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PostPosted: Fri Feb 04, 2011 4:24 am 
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FLYING THE SPITFIRE: Turning Performance 101

The agility of the Spitfire, its turning radius and rate is a subject of interest to many. The study of any aspect of aerodynamics and aeronautics is often voluminous and technically complex. While not in any manner intended to be an exhaustive or complete explanation, discussion or description of this subject, the following is an attempt to clarify and hopefully to, some degree, introduce it to those who may be interested and who may not have previously encountered or be familiar with this material.

Turning Performance - 101

Obtaining the best turning performance from the Spitfire or any aeroplane depends upon many factors, primarily: gross weight (wing loading), density altitude and true airspeed. Also, the power applied, the way the particular aeroplane is rigged, and not at all least, the skill of the pilot, all play a part in this as well. Under most combat circumstances, pilot skill being equal, the Spitfire can turn as-well-as and often better most of the best-known WWII era fighters, except the Hawker Hurricane and the Mitsubishi Zero-Sen.*

To obtain its maximum turning rate and smallest turn radius, the Bf-109 relies upon its automatic, aerodynamically-triggered wing slats to delay a stall at a high or near critical angle-of- attack (alpha), which slats have been known to not always perform as advertised. However, when they do, German pilots have reported that the 109’s turn rate is as good as or better than the Spitfire’s while perhaps not quite as good as the Hurricane’s. A comparison of the performance of these aeroplanes is a fascinating, but sometimes controversial topic (see performance charts and figures below). Please leave your guns at the door.

With regard to wing-loading (gross weight/total wing area), the area of the “clean” wing, i.e., without the extension of certain types of area-enhancing flaps, is a fixed value. The aeroplane’s gross weight is its empty weight + total load on board. The parameters of an aeroplane’s gross weight vary between its empty and its maximum permissible gross weight. Assuming the application of appropriate power and level flight, when near its heaviest gross weight and wing-loading**, an aeroplane’s turning radius will be relatively large, and its turning rate relatively slow since under such load it is necessarily already flying at a higher alpha in order to maintain level flight.

Critical alpha (stall), or greater (deep stall) will be rapidly attained in a hard, minimum radius, maximum rate turn under these conditions as the margin between level flight alpha and critical alpha is relatively small. The opposite is, of course, the case when flying at a lighter gross weight and wing-loading as the aeroplane is now flying at a relatively lower level-flight alpha and has a relatively greater margin before reaching critical alpha.

Density altitude, which is the local pressure altitude *** (atmospheric pressure expressed as height according to a standard scale), corrected for local temperature at that altitude, affects turning radius in direct proportion to its value. That is, the higher the density altitude (under certain conditions you can be at a very high density altitude indeed when actually even at or near sea level****), the greater the aeroplane’s turning radius and the slower its turning rate, and vice versa. This is because the wing “reads” and interacts with the air based upon the air’s pressure and temperature, notwithstanding the height above sea-level at which it may actually be.

The radius of turn and rate and the required angle of bank is proportional to the square of the aircraft’s true airspeed.***** Lower true airspeed = smaller turn radius and higher turn rate, and vice versa. At any given true airspeed (up to attaining critical alpha) a higher angle of bank will produce a smaller radius and a greater rate of turn. Also, when flying at a lower true airspeed, a shallower angle of bank is required for any given radius or rate of turn. You may have noticed that when flying more slowly, as when in the circuit above an airfield that is at or near sea level, for example, when on base leg at, say around 120 m.p.h. (airspeed at or near sea level is the same as the Equivalent Air Speed [EAS], see below), a relatively small angle of bank is required to make a turn to the runway’s heading; whereas, the same rate and radius of turn when flying at a higher true airspeed requires a steeper bank.

Except at very high true airspeeds, in order to make a steep turn while maintaining altitude, it will be necessary to increase power and/or pitch the nose above the normal level flight attitude.

“Bank and pull” is the mantra for turning hard; of course, there is a limit to how hard you may pull any aeroplane around in a turn. When turning, an aeroplane is actually partially “climbing” around the turn. Pulling too hard in a turn (applying too much “up” elevator) will produce an accelerated stall (airfoil brought to critical alpha) at any airspeed, just as pulling the control column back too hard in a climb, in a loop, or in a recovery from a stall will produce the same. As stated in the Spitfire Pilot’s Notes, the Spitfire’s elevators are very sensitive and do not become very heavy or stiff at airspeeds below 400 m.p.h. Even at that airspeed and above, the Spitfire’s elevators remain lighter than those of most other aircraft. This can lead an unwary Spitfire pilot into overstressing the airplane, or him/ herself. Historically and tragically that occurred on too many occasions.

Maximum turn rate is divided into two categories: instantaneous max. turn rate, i.e., a turn wherein energy is depleted; and sustainable max. turn rate, a turn wherein energy is sustained. Another factor to consider when discussing maximum turn rate is the maximum instantaneous and maximum sustained “g” permitted by the design of the airframe at the aeroplane’s gross weight at the time of the maneouver. Whether partial flaps are deployed will greatly affect both maximum turn radius and rate.

In combat, many WWII era fighter pilots deployed maneouvering flaps to increase turn rate and reduce turn radius; but in small amounts, for only short periods of time, and when in desperate situations, as the deployed flaps' drag penalty was enormous. In some combat circumstances, a useful tactic when being closely chased by an opponent was the sudden deployment of flaps. The concurrent, sudden increase in drag would sometimes cause a close-chasing opponent to overshoot and become an easy target. Of course, such flap deployment is almost never an option with the Spitfire, given its one-position flap setting (85º). This would clearly be too much flap to deploy in similar circumstances when in combat and would cause serious, possibly assymetrical damage to the flaps if they were so deployed above 140 m.p.h. The deployed Spitfire's flaps' extreme drag would, in any event, deplete too much Kinetic Energy whilst in a turning fight.

Energy management is perhaps the single most important factor in combat flying, particularly with regard to WWII era fighters engaging in turning fights. Remember, altitude= Potential Energy (PE), i.e., the available energy that has not yet been used; and airspeed=Kinetic Energy (KE), i.e., the energy due to the aircraft’s motion that is currently being used. These may be swapped, airspeed (KE) may be increased or maintained by using the force of gravity, i.e., by depleting altitude (PE); and altitude (PE) may be increased or maintained with the force generated by sufficient airspeed (KE) as it exists or is made available by the application of sufficient power. Total Energy Package (TEP)= PE+KE. All else being equal, and sometimes when things are not so equal, the aircraft possessing the greater TEP at any point in a fight will be in the better position to prevail at that point.

In a turning fight, the instantaneous maximum turn rate may be useful in an emergency, but it is dangerous to rely upon since it may not, by its definition, be sustained very long. If the wing is not unloaded, and if you either stall and/or run out of useful energy before your opponent does, you’re meat on the table unless you can apply such extra power as may be required; or, if you have the altitude, you can dive out of danger (see above). The sustainable maximum turn rate is, in most circumstances, a better and more effective choice. At this rate you can turn all day, as long as your engine is performing satisfactorily. Of course, in that instance, your aircraft’s sustainable maximum turn rate had better be greater than your opponent’s, or a different/additional strategy of action must be adopted, such as the use of high and/or low “yo-yos”, and the classic “hit, extend, hit again” tactic. However, in a pure turning fight, Corner Speed, also called “Peak Turn Rate” comes into play.

The Corner Speed is the minimum airspeed at which you may generate maximum “g” in a turn, and it is one of the most important factors in a turning fight. Flying the aircraft at its particular Corner Speed for the density altitude at which you are flying will insure that you are turning at the aircraft’s maximum turn rate and minimum turn radius. Attempting to turn at maximum “g” at an airspeed slower than the Corner Speed will quickly produce an accelerated stall. Avoiding an accelerated stall at this lower airspeed will cause the turn to be larger than the minimum turn radius and lower than the maximum turn rate. If turning at an airspeed faster than Corner Speed, the aircraft will reach its maximum structural ”g” , or you will, before having reached its best possible turn rate and minimum turn radius.

So, you can see that the Corner Speed is crucial to getting the best turning performance from an aeroplane. Turning at the Corner Speed of your aircraft is vital for success in a turning fight. What is the Corner Speed for various aircraft? Of course, that depends upon all of the factors mentioned above, gross weight (wing loading), density altitude and true airspeed, each of which will alter and affect the Corner Speed. Opinions about this subject vary widely; and while mathematical calculations and formulae exist, it is primarily through practical flight testing that an aircraft’s true Corner Speed may be discovered.

Other, more exotic factors may play an important part in turning performance in combat. For instance, referring to tractor, propeller driven aircraft, some have postulated that a shorter nose gives an aeroplane better turning performance. The idea is that because the longer nose puts the propeller farther away from the aircraft’s centers of gravity (horizontal and vertical), it tends, therefore, to impede instant turn performance. This is because the longer moment arm of the longer nose creates greater inertia which must be overcome in order to turn. It is considered that the longer nose also impedes sustained turn performance proportional to the power being applied because the propeller tends to pull the aircraft out of the turn.

Also, the amount of the wing’s dihedral is a factor in turn performance. Wings with more dihedral sometimes tend to decrease the bank (underbank) in a turn, and often tend to be less precisely controllable when sharply maneouvering as opposed to wings with no, or minimum dihedral. This is because of “Dihedral Effect” which, put simply, is the effect that yaw (rudder) has on the roll axis. The greater the dihedral of a wing, the greater the effect that yaw displacement will have on it. The Spitfire is designed to perform coordinated turns at moderate-to-high airspeeds without the need for rudder displacement. The Pilot’s Manual advises pilots not to place their feet on the rudder pedals at all at moderate-to-high airspeeds, or when flying with reference to instruments only (“blind” or “instrument” flying”).

However, in a swirling, desperate, adrenaline pumping, turning fight, the aeroplane is likely to get out of full lateral coordination with regard to yaw and roll from time to time. When this occurs, dihedral effect will influence roll performance and make precise turning and, accordingly, the aiming of weapons more difficult. Naturally, a stable and predicable gun platform is a most desirable characteristic for any fighting aircraft. The Hawker Hurricane was universally considered to be a more stable gun platform than was the Spitfire. The Hurricane’s dihedral angle is 3.5º, while the Spitfire’s dihedral angle is 6º; accordingly, the Hurricane’s wing is not as greatly affected by inadvertent yaw displacement as is the Spitfire’s wing. Wing thickness and planform also come into play regarding lateral stability, but the amount of dihedral (or wing-sweep, which produces the same result) is the major factor.

Here are some published performance numbers taken from actual flight tests (all airspeeds are indicated and are not true airspeeds) :

SPITFIRE Mk. i

Turn Performance
300mph - 1,000ft 5,000ft 10,000ft 15,000ft
One 360 - 12.2s 13.5s 14.7s -
Two 360s - 24.9s 28.2s 30.3s -

250mph
One 360 - 10.8s 12.8s 13.4s 14.1s
Two 360s - 24.4s 28.2s 29.9s 33.2s

Sustained
No Flaps - 14.8s 16.0s 17.8s 20.8s
Full Flaps - 15.1s 16.4s 18.1s 21.8s
Best Flap - none none none none
Speed/best - 125mph 125mph 125mph 120mph

Corner Speed and Radii (at 1,000ft)
Speed: 215mph
Turn Radius: 342ft

Minimum Sustained Turn Speed: 125mph
“ Turn Radius: 431ft

Corner Times 1,000ft 5,000ft 10,000ft 15,000ft
180 degrees - 5.0s 5.3s 6.0s 6.8s
360 degrees - 11.3s 11.8s 13.2s 15.2s

360º Roll Rate:
150mph: 6.9s
200mph: 5.1s
250mph: 5.7s
300mph: 7.1s
350mph: 10.4s
400mph: 14.6s

Bf-109E-4

Turn Performance
300mph - 1,000ft 5,000ft 10,000ft 15,000ft
One 360 - 12.9s 13.4s 15.4s -
Two 360s - 29.4s 31.2s 35.0s -

250mph
One 360 - 12.9s 13.7s 15.5s 16.7s
Two 360s - 31.0s 32.4s 36.5s 41.2s

Sustained
No Flaps - 18.0s 19.3s 21.2s 24.1s
Full Flaps - 19.0s 19.8s 21.7s 24.8s
Best Flap - none none none none
Speed/best - 120mph 120mph 120mph 115mph

Corner Speed and Radii (at 1,000ft)
Speed: 225mph
Radius: 367ft

Minimum Sustained Turn Speed: 120mph
“ Turn Radius: 503ft

Full Flaps Speed: 100mph
Full Flaps Radius: 442ft

Corner Times 1,000ft 5,000ft 10,000ft 15,000ft
180 degrees - 6.0s 6.4s 6.7s 7.1s
360 degrees - 13.8s 15.4s 15.8s 17.8s

360 º Roll Rate:
150mph: 4.8s
200mph: 4.3s
250mph: 4.2s
300mph: 5.5s
350mph: 7.2s
400mph: 11.9s

Hawker Hurricane Mk I

Turn Performance
300mph - 1,000ft 5,000ft 10,000ft 15,000ft
One 360 - 12.1s 12.4s 13.6s -
Two 360s - 24.2s 25.3s 30.0s -

250mph
One 360 - 10.2s 11.7s 12.9s 15.0s
Two 360s - 23.6s 26.2s 28.5s 33.2s

Sustained
No Flaps - 14.8s 16.4s 18.5s 22.1s
Full Flaps - 14.8s 16.6s 18.4s 22.2s
Best Flap - full full full full
Speed/best 105mph 105mph 100mph 100mph

Corner Speed and Radii (at 1,000ft)
Speed: 200mph
Radius: 291feet

Minimum Sustained Turn Speed: 125mph
“ Turn Radius: 436ft

Full Flaps Speed: 110mph
Full Flaps Radius: 384ft

Corner Times 1,000ft 5,000ft 10,000ft 15,000ft
180 degrees - 4.8s 5.3s 6.2s 6.4s
360 degrees - 10.8s 12.1s 13.3s 14.1s

360º Roll Rate:
150mph: 5.0s
200mph: 4.0s
250mph: 4.3s
300mph: 5.4s
350mph: 7.6s
400mph: 11.6s

Mitsubishi Zero-Sen A6M2 Reisen Model Type 21

Turn Performance
300mph - 1,000ft 5,000ft 10,000ft 15,000ft
One 360 - 11.2s 11.5s 12.5s -
Two 360s - 21.5s 23.2s 25.3s -

250mph
One 360 - 9.8s 10.4s 11.4s 12.5s
Two 360s - 21.6s 22.7s 25.7s 28.8s

Sustained
No Flaps - 13.2s 14.2s 16.7s 18.5s
Full Flaps - 13.5s 15.6s 17.3s 19.6s
Best Flap - none none none none
Speed/best - 100mph 95mph 95mph 95mph

Corner Speed and Radii (at 1,000ft):
Speed: 200mph
Radius: 291ft

Minimum Sustained Turn Speed: 110mph
“ Turn Radius: 339ft

Full Flaps Speed: 95mph
Full Flaps Radius: 299ft

Corner Times 1,000ft 5,000ft 10,000ft 15,000ft
180 degrees - 4.5s 4.7s 5.1s 5.8s
360 degrees - 9.9s 10.2s 11.7s 12.7s

360º Roll Rate:
150mph: 4.9s
200mph: 5.9s
250mph: 6.9s
300mph: 14.8s
350mph: 21.6s
400mph:

Please excuse the way the numbers lineup, this program is apparently not good for doing charts.


Footnotes:

*A number of IJAAF (Imperial Japanese Army Air Force) fighters could match or even surpass the vaunted Zero-Sen in terms of low-speed maneouverability, including turning performance. Some of these are: Nakajima Ki-43 “Hayabusa” (Oscar); Kawasaki Ki-61 “Hein” (Tony); Nakajima Ki-84 “Hayate” (Frank); and Kawasaki Ki-100 “Type 5” (no code name). While these impressive aeroplanes are not as well-known outside of aviation circles, they were all examples of some of the most maneouverable and best-turning aeroplanes ever built.

**The following is a “trick” question that I actually had on an, “Applied Aeronautics” final exam at school, some time in the last century:

Question - “When and under what circumstances can a powered aircraft be flown at its absolute maximum gross weight and/or absolute maximum wing-loading?”

Answer - “No powered aircraft can ever actually be flown at its absolute maximum gross weight, and accordingly, its absolute maximum wing-loading since some quantity of fuel and oil will have necessarily been depleted during starting and taking off, thus somewhat diminishing its gross weight and, accordingly, its wing-loading before actually taking flight. This does not, of course, apply to sailplanes.”

***To calculate pressure altitude (Pa):

Pa = 101325 (1 - 2.25577 10-5 h)5.25588

where: h = altitude above sea level (m)

(or, you may refer to a Pa table)

**** See: “Trapped on an Island - A Cautionary Tale About Density Altitude” - A2A Piper “Cub” POH - Flying the Cub, p.102

*****To calculate true airspeed at low to moderate airspeeds (less than Mach .7 - 70% of the local speed of sound), true airspeed can be calculated as a function of the equivalent airspeed and air density:

TAS= EAS √ρο/ρ

where: TAS is true airspeed
EAS is equivalent airspeed (airspeed at ISA= sea-level on a standard day (59ºF, 15º C, dry adiabatic lapse rate at 6.49 K (°C)/1,000 m (3.56 ° F or 1.98 K(°C)/1,000 Ft) from sea level to 11 km (36,090 ft.)

Note: EAS is the same as a sea-level reading on an airspeed indicator corrected for error.

ρ0 is the air density at standard sea level (1.225 kg/m3)

ρ is the density of the air in which the aircraft is flying


Last edited by Mitchell - A2A on Thu Feb 24, 2011 2:36 am, edited 3 times in total.

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PostPosted: Fri Feb 04, 2011 6:38 am 
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Brilliant post, very informative. Thanks very much for taking the time to write that Mitchell, much appreciated.

Regards
Matt

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PostPosted: Fri Feb 04, 2011 8:47 am 
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Great stuff Mitchell.

Thank you for sharing that. For those of you that don't know, Mitchell has more than one high end formal qualification in this field and significant practical experience.

Darryl

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PostPosted: Fri Feb 04, 2011 9:26 am 
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Excellent Mitchell;

My fingers hurt just thinking about this much typing :-))

Dudley Henriques


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PostPosted: Mon Feb 21, 2011 1:20 pm 
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Great post Mitchell! I second Dudley's comments on the amount of typing! :shock:

Quote:
Question - “When and under what circumstances can a powered aircraft be flown at its absolute maximum gross weight and/or absolute maximum wing-loading?”

Does a drop-launch from a mother-ship apply? Thinking X-35, X-1, etc...

Best regards,
Robin.

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PostPosted: Mon Feb 21, 2011 4:45 pm 
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I was also thinking any aircraft which can be aerial refueled. In fact, several aircraft have "absolute maximum" weights that have only been achieved through this (SR-71 being the most notable). In fact, there are several US aircraft which have a higher "max inflight weight" than their max takeoff weight for this reason. The F-15E is one of the first aircraft to have this as a documented feature as the Conformal Fuel Tanks, redesigned canopy, and several other improvements provide sufficient "lift recovery" (their shape fully offsets their drag or adds net lift to the aircraft) once airborne to lift weights that the landing gear cannot handle.

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PostPosted: Mon Feb 21, 2011 7:43 pm 
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VulcanB2 and CAPFlyer,

You both raise interesting, creative points and possible real-world exceptions to the “answer” to the posed exam question. However, neither an air-dropped or an in-flight refueled aeroplane would have been an acceptable correct answer.

It’s not that you are wrong; it’s my fault for not giving more information about the exam. As regarded virtually all exams in that and other similar courses (and on FAA exams), all questions specifically assumed, unless otherwise stated, an aircraft operating in a normal manner, i.e., taking off from the ground under its own power, using only the on-board fuel stated at time of takeoff, and landing at a typical airport.

As you might imagine, there were many questions on that exam that also involved performance parameters, engine operation, weather, navigation, endurance and range situations, as well as various approaches and landings. No answer that included a “sky-hook” or Parasite system (i.e., Curtiss XF9C-1,2 “Sparrowhawk”, Brodie Landing Systems, McDonnell XF-85 Goblin, or late-model Republic F-84 Thunderjet), or aircraft carrier-type catapulted takeoffs or wire- arrested landings, all of which we well-knew about, would have been accepted. Neither would any answer involving an aircraft that was refueled in flight have been permitted, since that would have rendered range and endurance and other questions moot or irrelevant; thus the “fuel on-board at takeoff” provision. However, a side-mention of any of these in the answer would likely have produced at least a chuckle from the instructor; and maybe would have garnered some extra credit, if not a beer or two at the canteen.

Mitchell


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PostPosted: Mon Feb 21, 2011 8:02 pm 
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Mitchell, of course that makes sense, but given those "assumptions for the purposes of testing", would not the glider "exception" be incongruous as for it to be an "exception" to the question, it would have to be an unpowered glider that required a tow or winch launch, thus not operating in the manner "assumed" for the other aircraft. :)

BTW, I've had these discussions with aviation professors and professionals in the past and it's always interesting how much discussion can be garnered out of something like looking at a test question and playing devil's advocate against each other and figuring out not only that the question is flawed in it's entire structure, but that there are so many "right" answers that you wonder how one ever really "tests" for knowledge with them. :)

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PostPosted: Tue Feb 22, 2011 1:44 am 
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CAPFlyer,

When I wrote the “answer” in the footnote, I added the bit about the sailplane; but I wasn’t thinking about the exam in detail and its pre-assumptions, etc. at that time.

Of course, you are correct; the pre-assumptions of the exam precluded a pure sailplane (but not a self-powered one) from consideration in the answer. I bet a number of students tried to answer it with affirmative examples instead of as it required. On the whole, I feel that it was a well-formed and effective exam question, effectively designed to test both the student's understanding of the subject and his or her ability to perform under pressure. It certainly left an impression on me after so many years. (BTW, as I recall, after a bit of brain twisting, I answered it correctly)

I'm sure that the point of that kind of “trick” question and many others of that ilk that were posed to us was to keep us on our toes, and to encourage us to think a bit outside the box; good pedagogical practice, I think, and very good training for prospective pilots.

Mitchell


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PostPosted: Sat Mar 26, 2011 6:23 am 
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Interesting and great post Mitchell.

I found that your calculation are very close with data which i got for Spitfire MK1 but also with German data for 109 E.

Look at these turn chart for SPitfire Mk1 sustained turn time at 12 000 ft:

Image


About 109 E-3 turn times:

" The pages deal with the official specification for the Bf 109E-3 model, and note the maximum speed of 500 km/h at Sea Level, and 570 km/h at 5000m, with +/- 5% tolerenace on top speed.
These figures are in close agreement with German, Swiss and French test results of Bf 109E-1 and E-3.

Of particular interest are the figures given in the German specifications as the smallest turning radius of the 109E.

These are, at Sea Level and at 6000 m, with and without deploying flaps to aid turning :

Without use of flaps :
at 0 m altitude - 170 m (557 feet), at 6000 m (19 685 feet) altitude - 320 m (1050 feet).

With use of flaps :
at 0 m altitude - 125 m (410 feet), at 6000 m (19 685 feet) altitude - 230 m (754 feet).

The report also gives figures for climb times and distances required take off and landing runs.


Similiar figures are given by a calculation by Messerschmitt AG on Bf 109E turn times and radius in an internal Messerschmitt report.

The calculation was based on a similiar set of data, but assumes the slightlly lower power output of the DB 601A-1 at 990 PS. Conditions in the calculation were 2540 kg weight, 990 PS output, an altitude of 0 m and no height loss. Under these conditions, the turning characteristics of the Bf 109E were as follows :

Turn time for 360 degrees: 18,92 seconds.
Turn radius for above turn: 203 m

Take note that the smallest turning radius and the best turning time do not occur at the same airspeed, which would

Further calculations were made for a diving turn of a descent rate of -50 m/sec, which would be equivalent translate to an overall power output

Turn time for 360 degrees in a -50m/sec diving turn : 11,5 seconds.
Turn radius for the -50m/sec diving turn above : 190 m"


http://www.kurfurst.org/Performance_tes ... turnradius




I wonder how do you calculate these ? What Clmax values did you used?

Also how you get roll rate times?

P.S.

Could you make similar calculation for 109 F-4, Spitfire Mk VB and Fw 190 A-5? ( i got some data if you need)


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PostPosted: Mon Mar 28, 2011 11:28 am 
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Kwiatec,

Thanks for the kind words.

The figures presented were all taken from practical flight tests. I don’t know about the 109F-4 or the Fw-190A-5. There are not too many of them around to fly from which to measure things; however, the Spit Mk Vb figures are more readily available and will surely be used to inform our girl's performance when we present her to you all.

Mitchell


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