jere at iki.fi

Nice add Eric.

If we are going to match up theory and experience we
need to match up based on true airspeed, since energy
is based on TAS.

Adding 5000 feet to elevation increases TAS by 10%
and pullup height by ~25%.

9B

At 02:42 10 September 2003, Eric Greenwell wrote:
In article ,
says...

100m~150m? Even the G103 will climb to 800' or so
from a 115kt pass.
I've seen closer to 1000 in standard class dry. About
800' from 100kts
in a Nimbus2 dry.

800 feet! Wow! What elevation are you flying at? I've
never seen
climbs like these in my ASW 20 or ASH 26 at 115 kts
(more like 400'),
but that's at density altitudes of about 2000'.

And, actually, the Grob should go 20-30% higher at
115 knots than the
Nimbus at only 100 knots, as the altitude gained goes
up by about the
square of the airspeed.
--
!Replace DECIMAL.POINT in my e-mail address with just
a . to reply
directly

Eric Greenwell
Richland, WA (USA)

Ok folks, let's try to put this one to bed.

This post is broken down into 3 sections
1) The Maths
2) An Experiment to prove the maths
3) Popular perception

1) The Maths
This isn't rocket science. Or perhaps it is! I'm sure
there's somebody from NASA out there who wants to take
a few minutes off from designing flying wings.
We have a number of variable here which all contribute
to whether the heavy glider wins.
1.1) Initial velocity - the faster we're going at the
start the greater the advabtage that the heavy glider
has. It's sink rate is lower at higher speed, and the
pull up takes longer.
If we started our pull up at 45kts I'm pretty sure
the light glider wins! If we start at 150kts (or 134
for you Discus drivers) then 'probably' the heavy glider
wins

1.2) Final velocity - If we pull up to the same speed
in both gliders the heavy one wins, no question. However
the light glider has a lower stalling speed than the
heavy one so can gain an advantage there.

1.3) Amount of ballast - This determines how great
the advantage the heavy glider has at the start of
the pull.

However the original post was for a glider at 100kts
with 100kg of ballast & I think the results are too
close to call.

2) An Experiment
This needs someone with a two-seater & a logger set
to 1 sec samples. Start your beat-up, racing finish,
whatever you choose to call it, at something above
the speed that you decide to start the pull-up.
When you get to the designated speed the P2 says 'GO'
& you pull (This why we need a 2 seat, so pilot can
keep their eyes out of the office).
Land, fill with ballast, & repeat. Compare logger traces


3) Popular perception
'Most' people think the ballasted glider wins. I'm
pretty sure it's 'cos they haven't carried out any
calibrated tests as described in (2) above.
What actually happens is...
You arrive back after your cross country, with no ballast,
and about 2.5 miles out you have 1000 ft on the clock.
This definately get you in so you lower the nose to
100kts.
This brings you over the airfield boundary 1.5 mins
later, you do your 'finish' at a few feet which takes
about 10 seconds & then pull up (starting somewhat
less than 100 kts - oops).

Meanwhile the guy with ballast arrives back at the
same point (2.5miles / 1000ft) and again lowers the
nose. Half a mile out this guy still has about 300ft
in hand so puts the nose down even further.
He does his finish at considerably more than 100 kts
& of course pulls up much higher!
(He had best part of 300ft in hand at the airfield
boundary remember)

My guess is that as long as the airspeed is within
a reasonable range (100kts, well below Vne) people
are not actually monitoring it that closely during
their 'finishes' so we're not really comparing like
with like

I think you'll find the polar on a 15m glider is quite
a lot flatter than that of a model. So at the entry
to the pull up the model is probably losing height
faster than the full-size ship.

The proportion of ballast you can carry in a model
is probably higher.In my Discus, weighing 320kg dry
(with me in it!) I can carry about 200kg of ballast
i.e about an extra 60%.
The models I used to fly 'when I were a lad' weighed
1-2kg, but could carry about 5kg ballast ('cos I was
less worried about pulling the wings off). This results
in a much greater benefit at high speed than you'll
get in the full-size object :-)

I also suspect the ballasted one is travelling faster
in the first place. How are you measuring the speed
of your models at the point you're starting the pull
up?

At 18:30 08 September 2003, Jim Vincent wrote:
(My money - if I had any - would be on the un-ballasted
one)


From my many years experience flying radio control
slope ships, there is a heck
of a difference in performance based on the amount
of ballast. Without ballast
I can get maybe one vertical roll; with ballast I can
get at least three or
four.
Jim Vincent
CFIG
N483SZ

I just tried this - but had to use a pair of bicycles.

Me (unballasted) and my boss (ballasted) on similar
bikes
at the same speed coasted up a small hill. He was going
significantly faster at the top.

Happens every lunch time so must be true.

At 13:30 08 September 2003, Szd41a wrote:
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

Jim
Next time, challenge your boss on an endless hill, not a small one!!! It is
obvious that at T=0 , if both your boss and you hit me, your boss will hurt
me more than you:-)))). Gee! Are we trying to prove that it easier to move
heavier load up the hill or what ???.
"Jim Britton" a écrit dans le message de
...
I just tried this - but had to use a pair of bicycles.

Me (unballasted) and my boss (ballasted) on similar
bikes
at the same speed coasted up a small hill. He was going
significantly faster at the top.

Happens every lunch time so must be true.

At 13:30 08 September 2003, Szd41a wrote:
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

In article ,
Jim Britton wrote:

I just tried this - but had to use a pair of bicycles.

Me (unballasted) and my boss (ballasted) on similar
bikes
at the same speed coasted up a small hill. He was going
significantly faster at the top.

Happens every lunch time so must be true.

Air drag and mass to drag ratio.


At 13:30 08 September 2003, Szd41a wrote:
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







--
Alan Baker
Vancouver, British Columbia
"If you raise the ceiling 4 feet, move the fireplace from that wall
to that wall, you'll still only get the full stereophonic effect
if you sit in the bottom of that cupboard."

As the thermal season's nearly over I've got time to
pick nits!

I'm sorry but the heavier glider is subject to more
drag at any given speed than the lighter one.

(Profile drag will be pretty much the same 'cos the
glider is the same shape - Induced drag will be higher
'cos the wings are having to work harder)

For most of the speed curve the heavier
glider will be subjected to less drag (that's why we
put ballast in in
the first place). Intuitively (and correctly) we perceive
it requires
more to slow it down.

Reckon the thermal season's nearly over.

In article ,
says...
As the thermal season's nearly over I've got time to
pick nits!

I'm sorry but the heavier glider is subject to more
drag at any given speed than the lighter one.

(Profile drag will be pretty much the same 'cos the
glider is the same shape - Induced drag will be higher
'cos the wings are having to work harder)

The heavier glider is flying at a higher L/D than the lighter one, so
it's drag is relatively less (absolute drag might be higher, but so is
it's energy). Because it is flying more efficiently, it will be able
to climb higher.

It's true it won't be able to slow down as much because it's stall
speed is higher, but the difference in energy between a stall speed of
40 knots unballasted and 42 ballasted (20% heavier glider) is very
small (typical values for the kind of gliders we are talking about),
and won't provide a significant height gain. If you doubt this, try it
in flight sometime, and see how much altitude you gain going from 42
knots to 40 knots.

The typical case of a pull up isn't down to stall speed anyway, but
more likely to pattern speed of around 50 knots or so.
--
!Replace DECIMAL.POINT in my e-mail address with just a . to reply
directly

Eric Greenwell
Richland, WA (USA)

Eric Greenwell wrote:
The heavier glider is flying at a higher L/D than the lighter one, so

I don't think that can be right.
The heavier glider will achieve the same max L/D ratio than the lighter
one, but at a higher speed.

Jere
jere at iki.fi