Throwing some light on rates of turn

[Holtzauge]

Originally Posted by Crumpp

We are not going to do another 100 pager because you lack formal education in aerodynamics.

EAS is the most common expression for velocity in all aircraft performance calculation. It is the preferred expression because it is so simple to use.

It is too easy to convert to TAS any performance derived with EAS and you don't have worry about density effects in the mechanics of the calculation. Just convert at the end.

It also a great approximation of Indicated Airspeed and very easy to convert to that with a PEC chart and a universal compressibility.






http://www.google.com/url?sa=t&rct=j...o9yenlVuG8g5Zw







If you are trying to quickly gauge relative performance you don't have to convert back to TAS. The specific numbers for rate and radius will change in proportion to density ratio which is a universal application.

The problem is that your turn time of 21 s at 20,000ft is physically impossible. No amount of posturing and posting irrelevant book quotes underlined in red will change that fact:

You have claimed R=900 ft turn radius and turn time T=21 s at 20,000 ft:

Since I'm a metrics guy I will convert R to SI units, i.e. 274.3 m

This gives a turn speed of 82.08 m/s (2*pi*R/T)

So from this we calculate the turn acceleration: a=v**2/R=24.56 m/s**2

So load factor is n= sqrt(a**2+g**2)/g=2.696

Let's calculate the Cl this would require:

n*m*g=0.5*ra*v**2*Cl*S

Spitfire data:

W=6000lb=2724 Kg
S=242 sqft=22.36 m**2
ra=0.65 (Approx at 6.1 Km alt)

Solving for Cl:

CL=(2.696*2724*9.81)/(0.5*0.65*82.08**2*22.36)=1.47

Now NACA claims Clmax for the Spitfire at 1.2 which is a bit low but according to RAE it is 1.36 tops. Your claim leads to a Cl of 1.47 which is clearly unrealistic and like you fails the sanity check.

BTW: I found a RAE report, R&M 2349, Notes on the turning performance of the Spitfire as affected by altitude and flaps.

On page 4 there is a figure 4 which gives the following results for the Spitfire at 20,000 ft: R=1045 ft and T=31.5 s

With my C++ simulations I get R=337 m (1106 ft) and T=31.65 s.

You claim 21 s turn time and 900 ft radius of turn. I get 31.65 s and 1106 ft while Morgan & Morris in R&M get 1045 ft and 31.5 s.

So on the one hand we have C++ simulation data and the data from the RAE report R&M 2349 which seems to tally and on the other hand we have your overbearing attitude and simplistic calculations leading to an off the chart Clmax. What could be the right number I wonder , 21 or 31 s?

Finally, I think the only thing we actually agree on is the other parties lack of formal aerodynamic training. We have been down this road before and as I've told you before I have an Mcs in aeronautical engineering from the Royal Institute of Technology in Stockholm from 1986 and more than 10 years in the business working in the defense industry for Ericsson and SAAB on the Viggen and Gripen fighter systems.

Tell me, What aeronautical companies have you worked with and the Msc in aeronautics from Embry-Riddle you claim to have, which year did you graduate and was that before or after your stint in US Special Forces?

[ATAG_Colander]

Math is good. Me likes math.

[ATAG_Snapper]

Originally Posted by ATAG_Colander

Math is good. Me likes math.

Me too. In fact, my favourite snakes are adders!

[Crumpp]

21 or 31 s?

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




115.6*1.3700 = 158.4 KTAS

Looks like 21s when we ask the US Navy or use any universal turn performance chart!!

Ha ha ha

[Crumpp]

we have C++ simulation data

The output is only as good as the input...

[Crumpp]

Yes Holtzauge, I am employed full time in aviation as a pilot.

Yes, I retired from the US Army before I went into aviation as a second career.

How about you? You do C+++++ simulations for a living?

[Crumpp]

Your claim leads to a Cl of 1.47 which is clearly unrealistic and like you fails the sanity check.

[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'.