A fundemental view on Weight and E state and its role in ACM

[humble]

OK....

1st and formost I greatly appreciated all the input here, now I'm trying to refine my understanding and relate the "math" to what I see as the practical application...especially in short duration "low speed" applications of mass related "E". As Mace stated early on the best way to engage an A-20 is to E fight it. When you get locked into an angles fight vs an A-20 that is not totally stripped of E it seems to be very adaptable if the pilot works his stability at high AoA...at least in my experience with it.

I can sort thru and find some more specific clips but I think the 2nd one I posted illustrates enough for discussion here. Again any/all (meaningful) comment/correction is appreciated.

At the end of the "zoom" I need to turn my attention to the Ki (I dont think my SA ever registered the 109). As the plane falls off I get lucky in that he's naturally in my initial view back since I'm falling off to the left. Initially my focus is on falling off and squaring up in a way that avoids getting shot, so I'm looking for space inside his arc...as soon as I get that angle off I'm looking to take the fight back up.

This is where I need a better grasp of both what the realities are and how I explain it. To me intuitively at the 16 second mark I'm golden. He's pulled for a shot that he cant hit and I'm going for a vertical scissor type thingie.

So at :09 on the clip i'm about topped out and in "rotate" at alt 3.0 speed 52, airframe is basically unloaded and falling of naturally with minimal inputs. At :16 he's taken his shot and we are engaged, film shows both planes at 2.5 with my speed at 145 and the Ki at 136. Now at :23 we're both showing 2.5 even though fight is going up with my speed at 125 and his at 150. At :29 as I roll back over to establish a position behind him at .2.9/85 and he is at 2.7 119...

So to me as an A-20 driver I went down, chopped throttle a bit at one point to make things "fit" angularly and popped back up while under modest G loading/control input while maintaining roughly equivalent E to my starting point while converting an angular gain of roughly 120 degrees and actually (IMO) bleeding a bit of E off the other guy. From my perspective a lot of this is due to the mass (and stability) of the a-20 in the low speed semi verticals. The flip side is that a lot of folks have commented over the years I can be a very "smooth" stick in this type of move.

So how much of this is the "zoom" (I think 80%) and how much is "smooth"?

[mechanic]

so...er.... where are all the threads you started to help newbies? 

[humble]

so...er.... where are all the threads you started to help newbies? 

Bat I could care less about what he does or doesn't do here. My "issue" is that he's basically an opportunist with minimal ACM skills. You want to fly around and pick people great, its your dime...but don't come in here and bash on stuff you've got no demonstrated ability with. I'm trying to explain something I've got some demonstrated ability with and put it in somewhat mathematical terms (no question incorrectly).

Now having sorted out a better understanding of the math, how do you break down the components. What I have gathered thanks to Mace, Badboy and dtango is that all the other factors cancel out the "zoom" very quickly. At the same time I can tell you from 1st hand experience that you can "cycle" the A-20 in the verts very efficiently if allowed. Mace and others I've run into do a very good job of making me go "the long way" as much as practical and no question the A-20 scrubs E badly in that situation. Were I can work a climbing cut back type of fight like linked the A-20 can gain both angles and E at the same time in relation to an opponent.

So...

Is this the mass, the low speed stability that allows more minimal control inputs, efficiency at those intermediate speeds compared to fighters or a combination + other factors I'm overlooking. The initial post refers to comments from others specific to sustained relatively low alt/low speed "dog fighting". I've found that if my SA holds up and i'm not forced to scrub massive E avoiding a B&Z/E attack from above I can "cycle" the A-20 for prolonged periods vs even multiple cons in a roughly co-e state. Normally either a higher inbound or a more cagey vet will loosely engage and draw the fight up via sustained climbing turn performance where I cant follow....but as long as guys are willing to furball the a-20 it just keeps chugging along.

What I'm gathering is that i have very efficient "short term" exchange within the initial flight parameters....meaning I can pop down and up within the alt band determined by initial height and some mid speed level unloaded dive that allows a very efficient recycling....but when i'm forced beyond that all the other variables offset and overwhelm that bit of "zoom" my mass generates... 

[dtango]

I’ve dusted off some old flight modeling spreadsheets to expound more on what Mace, Badboy, Bozon, and myself have been stating about zoom climb performance.

Specifically what we are seeing with the A-20’s energy retention in the vertical is primarily a function of it’s thrust, not it’s weight (mass).

Let’s analyze this through some basic modeling of a couple of aircraft. 

P-47 @ weight = 14,500 lbs
A-20 @ weight = 16,000 lbs
A-20 @ weight = 22,000 lbs

Unpowered Zoom Climb
First let’s examine the unpowered zoom climb.  The following is a graph showing a time-altitude history of our aircraft in an unpowered zoom climb where:

BHP~0 (thrust~0),
climb angle=63 degrees
g-load= 1g
initial airspeed = 400 mph,
initial altitude = 1000 ft.

 


The concept that many folks have in their mind is that mass (thus weight) effects energy retention.  We’re taught that the greater the mass, the more it takes to accelerate or decelerate it, thus the greater the mass the slower the energy bleed.  If we compare the two A-20’s, we see this at work where the heavier A-20 out zooms the lighter A-20.  So far we have no surprises.

However if we over generalize the concept of greater mass = slower energy bleed we start to run into problems.  We can see that even in an unpowered zoom climb that the P-47 (lighter by 8,000 lbs!) out zooms the heavier A-20.  What gives?  Since we have more analysis ahead, I’ll simply point out that this occurs because despite the greater weight (mass) of the A-20, the P-47 has a lower drag and drag/mass ratio compared to the A-20’s in our model.

The variance in drag-to-mass ratio should serve to remind us that we need to beware over generalization which leaves out other variables in the equation – in this case the impact of drag.

Accounting for ALL variables is important and we’ll continue to demonstrate that by now adding in thrust.

Powered Zoom Climbs
What happens when we add thrust to the equation?  The following is a graph showing a time-altitude history of our aircraft in a powered zoom climb where:

BHP= (P-47: 2600hp, A-20: 2 x 1600hp)
climb angle=63 degrees
g-load= 1g
initial airspeed = 400 mph,
initial altitude = 1000 ft.

 


Factoring in thrust, the P-47 continues to out zoom both A-20’s.  Comparing the A-20’s, the lighter A-20 now out zooms the heavier A-20.  Of course on the surface this graph doesn’t tell us anything particularly interesting.  After all thrust should make a difference to the zoom capabilities of our aircraft. 

However let’s take a look at a time-velocity history of our powered zoom climb.

 


Things start to get more interesting when we compare the change in airspeeds over the course of our powered zoom climb.  Comparing the A-20’s, the heavier A-20 initially bleeds airspeed just a hair slower than the lighter A-20.  At some point however the heavier A-20 bleeds airspeed faster and more pronounced than the lighter A-20. 

Even more interesting is that though the lighter A-20 bleeds airspeed faster than the P-47 for most of the zoom climb, there’s a cross-over point where the lighter A-20’s airspeed becomes greater than the P-47 as they near the peak of the powered-zoom climb.

Looking at the time-velocity graph we can obviously observe non-linear behavior which gives us a hint there are more complex things happening under the hood.  Let’s put our propeller-head hats on, give them a spin and dive a bit deeper shall we?

[dtango]

Anatomy of a Zoom Climb
What we are really interested in is analyzing the different variables in the powered zoom climb and how they impact zoom performance.  To do so we first should breakdown the basic equation of motion.  As Badboy points out a basic equation for forces in the axis of an airplane’s direction of flight is:

F = m*a = Thrust – Drag – Weight * sin (climb_angle)

If we solve for net acceleration of the aircraft we can re-arrange the equation to the following (similar to Badboy’s equation for acceleration):

a = Thrust/m – Drag/m – gravity * sin (climb_angle)

It’s the non-linear variation of this acceleration over time that results in the velocity curves in time-airspeed history of our powered zoom climb.  Four variables influence acceleration: thrust, drag, mass, and climb angle.

Since clearing up the impact of mass on zoom climbs is a focus here let’s spend some time discussing it.  As we can see in the equation the greater the mass we have, the lower the drag-to-mass ratio.  This means greater mass reduces the impact of energy bleed due to drag.  We can’t stop there however.  At the same time, greater mass also results in a lower thrust-to-mass ratio meaning that it also reduces the ability to gain energy through thrust.  We have to account for the impact of mass on all variables. 

Let’s take a look at thrust/mass and drag/mass [in other words acceleration (due-to-thrust) and deceleration (due-to-drag)] over the course of the zoom climb.

 


This is a graph of accel(thrust) [thrust/mass] and accel(drag) [drag/mass] over the zoom climb for our aircraft.  Drag/mass is plotted as a positive acceleration values for easier comparison with thrust/mass acceleration.  Comparing the A-20’s we can see that increased mass (heavier A-20) lowers drag deceleration vs. the lighter A-20, but it also lowers thrust acceleration as well compared to the lighter A-20. 

If we examine just the curves for a single airplane (either A-20) we make the following observations. 

First, drag deceleration is a greater factor at the start of the zoom climb but quickly diminishes.  This is phase of a zoom climb where greater mass helps energy retention.  But it doesn’t last long. 

Second, the cross-over point where thrust and drag acceleration are equal is less than 5 seconds into the zoom.  The significance of this convergence point is where the impact of greater mass starts to dwindle for energy retention.  Beyond this point greater mass becomes more and more of a detriment to energy retention.

Third, over the majority of the zoom climb thrust acceleration is the dominant factor in overall acceleration as evidenced by the time-history.  Greater mass is a detriment during this phase and thus the majority of our zoom climb.

These component acceleration graphs give us a glimpse to individual relative contribution of variables to zoom climb performance and some of the underlying complexities.  However what we want is to also better understand how these variables interact with each other IN COMBINATION between thrust, drag, mass, and climb angle and their combined effect on zoom climb performance.

As stated previously Specific Excess Power (P_S) is a measure of the rate of energy change of an aircraft.  It tells us the rate at which energy is gained or bled and defined as:

P_S = (T – D) * V / W = change_in_alt + change_in_velocity

This is a key relationship to understand.  Energy retention is a combination of these variables interacting with each other.

When P_S > 0 the aircraft is gaining energy.  When P_S < 0 the aircraft is bleeding energy.  As the P_S equation demonstrates it gives a combined interaction of thrust, drag, weight (mass), airspeed, and indirectly climb angle on the rate of energy change and thus a measure of the zoom climb performance of an aircraft and it’s ability to convert speed into altitude.

The following is a graph of the P_S of our aircraft in our powered zoom climbs.

 


Analyzing the graph we can make some observations.  First at the early phases of the zoom climb we see that the heavier A-20 bleeds energy less than the lighter A-20.  No doubt this reflects the contribution of greater mass.  However as seen that’s short-lived and soon the lighter A-20 retains energy better than heavier A-20.  This difference in energy retention dominates for the rest of the zoom climb between the A-20’s with the lighter A-20 retaining more energy.  This is reflective of the significant impact of thrust on a zoom climb but also the combined effect of how greater mass limits P_S of the heavier A-20 for most of the zoom climb.

A second interesting observation can be made.  As can be seen the P-47 has higher P_S value compared to the A-20’s until about 10 seconds into the zoom climb.  An interesting thing occurs.  The lighter A-20 actually begins to retain energy better than the P-47 throughout the remainder of the zoom climb.  As we noted in the component breakdown, this is not due to the greater mass of the A-20 but the impact of thrust on the majority of the powered zoom climb.  That being said the P-47 still has the highest average P_S of all three aircraft and therefore is able to reach a higher altitude at the peak though it reaches the peak a few seconds sooner than the lighter A-20.

The lighter A-20’s P_S margin in the later phases of a zoom climb I believe is the secret to it’s performance in the vertical.  In our comparison we see that though it doesn’t zoom as high as the P-47, it will stay in the zoom just a bit longer. 

This has a couple of potentials in air combat.  First, if the P-47 was behind the A-20 and trying to follow the A-20 up, the P-47 has to solve the problem of closure and possible overshoot because it will zoom higher than the A-20.  One obvious response is to chop throttle of the P-47.  But now we’ve seen that this could be a bad response because thrust is a big factor of determining zoom performance for most of a zoom climb. 

Second, if the A-20 is behind the P-47 instead and following the P-47 up, though the P-47 would peak higher it would peak and be on the way down while the A-20 would still be on the way up which presents all various positioning and eventual angles problems for the P-47.

So there we have it.  Analyzing the P_S of the aircraft in a zoom climb gives us insight into the A-20’s ability in a vertical fight.  It’s not greater mass that allows it to retain energy better, but rather it’s thrust.  I believe this is the secret to the success of the A-20 in the vertical.

Tango, XO
412th FS Braunco Mustangs

[moot]

Thank you.  I knew there was something fundamentally wrong with using off-power zooms as a metric for E retention and zoom ability.

[RTHolmes]

excellent stuff tango, clearly shows the slight advantage of extra mass in unpowered zoom, and that the extra mass is the greater factor for the first 8s of the A20's ~24s zoom-climb, untill the thrust/mass effect overwhelms it, as predicted


edit: the jug is a pretty hefty airframe though, it would be interesting to see how a much lighter fighter compares (as the thrust/mass effect will be more pronounced.) can the A20 use its mass to reel in any of our fighters in the initial phase of the zoom-climb?

[dtango]

excellent stuff tango, clearly shows the slight advantage of extra mass in unpowered zoom, and that the extra mass is the greater factor for the first 8s of the A20's ~24s zoom-climb, untill the thrust/mass effect overwhelms it, as predicted


edit: the jug is a pretty hefty airframe though, it would be interesting to see how a much lighter fighter compares (as the thrust/mass effect will be more pronounced.) can the A20 use its mass to reel in any of our fighters in the initial phase of the zoom-climb?

Sorry RTHolmes you're missing my point.  You want to bring it back to mass for some reason.  Mass only plays a small part to powered zoom climb performance and what advantage it plays early on is of little consequence.  You can see that in the velocity time history between the A-20's that there is little difference in airspeed in the early parts of the powered zoom climb.  You can't even see the separation distance advantage because it's only in mere feet, not even tens of feet.  This all gives way very quickly and dramatically with the plane with the greater (T-D)/W ratio retaining loads more energy because greater mass has a magnifying effect of reducing zoom climb performance since thrust grows very rapidly. 

More completely thrust and drag factor into the equation and it's thrust that provides most of the "energy" in a zoom climb not mass.  Zoom climb performance is determined by P_S of which thrust plays the dominant part in a powered zoom climb.  You can see it in the P_S comparisons.  The difference in weight between the P-47 and the lighter A-20 is ~2000 lbs while the difference between the Jug and the heavier A-20 is a whopping ~8000 lbs.  The P-47 easily out zooms the heavier A-20 by a significant margin.  I don't have key data plate points needed for modeling lighter aircraft with strong thrust/weight ratios like the N1K2-J, Spit 8, Spit 16, or Bf109-K4.  If I get that sorted out I'll model and demonstrate.

Tango, XO
412th FS Braunco Mustangs

[RTHolmes]

I understand your post, and we both agree that mass is the reason the heavier A20 zooms better for the first 1/3 of the zoom-climb, although the advantage as you say is slim, 1/3 of the zoom is significant. like I said, a slight advantage in the first 1/3 of the zoom, due to the extra mass, after which thrust becomes the more important factor.

[TonyJoey]

Kiss my grits you pompous little .....

 

[Mace2004]

Excellent post Dtango, nice work <S>.

If there's one take-away at all from this is to put to bed the myth that heavier weight helps zoom.

[dtango]

I understand your post, and we both agree that mass is the reason the heavier A20 zooms better for the first 1/3 of the zoom-climb, although the advantage as you say is slim, 1/3 of the zoom is significant. like I said, a slight advantage in the first 1/3 of the zoom, due to the extra mass, after which thrust becomes the more important factor.

Actually I quite disagree .  For our example mass gives an advantage 1/5 of the zoom climb.  The P_S convergence point between the A-20's is less than 5 seconds into the zoom climb.  This is the point where the impact of mass being a disadvantage is noticed.  After this point the (T-D)/W ratio favors the lighter A-20 and greater mass grows in greater detriment the more into the zoom climb we go.

Tango, XO
412th FS Braunco Mustangs

[RTHolmes]

indeed the P_S convergence is at 5s, but it takes some extra time to negate the previous effect of mass in terms of speed/alt. on the velocity-time graph the heavier A20 has the speed advantage up to about 8s when the lines intersect (about 1/3 of the zoom-climb). on the altitude-time graph the heavier A20 has the alt advantage up to about 14s (about 1/2 the zoom-climb). your posted theory is sound and I concur with the graphed results, so we must agree

[Karnak]

There will be differences of course, but look at the plane statistics. The range of power/mass, drag/mass values is not very big and as long as all the planes are underpowered, the differences are reduced even more. It is not like one will zoom twice as high as the other and disappear into the great blue yonder. We are talking about scale of 100ft or slightly more differences.

People expect larger differences that there really were.  I recall reading the US tests of the A6M as it compared to several US fighters and the rate at which our fighters pulled away in a dive or zoom climb was not nearly the "1-2 seconds of dive and I am out of gun range" a lot of people seem to think it was.

[dtango]

indeed the P_S convergence is at 5s, but it takes some extra time to negate the previous effect of mass in terms of speed/alt. on the velocity-time graph the heavier A20 has the speed advantage up to about 8s when the lines intersect (about 1/3 of the zoom-climb). on the altitude-time graph the heavier A20 has the alt advantage up to about 14s (about 1/2 the zoom-climb). your posted theory is sound and I concur with the graphed results, so we must agree

This is exactly what I mean about the dangers of over-generalization.  Looking at the velocity history you can't conclude the impact of mass.  The reason the velocity graphs cross at 1/3 is because the increasing thrust of both aircraft play a factor.   Thrust just doesn't kick all of a sudden even for the heavier A-20 but it's impact grows at some exponential rate.  What you're seeing with velocity history is also the interaction of the thrust of even the heavier A-20 that contributes.  The P_S curve uncovers what's going on and tells exactly when the effects of mass are negated.  The velocity curve doesn't.  Nor does the altitude-time history.

So we totally disagree .

Tango, XO
412th FS Braunco Mustangs