Thursday, February 19, 2015

The F-35 and the Infamous Transonic Acceleration ‘Spec’ Change:

Part 1: The Basics


About two years ago, F-35 critics were agog over the news that the F-35 was reducing its “Sustained G” and “Transonic Acceleration” Key Performance Parameters. As (the once-but-no-longer-promising-and-now -‘Punk’) ‘Journalist’ Dave Majumdar reported on
Turn performance for the US Air Force's F-35A was reduced from 5.3 sustained g's to 4.6 sustained g's. The F-35B had its sustained g's cut from five to 4.5 g's, while the US Navy variant had its turn performance truncated from 5.1 to five sustained g's. Acceleration times from Mach 0.8 to Mach 1.2 were extended by eight seconds, 16 seconds and 43 seconds for the A, B and C-models respectively…
Soon thereafter, I posted a short series where in the first part it was highlighted that the only truth one could conclusively draw from the Sustained G Spec change was that the F-35s would have slightly reduced sustained turn bank angles than planned. Anything else, including the relevance/significance of the change, would be speculation without additional knowledge.
We then explored what such a bank angle reduction MIGHT mean by performing parametric ‘what if’ exercises based upon certain assumptions. What we discovered was, is that the most important unknown appears to be aircraft total loaded weight and that the “baseline standard used [in developing the F-35 Spec] for the comparison was a clean Lockheed F-16 Block 50/52 with two wingtip Raytheon AIM-120 AMRAAMs”
In other words, the Sustained G spec was based upon an F-16 in a lightly loaded, and operationally-limited and therefore very non-typical ‘lightweight’ configuration. When an F-16A was loaded in a manner similar to the F-35’s ‘stealth’ weapons load, we found the F-35 may very well be significantly better than the F-16 in the ‘sustained turn’ category: It all depends on how heavily loaded each aircraft is relative to the other. 
For fun, we also showed that for the ‘spec’ F-35A to ‘turn like an F-4’ the F-4: 
1) had to be a late-model F-4E ‘slat bird’, 
2) had to be given every benefit of the doubt wherever there was any performance ambiguity, AND
3) it had to be loaded so lightly that it could only have a little over 8 minutes of fuel on board to achieve its maximum Sustained G turn performance. 

I also note here, once again, that ‘Sustained Turn’ is not now seen as important of a maneuverability parameter in the post-‘All Aspect’ missile era as it was before the all-aspect attack guided missile: Sustained Turn was more important when it was essential to get right on your enemy’s tail for a ‘kill’ while keeping him off yours.

Flash Forward: Today

I had left the transonic acceleration spec changes alone at the time it was ‘all the news’ because when I finished the ‘Sustained G’ posts, all the F-35 haters, anti-defense weak sisters, faint-of-heart, and the Joe Public mouth-breathers had pretty much moved on to complaining about something else. Also by the time I finished the Sustained G discussion, I didn’t really have the free time to quickly distill an explanation about transonic acceleration—or at least do so such that most people could understand the phenomenon if they put a little effort into understanding. After all, you can’t really simplify transonic acceleration with the same ease that you can with ‘sustained G’ because the former is about dynamic ‘change’ while the latter is about representing different states of equilibrium: nice and easy ‘steady state’ conditions.
A while ago though, I was reading a comment thread ‘someplace’ where there was ‘someone’ mixing claims about acceleration performance with top speed performance for the F-35C and complaining about the F-35 having to ‘dive’ to get to its top speed. I’m pretty sure he was referring to a comment made by a test pilot at PAX River (Naval Air Station Patuxent River)--also a while back--who talked about having to “accelerate, turn, unload, and accelerate” repeatedly within PAX’s range space to get the F-35C up to its top sustained speed of M1.6 using a ‘modified Rutowski’ procedure. I believe the commenter was incorrectly translating the ‘unload’ into a need to dive, versus the need to preserve speed during turns, just to make going through the exercise worth the effort within the limited range airspace allotted. This poor person’s mental flailing-about on something he clearly did not understand (alternatively, I suppose he could have been disingenuously misleading others--whatever) got me thinking again as to how we could best give some perspective as to what the announced changes to the transonic acceleration performance of the different F-35 variants might actually ‘mean’ without having someone pulling a synapse and then mentally limp right past the ‘Eureka!’ moment. Having thought about the subject for a while now, I now don’t think it’s too ‘hard’ of a write-up to produce – It’s just a tedious one.

Terminology Housekeeping

Because the media and others tend to use a shorthand to describe Key Performance Parameters (KPPs) as ‘specs’ or ‘Specifications’, we shall reluctantly do the same. KPPs are selected based upon their relevance to top level program requirements such as survivability, lethality, supportability, etc. The KPPs are the basis, as former F-35 PM Tom Burbage noted in 2012, “from which lower level detailed engineering specification are derived and Lockheed's job is to meet as many of those specifications as possible within the laws of physics”. In other words, KPPs are a vehicle used for deriving detailed engineering requirements from top-level operational requirements. They are initially established before the first design iteration comes out and it is not uncommon for them to be adjusted as more information about operational requirements and/or understandings of technical feasibility are refined. Though we will treat KPPs as requirements for the sake of simplicity, we need to understand that they are not immovable goals (or thresholds) that must be individually or collectively met, but instead are guideposts that show the way toward defining and then meeting engineering requirements that will support overall top-level program requirements. I’ve touched on this subject before, and this link still leads to the DoD Manual for the Operation of the Joint Capabilities Integration and Development System (JCIDS) which, with the references listed within the document, describe how requirements are determined and used, including the role of KPPs in the requirements process and the required steps/approvals to change KPPs.

Drag, Thrust and Acceleration

If you know all this already, go ahead and skip the discussion about aerodynamics. If you know his stuff and read this part anyway, you will see there will be a lot I’m leaving out or perhaps oversimplifying. But I do so on purpose. Once again we’re conveying enough information to get an idea across, and not enough to go design an aircraft. These are just the ‘basics’, on the ‘basic concepts’ needed to understand what we’re going to discuss.

Drag: Subsonic and Beyond!
The most important things to remember about ‘drag’ for this discussion are that not only does drag increase due to friction the faster an object moves through the air, but that the ‘nature’ of drag changes as the object moves through the air at ever increasing speed. The airstream over the object begins transitioning from a ‘compressible flow’ to an ‘incompressible flow’. This occurs even before the object reaches Mach 1, as it enters the ‘transonic speed region’, with some surface areas of the object going ‘Mach’ (Critical Speed) before other areas on the object (aircraft). The transition from subsonic to the supersonic region is typically described as .8 Mach to Mach 1.2. [NoteAbove Mach 1.2 is considered ‘supersonic’ until much higher Mach Speeds where the nature of the flow changes again and is then viewed as ‘Hypersonic’ with the object moving through a ‘Plasma’ flow beginning at around Mach 5.]

This change in the interaction between the aircraft and airflow results in a change to the relative contributions of various contributors to total aircraft drag:
Figure 1: Drag Contributors, Subsonic vs. Supersonic

Remember, not only do the relative contributions of the drag components change going from subsonic to supersonic, but the resultant drag for nearly all the ‘contributors’ increase as well. For example, here is a reconstruction of a typical straight wing drag profile, expressed in terms of drag coefficient (Cd): a dimensionless value used in calculating total drag (force). 

Figure 2; 'Straight Wing' Drag Coefficient increases through transonic region

From Figure 2, it is obvious that the wave drag contributors, particularly the contribution due to the effects of the wing wave drag, are the overwhelmingly dominant factors. I’m going to risk oversimplifying wave drag somewhat here and just note that wave drag is composed of two contributors: Wave drag due to volume (cross-sectional area for some fixed length), 

and wave drag due to lift . One of the earliest advances in overcoming wave drag was the recognition that there were two contributors, which allowed designers to methodically attack the wave drag problem. (Though the occasional spark of genius didn’t hurt)
The graphic above is scaled to reflect all values as a percentage of the maximum value. From this example we see that at Mach 1, the drag coefficient is but 75% of the maximum value reached around Mach 1.1, and that by Mach 1.6 the total Cd is less than 50% of the peak value. If we wished to calculate the total drag
force at any given speed, we could plug in the Cd value into the ‘Drag Equation’:

Figure 3: Drag Equation
The only mysterious-to-some element in this equation should be the Cross-Sectional Area. This is the cross-sectional ‘slice’ of aircraft area presented to the air stream, and is perpendicular to the airflow passing over the aircraft. As the equation indicates, given the drag coefficient and cross-sectional area of any aircraft, drag increases as airspeed increases and when air density increases (density altitude decreases). Keep this equation in mind as we go forward: we will be relying on and referring to it from this point forward.
While we do not know what the Drag Coefficient is for any of the F-35 variants at any of speed, we may have a general idea of what the ‘shape’ of the probable curve for each looks like. Here is a reconstruction of a typical swept wing aircraft drag profile, also expressed in terms of drag coefficient:

Figure 4: Swept Wing 'Drag Rise' Curve
Note the effect of using the swept wing configuration. It delays the rapid onset of drag rise and also pushes the peak drag coefficient to higher Mach numbers. Remember also that this graph is scaled against peak drag coefficient at around Mach 1.55, with horizontal gridlines spaced at ‘25% of peak’ increments.

Figure 5. F-35 'Straight Wing', Extracted from a photo at 
The F-35 wing is a straight wing with swept leading edges. I suspect the F-35’s drag curve may be shaped something like a hybrid of the sample straight and swept wing curves shown, with a bias towards the straight wing drag rise curve shape. The acknowledgement that the F-35 can go some distance above Mach 1.2 without afterburner (to be shown in ‘What we know or think we know’, Ref #2 in Part 2 coming up) is a good indicator of the F-35A's drop in drag coefficient after Mach 1.1 as shown in the straight-wing graph vs a peak at Mach 1.55 as shown in the swept wing example.

Why Straight Wing?

In case someone is asking the question, a simple NASA graphic drives home the point that a [swept] wing is ‘the way to go’ if a primary design concern is to reduce drag coefficient below about Mach 1.8. But there are other concerns, when it comes to fighter aircraft (such as 'maneuverability' and 'g-loading') that a straight wing provides certain advantages--such that a 'compromise' is often sought by sweeping the leading edges on an otherwise straight wing.

Figure 6: Straight vs Swept Wing Decision 

Thrust and Acceleration

To accelerate at any speed, the thrust must be greater than the drag opposing the thrust. Jet engine thrust also decreases as the aircraft speed increases, because the difference between the aircraft velocity and the velocity of the engine exhaust becomes smaller as the aircraft accelerates. This isn’t a complete explanation, but it is the conceptual ‘bottom line’ and I don’t want to get wrapped around variability of air mass and internal engine drag among other things. For a more detailed discussion on the topic, NASA’s K-12 site has a pretty good overview (some high school math and physics employed).

In closing Part 1...

The most important point to remember going forward is the obvious one: At a given altitude, when airspeed is lower, the thrust is higher and drag is lower. Therefore, acceleration is greater. 

Figure 7. (Updated/Corrected 21 Mar 15)

As the aircraft moves faster through the airstream, the thrust/drag ratio decreases (Figure 7). Therefore the rate of acceleration will becomes less and less as the aircraft approaches the end of an acceleration run through the transonic region. If we can reduce drag and/or increase thrust between the beginning and the end of an acceleration run, then the rate at which acceleration (rate of increasing speed over time) will be lower (still accelerating, just doing so at an ever-slowing rate) as the jet passes through the transonic region. (Paragraph corrected/revised 21 Mar 15)

In Part 2, we will have a go at a top-level analysis of F-35 transonic performance.


SMSgt Mac said...

Note. I'm at work and have corrected an egregious copy-paste error that I compounded by then committing another error last night. Corrections from my phone do not allow me to use the strikeout feature to preserve the original error, but if I left it until I got home tonight, dollars to donuts SOMBODY would have counts coup before I could correct it:-)

Unknown said...

Drag coefficient, and all other aerodynamic coefficients, need a reference area to make the coefficient dimensionless. In addition moment coefficients also need a reference length. Your use of cross section area is technically OK, but not done in practice. Nominal wing area is used as reference area, and mean aerodynamic chord is used as reference length for all aero coefficients, for basic airplane, for various external stores, control surface hinge moments, stability coefficients, etc.