Conservation of energy and pursuit tactics

[MANDOBLE]

Just a simple exercise in AH:
1 - Pick up a 190A8 4x20 75% fuel.
2 - Go up with substained climb to 15k
3 - Initiate a full power WEP-ON dive to 10k
4 - Level the plane for a bit, check speed and go vertical.
5 - Check the altitude where you stall.
6 - Repeat the process 1000 more times.
7 - Calculate the average altitude of stall.

Now do it with the lighter 190A5.
Now do it with the much lighter Spit V.
Now do it with the lighter Spit IX.
Now do it with the heavier P47.
Now do it with Niki, well, better dont do any test with Niki ...

Now try to elaborate some exotic physic formulaes that explain those results. If you tested the nikki, your formulaes surely will be as much exotic as inovative.

[Nuku]

 

Originally posted by Badboy:
They were not simply unloading, and this is a valid and aerodynamically correct procedure. I believe the technique is part of current USAF tactical doctrine.

I've just submitted an article that explains how and why it works to SimHQ and I'll post the link as soon as it goes live.

I want to see that article, and I hope you have references on it.  

I still want to know where the extra energy is coming from.  During my private pilot training, when the engine quits, we were instructed to trim for best glide, not porpoise up and down to stretch the glide.  The freight airlines don't porpoise to save fuel on those long transatlantic flights either (and I'm sure those pilots would LOVE to be able to do something mildly interesting during those long boring flights).

[funked]

 http://www.simhq.com/simhq3/sims/air_combat/co-e_chase/

[funked]

PS Badboy what I meant was that with thrust and drag in the picture, you don't get to turn all your PE into KE and vice versa.

PPS Nice article.  I still don't think you will get a long term advantage with a prop plane if both planes start at maximum level speed.  But it definitely works in the short term - I get into guns range against "faster" planes with my Seafire II this way all the time.  

[This message has been edited by funked (edited 02-02-2001).]

[Lephturn]

Very cool!  Thanks BadBoy!

So THAT is why this works.  I use tactics like this in the Jug, but I never knew why they worked.  I just marked it down to the Jug's tendancy to "work better" at high speed.  I can't tell you how many times I have used a 0 G extension to get to 300 IAS or so, and then used a very gradual high speed climb in the Jug.  It is one of the tricks to maintaining a good E position a plane like the P47.  It's good to know why it works.  

Badboy, I would LOVE to see that curve for the P47 in AH.  I suspect the Jug would show a higher speed for that "most efficient" energy transfer point than many of the other planes in AH, but I may be wrong.  It would be great to know of my instincts about the Jug are correct.  

------------------
Lephturn - Chief Trainer
A member of The Flying Pigs  http://www.flyingpigs.com
 
"A pig is a jolly companion, Boar, sow, barrow, or gilt --
A pig is a pal, who'll boost your morale, Though mountains may topple and tilt.
When they've blackballed, bamboozled, and burned you, When they've turned on you, Tory and Whig,
Though you may be thrown over by Tabby and Rover, You'll never go wrong with a pig, a pig,
You'll never go wrong with a pig!" -- Thomas Pynchon, "Gravity's Rainbow"

[Badboy]

Hi Nuku,

> I still want to know where the extra
> energy is coming from.

The extra energy comes from using what you have more efficiently. I have always found this technique to be most useful against bandits who attempt a climbing extension. If they get separation and then do a maximum rate climb their prop will typically be working well below maximum efficiency, and their aircraft will also be far from its maximum aerodynamic efficiency (AoA for maximum L/D ratio) and those factors alone conspire against the extending pilot. The other reasons are explained in the article.

> During my private pilot training, when
> the engine quits, we were instructed
> to trim for best glide, not porpoise up
> and down to stretch the glide.

Absolutely!!!
 

IMPORTANT NOTICE

Nothing I have said has any influence on the engine out procedure for any aircraft. Please do not... I repeat..DO NOT modify your current practice! Nothing I have ever said anywhere should be interpreted in the context of engine out performance!!!

Please don't take offense at this, I just do it for fun. I enjoy helping folk to fly simulations better, and helping them to understand why the simulated aircraft behave the way they do. I have no pretensions about the way any of that translates to the real world.

However, I get nervous when folk who fly real aircraft misinterpret my words and relate them erroneously to a potentially dangerous situation! But I'm sure you don't fly as carelessly as you read, so I guess everything is ok  

Take care!

Badboy

[Badboy]

 

Originally posted by Lephturn:
Badboy, I would LOVE to see that curve for the P47 in AH.  I suspect the Jug would show a higher speed for that "most efficient" energy transfer point than many of the other planes in AH, but I may be wrong.  It would be great to know of my instincts about the Jug are correct.

Thanks for the kind words...

Given time, I hope to analyse all of the aircraft in AH. It is currently my favorite sim! I believe your suspicions about the Jug are correct! Higher wing loaded aircraft tend to have their V speed numbers pushed up. If I do an analysis of the P47, what would you say would be the most interesting opponent to compare it with?

Badboy

[Lephturn]

Hmmm good question.

At first glance I would say the F4U, but I'm thinking they are too similar.  With the same engine and many similar traits, it may not be a very good comparison.  They may end up being very close in this regard, so it may not illustrate very much at all.

I think the George would be a better choice.  The N1K2 is one of the most populular planes in the game, so that puts it in contention.  It is also a plane that many folks have trouble with as an opponent, so more information may help.  The George is also the opposite of the Jug in many ways, (being a good accelerator but not so good at maintaining E at high speed) and so it should show more difference in the charts and demonstrate the theory better.  The George is faily representative of the lighter more TnB type planes in the arena, so this would possibly help make the information more applicable.

It sure would help to know the critical numbers for using energy most efficiently in the P47.    There are not many advantages we Jug pilots can exploit, so we need to maximize every tiny advantage we can!

Thanks Badboy!

------------------
Lephturn - Chief Trainer
A member of The Flying Pigs  http://www.flyingpigs.com
 
"A pig is a jolly companion, Boar, sow, barrow, or gilt --
A pig is a pal, who'll boost your morale, Though mountains may topple and tilt.
When they've blackballed, bamboozled, and burned you, When they've turned on you, Tory and Whig,
Though you may be thrown over by Tabby and Rover, You'll never go wrong with a pig, a pig,
You'll never go wrong with a pig!" -- Thomas Pynchon, "Gravity's Rainbow"

[Nuku]

The article explains very well the physics of  why a pursuer is able to get into guns range, but still doesn't detail how this advantage can be done more than once to *constantly* close the range.

In Shaw's "Fighter Combat", Figure A-7 shows that while Turbojets gain thrust with increasing airspeed, props LOSE thrust.

The green lines on your Es/Ps diagram  (known a H-M Diagram, or "altitude-mach" diagram) are lines of constant "specific energy" (effectively PE+KE).  In a frictionless closed system, any aircraft (or rock for that matter) follows those lines up and down, trading altitude for airspeed.  In my tail-chase scenario, the attacker, as he dives, moves down the green line, going faster, but losing altitude.  As he climbs back up, he loses airspeed and gets back to altitude exactly where he started.  

In order to jump from one green line to another green line, you need to pump energy into the system.  In the real-world, drag is constantly pulling you left into the lower green lines, and thrust helps you move right to the next line (or at least, helps you stay on your current line).

The blue lines on the diagram are lines of "specific excess power", which is a mixture of KE (zoom energy), thrust (raw extra energy), weight, and drag.  The blue lines as overlaid on your diagram match the thrust increases with airspeed that turbine engines get at altitude.  Prop engines however, don't have the "molar tooth" look: the blue lines for a WWII fighter go up and then slide constantly down (pretty steeply, like a parabola squished to the left).

In order to jump from one green line to another green line, your combination of airspeed and altitude must land on a blue line with a positive quantity.  Unfortunately, the blue parametric lines in your diagram are not labeled, so I can't tell exactly where you can jump to the next green line.  Actually, I don't know how you've overlaid those blue lines because in the tail-chase scenario, the attacker's Ps is zero (steady-state, thrust = drag, level flight).  So a blue line through point A in the diagram would be the "0" Ps line, aka as the maximum all-balls out level speed at a particular altitude (or max-performance envelope).

All blue lines OUTSIDE the 0 Ps line are negative, meaning the aircraft CANNOT jump to the next green line.  Blue lines INSIDE of the 0 Ps line mean the aircraft can move to the next highest green line (by accelerating level, or climbing).

I think this diagram is deceptive in that it shows the aircraft well inside its performance envelope.  I think Ps=0 is the outermost blue line in the diagram.

Diving to gain energy works for JET fighters because if you were already at Ps=0 at the edge of the last blue line, you could follow the green line across the "dip" and into the wave of increasing blue lines to go even faster.

A prop aircraft, as I said before, doesn't have this cusp, and the Ps countours are parabolic, and not as flattened at the top.  In the tail-chase scenario, the attacker is riding the Ps=0 line, and if he dives, he'll blow right outside the envelopes and never re-enter positive Ps territory to catch me.

That's where I'm confused.

[Lephturn]

Hmmm.

I'm not going to talk about the diagrams, because they are not specific for a prop plane and I think it will confuse the issue for me.  Badboy can explain the math.  

Lets look at it in a situation.  You and I are in P47's, roughly co E in a tail chase.  We are both at 10k and 200 IAS.  We both have excess power, since our planes will both do about 375 MPH at this altitude in WEP top speed.  The point is that the Jug and it's prop will more efficiently convert it's extra power into altitude or speed when it is moving faster than 200.  Lets just assume for a minute that the magic number is 350 Mph, WAG. (Wild Assed Guess)  So as you stay level and accelerate you are transferring your excess power into energy at low efficiency.  I use a 0G dive to get up around 300, and then zoom gently back up to your altitude.  The closer my plane gets to the 350 number, the more efficiently I am converting my excess power into speed or altitude.  You are still struggling along at a lower speed that is even less efficient, so you are converting that excess power to energy at much lower rate than I am.  I am gaining energy on you, mostly in the form of speed, and closing on you.

Now lets say I have done this once, but I am not in guns range.  Now I am not at my most efficient speed anymore after the zoom, lets say I fell back down to 275.  I again use a shallow 0G dive to accelerate, this time to 350, and then begin a gentle zoom back up to your altitude.  At this point I am now flying very close to the most efficient speed at which the Jug converts excess power into speed or altitude.  You have not accelerated as quickly, since you have been flying at a slower speed and hence a less efficient speed for converting your excess power into energy in the form of speed or altitude.  I can keep doing this and keep gaining energy on you as long as you are not at your most efficient speed for converting excess power to energy.  Once you reach 350 Mph at 10,000 feet, you are now converting your excess power into energy at the most efficient rate, so I can't make this trick work anymore.  What now?

Ok, now lets say I have done this twice, and gained on you, but not quite enough yet.  You have, by this time, reached your top level speed at 10k of 375 MPH.  Now, that number is over your most efficient conversion speed of 350.  By the same logic I should now be able to zoom gently at 350 Mph and gain E on you.  I will fall behind because of speed at first, but at this point you are not gaining energy, and I am.  If I climb at 350 while you run at 375 level (you have no excess power at this point), I will be gaining energy in the form of altitude.  If I have time, I should now be able to use another 0G dive to accelerate OVER 375 Mph and start catching you again.  Now this may not work as well due to higher drag and what not, but I am trying to illustrate the point.  

Now, at the time where you reached 350 Mph, your most efficient speed for converting excess power into energy... you could have held me at bay indefinately.  If you simply set auto-trim for speed at 350 Mph and let the plane climb at that speed, there is nothing I can do.  I am screwed, and no matter what I do I will not be able to gain energy on you.  You will have to turn, speed up, or slow down in order for me to have any advantage to exploit.

The trick is, how do we find out what that number is?  Badboy, can you suggest a test method that might allow us to find that number?  If you know the speed at which your plane converts excess power into energy at the most efficient rate for a give altitude, you can maximize your performance and either close on a similar bogey who is not maximizing his plane, or keep out of the guns range of somebody who is.  

Clear as mud?  

------------------
Lephturn - Chief Trainer
A member of The Flying Pigs  http://www.flyingpigs.com
 
"A pig is a jolly companion, Boar, sow, barrow, or gilt --
A pig is a pal, who'll boost your morale, Though mountains may topple and tilt.
When they've blackballed, bamboozled, and burned you, When they've turned on you, Tory and Whig,
Though you may be thrown over by Tabby and Rover, You'll never go wrong with a pig, a pig,
You'll never go wrong with a pig!" -- Thomas Pynchon, "Gravity's Rainbow"

[Westy]

"Clear as mud?"

Clear as all get out     This topic has helped me understand some behavior I'd previously thought of as odd.

 Thanks guys!  I appreciate all these posts and th efforts by all to help explain what is going on.

 -Westy

[Nuku]

   

Originally posted by Lephturn:

Lets look at it in a situation.  You and I are in P47's, roughly co E in a tail chase.  We are both at 10k and 200 IAS.

The situation I started this thread with was NOT the start of the chase, where acceleration counts.  That, I understand, and is the crux of Badboy's argument (especially when the defender is climbing below efficiency, and the attacker dips to hit his most efficient speed).  The bottom line is that the attacker is simply outaccelerating the defender.

It's at *steady state* when BOTH aircraft are at maximum speed (Ps=0 curve in the diagram). In your example, pursuer and attacker have already stabilizied  level at 375MPH and the attacker is out of range.  Now what?

By both your efficiency logic and the HM diagram, going any faster causes you to LOSE efficiency/energy.  Going straight at 375MPH (the defender) is more efficient than going into a dive at 400MPH (the attacker).  Prop efficiency drops at higher speeds (turbojet increases so this would work as Badboy states).  By the efficiency logic, the pursuer should CLIMB at WAG speed (350MPH), then dive to catch the defender.  

Stated another way, I think the distance gained in the dive above max efficiency, is lost during the climb AT max efficiency.   During the dive, thrust is dropping, but drag is increasing.  All that energy is pfffht.. gone.  At the nadir point, as the attacker pulls up all the extra KE goes pack to PE, and while he's above 350, parasitic drag sucks still more energy out until thrust and drag two balance at 350MPH.  By the time he gets back to the defender's altitude, I think he's at a deficit.

As I stated before, with prop planes, the attacker will dive right outside his performance envelope: he will generate less thrust, and parasitic drag will be greater than it was during level flight, so all the PE he converted to KE will get sucked right out, and he'll lose in the end.

The dive-zoom tactic is for a short-term snap-shot and works BEFORE both aircraft have hit their Ps=0 (max speed) points.

I'm still not convinced that once both aircraft have finished accelerating (level) that the pursuer can do anything to catch the defender if in a PROP plane.


[This message has been edited by Nuku (edited 02-03-2001).]

[This message has been edited by Nuku (edited 02-03-2001).]

[Badboy]

Hi Nuku

> The article explains very well the physics
> of why a pursuer is able to get into guns
> range, but still doesn't detail how
> this advantage can be done more than once
> to *constantly* close the range.

Optimal application does not involve repeating the procedure. It only needs to be repeated if the climb is started too soon, or too steeply. However, it still works when repeated because you are in effect oscillating between an optimum condition, and one only as bad as your opponents. So your energy transfer is better some of the time. It still works, but takes a little longer to get the kill.

> In Shaw's "Fighter Combat", Figure A-7
> shows that while Turbojets gain thrust >with increasing airspeed, props LOSE thrust.

Correct, but considering thrust alone doesn’t solve the problem. Because we are more interested in the maximum rate of energy transfer it is better to think in terms of efficiency, not just thrust. Prop’s produce less thrust as they get faster, but they also become more efficient, up to a point. Also the aerodynamic efficiency of the aircraft improves as the speed increases (until you reach the AoA for the best L/D ratio) and of course as the altitude increases the drag drops. It is a combination of all those factors, combined with their variation with speed, that is being represented in the diagram.

If it were only thrust that mattered, the Jet would want to get as fast as possible, and the Prop’ would be better off stationary! Neither of which is the correct thing to do and the theory wouldn’t work in either case.

> in the tail-chase scenario, the attacker's
> Ps is zero (steady-state, thrust = drag,
>level flight).

I never made the assumption that the fight began from zero Ps because it almost never does.

> I think this diagram is deceptive in that
> it shows the aircraft well inside its
> performance envelope.

The aircraft in this scenario never leave the envelope, that’s not deceptive, it is perfectly correct. The aircraft do not leave the envelope at any stage of the engagement I described.

> A prop aircraft, as I said before, doesn't
> have this cusp, and the Ps countours are
> parabolic, and not as flattened at
> the top.

That is correct, but the prop’ curves still yield a best energy transfer solution. They do so because the highest energy state along any Ps curve is the point where they are tangent to the Es curves and that is just as true for a prop’ fighter as it is for a jet. Of course the solution is different, but a solution all the same.

To imagine what it would like, picture the prop curve in Figure A-13 of shaw and imagine Es curves superimposed on them. Now the best energy transfer will occur at  points where they are tangent to each other. Yes, it will look different, but the solution will be just as valid.

> In the tail-chase scenario, the attacker
> is riding the Ps=0 line, and if he dives,
> he'll blow right outside the envelopes and
> never re-enter positive Ps territory to
> catch me.

The attacker doesn’t start at Ps=0 and should only dive to his best energy transfer speed. Of course if he dives right out of the envelope, he will almost certainly have lost it completely.


> Prop efficiency drops at higher speeds
> (turbojet increases so this would work
> as Badboy states)

Prop efficiency increases with speed, up to a point. It drops when Mach effects begin to have an influence, but the best energy transfer speed is well below that point.

> As I stated before, with prop planes, the
> attacker will dive right outside his
> performance envelope:

He should only dive until he gets to his best energy transfer speed.


> I'm still not convinced that once both
> aircraft have finished accelerating
>(level) that the pursuer can do anything
> to catch the defender if in a PROP plane.

Correct. The fight will have been neutralized once both aircraft have reached top speed at critical altitude. Whatever separation they have at that point is what they are stuck with. That’s the same for jets, the main difference being that they end up a lot higher, often somewhere just above 36000ft.

Hope that helps.


Badboy

[Badboy]

 

Originally posted by Lephturn:

The trick is, how do we find out what that number is?  Badboy, can you suggest a test method that might allow us to find that number?  If you know the speed at which your plane converts excess power into energy at the most efficient rate for a give altitude, you can maximize your performance and either close on a similar bogey who is not maximizing his plane, or keep out of the guns range of somebody who is.  

The best way is to actually produce the curves for it. I can do that, and I already have the data for quite a few of the AH aircraft. What I am short of right now is time!! As well as my full time teaching job, I'm on the point of signing the contract for another strategy guide. I just wish I didn't need to sleep  

It may take a little while, but I will come up with the goods eventually... I promise!

Badboy

[Rickenbacker]

Hmm, i can see this working for jets (after all, delta wings aren't very efficient at low speeds, so speeding up would lower drag, thus netting you energy), but I'm not sure why it works in prop fighters. Is the "magic" speed here the speed above which the prop starts "braking" the plane, or are we talking about engine performance at various alts only?

Rickenbacker