physics question about pull ups

I was trying to work out the expected height gain from a pull up
Experienced glider pilots say you will get a better pull up with a
heavier glider / water etc.
But I can't see this from my (probably incomplete) equations:

total energy = potential energy + kinetic energy

total energy before pull up = total energy after pull up

m * g * h0 + m * pow(v0, 2) * 0.5 == m * g * h1 + m * pow(v1, 2) * 0.5

with h0 v0 being height and speed before pull up
and h1 v1 being height and speed after pull up

mass cancels out of this equation

I think I need to include momentum in there somehow?

Hi John,

You are correct. The physics equations show that you will get the same
height regardless of the weight of the glider.

However, I think it is true that a heavier glider will have a slightly
higher pull-up. I don't think the difference is very much though. Both
gliders will have similar frictional losses and losses due to inefficiencies
during the pull-up.

Paul Remde

"John Rivers" wrote in message
...
I was trying to work out the expected height gain from a pull up
Experienced glider pilots say you will get a better pull up with a
heavier glider / water etc.
But I can't see this from my (probably incomplete) equations:

total energy = potential energy + kinetic energy

total energy before pull up = total energy after pull up

m * g * h0 + m * pow(v0, 2) * 0.5 == m * g * h1 + m * pow(v1, 2) * 0.5

with h0 v0 being height and speed before pull up
and h1 v1 being height and speed after pull up

mass cancels out of this equation

I think I need to include momentum in there somehow?

On Apr 20, 4:24*am, "Paul Remde" wrote:
Hi John,

You are correct. *The physics equations show that you will get the same
height regardless of the weight of the glider.

However, I think it is true that a heavier glider will have a slightly
higher pull-up. *I don't think the difference is very much though. *Both
gliders will have similar frictional losses and losses due to inefficiencies
during the pull-up.

Paul Remde

"John Rivers" wrote in message

...



I was trying to work out the expected height gain from a pull up
Experienced glider pilots say you will get a better pull up with a
heavier glider / water etc.
But I can't see this from my (probably incomplete) equations:

total energy = potential energy + kinetic energy

total energy before pull up = total energy after pull up

m * g * h0 + m * pow(v0, 2) * 0.5 == m * g * h1 + m * pow(v1, 2) * 0.5

with h0 v0 being height and speed before pull up
and h1 v1 being height and speed after pull up

mass cancels out of this equation

I think I need to include momentum in there somehow?

The kinetic to potential energy balance yields no difference as has
been pointed out. There are small drag differences that give some
advantage to a heavier glider since it has a higher L/D at any given
speed. Back of the envelope polar math says the difference in sink
rate at 150 knots with full ballast versus dry is about 100 feet per
mile (for a modern glider). At 100 knots it's about 50 feet per mile.
I'd estimate a typical pullup consumes about a quarter mile. Without
taking the time to integrate the declining sink rate difference over
the entire pullup, I'd guess the overall difference in altitude gain
would be around 20 feet. This ignores any differences in secondary
energy losses associated with pulling G's to make the pullup happen.
My intuition tells me that this would favor the lighter glider
slightly because it takes more energy to change the vector of a
heavier sailplane - how much I don't know except to say that the
harder the pullup the greater the drag losses.

All in all it's a barely measurable difference. I suspect the reason
people feel like they get a bigger pullup full of water is that they
are generally carrying more speed at the beginning of the pullup when
they are full of water.

9B

On Apr 25, 4:27*am, Andy wrote:
The kinetic to potential energy balance yields no difference as has
been pointed out. There are small drag differences that give some
advantage to a heavier glider since it has a higher L/D at any given
speed. *Back of the envelope polar math says the difference in sink
rate at 150 knots with full ballast versus dry is about 100 feet per
mile (for a modern glider). At 100 knots it's about 50 feet per mile.
I'd estimate a typical pullup consumes about a quarter mile. Without
taking the time to integrate the declining sink rate difference over
the entire pullup, I'd guess the overall difference in altitude gain
would be around 20 feet.

I agree.


This ignores any differences in secondary
energy losses associated with pulling G's to make the pullup happen.
My intuition tells me that this would favor the lighter glider
slightly because it takes more energy to change the vector of a
heavier sailplane - how much I don't know except to say that the
harder the pullup the greater the drag losses.

No, for sure not if the heavier glider doesn't pull so hard that it
goes above the angle of attack for max L/D.

Supposing that the speed for best L/D full of ballast (in level
flight) is 75 knots, at 150 knots you'll have to pull (150/75)^2 = 4
Gs before you get to the max L/D angle of attack. (and the
unballasted guy with a best L/D at 60 knots would have to pull 6.25
Gs)

If both gliders pull the same number of Gs at 150 knots then the
ballasted one will lose a lower percentage of its energy unless they
both pull over 4 Gs.

They are probably equally efficient at around 5 Gs. And the lighter
glider is for sure more efficient at 6.25 Gs -- the ballasted guy is
getting close to stalling by that point.


All in all it's a barely measurable difference. I suspect the reason
people feel like they get a bigger pullup full of water is that they
are generally carrying more speed at the beginning of the pullup when
they are full of water.

Yes, probably, and the smaller loses while cruising along the runway.

On Apr 25, 12:57*am, Bruce Hoult wrote:
On Apr 25, 4:27*am, Andy wrote:

The kinetic to potential energy balance yields no difference as has
been pointed out. There are small drag differences that give some
advantage to a heavier glider since it has a higher L/D at any given
speed. *Back of the envelope polar math says the difference in sink
rate at 150 knots with full ballast versus dry is about 100 feet per
mile (for a modern glider). At 100 knots it's about 50 feet per mile.
I'd estimate a typical pullup consumes about a quarter mile. Without
taking the time to integrate the declining sink rate difference over
the entire pullup, I'd guess the overall difference in altitude gain
would be around 20 feet.

I agree.

This ignores any differences in secondary
energy losses associated with pulling G's to make the pullup happen.
My intuition tells me that this would favor the lighter glider
slightly because it takes more energy to change the vector of a
heavier sailplane - how much I don't know except to say that the
harder the pullup the greater the drag losses.

No, for sure not if the heavier glider doesn't pull so hard that it
goes above the angle of attack for max L/D.

Supposing that the speed for best L/D full of ballast (in level
flight) is 75 knots, at 150 knots you'll have to pull (150/75)^2 = 4
Gs before you get to the max L/D angle of attack. *(and the
unballasted guy with a best L/D at 60 knots would have to pull 6.25
Gs)

If both gliders pull the same number of Gs at 150 knots then the
ballasted one will lose a lower percentage of its energy unless they
both pull over 4 Gs.

They are probably equally efficient at around 5 Gs. And the lighter
glider is for sure more efficient at 6.25 Gs -- the ballasted guy is
getting close to stalling by that point.

All in all it's a barely measurable difference. I suspect the reason
people feel like they get a bigger pullup full of water is that they
are generally carrying more speed at the beginning of the pullup when
they are full of water.

Yes, probably, and the smaller loses while cruising along the runway.

More calculation opportunities for the phyisics groupies.

Which glider gets you to the same altitude faster assuming the same
speed. Ballasted or non ballasted?

On Apr 25, 12:57*am, Bruce Hoult wrote:


On Apr 25, 4:27*am, Andy wrote:

The kinetic to potential energy balance yields no difference as has
been pointed out. There are small drag differences that give some
advantage to a heavier glider since it has a higher L/D at any given
speed. *Back of the envelope polar math says the difference in sink
rate at 150 knots with full ballast versus dry is about 100 feet per
mile (for a modern glider). At 100 knots it's about 50 feet per mile.
I'd estimate a typical pullup consumes about a quarter mile. Without
taking the time to integrate the declining sink rate difference over
the entire pullup, I'd guess the overall difference in altitude gain
would be around 20 feet.

I agree.

This ignores any differences in secondary
energy losses associated with pulling G's to make the pullup happen.
My intuition tells me that this would favor the lighter glider
slightly because it takes more energy to change the vector of a
heavier sailplane - how much I don't know except to say that the
harder the pullup the greater the drag losses.

No, for sure not if the heavier glider doesn't pull so hard that it
goes above the angle of attack for max L/D.

Supposing that the speed for best L/D full of ballast (in level
flight) is 75 knots, at 150 knots you'll have to pull (150/75)^2 = 4
Gs before you get to the max L/D angle of attack. *(and the
unballasted guy with a best L/D at 60 knots would have to pull 6.25
Gs)

If both gliders pull the same number of Gs at 150 knots then the
ballasted one will lose a lower percentage of its energy unless they
both pull over 4 Gs.

They are probably equally efficient at around 5 Gs. And the lighter
glider is for sure more efficient at 6.25 Gs -- the ballasted guy is
getting close to stalling by that point.

All in all it's a barely measurable difference. I suspect the reason
people feel like they get a bigger pullup full of water is that they
are generally carrying more speed at the beginning of the pullup when
they are full of water.

Yes, probably, and the smaller loses while cruising along the runway.

I'm not totally sure about this but here's my logic (been a while
since engineering school). If you assume the ballasted and unballasted
gliders fly the same profile then they need to pull the same number of
Gs to execute the pullup. We've already accounted for the steady-
flight L/D effects in the initial calculation so all we need here is
how much energy is lost in pulling the same number of Gs to initiate
the climb. It's the same glider except for the ballast so the form
drag is the same which means we only have to account for the
difference in induced drag. The formula for that is:

D=(kL^2) / (.5pV^2S(pi)AR)

At the start of the pullup all these variables are the same except for
L which equals the weight of the glider times the G's being pulled. If
the heavier glider is 1.5 times as heavy the induced drag is 9 times
as great at 2 Gs. Keep in mind that at redline the induced drag term
overall is small because the speed is high, but still the advantage
should go to the lighter glider for the G-losses part. If you
calculate the L/D in accelerated flight you still end up with a weight
times Gs term in the denominator. I haven't done the math fully
through with real numbers, but that's how the formula looks to me.

Bruce's comment generated one additional thought. The energy balance
calculation we all did assumes the ballasted and unballasted gliders
both start at the same speed (redline) and end up at the same speed.
However, the ballasted glider has a higher stall speed, min sink speed
and best L/D speed - in my case by around 10 knots. If both gliders
pull up to their respective best L/D speeds the unballasted glider
gets about 65 feet higher due to being able to turn that last 10 knots
into altitude. Of course if both gliders went ballistic and did a
hammerhead stall at the top you wouldn't get this difference - but I'm
assuming typically you'd pull up to the same margin above stall speed,
which translates to a slower speed for the lighter glider.

So, by my new calculation the unballasted glider has a slight
advantage. It loses 20 feet to the ballasted glider due to L/D
effects, but gains 65 feet by being able to top out at a lower speed
and gains an unspecified amount (probably small) from G effects on
induced drag at the start of the pullup.

As an aside - the strong G-effect on induced drag is the main reason
why you should try to avoid hard pullups into thermals - you give away
a bunch of altitude.

9B

On Apr 20, 5:06*am, John Rivers wrote:
I was trying to work out the expected height gain from a pull up
Experienced glider pilots say you will get a better pull up with a
heavier glider / water etc.
But I can't see this from my (probably incomplete) equations:

total energy = potential energy + kinetic energy

total energy before pull up = total energy after pull up

m * g * h0 + m * pow(v0, 2) * 0.5 == m * g * h1 + m * pow(v1, 2) * 0.5

with h0 v0 being height and speed before pull up
and h1 v1 being height and speed after pull up

mass cancels out of this equation

I think I need to include momentum in there somehow?

You have included momentum :-)

I think the answer is in where on the L/D curve the glider is flying
during the pullup. And how close you can get to the optimal flight
path.

Your formula is correct but incomplete. It does not account for the
energy lost due to drag. Also, v1 (assuming it is stall speed) will
have some dependence on mass. However these are higher order effects;
in the first approximation you are correct.

On Apr 20, 1:06*am, John Rivers wrote:
I was trying to work out the expected height gain from a pull up
Experienced glider pilots say you will get a better pull up with a
heavier glider / water etc.
But I can't see this from my (probably incomplete) equations:

total energy = potential energy + kinetic energy

total energy before pull up = total energy after pull up

m * g * h0 + m * pow(v0, 2) * 0.5 == m * g * h1 + m * pow(v1, 2) * 0.5

with h0 v0 being height and speed before pull up
and h1 v1 being height and speed after pull up

mass cancels out of this equation

I think I need to include momentum in there somehow?

On Apr 20, 5:06*am, John Rivers wrote:
I was trying to work out the expected height gain from a pull up
Experienced glider pilots say you will get a better pull up with a
heavier glider / water etc.
But I can't see this from my (probably incomplete) equations:

total energy = potential energy + kinetic energy

total energy before pull up = total energy after pull up

m * g * h0 + m * pow(v0, 2) * 0.5 == m * g * h1 + m * pow(v1, 2) * 0.5

with h0 v0 being height and speed before pull up
and h1 v1 being height and speed after pull up

mass cancels out of this equation

I think I need to include momentum in there somehow?

You've also forgotten what the initial speeds are. When you are
flying with a heavier wing loading you are flying faster before the
pullup than you are with a lighter wing loading. Therefore, you'll
end up higher.

-- Matt

mattm wrote:
On Apr 20, 5:06 am, John Rivers wrote:
I was trying to work out the expected height gain from a pull up
Experienced glider pilots say you will get a better pull up with a
heavier glider / water etc.
But I can't see this from my (probably incomplete) equations:

total energy = potential energy + kinetic energy

total energy before pull up = total energy after pull up

m * g * h0 + m * pow(v0, 2) * 0.5 == m * g * h1 + m * pow(v1, 2) * 0.5

with h0 v0 being height and speed before pull up
and h1 v1 being height and speed after pull up

mass cancels out of this equation

I think I need to include momentum in there somehow?

You've also forgotten what the initial speeds are. When you are
flying with a heavier wing loading you are flying faster before the
pullup than you are with a lighter wing loading. Therefore, you'll
end up higher.

-- Matt

I think that this is the best brief answer too...


Brian W