Blackbird
Topic Author
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### Energy Maneuverability Equation

Okay, from what I remember
-The higher the thrust/weight ratio you have, the more aggressively you can turn without losing speed
-The lower the wing-loading at low airspeed for the same T/W ratio, the tighter you can turn without losing speed
-The higher the wing-loading at high airspeed for the same T/W ratio, the tighter you can turn without losing speed

Doesn't the wing's L/D ratio factor into this equation? Because I was thinking, you could have a huge wing which is an aerodynamic piece of crap, and a small wing which is extremely efficient. Also, swing-wings which have very large wing-areas even swept back seem to do very well at high IAS in terms of sustained maneuvering (which appears to be because with a high-sweep, the L/D ratio changes).

Andrea Kent
BTW: Should I disappear, get a heart-attack, commit-suicide, die suspiciously, contract some incurable disease, or end up arrested on bogus charges, you know who's to blame for it.

[Edited 2008-07-17 20:13:35]

rwessel
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Joined: Tue Jan 16, 2007 3:47 pm

### RE: Energy Maneuverability Equation

In short your ability to turn is based on how much lift your wing can produce. Avoiding a loss of speed (assuming we're talking about a level turn) requires that your engine produce enough thrust to compensate for the drag the wings (plus any parasitic drag) produce creating that lift. So yes, it's fundamentally a function of available thrust and L/D. Remember that L/D is not a constant, but varies considerably over the flight regime.

Consider an aircraft weighing 100,000lbs, in a level 3G turn, with an L/D of 10:1 (in that particular set of flight conditions). To avoid losing speed, the engines need to be producing 30,000lbs of thrust.

kellmark
Posts: 550
Joined: Thu Dec 21, 2000 12:05 pm

### RE: Energy Maneuverability Equation

This might help.

The Energy-Maneuverability Equation that was created by Air Force fighter pilot/engineer John Boyd is as follows:

The specific energy rate of an aircraft , ie an aircraft at 30,000 feet at 450 knots and pulling 6 Gs, is equal to thrust minus drag over weight, multiplied by velocity.

Boyd revolutionized air-to-air tactics and fighter design.

Blackbird
Topic Author
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Joined: Wed Oct 06, 1999 10:48 am

### RE: Energy Maneuverability Equation

Understood...

Just out of curiousity. While I know that an unstable design with super-maneuverability with light wing-loading doesn't bleed off as much airspeed when flying at high IAS (where light wing-loading doesn't typically do so well)?

Especially considering such high alphas generally generate a lot of drag...

Andrea Kent

Blackprojects
Posts: 527
Joined: Wed Jul 25, 2007 5:22 am

### RE: Energy Maneuverability Equation

Ps = [T-D]V
W

P sub S =Thrust - Drag / Weight * Velocity

Comes to mind as i have seen it written out before by a Proffesor i know.

Personaly it is all Squirrel food to me as that would soon drive me NUTS trying to make heads or tails out of it.

Blackbird
Topic Author
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### RE: Energy Maneuverability Equation

What's "Psub"?

Andrea Kent

Blackprojects
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### RE: Energy Maneuverability Equation

http://www.d-n-i.net/fcs/boyd_thesis.htm

kellmark
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Joined: Thu Dec 21, 2000 12:05 pm

### RE: Energy Maneuverability Equation

What I would suggest is that you try to obtain a copy of the book.

"BOYD, The Fighter Pilot Who Changed the Art of War".
By Robert Coram
Back Bay Books

It has an entire chapter devoted to the energy-maneuverability theory. Note that it is not about the math itself, but the theory behind it. But it goes into the processes of how Boyd came up with it.

Boyd is considered by many to be the greatest air tactics theorist to have ever lived. And he applied this to fighter design, specifically the F15 but especially the F16. Also he expanded into all forms of military strategy, and is considered by many to be the pre-eminent military strategist since Sun Tzu, in 400 BC. The US Marine Corps, as noted above at the link, took him to heart and changed their strategies/and tactics due to his influence.

I have now just read that book by Coram for the third time, and each time I get something new out of it.

One example that Boyd figured out was one reason why the F-86 was able to do so well against the MIG-15 in the Korean War. The MIG flew higher, could turn tighter and had heavier armament. The F-86 should have been inferior. But it had hydraulic flight controls, while the MIG did not. It meant that an F-86 could be much quicker in reversing maneuvers, and was not limited by manual forces that could be applied by the pilot.

He was a huge advocate of a smaller, lighter, highly maneuverable fighter. Without him, we would not have the F-16.

Blackbird
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### RE: Energy Maneuverability Equation

Ironically, his theory helped spawn the F-15, but then he became an opponent of it...

Andrea Kent

kellmark
Posts: 550
Joined: Thu Dec 21, 2000 12:05 pm

### RE: Energy Maneuverability Equation

 Quoting Blackbird (Reply 8):Ironically, his theory helped spawn the F-15, but then he became an opponent of it... Andrea Kent

Yes, he was an advocate of the F-15 as he felt it should have been designed, but what happened was that the Air Force proceeded to "gold plate" it with what he considered was much too much extra weight, and a subsequent drop in performance. He had the saying of for every extra pound of "BS" you put on it, it meant that you had to add 20 pounds to carry it, for no good reason. He considered the F-15 as it was supposed to be designed as a good aircraft, but what was actually produced was NOT what he wanted at all. He considered it far too heavy. This then ultimately gave him the motivation to get the Air Force to acquire a smaller lighter fighter, which the Air Force did not want. They wanted the F-15. They fought the F-16 design, saying it was a short ranged aircraft that had far less capability than the F15, as they did not want to take funding from the F-15. When it was shown that the F16 not only could out-turn the F15, but also had greater range due to its greater fuel fraction, produced at far less cost, he beat them and they had to accept the F-16. It turned out that he was right.

Another interesting thing that he did prior to all of this was to analyze the existing US fighter aircraft versus the existing Soviet aircraft, and found that in most cases, the US aircraft fell short on energy and maneuverability. They were fast but couldn't accelerate or turn as well. He was particularly critical of the swing wing F111 and the B1 Bomber, which never met their original specifications. It was said of the F4, that a brick could go Mach 2 if you put enough power on it. Later, in Vietnam, the F4 had a difficult time dealing with the much more maneuverable MIGs. He was right.

He made a lot of enemies in the Air Force, with his frank analysis, but his numbers were right and he did his homework. And he knew airplanes inside out and what they could or could not do.

ferrypilot
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### RE: Energy Maneuverability Equation

 Quoting Rwessel (Reply 1):Consider an aircraft weighing 100,000lbs, in a level 3G turn, with an L/D of 10:1 (in that particular set of flight conditions). To avoid losing speed, the engines need to be producing 30,000lbs of thrust.

An aircraft weighing 100,000lbs would be a pretty big plane to be hauling around with a 70degree bank angle and which is what you would have if pulling a level 3G turn.

rwessel
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### RE: Energy Maneuverability Equation

 Quoting Ferrypilot (Reply 10):An aircraft weighing 100,000lbs would be a pretty big plane to be hauling around with a 70degree bank angle and which is what you would have if pulling a level 3G turn.

An F-111 would be in the ballpark, but it was just a round number for sake of illustration... But even so, something like a 737 is physically capable of a 3G turn, even though it's not often flown that way.

Blackprojects
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### RE: Energy Maneuverability Equation

A BONE(B1b) does a lot of HI G turns and Rolls a lot so large heavy machines if Designd rite can do every thing a smaller machine can do just with 5 or 6 times the War load and 4 or 5 times the range.

A BONE is rearly just a very large F-111 or a Strike Eagle on Steroids!

Blackbird
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### RE: Energy Maneuverability Equation

How many G's can the B-1A / B-1B pull?

Blackbird

ferrypilot
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### RE: Energy Maneuverability Equation

 Quoting Rwessel (Reply 11):But even so, something like a 737 is physically capable of a 3G turn, even though it's not often flown that way.

I haven't flown the 737. ...However I have seen the max. g limit for it advertised as being 2.5 And in which case it would be quite adventurous to attempt to fly even a 60 degree banked turn requiring only a 2 g pull in the type.
...And I suggest to you that were an average pilot to attempt a 3 g level turn (corresponding to 70degrees bank < ) in the 737 there would be a very high risk of an accident occurring. ...As an accidental over bank of only 10 degrees during any part of that turn would suddenly require a 6 g pull to stop the nose dropping and to maintain height. And which I would have to suspect would most likely cause catastrophic structural failure of the airframe.

rwessel
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### RE: Energy Maneuverability Equation

 Quoting Ferrypilot (Reply 14):However I have seen the max. g limit for it advertised as being 2.5 And in which case it would be quite adventurous to attempt to fly even a 60 degree banked turn requiring only a 2 g pull in the type. ...And I suggest to you that were an average pilot to attempt a 3 g level turn (corresponding to 70degrees bank < ) in the 737 there would be a very high risk of an accident occurring. ...As an accidental over bank of only 10 degrees during any part of that turn would suddenly require a 6 g pull to stop the nose dropping and to maintain height. And which I would have to suspect would most likely cause catastrophic structural failure of the airframe.

Oh, I agree. My "but it isn't often flown that way" was a bit too flippant - a 737 would never actually be flown that way in anything other than flight test or if the pilot suddenly saw a whole lot of granite in the windscreen. My point was that a 3G turn is not inherently far-fetched for an aircraft of that size.

Blackbird
Topic Author
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Joined: Wed Oct 06, 1999 10:48 am

### RE: Energy Maneuverability Equation

Ferrypilot,

Rwessel's statement is correct. A plane that size could physically pull such a maneuver off, therefore it would not be far-fetched to say a plane that size could pull such a maneuver off.

Of course such a maneuver would only be done in an emergency...

ferrypilot
Posts: 623
Joined: Mon Sep 11, 2006 1:19 pm

### RE: Energy Maneuverability Equation

 Quoting Blackbird (Reply 16):A plane that size could physically pull such a maneuver off, therefore it would not be far-fetched to say a plane that size could pull such a maneuver off.

Well I believe it is "far fetched" to imagine that an intelligent pilot would ever think of trying to fly a level 3g turn in a 737. ...I would be very surprised if any Boeing test pilot has tried that! ...My personal view is that you need an airframe that is advertised by the manufacturer as good for a minimum of 6g in order to plan on having a sufficient safety margin in a 3g / 70degree banked level turn.

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