Richard Bytheway wrote
> Sent: 04 May 2004 10:42
> To: FlightGear developers discussions
> Subject: RE: [Flightgear-devel] Spitfire Propeller vs. YASim
>
>
> > I had already shown by some pretty simple math that at 2850
> > rmp the tips of
> > a 1.65m radius propeller would be supersonic and therefore highly
> > improbable, but we now know that the data of hp, gear ratio,
> > rpm etc all tie
> > together.
> >
> > Thanks
> >
> > Vivian Meazza
> >
>
> I have a memory from years back of being told that the reason
> the Spitfire had such a distinctive sound was that the
> propellor tips _were_ supersonic. Maybe it was just heresay.
>
> Richard
>
I think it is possible that the propeller tips went supersonic in the
corners of the flight envelope of some of the later versions. However, the
math seems to show that in most circumstances they were not. It seems
unlikely that this could explain the distinctive sound when heard from the
ground.
Here are some calculations on propeller rpm.
The propeller the tip speed should be as high as possible with the only
limitation being that the tip should not get into the region of aerodynamic
compressibility. Typically a figure of Mach 0.85 is used as the magic number
that should not be exceeded. (This makes some allowance for the speed
increase as the air passes over the aerofoil curved surface and the increase
in air velocity caused by the propeller operation.)
If we take 8000 ft as the operating altitude then Mach 1 = 1085 ft/sec
(approx)
Assuming that the forward velocity of the aircraft is 300 mph = 440 ft/sec
Then the maximum rotational velocity may be calculated by Pythagoras:
Max Rotational Velocity = ((M *1085)^2 - (V)^2)^0.5
where M is the designed Mach Number (0.85) and V is the aircraft forward
velocity
= ((0.85*1085)^2 -(440)^2)^0.5 = 810.52
ft/sec
RPM at Max rotational velocity is given by:
RPM = Max rotational velocity*60/(PI * D)
Where D is the propeller diameter (ft)
= 810.52*60/(PI * 10.75) = 1439.98 rpm
At 3000 rpm the propeller rpm is 1431 rpm, but the Merlin only did this when
the throttle was through the gate, and the Boost Control Valve Cutout was
operated. This was allowed for 5 minutes.
We can calculate the Max Rotational Velocity @ 1431 rpm
Max rotational velocity (PI * D) = (RPM/60) * (PI * D)
= (1431/60) * (PI * 10.75)
= 805 ft/sec
We can also calculate the Mach Number (M) of the tip by rearranging and
substituting
M = ((805^2+440^2)^0.5)/1085
= 0.8459
I hope that all the maths are correct.
I think all this shows that under normal operating conditions, and observing
the normal operating limit of 2850 rpm, it is unlikely that the propeller
tips would exceed M1.
Regards
Vivian
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