snips..
Hi Paul,
I took your current formula and updated the spreadsheet. I've also
rearranged it and separated all of intermediate calculations.
I ran into a problem when I got to the induced drag
calculation. I get
a value of .0045. If I do an estimate based on your formula, I
get:
AspectRat = 3 / AvgCord
=3 / .34 is approximately 9
(My Avg Cord agrees with yours)
Now,
InducedDrag = (CsubL ^ 2 / ( 3.1416 * AspectRat)) / 2
= (.5 * .5 / (3 * 9)) / 2
= (.25 / 27) / 2 is approximately .005
Yet your program calculated 4.24, and I cannot see what I'm doing
differently. Once that is fixed, the total torque and HP will
agree.
Outside of that, this version should be easier to update and
modify.
Bob W.
--
http://www.bob-white.com
N93BD - Rotary Powered BD-4 (first engine start 1/7/06)
Custom Cables for your rotary installation -
http://www.roblinphoto.com/shop/
Thanks Bob.
I wrote that at home with out my Von Doenhoff Theory of Wing
Sections so I got it wrong. Here is the correct formula.
C sub D = C sub d + (C sub L)^2 / pi * (aspect ratio)
C sub d is the section drag coef. which we are summing up.
So you have to multiply (CsubL^2/(pi*AR)) times air density
times velocity^2 times blade area I think. I need to work
on this a bit more.
Aspect ratio is also span squared divided by wing area.
Which is easier to implement.
---------------------------------------------------
Hi Bob,
I added a couple of columns for coef. of lift and coef.
of drag as they vary with Mach number. This is
important as so many prop tips operate near Mach one.
I have not chosen the values yet. I hope it does not bust
the rest of the spread sheet. Here is a couple of scans on
the subject from Theory of Wing Sections.
I was kind of surprised about the temporary drastic rise in
in the lift coef. at a 2 degree and above angles of attacks
with mach number. I think we should start with the 4 degree
angle of attack curve. There is a huge rise in the coef.
of drag starting at only .7 Mach at 4 degrees angle of attack.
We will have to add a calculated column for Mach number.
As far as the induced drag torque is concerned probably using
the Coef. of lift and the overall aspect ratio
for the last area segment torque might work in the absence
of a full blown 3D CFD.
Paul Lamar ...No rotor no motor.
Dumb question:
Does aspect ratio really exist on a wing which has such vastly different
airspeed between the root and the tip (such as a prop)?
Regards,
Matt-
Good question Matt. Been pondering that. Aspect ratio mainly
affects the drag of the tip. Air tends to flow radially outward
from the bottom of the wing up and over the top of the tip.
In a prop this effect could be enhanced or limited
(take your pick) by the centrifugal effects on the
air molecules.
This causes a horrendous high energy tip vortex. Happens
at high angles of attack. I suspect a prop program
will never be very accurate until this flow is accounted
for. I also suspect the drag increment due to aspect ratio
effects is applied to the tip contributing a huge
negative torque and consequently huge consumer
of engine HP due to the longer lever arm. Large diameter props
seem to be more efficient which would support this theory
despite the tips operating at higher Mach numbers.
It could also happen at the hub end of the blade if you assume
the centrifugal effects are minimal. In this case
Paul Lipps's prop design scores as the spinner is used
as an end plate limiting the radial flow from bottom to top.
Any time you apply an end plate to a
wing intersection drag occurs. That is perhaps why Paul
uses a 45 degree tip sail on his wings with a
generous radius. For more info on this check Sig Hoerner's
book Fluid Dynamic Drag first published in 1965.
BTW as an interesting aside Klaus claims to have dated
Sig's daughter:) My claim to fame is Sig autographed
my copy in 1966 before he died :)
The day will come when 3D CFD will be available
at low cost. Perhaps 10 years. All turbofan engine
builders are using it now.
Paul Lamar ...No rotor no motor.
Aha.. What you're saying makes sense. Actually, now that you mention
it, on a conventional wing, aspect ratio might be a catch-all spec which
accounts for both root intersection and tip loss effects. The
longer/skinnier the wing, the more 'ideal' the wing behaves. Careful
handling of the root and tip can probably make the wing look like it has
more aspect ratio.
On a prop, the aspect ratio of the tip seems useful to consider. The
airspeed at the root is so low that it seems that a different type of
calculation might make more sense. Also, the aspect ratio of a prop is
so high that changing it a little in the calculation probably doesn't
have that much effect on the result.
Centrifugal/centripital forces likely are related to how thick the
boundary layer is, as that's the air that's going to ride along on the
propellor for any amount of time, and get moved on a curving path. So,
that says that there's going to be more outward going spanwise flow the
further back along the chord that you look. Near the trailing edge,
where the boundary layer is thickest, the spanwise flow due to
centrifugal force is probably high.
CFD. Yeah.
Regards,
Matt-
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