Post by bbroughtPost by EunometicYou could also factor in a simple compressability correction factor
also.
No, to account for compressibility here you need to look at the
influence that shock formation would have on CD over the entire
aircraft. As mentioned, at Mach 0.73 we are in the region where local
shocks will start forming all over the place, especially with an
aircraft with this type of shape. A simple first order compressibility
correction such as Prandtl-Glauert cannot be used anymore. Regardless,
compressibility will increase the drag coefficient for the Do-217P, so
it will make the 488 mph even less plausible.
I have a graph, created by John Stack of the NACA when he first started
pushing for a research aircraft that eventually became the Bell X-1.
His calculations for a small research aircraft of NACA 0018 at the root
and NACA 0009 at the tip verified in the VDT suggest that
compressability requires an increase from 1100hp to 1550hp at 480mph to
account for transonic effect. The Bell X-1 conceptual roots go back to
a piston engined aircraft in 1933 using an 2300hp Rolls Royce engine.
(the R engine used on the Schneider Trophy Series). The wing sounds
thick but note it is symetrical and of zero camber.
Prandle-Glauert equation is
Cl = Cl0/(SQRT(1-M^2)) and is considered good till Mach 0.7.
Incidently Hermann Glauert was British and derived the equation despite
his German sounding name, association with Prandle and the equation.
Post by bbroughtPost by EunometicThis is not entirely inconceivable.
I completely agree with the part that you now have a supercharger
helping to maintain power much better than on the earlier engines, and
I have also noted this several times. Yet, what we are talking about
here is a huge increase in power - you are asking for power that goes
far beyond what engine refinement alone can achieve,
The DB603 was actually capable of this increase in power and
demonstrated this though I'm not claiming it was used on the Do 217P.
The DB603 was actually a huge V12 of about 42L. Early versions
achieved its power of around 1800hp on B4 fuel. This is German for
fuel that is rated at 87 Octane Lean and 81 Octane Rich using the
Performance Number method. In other words the engine would have run
worse on rich mixture which is why the Daimler Benz engines tended to
use water methanol injection when overboosting and the British engines
used rich mixtures when over boosting since British aromatic fuel was
100/125 or 100/130 lean/rich At this time German C3 fuel of 92 lean
and 110 rich was also available but its use was reastructed to fighters
eg DB601E of the Me 109F and BMW801 of the Fw 190 since the BMW engine
didn't like water methanol (cylinders cracked) so C3 injection was used
instead. Bombers used B4 and even the Me 109G had to use B4 untill
later versions of the 109 started using C3 from mid 1944 onwards.
Around the begining of 1943 British analysis of the fuel tanks of
captured German aircraft started picking up that C3 fuel increased in
rating from about 87/110 to 96/125. This coincided with the use of an
additional hydroforming process which was used to synthesise armomatic
fuel out of the fuel that was obtained from hydrogenation of coal that
usually gave B4 directly. Also at this time two alkylation plants
opened to produce iso-octane like alkylates. Prior to this the Germans
had synthesised iso-octane from syngas via a precursor that involved
iso-butane and unfortunatly iso-butane was in gread demand for
production of synthetic rubber.
The DB603N (two stage super charger) using this fuel the one prototype
engine achieved a sustainable 2700hp which I think is twice as much as
a standard DB603 was achieving at 5600m. Standard way of increasing
performance in WW2 was to increase RPM through better metallurgy and
balancing, improve aspiration (eg valves) and increased boost pressures
through better cooler spark plugs, higher octane fuel, better engine
cooling, superidor fluid dynmaics or the addition to charge precooling
or intercooling.
So it is within the capability of the basic engine especially hand
built ones.
and as explained
Post by bbroughtthe comparison did not even include the additional drag due to
compressibility. Then of course there is the fact that propeller
efficiency starts dropping off very quickly at these high mach numbers.
With the aircraft going at Mach 0.73, the propeller tips are way past
the drag divergent mach number. A more realistic requirement to get to
that speed is probably at least a doubling in shaft horsepower, and
even then I have my doubts.
Post by EunometicAnother thing to consider is that these engines were probably producing
at least 440llbs of jet thrust and probably much more in the thinner
atmosphere since the main engines were opperating at full pressure and
acted as jet engines in consideration of the pressure they were being
fed. (440lbs is the the thrust of a supercharged single stage 36 L
Jumo 213).
Since we are working with a comparison (i.e. incremental values), you
need to look at the increase in jet thrust (I assume you are refering
to the "thrust augmentation" you are getting from the exhausts) from
the engines in the P model over that in the M-1 model. Do you really
think that increment would have been significant, especially in the
light of the type of claimed speed increment we are talking about here?
I do, since 440lbs of jet thrust equates to 200kg or 2000N which at a
speed of 200m/s(440mph) from Power = force x velocity = 400kW.
Considering propellor inefficiencies this equates to 500kW at the
shaft.
With the Do 217P engine opperating at sea level conditions at the inlet
but experiencining very little back pressure at its 'reaction nozzles'
the jet thrust would be even higher.
Post by bbroughtPost by EunometicAlso at higher speeds the dynamic pressure causes a ram air
effect that adds to the power of the engines of around 10% or more.
Oh come on - the ram effect adds pressure to the inlet of the
supercharger and may allow you to get to a slightly higher altitude
before power starts dropping off. But you said yourself the engine is
probably already producing close to its maximum power at this altitude
with that third engine running the supercharger, so you would gain
virtually nothing from the ram effect. If the supercharger cannot quite
cope with the low density at this altitude, then the ram effect may
help a little to recover a bit of that lost power, but it certainly is
not going to add another 10%.
The following is a graph of the DB601N engine of the Me 109F-4. The
powers for four different dynamic pressures when opperating at 2500rpm
and 1.3 atmopheres maximum boost are shown. Dynamic pressure is given
in metric cgs rather than metric SI. The term 'staudrukhoehe' means
stagnation pressure or dynamic pressure in english. As you can see
above the full pressure altitude at which engine power falls of rapidly
the increase in shaft horsepower is actually more like 20% compared to
the zero speed rating.
http://www.beim-zeugmeister.de/zeugmeister/index.php?id=30&L=1
Horse power ratings that don't include altitude, supercharger
gearing/settings, impellor diameter and dynamic pressure are almost
pointless.
Post by bbroughtPost by EunometicSo because of its higher opperating altitude the Do 217P experience
less than 63% as much air density and due to its central supercharging
engine had around 33% more power. That commutes to about two and so
the cube root of 2 is 1.25. So I come up with a speed of about 340mph
x 1.25 = 425mph.
I think we would both agree that 33% more power would be impressive,
right? Especially if you look at the rated power of the engines, where
the engines in the P-model were only rated at 6% more power than that
of the M-1 model. Even assuming the power on the M-1 already dropped at
5700m while the engines on the P model are still going full blast at
9600m (which would in itself be very impressive), then 33% still seems
extremely optimistic. But lets say you are correct: Go and have a look
at how much more power is needed to get to 488 mph...
Answered above. The basic 1750/1800hp engine could produce around
2200hp with MW50 injection and potentially 2700hp with the use of C3
fuel. The basic engine block was capable of it.
The various tyrpes of emergency boost powers for German engines can
confuse the issue. I'm not suggesting that the Do 217P engine was fed
on MW50 but that it was fed by pressurised air that had been cooled in
a heat exchanger and that it could have been producing at least 1750hp
at the shaft, maybe more, but that it also would have had impressive
jet thrust.
Post by bbroughtPost by EunometicOfcourse I don't factor in Jet thrust which speeds
the aircraft up, mach effects which slow it a little and the increased
drag of the installation of the central engine.
"Jet thrust", and in this case an increment in jet thrust, is normally
considered a second order effect, while Mach effects (on the airframe
and even more so on the propeller) would become very significant by the
time you get to Mach 0.73.
Jet thrust was a substantial contributer to WW2 fighter aircraft speed
and I think would have provided around 1/3rd the equivalent shaft horse
power second order maybe but still to substantial to be ignored. 200kg
thrust is a lot when you consider that the 1000kg thurst WW2 jet s were
only pushing out 380kg thrust or so at 10,000m. One reason Rolls Royce
never invested much effort into turbo charging the Merlin was that they
didn't want to give up that 300lbs of jet thrust.
As you know, to get a 10% increase in speed requires approximtely a
cubed increase in power whereas it requires only a squared increase in
thrust.
Post by bbroughtEven if we are extremely optimistic and assume the increment in Jet
thrust effect cancels out the compressibility effects on the airframe
and propeller as well as the extra drag due to the installation of the
extra engine, then we are back to requiring 1.75 times as much power as
what the engines on the M-1 model could deliver at 5700m.
Post by EunometicThe Do 335 if equiped with two DB603L could do around 494mph.
And it is an entirely different aircraft.
Indeed.
Post by bbroughtPost by EunometicThe 360mph top speed of the Do 217P in Greens book also doesn't make
sense.
It fits in much better with the type of increments you typically expect
from small increases in engine power. However, if test data showed it
reached around 400 mph I would not be able to argue, especially since I
don't have data of the airframe and propeller characteristics or a
detailed power curve of the engine installation. However, an increment
to 488 mph is ridiculous in every way. Remember the two main
improvements over the earlier model were only better supercharging of
the engine and a 6% increase in rated power. Also see my second post to
Rob on the Do-317 example.
I think there must be a much greater than 6% increase in power since
the Do 217P's engines would not decline in power at all till around
10,000m whereas the Do 217M would have lost about 25% of its power at
5600m and would have very good jet thrust.
The 317 was a completely new airframe.
Post by bbroughtThe additional considerations mentioned in this discussion: thrust
effects from the exhausts, ram pressure, etc - these are generally
second order effects. They will explain the difference between
predicting 400 mph and measuring 390 or 410. They cannot possibly
explain the claimed maximum speed of 488mph.
Possibly someone plugged in the 2700hp rating of the DB603N engine in
and came up with this hypothetical figure.
The aircraft had very low aspect ratio wings AFAIKT and must have been
flying fast, perhaps near coffin corner that tiny space between mach
tuck and stall.