BALANCE OF
PROPELLER/ENGINE
From Graham Patterson of Upper Orara in NSW
comes this months winning question, straight off the Internet. Over now to our patient.
Q. An article on the Internet was extolling the virtues of fitting an
unbalanced propeller with the heavy blade opposite the piston at TDC to help balance the
engine.
My interest is in vintage team race engines with iron pistons: my question is whether a
weighted hub
or blade on the propeller would have any benefit or am I having myself on?
A. My diagnosis is idiopathic delusions arising from too much rotation at F2C speeds.
In short, I don't know the answer to your question.
The system you are describing is complex, involving a reciprocating piston, an oscillating
conrod and rotating counterweights and propeller:
all of these have some degree of elasticity, and I aint Euler or Newton.
There is a theory that may help us to some degree, so
lets consider.. With Mp the mass of the piston, r the crank length,
w the angular velocity and that the momentary angle between the
crank and line of motion of the piston, the primary disturbing force Frecip caused by
motion of piston alone is given by:
This primary unbalance could be cancelled by a second piston moving the
opposite way, as in a horizontally opposed twin. However all we have is a rotating
counterweight,
so lets look at that. With Mb the mass of the counterweight, rb the length
of the crank supporting Mb, then the centripetal force Fb due to this rotating mass is
given by:
This force has 2 components, one parallel to the line of stroke and
one across the line of stroke. These are in turn:
To cancel out Frecip we want to use the countervailing force Fparallel,
as these are oppositely directed. Thus we have full primary balance when:
Substituting the above equations yields:
This is fine, but we still have F across acting without any countervailing force.
Things keep on shaking just the same, but in a different direction!
The introduction of the rotating balance mass merely served to change the direction
of the disturbing force from parallel to the line stroke to across the line of stroke!
It is preferable then to only partially balance the primary force.
Thus we set:
The number c is chosen arbitrarily, but the unbalanced force on the
engine mount is least when c = .5. Note that we have not considered the
unbalance due to the weight of the conrod.
It turns out that a counterbalance for the rod must spin at twice the engine RPM,
something of a nuisance, I think you will agree !
Now reconsider that unbalanced prop set opposite top dead centre.
If we like , this can be considered an additional weight added to the
counterbalance.
It will therefore have the same characteristics, altering the primary partial balance.
If the engine manufacturer has carefully set c = .5, then c will no longer
have this value and force at the engine mount will be greater.
According then to this theory, perhaps using unbalanced props may
not be so smart: unless, of course, the manufacturer screwed up anyway.
This may well be the case. Graham points out that Metkemeyer
and Flores of FMV T/R fame had to go to great lengths with
tungsten counterweights to achieve c = .5 However,
there is more to this story. At least the counterweight is
almost in line with the reciprocating mass of the piston, and
is thus slightly dynamically unbalanced on the shaft axis.
But the propeller unbalance weight is well forward
of the piston, by the length of the shaft, so there is a couple
formed between the piston and the prop unbalance.
This couple introduces a rocking mode of vibration, and I think we
don't really want to add new modes of unbalanced vibrations ! Indeed,
if we want to improve the piston/counterweight dynamic balance,
the heavy prop tip should be on the same side as TDC
!Perhaps one could conclude, for prop imbalance opposite TDC,
that primary balance may be improved for engines with c somewhat less than .5,
but possibly at some small expense of dynamic balance ,
which loads the front and rear bearings. It may well be worth a try !
To finish off,I will dwell briefly on the 3 modes a propeller must be
balanced. Firstly, if you set your prop horizontally on the
balancer and file the tips to get balance, you have achieved radial static balance.
My feeling is that this is the most important balance mode, despite the Internet
ravings.
Secondly, you may set the prop vertically on the balancer and remove
material from the sides of the hub, so that the prop stays vertical. This achieves
lateral static balance.
Thirdly, you may spin the prop and check the tracking of the tips.
By removing facing material from the hub, you can get the tips to track true.
You have then (hopefully !) achieved dynamic balance.
I know Merv Bell, with his superb propellers, took great pains with this tracking.
Well I hope you are feeling better now Graham, those
Internet viruses can be hard to shake off! Let me know what you would like as
a prize to the value of $30 of Supercool props or my book Propeller Dynamics.
So readers do send in your questions, give the Prop Doctor a call, maybe you could win !
Reference: Machine Design 2, Volume 2, P. Weir, 1983.
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| PROPELLER TIPS from Joe Supercool
Pitch comparison between propellers of different makes
In the February issue of VCLN, I noticed in Bendix Tales a reference to
APC, Bolley and assorted unmentionable other brands of propellers.
This set in train a thought process that said:
" Can one compare propellers by their pitch ?"
Reaching for a bucket .. (relax, John) .. of broken propellers, I scraped
the paint off them, then sliced through them at the 70% radius.
This revealed all sorts of airfoil sections, some flat bottomed, some undercambered,
some almost symmetrical. If one is to
compare propellers by their pitch, then surely this polyglot
of sections must confuse the issue: after all,if the performance of a
propeller does not depend on its airfoil section, then what on Earth does it depend on ?
Furthering this spirit of enquiry, I measured the pitch
at the 70% radius. Not entirely to my surprise, this pitch bore
little resemblance in some cases to the manufacturers stated value.
One 14 X 12 was a 14 X 14, and a 10 X 6 was a 9.7 X 7. If the
manufacturer can't even state the correct value, what hope for the modeller ?
Clearly you need your own pitch gauge. The Prather is well known, and a similar unit is
available from:
Edmunds Engineering in the
US for US$50 (Fax: 0011 1 301-702-2136)
Then at least you can decide what the pitch is for yourself.
In "Propeller Tips" last month I covered "face pitch", which
is the pitch measured to the bottom of the airfoil at the 70% radius.
Its a useful concept, especially if the blade is flat on the bottom, but gets
confusing if the
section is semi-symmetrical. Did you spot the deliberate error in that
article. " slipstream was 34%" should have been "slipstream was 24%".
Slightly more useful is the "geometric pitch", which is the same as face pitch
but measured to the airfoil chord-line, rather than the bottom. The chord-line joins
the extreme trailing edge to the extreme leading edge. It has the advantage that it
can
always be measured, irrespective of the airfoil shape.
Since nothing comes for free, it has the disadvantage
that you have to eyeball just where you think these extreme points are: the TE is
not so bad, but the leading edge is often round, making the chordline position there a bit
of a guess.
Still, any guess is better than no guess.
But we still have not answered the question,
which, in case you've glazed over, was
"Can one compare propellers by their pitch ?". Unfortunately the geometric
pitch
doesn't help either, as the dependence on airfoil shape has still not been accounted
for, yet.
This leaves "experimental pitch", which is the pitch (rough enough) measured
this
time to the zero-lift line of the airfoil. This time we've hit the jackpot .. propellers
with the same
experimental pitch will behave the same with respect to pitch, irrespective
of the airfoil shape. This is because all airfoils produce about the same amount of
lift for
each increment in angle of attack: since we're starting at zero lift, they compare
directly. Hence if you have more experimental pitch, that propeller will want to go
faster.
Now if you thought measuring geometric pitch was a bitch, how on earth
can you measure to the zero-lift line,when you have no idea where that is? It turns
out that the zero-lift angle, measured relative to the chordline, can be easily
calculated.
The formula for airfoil zero-lift angle is given by:
Zero-lift angle = arctan ( m /( 1 - p )) * 1.07
The symbol m is the airfoil camber, and is a number like .04 for a flat bottomed section,
and zero for
a symmetrical section. The camber line, like the chord-line, joins the extreme leading and
trailing
edge points, but not with a straight line. Rather, with a curved line that
splits the airfoil neatly in twain. The maximum height of the camber line above
the chord-line is the camber, and must be divided by the chord to get m. The symbol
p is the distance
of the camber maximum point from the leading edge, divided by the chord. It has a value
like .3 or .4.
The value 1.07 is a fiddle factor to adjust roughly for variation of the formula
between airfoils. Consider the famous Clark Y airfoil, often used for propellers,
even to this day. Clark Y has camber .0355 and high point of .35 (near enough).
Then:
Zero-lift angle = arctan ( .0355 /( 1- .35)) * 1.07
= arctan ( .0546 ) * 1.07
= 3.126 * 1.07
= 3.34 degrees
This agrees with Soartech 8 data, at a Reynolds number
of 150000, which is useful for us modellers.
I leave it to you to relate this angle to the geometric pitch angle, and thereby
derive the experimental pitch. Just remember that pitch is advance per revolution, you'll
figure
it out OK. Be careful with the above calculations, sometimes you get the
answer in radians and have to multiply by 180/pi to get degrees, where pi = 4 * atn(1) or
3.141592.
Next month in Propeller Tips: Transonic airfoils for F2A props.
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