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Elite 1K Joined: Aug 19, 2004 Posts: 1092

Nobody's even agreed to solve my homework problem? That's so lame!

bf-fly wrote:

First off, I'm not confused in the slightest. Secondly, if you had read what he wrote he used an aircraft for his example that was FAA certificated as a "normal" catagory aircraft. Which as you know (actually it seems not) is limited to 3.8 G's. (plus of course a 150% tolerance)

Ummm... do you think an aircraft certified by the FAA as a "normal" category aircraft can pull 3.8g (or even 1.5*3.8g) at the airspeed that will actually give it the minimum turning radius? This airspeed would be the level turn stall speed, Vsturn. The chances of any airplane pulling that one off is slim to none. Once again you fail to realize the difference between a limit and an aerodynamic ability. An aircraft that is limited by some FAA restriction to 3.8g probably won't attain its minimum turning radius by flying at an airspeed just great enough to sustain 3.8g at whatever the bank angle. It might attain its minimum turning radius by flying at a speed just great enough to sustain a 1.8g level turn.

As for these speeds that your precious manual gives you, they're probably not the actual speeds for which absolute minimum turn radius can be achieved. They are probably safe turning speeds (given aircraft weight, altitude, configuration, etc) set by either the aircraft manufacturer or FAA regulations. If the speeds you're referring to from the manual are the actual speeds which give minimum turn radius, maximum turn rate, or whatever, then they're calculated exactly the way I outlined based on the aircraft's CLmax value determined during flight testing. You don't actually believe that minimum turn radius is determined directly during flight testing, do you? That's not how it works. When you flight test an aircraft, the pilot performs certain pre-determined maneuvers designed to give engineers back on the ground the necessary raw data from which they can determine things like CL vs. AoA all the way up to the aircraft's CLmax. Once they know what CLmax is, they can determine numerically what Rmin will be. This will be a true Rmin value and not one based on FAA regulations placed on bank angle, minimum airspeed, or what have you.

When it comes to fighters, however, maximum performance figures like minimum turning radius are based solely on what the aircraft is physically capable of. Perhaps you need to start thinking in terms of aircraft in general and not some specific aircraft for which you've read the manual and associated FAA rules and regulations governing its safe operation. I hope you realize how ridiculous you sound when you say something like, "The manual tells you the speeds." Talk about someone who isn't aware of the basic principles of flight. So you're saying that to determine the speed at which an aircraft attains its minimum radius turn, you simply look at the manual? Well dude... what if I was the engineer who had to calculate the minimum turning radius of an F-16 or F-22 based on flight test data for inclusion IN THE MANUAL ITSELF??!!! Would I have some manual handed down to me by God himself that told me what speeds and load factors to use in calculating the aircraft's minimum turn radius for ANY conceivable altitude, aircraft gross weight, etc? And once again... this kind of arbitrary information isn't determined directly through flight testing. If they did, you wouldn't have sea level turn performance charts for an F-16. Or wait... maybe the F-16 test pilot took his test bird out to Death Valley and max performed it all day long at exactly sea level. Righto! Brilliant!

Do the homework I've assigned you and maybe you'll learn something.

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Elite 1K Joined: Aug 19, 2004 Posts: 1092

Tinito_16 wrote:

ok, it's like 3:30 am where I'm at and I gotta get some shuteye, but I'll close with this: basically, bf-fly seems to be right on one thing, and Raptor_One seems to be right in another. Right now (I havent finished the book it's quite long) I think fly's right (mostly) about the g's/bank angle thing, and Raptor's right (mostly) when he says bank angle does not necessarily give you the Rmin. Given the F-22's good wing loading and excellent thrust, I don't think the pilot's gonna think twice about lighting the burners and banking about 90 degrees and just turning the nose as fast as possible to get whatever threatens him or her on the Raptor's sights. Unless the guy is 100 feet off the ground.

Tinito,

This whole debate is over Rmin and nothing else. bf-fly suggested that an aircraft's minimum turning radius is determined by its bank angle (and some other nonsensical relationships he added along the way). That's THE debate. There is no argument over the relationship n = 1/cos(Φ). I hope you understand that. I NEVER said that this was not a valid relationship... just that it can't tell you what an aircraft's Rmin is. I told you in words and with equations exactly why this is. You are in no position to be telling me who is right and who is wrong either. How many textbooks do you think I have on aerodynamics (which really isn't the subject we're debating) and aircraft performance/flight mechanics (which is the subject we're debating)??? You can read that textbook you just got till you're blue in the face and you still won't be in any position to tell me what's what and who's right about this or that.

Not that I consider myself an expert, but I've probably forgotten more about aircraft performance than you've learned to date. If you cannot solve the problem I gave you in a few days time, you probably don't have the necessary math skills and computational analysis knowhow to be involved in this debate to begin with. You could calculate Rmin by hand, but it would probably take you an entire day to come up with a reasonable approximation. If you understand how to do the problem by hand using some graph paper and a calculator to evaluate functions at various points, just plot a few values of nmax vs. V. Using those points you plotted, construct a graph of R vs. V. Remember that R is a function of both nmax and V, so make sure you use the proper [nmax,V] values when plotting R vs. V. Once you've (correctly) plotted R vs. V, you will clearly see that one of these R values is smaller than the rest. That's your minimum turn radius based on the few points you chose to analyze. Now imagine doing the same thing but with thousands of discrete velocity values, which would give an equal number of discrete nmax values, which together in turn would give you an equal number of R values. Despite having thousands of discrete R values, there should be a single minimum value for R if you've done everything correctly. Oh... and the value of V which corresponds to the minimum value of R is the aircraft's approximate stall speed in a level turn. The nmax which corresponds to the minimum R value is the nmax you can now, FINALLY, use to calculate the bank angle Φ = arccos(1/nmax).

Again, you couldn't have known what nmax value corresponded to the aircraft's minimum turn radius ahead of time, so bank angle obviously doesn't tell you anything about Rmin. It's the other way around. The information you use to determine Rmin (some nmax value at some specific velocity) can also be used to determine what your bank angle will be while performing a minimum radius turn at a given altitude and weight.

Active Member Joined: Aug 28, 2006 Posts: 191

Quote:

The information you use to determine Rmin (some nmax value at some specific velocity) can also be used to determine what your bank angle will be while performing a minimum radius turn at a given altitude and weight.

Really, do ya think? Wow, I couln't have said it better myself. If you haven't done this final step, then you haven't completely answered the problem. You have only assigned a nebulous value to the bank angle. When you have done this, you'll find the minumum speed and maximum bank angle to attain the minimum radius of turn.

Elite 1K Joined: Aug 19, 2004 Posts: 1092

bf-fly wrote:

Quote:

The information you use to determine Rmin (some nmax value at some specific velocity) can also be used to determine what your bank angle will be while performing a minimum radius turn at a given altitude and weight.

Really, do ya think? Wow, I couln't have said it better myself. If you haven't done this final step, then you haven't completely answered the problem. You have only assigned a nebulous value to the bank angle. When you have done this, you'll find the minumum speed and maximum bank angle to attain the minimum radius of turn.

Son... you're still making a fool out of yourself. Do the homework I've assigned you, otherwise you're out of gas.

Active Member Joined: Aug 28, 2006 Posts: 191

I think you know what you can do with your assignment.

The man who poses as the teacher yet says stuff like this:

Quote:

You can't start drawing direct relationships between bank angle and stall speed simply because there's an approximate trigonometrical relationship relating load factor and bank angle in a level turn.

From NASA

"The value of the load factor is UNIQUELY DEFINED by the aircraft angle of bank. For example, 2-g and 5-g turns require bank angles of 60 and 78.5 respectively."

http://www.hq.nasa.gov/pao/History/SP-468/ch11-6.htm

FAA Advisory Circular 61-67C

"The aircrafts stall speed increases in proportion to the square root of the load factor"

Quote:

bf-fly suggested that an aircraft's minimum turning radius is determined by its bank angle (and some other nonsensical relationships he added along the way).

AHH, no. Never said bank alone, now you are changing what I have said; The highest possible load factor at the lowest possible velocity.

Nonsensical relationship? You mean the ones NASA, numerous other sources I've posted including Embry Riddle, and the FAA concur with?

Here is my very first post:

"There is a vertical component of every turn, hense why a 90 degree bank it's impossible to maintain level flight, no vertical lift. Since pitch authority plays a role in that vertical component, I suspect that for the Raptor to exceed the turn radius of say a F-16 in a purely aerodynamic constant speed turn, two thing must occurr, excess thrust to maintain that speed with increasing G's, and secondly, a greater AOA limit so it's higher angle of attack abiliity allows for an increase in lift to offset the G's. Lastly (but certainly not all inclusive) it's TVC pitch authority assist aerodynamic control, but my also overwhelm normal aerodynamic forces."

Here is what NASA days:

"In steady, turning flight the lift developed by the wing must balance not only the weight of the aircraft but the centrifugal force generated by the turn. (The term "balance" is used here in a vector sense; that is, the lift vector must equal the sum of the weight and centrifugal force vectors.) The load factor is defined as the ratio of the lift in the turn to the weight of the aircraft and is usually expressed in g units, where g is the acceleration due to gravity. Thus, a 2-g turn is one in which the wing must develop a lift force twice the weight of the aircraft. The value of the load factor is uniquely defined by the aircraft angle of bank. For example, 2-g and 5-g turns require bank angles of 60 and 78.5 respectively. Finally, for a given bank angle and thus load factor, the turning radius varies as the square of the speed; for example, doubling the speed of the aircraft increases the turning radius by a factor of 4. It would then appear that two different aircraft flying at the same speed would have the same turning radius; however, this conclusion is not necessarily correct. The maximum load factor and associated turning radius may be limited by wing stalling. For a given speed and altitude, stalling occurs as a function of the wing maximum lift coefficient and the wing loading in straight and level flight. Clearly then, the turning capability of different aircraft types may vary widely"

" Two other important aircraft physical parameters may also limit turning performance. First, at a given speed and altitude, the aircraft drag increases rapidly with lift coefficient; as a consequence, the available thrust may not be sufficient to balance the drag at some load factors that the wing can sustain. In this case the aircraft loses altitude in the turn, an undesirable situation in combat. As for maximum lift coefficient, the drag rise with increasing lift depends upon the wing design and Mach number, as well as upon the added drag required to trim the aircraft at high lift coefficients. Finally, the turning performance may be limited by the control power available in the horizontal tail for trimming the aircraft at the high maneuvering lift coefficients."

Quote:

I've probably forgotten more about aircraft performance than you've learned to date

You've clearly forgotten more than you think.

"You can't start drawing direct relationships between bank angle and stall speed"

Ahh, yes teacher, the FAA says "The aircrafts stall speed increases in proportion to the square root of the load factor" NASA says "for a given bank angle and thus load factor"

The teacher, R1 says "there's an approximate trigonometrical relationship relating load factor and bank angle in a level turn"

NASA says "The value of the load factor is UNIQUELY DEFINED by the aircraft angle of bank"

These are very basic errors Raptor1. You hail yourself as being correct yet you make monumental errors on the basics. Yes you are better than me at formulas. But your lack of knowledge of the basic tenents of aerodynamics has been blatently exposed. Your attempt to cover up that with a childish game of "do your assignment or you lose" is quite easily exposed for what it is, an attempted distraction from your very obvious errors. Lastly (and I mean lastly) you have never provided a single source to back up your claims while I have provided at least 8.

Your formula for Rmin is not the correct formula for the absolute min radius of turn, only the radius of turn for the value assigned to "n".

Elite 1K Joined: Aug 19, 2004 Posts: 1092

Forget about it. My homework assignment wasn't a very good one anyway. You get minimum instantaneous turn radius at your aircraft's corner velocity which you can calculate exactly. The method I gave is sort of what you'd have to do to determine minimum SUSTAINED turn radius, but you'd have to include thrust and drag in the calculation procedure. You can calculate sustained Rmin exactly if you use an idealized equation for an aircraft's drag polar. The method I gave is also what you'd have to do to calculate minimum turn radius (sustained and instantaneous) for an aircraft like the F-16 where maximum available load factor is a function of angle of attack. The F-16's minimum instantaneous turn radius does NOT generally occur at its maximum instantaneous turn rate.

Anyway, if you want to find Rmin instantaneous, you just calculate Rmin as:

Rmin = (Vs^2 * nmax) / { g * (nmax^2 - 1)^0.5 }

nmax is your structural load limit. Vs is your 1g (i.e. level flight) stall speed.

I'm not going to argue with you anymore though. Here's the equation for load factor, n based on bank angle:

n = 1 /cos(Φ)

Or if you prefer...

n = sec (Φ)

If you prefer to calculate your turn radius as...

R = (Vs^2 * sec(Φ) ) / { g * (sec(Φ)^2 - 1)^0.5 }

.... be my guest.

It's just a different way to represent load factor in a level turn. And yes, n=sec(Φ) is a trigonometric relationship valid for an aircraft in a level turn. And yes, it's somewhat approximate in the sense that a real aircraft might not have a bank angle in a 9g level turn that's exactly predicted by Φ = arccos(1/9).

I don't feel like wasting my time with you anymore. At least I'm secure enough to tell you I goofed on the little homework problem I gave out. You're obviously afraid to admit you might be wrong about some things. So afraid that you've worked as hard as possible to avoid seeming wrong. Fine, you're right. I was so foolish to challenge you. I really need to go back and hit the books, but I realize I won't ever become as knowledgeable as you because you're a pilot with 8000+ hours and countless certificates. I guess it's pointless. I'll defer to you on everything related to flight because you obviously showed me. Golly gosh darn it!

Wow, I go afk for a week and look what happens.
I have only skimmed the recent additions, and don't want to take the time to address each little point, but...

BF - In general, I think you could save yourself alot of grief on this board by simply admitting that as a pilot you 'see' the world from a different point of view and admitting that there are times when what you see view as a "cause" is actually an "effect" (and visa versa) when viewed from the god's-eye view of the engineer. The fact is that no matter how many hours you may have in the seat, you don't (and don't need to) understand everything that's going on 'under the hood' - in this particular case all of the detailed flight dynamics that you cannot directly affect or control. The simple fact is that pilots already have enough to remember and think about, especially in times of emergency. Information in flight manuals and other pilot-used documents are meticulously scrubbed to make them them as simple as possible, while still be 'accurate enough' to be useful.

Along these lines...

bf-fly wrote:

From NASA
"The value of the load factor is UNIQUELY DEFINED by the aircraft angle of bank. For example, 2-g and 5-g turns require bank angles of 60 and 78.5 respectively."

Nobody has ever said the "1/n" relationship is wrong, but in fact it is only completely accurate for a point mass. Any real-world aircraft must carry some sideslip and/or rudder in a bank. As such, there will be aerodynamic forces created in the directional axis which will change that relationship - and that change can be dramatic depending on the aircraft shape. The relationship is useful for a pilot as an approximation, but is fairly worthless to an engineer. For example, the guy designing the wing/root attachment structure is really only concerned about what load factor he has to design to. It makes no real difference whether that load is ultimately generated in a bank, or in a symetric manuever (like a pull-up, or loop). At least for fighter-type aircraft, you would never tell a test pilot to go fly a 60 degree bank turn. You would tell him to fly a 2-g turn. Sure, he would initially bank to about 60 degrees, but would adjust that as required to maintain altitude. He would be keying off of the load factor display, not bank angle.

bf-fly wrote:

FAA Advisory Circular 61-67C
"The aircrafts stall speed increases in proportion to the square root of the load factor"

Again, an approximation that is usually 'good enough' that gives pilots something they can easily remember. The assumption here, of course, is that Clmax doesn't change with airspeed or load factor. Again, depending on the aircraft design, it can change with both. Both the value of Clmax and the AOA at which it occurs can be a fairly strong function of speed (usually the relationship is with Mach), especially as Mach increases above about 0.6. Also, Clmax is affected by wing shape. So, the value can change as the wings bend (change shape) as load factor increases. For most G/A and commercial aircraft these effects are pretty small, as the airspeed and load factor envelopes are fairly limited. But if you are going to refer to a statement like this to support an argument, you cannot ignore it's limitations in the general sense.

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