Reply to topic  [ 28 posts ]  Go to page 1, 2  Next
130: deep jumps vs. white dwarves 
Author Message

Joined: Sat May 05, 2018 3:08 am
Posts: 3
Post 130: deep jumps vs. white dwarves
Actually, that's not how General Relativity works. The depth of a well depends on a star's mass, no matter what diameter it is. Gravity always decreases with the square of the distance. There cannot be such a thing as a "shallow but deep" gravity well.

What's actually dangerous is hitting the star itself, and the probability of *that* depends on the star's diameter. Thus a white dwarf is reasonably safe; what you should really be concerned with is jumping to a red giant – same mass but a whole lot bigger, thus more likely to end up inside of. (When our sun becomes a red giant it'll extend beyond Earth's orbit!)


Sat May 05, 2018 3:20 am
Profile
Online

Joined: Mon Jan 26, 2015 2:00 pm
Posts: 1285
Location: Athens, Greece
Post Re: 130: deep jumps vs. white dwarves
MatthiasU wrote:
Actually, that's not how General Relativity works. The depth of a well depends on a star's mass, no matter what diameter it is. Gravity always decreases with the square of the distance. There cannot be such a thing as a "shallow but deep" gravity well.

What's actually dangerous is hitting the star itself, and the probability of *that* depends on the star's diameter. Thus a white dwarf is reasonably safe; what you should really be concerned with is jumping to a red giant – same mass but a whole lot bigger, thus more likely to end up inside of. (When our sun becomes a red giant it'll extend beyond Earth's orbit!)


I think that you misunderstood how Jump drives work. Large Mass = Greater pull/Bigger gravity well.

A Big red giant has a greater pull which also means that its gravity well is both deeper and wider. It's a safer bet to jump into a red giant system because the jump points are larger due to the deeper/wider gravity well. The 'landing' angle is easier and you have a bigger 'landing strip' of shorts to safely jump.

A white dwarf has a smaller gravity well but this means that it is harder to jump into, smaller jump points and the 'walls' of the gravity well are far steeper. The well isn't deep but the diameter is vastly smaller with everything that entails in regards to the safety margins of a jump.

_________________
My fan fics

Looking forward to the Mirror (Delayed Editing)
The pale horse (Completed)
Reforged (Semi regular updates)


Sat May 05, 2018 5:18 am
Profile

Joined: Sat May 05, 2018 3:08 am
Posts: 3
Post Re: 130: deep jumps vs. white dwarves
dragoongfa wrote:
I think that you misunderstood how Jump drives work. Large Mass = Greater pull/Bigger gravity well.

Umm, that's what I was saying. "Bigger" as in "wider" / "greater pull" depends on the mass. "Bigger" as in "deeper" / "how close to the star can you get without being inside" also depends on the mass' density, but that's irrelevant, as outside of a system only the mass affects your trajectory – not its distribution.

In any case there is no such thing as a narrow-but-deep gravity well. If you draw the gravity wells of multiple stars on top of each other, in the same scale of course, the lines of these graphs do not cross (unless you're inside a larger-diameter star). Also, at the star's center the gravity is zero, so there's an upturned triangle-or-whatever at the center of the gravity well, not a trough in which the star sits.

As the graph in #130 shows, you enter jumpspace at a certain "angle", for want of a better word, at the source system, in order to end up close enough to the destination star without hitting it. As red giants and white dwarves may have the same mass, I don't see how the latter could per se exert a larger pull on you.

If you assume that a ship ends up inside the star whenever it overshoots the edge of the gravity well, the actual diameter of the star is irrelevant.


Sat May 05, 2018 8:14 am
Profile
Online

Joined: Mon Jan 26, 2015 2:00 pm
Posts: 1285
Location: Athens, Greece
Post Re: 130: deep jumps vs. white dwarves
Not a physicist and I think am now sure that I made a mess of my previous post in regards to the gravity well.

Looking into it some more I realized/recalled that White Dwarfs have far greater surface gravity than normal stars and red giants, red giants having the weakest surface gravity of all stars. If we go by surface gravity then a white dwarf should have a far greater pull in a hyperspace jump if a ship deep jumps.

A red giant has a far greater diameter but since it has far lower surface gravity due to said diameter it shouldn't affect space ships that jump into a red giant system that much but the greater diameter should forbid deep jumps at the first place. Sol's normal Jump points are around Jupiter's orbit and considering that Sol will expand up to Earth's orbit it should leave normal jumps relatively intact in regards to safety but deep jumps up to the Asteroid Belt should still be safe if not of any use at all, anything deeper than that puts you too close to the sun and you risk getting cooked even if you don't get eaten by the red blob.

EDIT: To make it clearer since my graphing skills are shit and I have the nasty habit of posting half backed stuff before truly comprehending shit.

If we go by mass a red giant and a white dwarf of equal mass should have their jump points at roughly the same points in space unless the distance and location are directly affected by the star's surface gravity.

Normal jumps into both of these stars are still safe but deep jumps in red giants should be done 'swallower' since the large diameter of the sun means that you will end too close or into the sun if you deep jump. In such a case there should be no reason to deep jump into a red giant system since the rewards aren't enough to overshadow the risks involved.

Deep jumps into a white dwarf should be even riskier, the sun isn't big but its surface gravity is far greater, exercising greater pull the closer you Jump to the sun but the reward is far greater due to the lower diameter of said sun which put you deeper into the system if you manage to pull it off. In a red giant you have the risk of getting fried if you jump deep without much of a reward but in a White dwarf the reward is getting far closer to the sun without getting cooked in your own ship.

_________________
My fan fics

Looking forward to the Mirror (Delayed Editing)
The pale horse (Completed)
Reforged (Semi regular updates)


Sat May 05, 2018 9:34 am
Profile
User avatar

Joined: Thu Aug 27, 2015 10:43 am
Posts: 87
Location: Saint-Petersburg, Russia
Post Re: 130: deep jumps vs. white dwarves
The gravity pull of any object is defined by it's mass and distance from it's center. So, the lower surface gravity of red star is explained just by it's far bigger size.
The gravity pull of a black hole of the same mass on same distance would also be same, for example.

_________________
Outsider in Russian
Image


Sat May 05, 2018 10:16 am
Profile
Site Admin
User avatar

Joined: Fri Mar 04, 2011 9:19 pm
Posts: 2583
Location: San Jose, CA
Post Re: 130: deep jumps vs. white dwarves
MatthiasU wrote:
In any case there is no such thing as a narrow-but-deep gravity well.

Sure there is. A black hole has an infinitely steep gravitational slope at the singularity, but black holes vary greatly in mass. In theory you can make a very small black hole that has a total gravitational pull that's much less than that of a star, but still has an infinitely deep well.

A stellar mass black hole has a gravity slope that's so steep at the event horizon that the tidal forces will tear any matter apart before it even reaches the horizon, but a supermassive black hole with a thousand solar masses has a much milder gravity slope at the event horizon; you could easily cross the event horizon without experiencing any significant tidal stresses. The volumes described by the two event horizons have different effective densities; the two gravity wells are not the same shape.

Now, you could argue that a white dwarf isn't dense enough to significantly affect the slope of the gravity well, and I haven't done the math to contradict you, but in principle a denser object has a steeper gravity well.

_________________
Outsider


Sat May 05, 2018 12:30 pm
Profile WWW

Joined: Fri Jan 12, 2018 4:53 am
Posts: 212
Post Re: 130: deep jumps vs. white dwarves
A gravity well is only a model, the 3D plot of the gravity field strength (gravitational pull) of an object against the distance from said object, with said object being at the bottom of this "well". This relationship is hyperbolic and the plot thus looks like a funnel. The plot for a black hole looks like a funnel with the walls becoming vertical and infinite at the diameter of the hole's event horizon (a black hole has no physical surface or a diameter, what we commonly refer to as a black hole is it's event horizon - the distance from the hole where the gravity is so strong that it's escape velocity exceeds the speed of light) In layman's terms the "depth" and slope of this funnel are proportional to the gravity field strength of the object in question and the mass of the object, because gravity is determined by mass.

Thus, different objects of equal mass (regardless if they are a main sequence dwarf star, red giant, neutron star or a stellar mass black hole) will have equal depth gravity wells and thus equal conditions for jumping into them, all other factors being equal. Rapidly rotating objects like neutron stars and pulsars, especially if they are in close binary systems, are a different story altogether because they produce gravity waves and thus "fluctuating" gravity wells.

Objects with low mass = weak gravity = shallow gravity wells (red/brown dwarfs, white dwarfs, gas giants) are difficult to jump to - the optimal jump arrival areas will be comparatively small and close to the object with very little margin for error (just a bit too far out and you'll bounce back into hyperspace, too close and you'll get pulled into the star or exit hyperspace inside the star). The difference between an optimal, deep and shallow jump will be within a couple AUs, when in comparison the optimal jump arrival zone for a main sequence dwarf star (like Sol) starts around 5 AU from the star (Jupiter orbit) and would extend to about 9-10AU (Saturn's orbit) with deep jumps down to almost 1 AU being possible.

The more massive the object, like a main sequence giant star, the easier it would be to do a hyperspace jump to it and it will have a rather broad jump arrival zone. Unless there are more Arioch's Hyperspace Laws which I'm not aware of, it is possible to do a hyperspace jump into a black hole system, if the precise location and mass of the black hole is known and the hole isn't currently absorbing another massive object. The Well Of Souls black hole is currently not "jumpable" because it has an unstable (fluctuating) gravity well and thus appears to be in a close binary system.

Leido is a very compact white dwarf system (mass unknown, but white dwarfs are usually come in at around 0.6 Solar masses) and is thus much more difficult to correctly jump into than, say, Sol (which itself has 7 usable jump links, according to Insider), but is strategically important since it has 5 other stars within optimal jump distance (less than 10LY apart).

*wow, that was a truckload of pseudo science BS*


Sat May 05, 2018 1:17 pm
Profile

Joined: Mon Mar 21, 2011 9:37 am
Posts: 62
Post Re: 130: deep jumps vs. white dwarves
entity2636 wrote:
A gravity well is only a model, the 3D plot of the gravity field strength (gravitational pull) of an object against the distance from said object,


this may be a picking nits as it were but a gravity well is a model of how much an objects gravity has warped space not how strong the field is. the strength of gravity is always constant its the mass and density of the target object that determines how warped the space around it is

so two objects of equal mass but different densities will have very different gravity well. they may be the same size but the denser object will bend space more in that distance


Sat May 05, 2018 5:10 pm
Profile
User avatar

Joined: Sun May 07, 2017 2:10 pm
Posts: 37
Location: Taton mi Dshaneiro
Post Re: 130: deep jumps vs. white dwarves
Arioch wrote:
Now, you could argue that a white dwarf isn't dense enough to significantly affect the slope of the gravity well, and I haven't done the math to contradict you, but in principle a denser object has a steeper gravity well.


I've done a quick investigation, and I feel it is safe to say that they do. White Stars are absurdly dense, because they're made of Electron-Degenerate matter. In a way, they're just one step behind Neutron Stars, density-wise. For reference, Sirius B, our nearest White-Dwarfy neighbour, has a density of mind-boggling 2.1x10^6 grams per cubic centimetre! That is quite enough to generate a steep gravitational gradient, indeed.

(As an addendum, in Space Engine you can actually get to see just how dense White Dwarfs are by watching the gravitational lensing they cause around them. Video inside the Spoiler; for White Dwarf, skip to 1:41.)
Spoiler: show

_________________
Tauntingly: "Enzin tii Eilis mé sibreg ranii tó lanzedad..."


Sat May 05, 2018 5:37 pm
Profile

Joined: Fri Sep 23, 2011 9:33 pm
Posts: 703
Post Re: 130: deep jumps vs. white dwarves
GabrielGABFonseca wrote:
Arioch wrote:
Now, you could argue that a white dwarf isn't dense enough to significantly affect the slope of the gravity well, and I haven't done the math to contradict you, but in principle a denser object has a steeper gravity well.


I've done a quick investigation, and I feel it is safe to say that they do. White Stars are absurdly dense, because they're made of Electron-Degenerate matter. In a way, they're just one step behind Neutron Stars, density-wise. For reference, Sirius B, our nearest White-Dwarfy neighbour, has a density of mind-boggling 2.1x10^6 grams per cubic centimetre! That is quite enough to generate a steep gravitational gradient, indeed.

(As an addendum, in Space Engine you can actually get to see just how dense White Dwarfs are by watching the gravitational lensing they cause around them. Video inside the Spoiler; for White Dwarf, skip to 1:41.)
Spoiler: show
Sirius B also has a total mass close to that of the Sun, and thus at meaningful distances from it the space-time slope should approximately match that of the Sun.

In essence, once you get far enough away to reasonably treat an object as a single point, only it's mass (and maybe spin) matters to the space-time slope. Density and other such things basically just matter when close enough that you should model it as a multi-point object (because you can differentiate forces from one side and the other).

Same thing happens with radio antennas: if you stick two antennas within a certain distance (1/2 wavelength I think) then they act like a transformer (albeit usually not a good one), with close to 0.0 transformer action (and thus 1.0 antenna action) at 1/2 wavelength, and 1.0 transformer to 0.0 antenna (well, not necessarily, circuit details) at physical contact, because a photon's size matches it's wavelength.


Sun May 06, 2018 12:24 am
Profile
Online

Joined: Mon Jan 26, 2015 2:00 pm
Posts: 1285
Location: Athens, Greece
Post Re: 130: deep jumps vs. white dwarves
I love being in forums with people who know more than I do. :)

_________________
My fan fics

Looking forward to the Mirror (Delayed Editing)
The pale horse (Completed)
Reforged (Semi regular updates)


Sun May 06, 2018 1:03 am
Profile

Joined: Tue Dec 11, 2012 1:46 am
Posts: 172
Location: Czech Rep., European Union
Post Re: 130: deep jumps vs. white dwarves
I have a tangential question about jumping, which I've never seen explained in detail: how, specifically, do ships jump? I mean the procedure, I'll clarify.

We know the ship has to have the "jump generator" device and sufficient "capacitors" to accumulate the sufficient energy that's needed to active it. That's understood. Then, the ship needs to be on the proper vector to the target star (right distance from the outbound star, right direction). The third component, the one I am interested in, is the "hyperspace momentum". How is this achieved?

Do ships need to activate the jump generator at a very specific real-space speed? I've always thought that the only thing the jump generator does is that it allows the ship to disconnect from the real-space "plane", translating its real-space speed into hyperspace momentum. This brings certain implications:

(a) can ships jump while under acceleration, or not? If they must be moving at constant speed, this will very seriously increase their vulnerability during the jump sequence (hitting a predictably moving, non-accelerating target is much easier);
(b) how high/low is the correct jump speed (the range of acceptable jump speeds)? If a fleet is now running towards the jump link at full acceleration, does it mean it will have to slow down to successfully jump? This will again make the jumping fleet vulnerable, because it allows the enemy to catch up and engage in combat.

It seems to me that attempting a jump while the enemy is on your tail is a pretty risky, possibly suicidal move.

Any comment on this?


Sun May 06, 2018 1:19 am
Profile

Joined: Sat Jan 24, 2015 1:42 pm
Posts: 70
Post Re: 130: deep jumps vs. white dwarves
entity2636 wrote:
Objects with low mass = weak gravity = shallow gravity wells (red/brown dwarfs, white dwarfs, gas giants) are difficult to jump to - the optimal jump arrival areas will be comparatively small and close to the object with very little margin for error


Absalom wrote:
In essence, once you get far enough away to reasonably treat an object as a single point, only it's mass (and maybe spin) matters to the space-time slope.


Apart from all of this being applied to non-existent technologies, that sounds about right.


Sun May 06, 2018 2:15 am
Profile
Site Admin
User avatar

Joined: Fri Mar 04, 2011 9:19 pm
Posts: 2583
Location: San Jose, CA
Post Re: 130: deep jumps vs. white dwarves
Victor_D wrote:
Do ships need to activate the jump generator at a very specific real-space speed? I've always thought that the only thing the jump generator does is that it allows the ship to disconnect from the real-space "plane", translating its real-space speed into hyperspace momentum.

A specific range of speeds, yes. For each pair of stars there is an "optimal" setting of location + velocity for the safest jump. These values can be varied (say between 50-100% in either direction) with semi-predictable results (higher velocity or farther from origin star = deeper jump into the destination star), but the farther away you get from the optimal setting, the greater the chance that a random deviation while in hyperspace will push you into a failure mode.

While you can theoretically jump while under acceleration (as long as that acceleration is only along the jump vector, and doesn't push you laterally off course), it is an additional risk. A jumping ship is vulnerable; in addition to needing to use most or all of its power to charge the jump accumulators, it can't perform evasive maneuvers, and receiving any kind of hit at the moment of jump could add unwanted momentum. So in practice, the enemy can essentially deny the use of an outbound jump link just by having ships within weapons range.

_________________
Outsider


Sun May 06, 2018 9:25 am
Profile WWW

Joined: Thu Jun 16, 2016 10:01 pm
Posts: 368
Post Re: 130: deep jumps vs. white dwarves
Arioch wrote:
While you can theoretically jump while under acceleration (as long as that acceleration is only along the jump vector, and doesn't push you laterally off course), it is an additional risk. A jumping ship is vulnerable; in addition to needing to use most or all of its power to charge the jump accumulators, it can't perform evasive maneuvers, and receiving any kind of hit at the moment of jump could add unwanted momentum. So in practice, the enemy can essentially deny the use of an outbound jump link just by having ships within weapons range.


Hey, if it's the difference between guaranteed death under enemy guns and *probable* death by Slaneesh, it might be worth putting your most blindly self-confident pilot on the helm and saying "wow me."


Sun May 06, 2018 9:31 am
Profile

Joined: Sat May 05, 2018 3:08 am
Posts: 3
Post Re: 130: deep jumps vs. white dwarves
dex drako wrote:

this may be a picking nits as it were but a gravity well is a model of how much an objects gravity has warped space not how strong the field is. the strength of gravity is always constant its the mass and density of the target object that determines how warped the space around it is

so two objects of equal mass but different densities will have very different gravity well. they may be the same size but the denser object will bend space more in that distance


Umm, no. Two objects of equal mass will have the exact same gravity well, i.e. cause the same amount of space-time distortion – outside of the larger object's radius of course. The differences inside said radius don't affect the space outside (other than tidal effects and whatnot, but these don't matter at interstellar distances).

Yes this is all non-existent tech, but its real-space component still should conform to what we know about real-space physics.


Sun May 06, 2018 12:22 pm
Profile
User avatar

Joined: Tue Nov 12, 2013 4:31 pm
Posts: 162
Location: Tallmadge Ohio
Post Re: 130: deep jumps vs. white dwarves
Those Buggies are freaking crazy with hate for the Loroi if they don't mind risking life and limb on a possible chance of being behind enemy lines. I mean really jumping into a white dwarf these guys have some crazy dedication.

_________________
An amazing life changing Service http://blsmailbag.com/direct.php?id=B17 ... r_services


Sun May 06, 2018 2:45 pm
Profile WWW
Online
User avatar

Joined: Sun Mar 06, 2011 10:10 am
Posts: 320
Post Re: 130: deep jumps vs. white dwarves
Quote:
Umm, no. Two objects of equal mass will have the exact same gravity well, i.e. cause the same amount of space-time distortion – outside of the larger object's radius of course. The differences inside said radius don't affect the space outside (other than tidal effects and whatnot, but these don't matter at interstellar distances).


This is true, outside the larger object's radius. But once you're inside that radius you reach levels of distortion around the denser object that you wouldn't experience inside the less dense object if you could somehow travel within it. The gravitational forces start to cancel out. In the rubber sheet visualization once you hit the outside of an object the sheet starts to flatten back out, so the denser object will ultimately reach deeper. This doesn't actually have a detectable effect on objects in the real world out in the jump zone distances, but I have no problem believing that it has a different impact on the broader shape of hyperspace.

_________________
Atomic Space Race, a hard sci-fi orbital mechanics puzzle game.
Homeworld Fulcrum, a Homeworld Remastered Mod


Sun May 06, 2018 5:43 pm
Profile

Joined: Wed May 20, 2015 2:14 am
Posts: 610
Post Re: 130: deep jumps vs. white dwarves
Since current knowledge tells us nothing about how gravity contorts realspace for hhyperspace transitions, whetever Arioch tells me, I'll accept.
For the story, and since that science simply is unknown, as of now.

Otherwise, I have my own opinions, and as someone here mentioned, most current sci-fi stories don't hold up when examined with sufficient detail.
We'll just add some analogs to Star Trek's Heisenberg compensator, and the story continues.

BTW, the current increase in update frequency is very much enjoyed here, and makes me hopeful, that this comic reaches its planned end before Humans start leaving the solar system for real.

_________________
Vote for Outsider on TWC: Image
charred steppes, borders of territories: page 59,
jump-map of local stars: page 121, larger map in Loroi: page 118,
System view Leido Crossroads: page 123


Mon May 07, 2018 12:46 am
Profile
User avatar

Joined: Sat Mar 05, 2011 1:35 pm
Posts: 1071
Location: Middle of Nowhere
Post Re: 130: deep jumps vs. white dwarves
hi hi

So, I went ahead and ran the math on it. I used Sirius B's radius since it is so close to Sol in mass, even if that is on the heavy side for white dwarfs, and Sol. At 1 AU distance, there's not much of a difference, but there is still a slight difference in the gravitational pull.

At the distances that normal jumps are made, 4 or 5 AU, the gravitational gradient is much shallower, and the gravitational pull is much weaker than 1g, to say nothing of the 440,000g surface gravity of a white dwarf. So perhaps such slight differences are actually important.


Mon May 07, 2018 11:07 am
Profile WWW
Online

Joined: Mon Jan 26, 2015 2:00 pm
Posts: 1285
Location: Athens, Greece
Post Re: 130: deep jumps vs. white dwarves
The 1 AU distance has been retconned to an estimated 64 solons distance from the star, a little more than 1 light minute, which as a distance is 1/3 of the distance between sun and mercury. The Shells jumped danger close.

_________________
My fan fics

Looking forward to the Mirror (Delayed Editing)
The pale horse (Completed)
Reforged (Semi regular updates)


Mon May 07, 2018 12:55 pm
Profile
Site Admin
User avatar

Joined: Fri Mar 04, 2011 9:19 pm
Posts: 2583
Location: San Jose, CA
Post Re: 130: deep jumps vs. white dwarves
1 AU was meant to be the diameter of the entire system. That's what the transit times are based on.

_________________
Outsider


Mon May 07, 2018 1:54 pm
Profile WWW
User avatar

Joined: Sat Mar 05, 2011 1:35 pm
Posts: 1071
Location: Middle of Nowhere
Post Re: 130: deep jumps vs. white dwarves
hi hi

So, at 64 light solon, that's about 69.888 light seconds. Around that distance, given Sol mass white dwarf, the gravitational pull is about 0.302 m/2^2 That's nothing to scoff at, but not unreasonably close either.


Mon May 07, 2018 5:26 pm
Profile WWW

Joined: Mon Jun 04, 2018 4:11 pm
Posts: 1
Post Re: 130: deep jumps vs. white dwarves
Krulle wrote:
Since current knowledge tells us nothing about how gravity contorts realspace for hhyperspace transitions, whetever Arioch tells me, I'll accept.
For the story, and since that science simply is unknown, as of now.


Seems to me that's the issue - the given explanations don't make sense.

Attempting a deep jump into a white dwarf system should be less dangerous, not more, than attempting to do so into a red giant of the same mass.

Outside the red giant's diameter, the slope of the wells should be equivalent for the two cases, and inside the red giant's diameter - well you've already collided with the red giant, whereas you at least still have a chance of re-entering realspace outside the white dwarf.


Last edited by Myrddin on Fri Jun 08, 2018 7:48 pm, edited 1 time in total.



Fri Jun 08, 2018 5:14 pm
Profile

Joined: Mon Dec 14, 2015 8:08 pm
Posts: 63
Post Re: 130: deep jumps vs. white dwarves
I assumed it was more of a function of gravity in general more than the White/Red comparison.

Essentially, the low gravity means that there's a very limited acceptable zone of ingress from hyperspace. You need to get very close to the star's well to overcome the limited gravity.

To recall the diagram of the hyperspace 'well' in the Insider page, the White Dwarf would have a very shallow, very narrow 'dip', and thus be a difficult target. Assuming a certain dispersion on the X-Axis of the same diagram, one can see that such a small target is difficult to hit.


Fri Jun 08, 2018 7:06 pm
Profile
Display posts from previous:  Sort by  
Reply to topic   [ 28 posts ]  Go to page 1, 2  Next

Who is online

Users browsing this forum: dragoongfa, Siber and 5 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum

Search for:
Jump to:  
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group.
Designed by STSoftware for PTF.