Throwing some light on rates of turn

[MiG-3U]

Originally Posted by Crumpp

It is not hard to do at all. We can use the first entry for flaps up turn performance at 12000 feet.

V = TAS/SMOE = EAS

Standard Means of Evaluation at 12,000 feet = 1.2011

Flaps up TAS at 12,000 feet = 160 mph TAS

160/1.2011 = 133 mph EAS

133 mph EAS * .869 = 115.6 KEAS

Oh check it out....They give you EAS on the report. Gee, wasn't that another 100 page discussion on these forums?

Anyway, once you have EAS you can easily convert the performance to any atmospheric condition you want.

I like working with BGS but the units do not matter. Just don't put the correction factors like "1091" and "11.26" if you are using metric and keep your units straight.

Our formula becomes:

Radius = (VKeas * SMOE)^2 / 11.26tan <theta>

<theta> = angle of bank which is a fixed relationship with load factor irregardless of altitude

If you use the above formula and knots, our radius calculates out to be 693 feet and the RAE measurement is 695 feet. Pretty good agreement.


Radius is not the primary turn characteristic in a fighter. It not so important how small the circle but how fast we can bring the nose around to put guns on target.

So lets check our rate of turn based on the document:

Flaps up = 160 TAS * .869 = 139 KTAS

1091(tan 68 ) / 139 KTAS = 19.42 degrees a second

360/19.42 = 18.56 seconds to complete a 360 degree turn

18.6 and 18.56 are a match....

Now let's see what it does at 20000 feet:

160 TAS at 12000 feet = 133 mph EAS


133 mph EAS * .869 = 115.6 KTAS

SMOE @ 20000 feet from our Standard Atmospheric Data = 1.3700

Radius = (VKeas * SMOE)^2 / 11.26tan <theta>

Radius = {115.6*1.3700}^2 / 11.26tan <68>

= 899.97 or just 900 feet @ 20,000 feet

Rate = 1091(tan 68 ) / (115.6KEAS*1.3700)

= 17.05 degrees a second

= 360/17.05 = 21 seconds to complete a 360 degree turn at 20,000 feet

All you calculate here is the turn times at constant KEAS and constant g load (2.68 g which corresponds angle of bank 68 deg) at two altitudes, 12k and 20k. Then you claim that an airplane which can do this kind of sustained turn at 12k, can do sustained turn at same g load at 20k at same given KEAS. Note that your calculation does not account the engine power and the power might be different at 12k than at 20k.

Now, think this for a minute instead insult the other members of the board.

Originally Posted by Crumpp

Another interesting fact about basic aerodynamics. Coefficient of lift is independent of altitude and corresponds to an specific angle of attack.

In otherwords, the angle of attack for best turn performance will be the same no matter what the altitude.

Amazing that some simple calculations reflect that basic fact. OHH the INSANITY OF IT ALL!!!

Mh. IIRC CL does depend on Mach number even at subsonic speeds and thus indirectly on altitude as for the same IAS the Mach number changes with altitude, the speed of sound being intimately linked to temperature.

[nakedsquirrel]

Originally Posted by ATAG_Colander

Math is good. Me likes math.

It's not fair. I see all of the math but I still can't shoot anybody down =(

I don't like math.

[Crumpp]

IIRC CL does depend on Mach number even at subsonic speeds

Yes it does but the RAE was using subsonic incompressible flow theory in that report.

In subsonic incompressible theory, Coefficient of Lift is independent of altitude and mach number.

A compressibility correction to velocity is used to account for it.

In the formulation, compressibility is factored in when converting from CAS to EAS.

How does the lift coefficient for maximum range vary with altitude? (No compressibility effects.)

A: The lift coefficient decreases with increasing altitude.
B: The lift coefficient is independent of altitude.
C: The lift coefficient increases with increasing altitude.
D: Only at low speeds the lift coefficient decreases with increasing altitude.

Answer: B

http://www.thedailyatpl.com/atpl/per/how-does-the-lift-coefficient-for-maximum-range-vary-with-altitude-no-compressibility-effects/

All you calculate here is the turn times at constant KEAS and constant g load (2.68 g which corresponds angle of bank 68 deg) at two altitudes, 12k and 20k. Then you claim that an airplane which can do this kind of sustained turn at 12k, can do sustained turn at same g load at 20k at same given KEAS. Note that your calculation does not account the engine power and the power might be different at 12k than at 20k.

That certainly depends on which merlin and which variant we are discussing. I don't know as only snippets of the report have been posted and would only be guessing.

If you read the thread, the question was how to convert that performance to other altitudes.

The answer to that is to use the EAS scale provided in the RAE chart and convert to what ever density altitude you wish.

[Al Schlageter]

Originally Posted by Crumpp

That certainly depends on which merlin and which variant we are discussing. I don't know as only snippets of the report have been posted and would only be guessing.

On the first page it says 'Merlin II Spitfire'.

[MiG-3U]

Originally Posted by Crumpp

That certainly depends on which merlin and which variant we are discussing. I don't know as only snippets of the report have been posted and would only be guessing.

If you read the thread, the question was how to convert that performance to other altitudes.

The answer to that is to use the EAS scale provided in the RAE chart and convert to what ever density altitude you wish.

So, what's the point of your calculation then? You did not quess any power value but claim a time, 21 sec for 360deg, for sustained turn at 20k which is unrealistic given that power is lower at 20k than at 12k (Merlin II).

The scale does not matter, EAS or TAS, it's just slightly different calculation.

[CaptainDoggles]

Originally Posted by Crumpp

If you read the thread, the question was how to convert that performance to other altitudes.

The answer to that is to use the EAS scale provided in the RAE chart and convert to what ever density altitude you wish.

While your work looks ok to me, I think the original question's intent was "can we convert this data to see what the a/c would be capable of at higher altitudes" which is not answered by the math you posted. Rather, we would need to check available power at the relevant altitude.

[Crumpp]

I wonder if its possible to convert the figures to different altitudes..?

Is the question asked and I answered.

http://forum.1cpublishing.eu/showpos...&postcount=166

My post was not a treatsie on specific aircraft performance.

It took a few seconds to say, "Yes you can use EAS to convert the performance to any altitude" with any airplane.

And did the correct mathmatical mechanics to show the process to change altitudes given a speed and angle of bank.

As for the other baloney posted, it will always reach CLmax at the lift line irregardless of altitude in the theory the RAE is using.

That should not be a surprise to a MSc Aerospace Engineering.

Any undergraduate who has taken a Basic Aerodynamics course understands that. It is a principle of subsonic incompressible flow theory.

[IvanK]

This document was written around the Spitfire MKIII (never went into production only prototype stage) powered by the Merlin XX. All the data tables and graphs refere to merlin XX equipped aircraft.

There is a single Reference to Merlin II spitfire on the first page.

[Crumpp]

The reason why the RAE provided the EAS scale is to quickly convert to different altitudes and conditions.

Crazy Huh??