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>
> > Found a table of air density vs
Altitude
> >
> > Sea level Density = .00237 Slug/Ft^3
>
> Density at 20,000 = 0.001267 Slug/Ft^3 or a 47% decrease
>
>
> > So taking formula for air mass W = p*V*A with p 47% less
than at sea
> level
> > means you would get 47% less air mass
flow (with the same cubic
> feet/minute
> > of air volume flow)
at 20,000 ft compared to what you would get at sea
> level
> >
for the same volume flow.
> >
> > While cooler temps would
help, it would not compensate for a 45% less air
> > mass flow.
>
>
> > Ed
>
> But Jim does have a point.
>
Indicated Air Speed should be an indication of mass air right?
> So if it
cools enough at X mph IAS, it will work at any altitude at X mph
>
IAS?
> And this should mean that the cooler air would give an advantage as
the mass
> air is cooler.
>
> P.S.
> I, as many I am
sure, deeply appreciate your work in our behalf. If we may
> ever
assist you please let us know.
>
Thanks, Eric! how much money can you spare?
{:>)
I don't really know the answer, doesn't seem
unreasonable, but I think we can check that theory fairly easily.
Lets consider that point. Will IAS provide
an indication of air mass flow if the IAS is the same at two different
altitudes?
The same indicated air speed at any altitude
implies that the dynamic pressure (as that is what the pitot tube measures) is
the same. Again looking at our two equations we have
Pd = 1/2*p*V^2
(dynamic pressure) and W = p*V*A (for mass
flow)
Were p is density and V velocity and A area of our
duct (1ft^2)
The density at sea level is 0.00237 Slug/ft^3
whereas the density at 20000 ft is 0.001267 slug/ft^3 according to the chart I
have.
So if we have the same indicated airspeed at both
altitudes then that means the dynamic pressure is the same at both
altitudes. Dynamic pressure at sea level for 120 mph TAS (has to be true
airspeed for V as that is the speed at which we are moving through the air
mass) = .00237*(176 ft/sec)^2 =.00237*30976 = 73.41312 lbf/ft^2 = 73.4/144
= 0.51 psi dynamic pressure.
So 0.51psi gives us an indicated airspeed of
X IAS (would have to know, temperature, pressure altitute, instrument and
installation errors to really get IAS from this) for 120MPH TAS at sea
level.
and at sea level the Mass flow = 0.00237 *(176
ft/sec)*(1 ft^3) = 0.41712 Slug/Sec
So lets now go to 20,000 altitude.
Now while we don't know what X IAS was a sea level,
but we know we want it to be the same so that means the same dynamic pressure
has to be present in the pitot tube.
So Pd = 0.51 psi =73.4 lbf/ft^2 has to be the same
at 20,000 as it was at sea level to give us the same IAS. So
working backwards and recalling that the density is now 0.001267
slug/ft^3
Pd = 1/2*p*V^2 and solving for V^2 = 2*Pd/p and V =
Squareroot(2*Pd/p)
V (TAS) = Sqrt(2*Pd/p) = sqrt(2*73.4
lbf/ft^2/.001267 slug/ft^3) = sqrt(115864) =340 ft/sec = 232 mph
TAS.
So to get the same indicated airspeed at sea level
given by a true air speed of 120mph we would have to be traveling at 232 MPH TAS
at 20,000 ft.
So looking at out mass flow again at this true
airspeed (232mph) and air density(.001267)
W = .001267 slug/ft^3*(340 ft/sec)(1 ft^2) = 0.4307
slug/sec of mass flow
So comparing our sea level mass flow of 0.417
slug/sec with that at 20,000 of 0.4307 slug/sec
there is only an approx 3% difference (could be I
lost it rounding numbers, but in any case not signficantly
different)
So, unless I've screwed up the math badly,
it does indeed appears that indicated airspeed provides a fairly
good indication of mass flow at any reasonable altitude provided we are not so
fast as to encounter compressibility.
Ed Anderson
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