Arggg!
Props!
Ok,
Bill – here is my stab at it. The following equation tells the tale –
well some of it.
(1)
|
where: |
|
T |
thrust |
[N] |
|
D |
propeller
diameter |
[m] |
|
v |
velocity of incoming
flow |
[m/s] |
|
|
additional velocity, acceleration by
propeller |
[m/s] |
|
|
density of
fluid |
[kg/m³] |
|
|
(air: = 1.225 kg/m³,
water: = 1000
kg/m³) |
|
Thrust
is about increasing the momentum of the air mass passing through the prop
disc. Static thrust occurs while sitting still - therefore
v
(the air velocity of
air in front of the prop disc) =
0. So the addition momentum imparted to the air mass by our spinning
prop is p*DV.
Since
the air mass p during our run up
is essentially constant ), that leaves two variables - the diameter of the
prop D and the amount the
spinning prop accelerates the air (Dv) to affect the
thrust (T)
generated.
The
following are extracts from some of the better article (more understandable)
material I have read about props and static thrust. As it concludes and
Tracy points
out Static Thrust does not really tell the whole
story.
For a typical, fixed pitch
propeller, the largest induced velocity occurs under static conditions, where the efficiency is small.
It decreases with increasing flight speed, until it reaches zero: no thrust is
generated.
For a given power P, it is always
desirable to use the largest possible propeller diameter D, which may be limited by mechanical
restrictions (landing gear height) or aerodynamic constraints (tip Mach
number). That's why most man or solar powered airplanes use large, slowly
turning props. These catch a large volume of air and accelerate it only
slightly to achieve the maximum efficiency.
As long as an aircraft does not
move, its propeller operates under static conditions. There is no air moving
towards the propeller due to the flight speed, the propeller creates its own
inflow instead. A propeller, with its chord and twist distribution designed
for the operating point under flight conditions, does not perform very well
under static conditions.
As opposed to a larger helicopter
rotor, the flow around the relatively small propeller is heavily distorted and
even may be partially separated. From the momentum theory of propellers we
learn, that the efficiency at lower speeds is strongly dependent on the power
loading (power per disk area), and this ratio for a propeller is much higher
than that for a helicopter rotor. We are able to achieve about 80-90% of the
thrust, as predicted by momentum theory for the design point, but we can reach
only 50% or less of the predicted ideal thrust under static
conditions.
So much for
theory. My personal experience when I went from the faster turning
68x72” prop to the slower turning (2.85 gear box) 76x88 prop – my take off
acceleration increased significantly indicating (in my opinion) more thrust
was being generated. With the 76x88 prop and my old 13B I would
generate 5800 rpm static (for what its worth), with it cut down to 74x88 I
picked up 200 rpm for a static of 6000 rpm. Plus I got another inch of
ground clearance – needed on my nose geared Rv-6a.
Interestingly enough
the larger slower turning prop not only did not hurt my top speed it actually
increase around 4 mph – perhaps due to the increased HP due to high rpm of the
lighter loaded engine?
Ok, Bill that’s my
take and what I could pull out of references. Don’t know if it really
tells us a whole lot – there are some good NACA studies on Prop – but the math
makes my head hurt.
Ed
From:
Rotary motors in aircraft
[mailto:flyrotary@lancaironline.net] On
Behalf Of Bill Bradburry
Sent: Wednesday, March 03, 2010 5:01
PM
To: Rotary motors in aircraft
Subject: [FlyRotary] Re: single
rotor
I would like to get some educational (for me)
discussions going on this.
A prop of 76 X 88 is pretty common in our usage.
Tracy, Ed, and I have a Performance Prop in this dimension. Dennis and
maybe others have a Catto prop in this dimension. We all seem to be
getting static rpm of about 52-5400 rpm (except for Dennis with his new DIE
manifold). Tracy and Ed had their prop cut down to 74 X 88 and are
getting increased static to around 6000 rpm. Higher rpm = higher HP for
the rotary. We should get higher thrust with a slightly smaller diameter
prop? This has something to do with the idea of sizing the prop to the
engine. I wonder what is the proper size? What is the proper
static rpm for best performance with the rotary? What did Tracy and Ed
lose in prop performance and what did they gain in total performance when they
cut the prop down?
It seems to me that a prop sized for climb would allow
around 7500 rpm at about Vx or Vy? Max speed would require 7500 rpm at
WOT sea level? I wonder what rpm our props allow at these speeds?
If you had a prop that would do the above, I wonder what the static rpm would
be? Then since most of us have fixed pitch props, I wonder where we
should try to be for the best of both worlds (a
compromise)?
We have some really good engineers in this group and
they have made these selections. I know they know why they made the
selection they did. How about sharing?
:>)
Don’t worry, you can not ramble on too much for
me!
Bill B
From:
Rotary motors in aircraft
[mailto:flyrotary@lancaironline.net] On
Behalf Of Tracy Crook
Sent: Wednesday, March 03, 2010 2:32
PM
To: Rotary motors in aircraft
Subject: [FlyRotary] Re: single
rotor
Al is correct about it taking HP to make static thrust
with a prop but the assumption about the relationship between HP and static
thrust is subject to a lot of variables. There is no fixed relationship
between static thrust and HP. If there were, you could not account
for the ability of most helicopters
to hover.
You could easily increase static thrust by 1.18
by increasing the diameter of the prop and the reduction ratio of
the redrive with NO increase in HP.
But my real point was that static thrust is not a very
useful measurement to us.
On Wed, Mar 3, 2010 at 11:06 AM, Al Gietzen <ALVentures@cox.net>
wrote:
Looking at the two
sizes of the engine, it takes 1.6 times as much horsepower to develop 1.18
times as much static thrust! Somehow this does not compute for me….I
always doubt the performance figures in a sales presentation and when they
don’t make sense to me…..???
Bill B (hoping
this generates an educational experience for me :>)
We’re talking about
the amount of force exerted by the prop with the plane (motor) standing
still.
So, it seems to
make sense to me that the power needed to accelerate the air to generate the
thrust would go as the cube root; and the cube root of 1.6 is very close
1.18.
To move the amount
of air it takes to generate the thrust certainly does take horsepower.
Very much the same as the power it takes to drive the pump (or generator) on a
dyno. So I don’t know how Tracy was interpreting the
question.
Al
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