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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